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Improved connectivity analysis using multiple low-cost paths to evaluate habitat for the
endangered San Martin titi monkey (Callicebus oenanthe) in north-central Peru
by
Nathan Walker
Dr. Jennifer Swenson and Dr. Dean Urban, Advisors
April 28, 2017
Masters project submitted in partial fulfillment of the
requirements for the Master of Environmental Management degree in
the Nicholas School of the Environment of
Duke University
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Executive Summary A major cause of species loss is habitat destruction and fragmentation. One of the primary approaches conservationists can take to preserve species, therefore, is increasing the amount of habitat available to a species, and increasing connectivity between the remaining patches. Increased connectivity can improve population and species viability, maintain genetic diversity, and give a species the flexibility to move around the landscape in response to changing resources and threats. This is an active area of research in the field of conservation science, focused on developing improved methods for identifying priority connectivity areas for protection and restoration. In this report, I discuss novel connectivity methods I have developed to advance this research.
I introduce two major refinements of connectivity analysis methods here. First, one major approach to analyzing connectivity is the use of graph theory: breaking complex landscapes down into the components of nodes (representing patches), and links (representing connections between patches). Typically in ecological applications there is a single link connecting a pair of nodes, representing a least-cost path between those patches. Instead, I am using a multigraph approach, where nodes can be joined by many links, representing multiple low-cost paths between patches. This allows conservation planners to identify not just which patches are closest to each other, but which patches have the most connecting routes. Knowing which patches are connected by only a single narrow route, and which have hundreds of connecting paths, can help us better understand the vulnerability or resiliency of different habitat connections, as we make conservation prioritization decisions.
Secondly, as with many connectivity analyses, my methods are based on the use of a cost surface (where low cost areas are relatively safe and easy for an animal to travel through, and high cost areas are relatively dangerous or difficult for an animal to travel through). As with other researchers, I wished to perform a sensitivity analysis, to understand how these results would change if the assumptions of the underlying cost values were altered. However, in addition to changing all values across the entire landscape (e.g. all agricultural areas have lows costs, or all have high costs), I explored the effects of varying the cost values spatially (e.g. what if one agricultural area has low costs, and another has high costs?). This allowed me to explore another effect of uncertainty in this analysis: not just “what if the cost values are incorrect?” but “what if there are unknown local effects on cost values?”
I applied these analyses to perform a connectivity prioritization for the endangered San Martin titi monkey (Callicebus oenanthe), located in the San Martín department of north-central Peru. This is one of the top 25 most endangered monkey species in the world, and is endemic to a small region in Peru. Relatively little is known about this species; therefore, developing new analytical methods for this species could also be useful for the conservation of other species of concern, in data-poor regions. This species is also under imminent threats from deforestation, land conversion, and fragmentation; an improved connectivity analysis for this species can help local conservationists identify priority areas for land protection and restoration.
For my analysis, I first modified a land classification to capture the different land cover types relevant to the movement of this species, based on consultation with species experts. I then used this dataset to create a variety of different cost surfaces, bounded by low and high cost estimates for each land class from the species experts. Next, I identified habitat patches for this species, to represent the nodes in the graph analysis. I then identified a set of low-cost paths connecting each of these patches, using the cost distances from the source patch to all reachable cells along the edge of the destination patch.
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I used these to build a multigraph, then evaluated connectivity for this using an iterative approach. In this approach, connectivity metrics are evaluated for each patch, then a link is removed from each pair of patches, then the metrics are recalculated, and these steps are repeated until all links have been removed. This provides information not just of the initial connectivity of a network, but on the resilience of connectivity: how the connectivity would change if habitat is lost throughout the landscape, and how this would affect conservation priorities. Finally, I repeated this analysis for each of the different cost surfaces, in order to perform a sensitivity analysis, evaluating the effect of changing cost surfaces on the priority patches identified. I then explored several methods for conducting a final prioritization, taking into account all this information on patch connectivity.
The priority habitat patches I identified for this species were robust to differences in cost surfaces, with high average correlations between cost surfaces for 10 of the 11 methods I used to rank patches. For the final prioritization method I selected, I counted the number of times a patch was in the top 100, for 15 different cost surfaces, 3 different connectivity metrics, and hundreds of iterations of link-removal. I found that of more than 4300 habitat patches in my study area, the same 100 patches were in the top 100, 63% of the time. If protected, these patches would help maintain connectivity that should, in turn, help to maintain persistent monkey populations.
These methods provide a far more robust analysis of connectivity than a typical least-cost path analysis, identifying not just which patches are closer to each other, but which patches have more possible routes between them, and better evaluating how the prioritization of patches would change when using different cost surfaces. These analysis methods represent an important step forward in connectivity analysis, and they should be broadly useful for the conservation of other species threatened by fragmentation.
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Table of Contents
Executive Summary ....................................................................................................................................... ii
Table of Contents ......................................................................................................................................... iv
List of Tables ................................................................................................................................................ vi
List of Figures .............................................................................................................................................. vii
Introduction and Background ....................................................................................................................... 1
Study Area ................................................................................................................................................. 1
Life History of the San Martin Titi Monkey ............................................................................................... 2
Threats to the San Martin Titi Monkey ..................................................................................................... 4
Conservation of the San Martin Titi Monkey ............................................................................................ 4
Connectivity .............................................................................................................................................. 6
Consequences of Connectivity .............................................................................................................. 7
Analytical Approaches ........................................................................................................................... 8
Graph Theory ...................................................................................................................................... 10
Habitat Patches ................................................................................................................................... 11
Habitat Links........................................................................................................................................ 12
Multiple Low-cost Paths...................................................................................................................... 13
Resistance Surfaces ............................................................................................................................. 14
Uncertainty Analyses .......................................................................................................................... 16
Evaluating Connectivity ....................................................................................................................... 18
Other Considerations .......................................................................................................................... 20
Methods ...................................................................................................................................................... 22
Data ......................................................................................................................................................... 22
Land Cover .......................................................................................................................................... 22
Habitat Patches ................................................................................................................................... 24
Resistance Surfaces ............................................................................................................................. 25
Multigraph Creation ................................................................................................................................ 27
Analysis of Multigraphs ........................................................................................................................... 28
Results ......................................................................................................................................................... 34
Land Cover and Habitat Patches ............................................................................................................. 34
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Resistance Surfaces ................................................................................................................................. 37
Multigraph Creation ................................................................................................................................ 40
Analysis of Multigraphs ........................................................................................................................... 42
Discussion.................................................................................................................................................... 52
Limitations and Extensions ..................................................................................................................... 53
Conclusion ............................................................................................................................................... 56
Acknowledgements ..................................................................................................................................... 57
References .................................................................................................................................................. 58
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List of Tables
Table 1. Method parameters and the value(s) tested. ............................................................................... 31 Table 2. Land classes and habitat patches .................................................................................................. 34 Table 3. Correlations of values for each patch, between 15 cost surfaces ................................................ 47
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List of Figures
Figure 1. Photo of the San Martin titi monkey ............................................................................................. 2 Figure 2. Distribution of the San Martin titi monkey .................................................................................... 3 Figure 3. Land uses within the C. oenanthe species range ........................................................................... 5 Figure 4. Comparison of steps for least-cost path and multiple low-cost path analyses ........................... 29 Figure 5. Comparison of graph and multigraph representations ............................................................... 30 Figure 6. Land cover map of the species range .......................................................................................... 35 Figure 7. Habitat patches in the species range ........................................................................................... 36 Figure 8. Ranges of resistance values for each land cover class. ................................................................ 38 Figure 9. Four resistance surfaces. ............................................................................................................. 39 Figure 10. Effects of different resistance surfaces on connectivity ............................................................ 40 Figure 11. Multigraphs from four different resistance surfaces. ................................................................ 41 Figure 12. Number of remaining patches in the graph as links are removed ............................................ 42 Figure 13. Values for three metrics, at different levels of connectivity ..................................................... 43 Figure 14. Examples of changing values for two different patches. ........................................................... 44 Figure 15. Overlap in top 100 patches, between cost surfaces .................................................................. 44 Figure 16. Mean and variance in patch ranks, across all iterations and cost surfaces ............................... 45 Figure 17. Mean patch rank, for all iterations and cost surfaces ............................................................... 46 Figure 18. Proportion of the iterations in the top 100 patches .................................................................. 48 Figure 19. Top patches, for combined metrics. .......................................................................................... 50 Figure 20. Proportion of iterations in the top 100 ...................................................................................... 51
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Introduction and Background A major cause of species loss is habitat destruction and fragmentation. One of the primary approaches conservationists can take to preserve species, therefore, is increasing the amount of habitat available to a species, and increasing connectivity between the remaining patches. Increased connectivity can improve population and species viability, maintain genetic diversity, and give a species the flexibility to move around the landscape in response to changing resources and threats. This is an active area of research in the field of conservation science, focused on developing improved methods for identifying priority connectivity areas for protection and restoration. In this report, I discuss novel connectivity methods I have developed to advance this research.
I introduce two major refinements of connectivity analysis methods here. First, one major approach to analyzing connectivity is the use of graph theory: breaking complex landscapes down into the components of nodes (representing patches), and links (representing connections between patches). Typically in ecological applications there is a single link connecting a pair of nodes, representing a least-cost path between those patches. Instead, I am using a multigraph approach, where nodes can be joined by many links, representing multiple low-cost paths between patches. This allows conservation planners to identify not just which patches are closest to each other, but which patches have the most connecting routes. Knowing which patches are connected by only a single narrow route, and which have hundreds of connecting paths, can help us better understand the vulnerability or resiliency of different habitat connections, as we make conservation prioritization decisions.
Secondly, as with many connectivity analyses, my methods are based on the use of a cost surface (where low cost areas are relatively safe and easy for an animal to travel through, and high cost areas are relatively dangerous or difficult for an animal to travel through). As with other researchers, I wished to perform a sensitivity analysis, to understand how these results would change if the assumptions of the underlying cost values were altered. However, in addition to changing all values across the entire landscape (e.g. all agricultural areas have lows costs, or all have high costs), I explored the effects of varying the cost values spatially (e.g. what if one agricultural area has low costs, and another has high costs?). This allowed me to explore another effect of uncertainty in this analysis: not just “what if the cost values are incorrect?” but “what if there are unknown local effects on cost values?”
I applied these analyses to perform a connectivity prioritization for the endangered San Martin titi monkey (Callicebus oenanthe), located in the San Martín department of north-central Peru. This is one of the top 25 most endangered monkey species in the world, and is endemic to a small region in Peru. Relatively little is known about this species; therefore, developing new analytical methods for this species could also be useful for the conservation of other species of concern, in data-poor regions. This species is also under imminent threats from deforestation, land conversion, and fragmentation; an improved connectivity analysis for this species can help local conservationists identify priority areas for land protection and restoration.
Study Area The tropical Andes, stretching along the mountains from Venezuela south to Chile and Argentina, are widely regarded as a global biodiversity hotspot (T. M. Brooks et al., 2006; Myers et al., 2000; Zador et
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al., 2015). Myers et al. (2000) found that the tropical Andes contained at least 20,000 endemic plants and more endemic vertebrates than any other area; indeed, its importance was such that the authors considered it to be a ‘hyper-hot’ hotspot.
Peru, which covers a large portion of this hotspot (Zador et al., 2015), has been rated one of the top three countries in the world for biological diversity (Grupo de Trabajo Multisectorial, 2008). Peru ranks second in the planet for bird diversity, with more than 1800 species, and third for amphibians and mammals (more than 400 each, among them 49 endemic mammals) (Grupo de Trabajo Multisectorial, 2008; Pacheco et al., 2002). That includes 32 primate species, 8 of them endemics, such as the critically endangered Peruvian yellow-tailed wooly monkey (Oreonax flavicauda), believed extinct until 1974, and the San Martin titi monkey (Allgas et al., 2016; Pacheco et al., 2002; Zador et al., 2015), described in more detail below.
The department of San Martín, in north-central Peru, is an area of particularly high biodiversity (Instituto de Investigaciones de la Amazonía Peruana, 2006). It has a complex geology, a rich variety of different ecosystems, and a high level of endemism: 544 of its 3827 species are endemic to the region (Instituto de Investigaciones de la Amazonía Peruana, 2006). There are at least six endangered species in this region, of which the Instituto de Investigaciones de la Amazonía Peruana (2006) highlighted C. oenanthe as being in particular danger.
Life History of the San Martin Titi Monkey The San Martin titi monkey (Figure 1), also called the Rio Mayo titi monkey, the mono tocón (in Spanish), and the sugkamat (in the indigenous Aguaruna language) (DeLuycker, 2007) has been classified as critically endangered by both the International Union for Conservation of Nature (IUCN) and the Peruvian government (El Presidente de la República, 2014; IUCN, 2013). It has been listed as one of the top 25 most threatened species of primates in the world, with more than 80% of its population lost in the past 25 years (Vermeer, 2015).
Figure 1. Photo of the San Martin titi monkey. (Photo credit: Nathan Walker)
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Titi monkeys are small (about 1 kg), arboreal, and frugivorous (DeLuycker, 2007). As with other members of its genus, C. oenanthe is generally found in small groups, with an adult male and female accompanied by as many as three offspring (DeLuycker, 2007). This genus is typically monogamous, pair-bonded, and shows strong paternal care, setting it apart from most other monkeys (DeLuycker, 2007). This genus is territorial, and uses loud morning duets to maintain its territory spacing (DeLuycker, 2007).
C. oenanthe is found in low to mid-elevation areas of the San Martín department, north of the Río Huayabamba and west of the Río Huallaga (Allgas et al., 2016) (Figure 2). This area is categorized as a humid premontane tropical forest, with a mix of flat terrain, hills, and mountains (DeLuycker, 2007). The San Martin titi monkey is found in a mix of different habitats within this zone, including flooded forests, drier zones, both primary and secondary forests, and disturbed areas (Bóveda-Penalba et al., 2009).
These monkeys are difficult to study because of their cryptic behavior, small size, and rarity (Schaffer-Smith et al., 2016; van Strien, García-Suikkanen, et al., 2016). C. oenanthe was first described in 1924, but was not studied intensively until the mid-2000s (Vermeer, 2015), when Anneke DeLuycker delivered first a preliminary study on the ecology of this species, then a more detailed report (DeLuycker, 2006, 2007). A distributional analysis was performed by Bóveda-Penalba et al. (2009), which was followed by a density analysis, performed by van Kuijk et al. (2016). The first range maps were completed as part of gap analyses performed by Young (2007) and Swenson et al. (2012); these was updated by Schaffer-Smith et al. (2016) as part of a connectivity analysis. Another method of connectivity analysis was completed by Ernest (2015) for a portion of the species range.
Figure 2. Distribution of the San Martin titi monkey; species range from Schaffer-Smith et al. (2016).
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Threats to the San Martin Titi Monkey The biggest threat to the San Martin titi monkey is habitat fragmentation and loss (Bóveda-Penalba et al., 2009; DeLuycker, 2006; Pacheco et al., 2002; Purvis et al., 2000). The range for this species is small to begin with, less than 14,000 km2, and of the lowland forest in its northern range, 34% has already been lost (Schaffer-Smith et al., 2016). Of the remaining habitat fragments, almost 95% are unlikely to be of sufficient size to sustain viable populations, and less than 8% are on conserved lands (Schaffer-Smith et al., 2016). In a study by DeLuycker (2007), this species spent only 0.2% of its time on the ground; as with other species that rely upon forest canopy for movement, habitat fragmentation is of particular concern (Isaac & Cowlishaw, 2004). This fragmentation makes it difficult for titi monkeys to move to new habitat patches to reproduce or establish territories (Bóveda-Penalba et al., 2009; DeLuycker, 2007), which may increase the extinction risk for this species (Fahrig, 2002).
The fragmentation of habitat is caused by a combination of deforestation and land conversion, with 50,000 to 100,000 ha of forest lost per year, among the highest rates in Peru (DeLuycker, 2006; S. Shanee et al., 2013). The region of San Martín represents 6.5% of the Peruvian Amazon’s area, but more than 21% of the deforested area (Instituto de Investigaciones de la Amazonía Peruana, 2006). Logging, legal and illegal, results in forests being cleared for cooking fuel and for construction materials (DeLuycker, 2006; S. Shanee et al., 2013). Overall, 40% of the forests in San Martín have been lost (S. Shanee et al., 2013). The remaining habitat has become more isolated, surrounded by agriculture and grazing lands (DeLuycker, 2006). Slash-and-burn agriculture removes forest habitat, to allow the planting of rice crops in the plains and river valleys, and cacao on the slopes (DeLuycker, 2006; S. Shanee et al., 2013). Even coffee crops, which could be compatible with some level of habitat conservation, are generally not shade-grown, with forests cleared to create coffee plantations (DeLuycker, 2006).
Most of the fragmentation of C. oenanthe habitat is fairly recent, starting in the 1950s and accelerating more recently (S. Shanee et al., 2013). In the 1980s, large numbers of immigrants came to this region, attracted by the nation’s second largest agrarian program, which contributed to increasing deforestation (DeLuycker, 2006). This was followed by the construction of a new highway, with paving completed in 2003, bringing with it another influx of immigrants (DeLuycker, 2006). Immigration to San Martín is currently twice the national average (Schaffer-Smith et al., 2016), with a 131% increase in population from 1981 to 1993, and a further 300% increase from 1993 to 2007 (S. Shanee et al., 2013).
As immigrants arrived in the region, they founded new settlements following the highway, further into the forests and further up the valleys than the earlier settlements (DeLuycker, 2006; S. Shanee et al., 2013), and deforested lands as a way of asserting property rights or for land speculation (Monteferri & Coll, 2009; N. Shanee & Shanee, 2016). Indigenous community members also annexed new lands, causing further forest loss (DeLuycker, 2006). Meanwhile, the fraction of the Amazon with rights granted for oil exploration and exploitation has risen from 15% to more than 72% in a few years (Monteferri & Coll, 2009). All of these issues result not just in more habitat being lost, but in habitat being lost in new spatial configurations than before, further fragmenting habitat for this species (DeLuycker, 2006).
Conservation of the San Martin Titi Monkey Currently 18 million ha of public land are protected in Peru, roughly 14% of Peru’s area (Monteferri & Coll, 2009). Additionally, Peru currently has more privately protected lands than any of the seven other
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Amazonian countries, with 1.2 million ha in conservation and ecotourism concessions, ecosystem service zones, and other protected lands (N. Shanee et al., 2016). In San Martín, there are currently two national parks and one protected forest, including almost 1 million ha, almost 20% of the region (Instituto de Investigaciones de la Amazonía Peruana, 2006). These areas are relatively undisturbed; as recently as 2003 there was not a single visitor reported at any of these protected areas (Instituto de Investigaciones de la Amazonía Peruana, 2006).
Unfortunately, protected lands are not enough by themselves to protect the whole landscape (N. Shanee et al., 2016). Furthermore, the San Martin titi monkey, like many other species endemic to Peru, has a large portion of its range outside of protected areas. Swenson et al. (2012) found that only 20% of high-endemism areas, and 20% of irreplaceable areas, were in protected lands, and that 40% of ecological systems were classified as “in serious need of protection,” with less than 2% of their ranges found within protected lands. Rodrigues et al. (2004), in a global gap analysis, found that the Andes were an extremely high priority for new land conservation efforts. In the case of C. oenanthe, the species range is almost entirely on lands that lack conservation protections (DeLuycker, 2007; Instituto de Investigaciones de la Amazonía Peruana, 2006; Schaffer-Smith et al., 2016). Based on generalized land use data from Gobierno Regional San Martín (2013), roughly 58% of the species range is in agricultural and ranch lands, including 14% for corn crops, 12% for ranching, 6% for coffee, 4% for rice, and 21% for mixed use (Figure 3).
Figure 3. Land uses within the C. oenanthe species range (Gobierno Regional San Martín, 2013).
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Land conservation is therefore a high priority. Areas can be protected through a variety of measures, using government protections (at the local, regional, or national level), or various types of private and community initiatives (N. Shanee, 2016; S. Shanee et al., 2013). Protections of lands can include not just forest patches for C. oenanthe to inhabit, but the creation of corridors to connect isolated fragments, allowing groups and individuals to travel between patches for mating or colonization (DeLuycker, 2006, 2007), described at greater length in the Connectivity section below. In practice, such corridors are often established by conserving riparian forest or the edges of agricultural lands (N. Shanee et al., 2016).
Habitat conservation can also include replanting of deforested areas (Allgas et al., 2016). Secondary forests often have greater primary production (Allgas et al., 2016), and C. oenanthe has shown a preference for this type of habitat (Bóveda-Penalba et al., 2009; van Strien, García-Suikkanen, et al., 2016). In particular, enrichment planting, which supplements natural regrowth by planting saplings of key forest types, can speed recovery of suitable habitat, and attract primates (Allgas et al., 2016). Such activities are particularly helpful for relatively small species with small ranges (Allgas et al., 2016; N. Shanee et al., 2016), particularly those that are more tolerant of edge effects and disturbed forests, such as the San Martin titi monkey (Bóveda-Penalba et al., 2009; van Kuijk, 2013; van Strien, García-Suikkanen, et al., 2016). Species can also be protected through the use of community conservation programs, including local ordinances by communities to restrict or eliminate hunting or deforestation within certain zones, establish new protected areas, or promote tree planting campaigns (Allgas et al., 2016; N. Shanee et al., 2016).
A variety of non-governmental organizations (NGOs) work on wildlife issues in Peru, including local, national, and international organizations. In particular, the local organization Proyecto Mono Tocón (PMT), which assisted with this project, is dedicated to the conservation of the San Martin titi monkey, and contributes to research, conservation, and environmental education in this area (Gaultier et al., 2015; Proyecto Mono Tocón, 2013, 2017). PMT also partners with well-known international NGOs such as Conservation International and the Rainforest Trust (Rainforest Trust, 2016). Similarly, other NGOs also have local educational initiatives to promote habitat protection and raise awareness of threats to this species (S. Shanee et al., 2013).
Connectivity For all these organizations, governmental and non-governmental, to conserve C. oenanthe and other species of concern, they must be able prioritize areas for protection, restoration, research, or other conservation initiatives. Conservation biology is a crisis discipline, which requires that decisions be made to protect species or ecosystems before all the relevant data have been collected (Soulé, 1985). Bennett et al. (2006) describes four major topics of conservation in practice: conserving more lands, enhancing the quality of existing habitat, mitigating damages from nearby lands, and increasing the connectivity between different areas of habitat. All of these approaches should be rooted in science, but require the prioritization of different possible actions before all the relevant facts can be known.
Instead of being paralyzed by the unknown, however, conservationists must weigh the consequences of action against those of inaction. Destruction and fragmentation of habitat are the greatest immediate threats to biodiversity (K. R. Crooks & Sanjayan, 2006; Wilcove et al., 1998). Even the largest protected area is often not large enough to preserve a species by itself (K. R. Crooks & Sanjayan, 2006; Newmark,
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1995). Fragmentation can interact with other threats to increase extinction risk and increase the amount of habitat required for conservation (Fahrig, 2002; Laurance et al., 2002; Laurance et al., 2000). In particular, for neotropical primates, costs to species biomass and persistence from fragmentation have consistently been found, beyond what would be expected from the reduction in patch size alone, due to increased human pressures and loss of genetic connectivity in fragmented landscapes (Benchimol & Peres, 2013). For this reason, rather than just attempting to establish new protected areas, one of the major goals of conservation is to provide better connections between existing protected areas, between habitat patches, or between isolated species populations (K. R. Crooks & Sanjayan, 2006). Thus, even if a pair of patches are individually too small to maintain a population or species, if individuals have a way to travel between these patches, there will be a greater chance that the populations will survive (K. R. Crooks & Sanjayan, 2006).
Consequences of Connectivity Connectivity has been defined generally as “the degree to which the landscape facilitates or impedes movement among resource patches” (Taylor et al., 1993). ‘Movement’ here can imply not just demographic exchanges, the flow of animals between areas, but also to trophic, environmental, behavioral, and genetic exchanges (Talley et al., 2006). In this section, I describe a variety of positive and negative effects of connectivity, and what these mean for C. oenanthe. In the following sections, I describe major methods and considerations for the analysis of connectivity.
Research into connectivity and corridors has been steadily increasing for the past several decades (K. R. Crooks & Sanjayan, 2006). In that time, researchers have looked into a variety of benefits of connectivity, including increased population and species viability, improved species diversity and genetic variation, greater area for daily and seasonal movements and for individual dispersal, facilitation of range shifts in response to climate change or other threats, and the provision of a variety ecosystem services (summarized by K. R. Crooks and Sanjayan (2006); see also Neville et al. (2006) and Pringle (2006)). Some of these benefits are direct: for example, a dispersing individual in a connected landscape is more likely to find available high-quality habitat than an individual in isolated habitat (Fahrig, 2007); other benefits, such as those related to ecosystem services, may be provided indirectly.
Ecosystem services provided by enhanced connectivity include seed dispersal (Levey et al., 2005; Levey et al., 2008), nutrient exchange (Pringle, 2006; Wipfli, 2005), and pollination (Ricketts et al., 2006). In the case of monkeys, these are important pollinators (Janson et al., 1981) and dispersers of fruit seeds (Link & Di Fiore, 2006) in the Amazon, and can increase both biodiversity and seed germination rates (A. Estrada & Coates-Estrada, 1984). In fact, one of the topics for education work by Proyecto Mono Tocón is raising awareness of the environmental services provided by C. oenanthe (Fuertes, 2017). Ricketts et al. (2006) argues that corridors of native habitat provide valuable ecosystem services to the surrounding agricultural areas, and that more pollinator species provide added benefits. Improved connectivity may therefore be valuable in bringing the ecosystem service benefits provided by this species to a greater number of people.
Additionally, in instances where conservation efforts are directed towards a single focal species, this can act as an umbrella species, providing connectivity benefits for many other plants and animals (see Haddad et al. (2003), Richard Walker and Craighead (1997), and Pringle (2006) for examples). This may
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be especially true for the conservation of rare species, where the distribution of the rare species is nested within the distribution of other more common ones, and where conserving the rare species can aid many others (Dale & Fortin, 2010). In this case, improving connectivity for C. oenanthe may also provide benefits for an unknown number of other species in this region.
On the other hand, some have pointed to potential disadvantages of increased connectivity (K. R. Crooks & Sanjayan, 2006; Haddad et al., 2014), such as the spread of wildfire and other disturbances, synchronization of population dynamics, decreased genetic variation and fitness, and in particular, the greater spread of disease and invasive species (J. Crooks & Suarez, 2006; McCallum & Dobson, 2006; Pringle, 2006; Rudnick et al., 2012). Human-assisted connectivity has rapidly spread pollution, invasive species, and other negative impacts around the world (J. Crooks & Suarez, 2006; Lovejoy, 2006; Talley et al., 2006).
Nonetheless, in a variety of meta-analyses, all came to the conclusion that the positive effects of corridors outweighed the negatives, and all found substantial evidence that corridors increase movement and gene flow between otherwise disconnected patches of habitat (Beier & Noss, 1998; Haddad et al., 2014; Haddad & Tewksbury, 2006). To the concerns about corridors spreading invasive species, Minor et al. (2009) found that improved connectivity may help native species more than invasive ones, while McCallum and Dobson (2006) pointed out that while corridors might contribute to the spread of some diseases, they could also contribute to the spread of resistance against them. McCallum and Dobson (2006) also make the point that while disease dynamics can be complicated, too little genetic connectivity inevitably leads to extinction, regardless of disease prevalence.
Looking specifically at whether corridors improved population viability, Haddad and Tewksbury (2006) found that most studies showed positive effects, despite some caveats. Models suggest that corridors will likely be most beneficial to species of conservation concern that are undergoing long-term declines in population (Haddad & Tewksbury, 2006). Both models and experiments have shown that only a few migrants per generation are enough to prevent impacts from inbreeding (Frankham, 2006). Thus, even minor improvements to connectivity may in some circumstances provide major benefits to population viability.
Analytical Approaches Conservationists may promote connectivity by protecting or restoring corridors, or by reducing threats in high connectivity regions. Before doing any of these activities, however, they must determine which areas should be priorities for connectivity conservation. There are a variety of approaches available to analyze this, depending on the amounts and types of input data available, and the degree of output detail desired (Calabrese & Fagan, 2004). Below I describe the broad categories of analyses, and the factors that led me to select both the general analysis category and the specific analytical method that I did.
At the most basic level, there are two types of connectivity analyses: structural and functional (K. R. Crooks & Sanjayan, 2006). Structural connectivity analyses describe only the physical arrangement of habitat and other landscape characteristics, without any consideration of the movement capabilities of particular species (K. R. Crooks & Sanjayan, 2006). This can be evaluated using approaches such as
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morphological image processing (Piquer-Rodríguez et al., 2012; Vogt et al., 2009), percolation theory (Gardner et al., 1989), or the software package Fragstats (Kuttner et al., 2013; McGarigal et al., 2012).
Functional connectivity analyses, on the other hand, consider not only the physical configuration of the landscape, but how species, individuals, or processes will respond to this configuration, and the effects of their responses (K. R. Crooks & Sanjayan, 2006; Wiens, 2006). Structural connectivity is easier to quantify and visualize, but may have low predictive power (Winfree et al., 2005), and is generally less informative than functional connectivity, “a stage […] without the players” (Wiens, 2006). Importantly, habitat may be functionally connected without being structurally connected, or may be structurally connected without being functionally connected (Taylor et al., 2006; Tischendorf & Fahrig, 2000).
Fagan and Calabrese (2006) furthers divide functional connectivity analyses into those based on potential and actual connectivity. Potential connectivity combines general information on the physical attributes of the landscape with coarse information about a species’ movement patterns (for example, estimated travel distances or energy budgets) (Fagan & Calabrese, 2006). Actual connectivity requires direct observations of the species’ movement through the landscape, or between habitat patches (Fagan & Calabrese, 2006). Both types of functional connectivity have greater information requirements than analyses of structural connectivity, requiring species-specific information such as movement rates, mortality, dispersal range, and response to fragmentation (for example, see Hansen and Urban (1992)) (Taylor et al., 2006; Tischendorf & Fahrig, 2000).
More specifically, Fagan and Calabrese (2006) and Calabrese and Fagan (2004) break down the general types of analyses by the types of data they require:
1) patch occupancy data (e.g. nearest neighbor analyses); 2) spatially explicit habitat data (e.g. spatial pattern indices); 3) point or grid-based occurrence data (e.g. scale-area slope relationships); 4) both spatially explicit habitat data and information on dispersal distance (e.g. graph-theoretic
analyses); 5) spatially explicit habitat data, patch occupancy data, and dispersal data (e.g. buffer radius and
incident function measures); 6) individual movement data (e.g. using telemetry data).
Of these, the first three only provide information on structural connectivity, not functional, while the last two require detailed data on patch occupancy or individual movements (Calabrese & Fagan, 2004; Fagan & Calabrese, 2006), which do not exist at landscape scales for the San Martin titi monkey. Given the data I have available (detailed habitat data and some limited information on species movement patterns and preferences), the fourth category provides the most detailed outputs. And, indeed, these authors recommend this category of analyses in general, and graph theory in particular, as providing the most benefit for the least data on landscape-scale conservation issues. Methods such as graph-theoretic analyses require only spatial data on habitat, not long-term population data, which can make these a more rapid method of assessing landscape connectivity (Urban & Keitt, 2001). Within this category, there are a variety of specific methods that can be used to assess connectivity:
Graph Theory: in graph theory, a landscape is simplified into a set of points (or nodes), connected by lines (or edges/links), where the nodes represent patches of habitat, and the links represent connections between them (Dale & Fortin, 2010; Fall et al., 2007; Minor & Urban, 2008; Urban & Keitt, 2001; Urban
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et al., 2009). Nodes are evaluated as connected or disconnected based on the dispersal capabilities of the species being analyzed (Bunn et al., 2000; Fall et al., 2007; Keitt et al., 1997; Minor & Urban, 2008; Urban et al., 2009). This approach is described in greater detail below.
Circuit Theory: Circuit theory, using the software package Circuitscape, developed by McRae et al. (2014b), involves treating a landscape as if it were a circuit board: areas are classified with varying levels of resistance, and current is run through this to identify areas of higher circuit flow (Carroll et al., 2012; McRae, 2006; McRae et al., 2008; Rayfield et al., 2015). In this conception, resistance indicates opposition to movement through a landscape, current indicates net movement probabilities, and voltages indicate the probability of successful dispersal (McRae et al., 2008). The resistance distance indicates the isolation between any two habitat patches, and is predicted to be correlated with genetic variation (McRae, 2006; McRae et al., 2008). This is related to graph theory, and can be used for many of the same purposes, with the added advantage that it can easily visualize multiple connections between patches (Carroll et al., 2012; McRae et al., 2008; Urban et al., 2009). This approach also offers extensions for the identification of barriers, pinch points, and key linkages (Carroll et al., 2012; McRae et al., 2012; Pelletier et al., 2014).
Individual-based Models: Another approach involves individual-based models, which release randomly or semi-randomly moving animals around the landscape, and evaluate the degree of connectedness between patches based on the movement of virtual animals between them. The movement of the virtual animals may be purely random (Karlin & Raghavan, 1995), or may depend upon a combination of other factors, such as a cost distance surface (Coulon et al., 2015; Gardner & Gustafson, 2004; Hargrove et al., 2005; Lookingbill et al., 2010; Morzillo et al., 2011; Palmer et al., 2011), response to linear features (Vuilleumier & Fontanillas, 2007), response to changes in land cover (Schippers et al., 1996; Tracey, 2006), or a bias against an abrupt change in movement (Hein et al., 2004). An advantage of this approach is that unlike other methods, it does not assume omniscience in a dispersing animal: a virtual animal can only perceive its neighboring cells, not all the cells on the landscape, which can produce more realistic movement paths (Coulon et al., 2015). However, this requires more data to parameterize correctly, increasing the potential for error, and it may be overly prohibitive in its processing time requirements for large landscapes (Bunn et al., 2000; McRae et al., 2008; Minor & Urban, 2007).
Other: While the methods described above appear to be the most common, a variety of other approaches exist to assess functional connectivity, many with similar data requirements to those described above. These include approaches using resistant kernels (Compton et al., 2007; Cushman et al., 2013; Wasserman et al., 2012), vector-based methods (Matisziw et al., 2015; Vuilleumier & Metzger, 2006), gradient-based analyses (Cushman, Gutzweiler, et al., 2010; Moilanen, 2011; Moilanen et al., 2005), and corridors designed to maintain connectivity in response to climate change (Beier et al., 2011; Brost & Beier, 2012; Cushman et al., 2013; Rudnick et al., 2012).
Graph Theory After reviewing the major approaches available, I elected to use graph-theoretic methods for my analysis, for several reasons. First, while graphs are a simplification of a landscape, they allow important landscape characteristics to be retained, including the size or quality of habitat patches, as well as distance between patches and other route information (Galpern et al., 2011). Graph theory also offers
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better analytical capabilities, to evaluate not just a patch’s connections to its immediate neighbors but the patch’s stepping stone importance (for connecting more distant patches), the network’s redundancy to habitat loss, the value of separate subgraphs or other structures within a larger graph, and the landscape as a whole (Awade et al., 2012; Benson et al., 2016; Bodin & Norberg, 2007; C. P. Brooks, 2006; Girvan & Newman, 2002; Urban & Keitt, 2001). While constructing large graphs can be time-consuming, once a graph is constructed, many analyses are extremely fast, allowing experiments to be performed easily (for example, removing a habitat patch or link, and re-evaluating the network) (Bodin & Saura, 2010; Bunn et al., 2000; Estrada-Peña, 2005; Keitt et al., 1997; Proulx et al., 2005; Urban & Keitt, 2001; Urban et al., 2009). Many of these analyses cannot easily be performed using other methods, and could be extremely helpful when setting priorities for conservation and restoration (Awade et al., 2012; Jordán et al., 2007; Schick & Lindley, 2007).
An additional strength of graph theory is the ease with which it can be combined with other data sources or approaches. This includes using datasets for multiple species, to optimize corridor networks for a suite of species simultaneously, or incorporating costs and feasibility into prioritization activities (Brás et al., 2013; Dilkina et al., 2013; Dilkina et al., 2011; Lai et al., 2011; Le Bras et al., 2013; Robert Walker et al., 2013). If new species observation data became available, these could be used to evaluate graph connectedness (Dilts et al., 2016), or to weight nodes or links (Jordán et al., 2007), to improve existing analyses.
These strong advantages made graph theory a better approach for my project than circuit theory, which is better suited for visualizing connectivity, but does not offer the same analytical capabilities (in particular, for the isolation or removal of particular network connections). Additionally, the software Circuitscape faces limitations in the size of the landscape that can be analyzed, particularly for more advanced features (McRae & Kavanagh, 2013; McRae et al., 2014a). Work by Poor et al. (2012) also found that while Circuitscape performed well at estimating dispersal rates, it was not an effective method for identifying corridors, while derivations of graph analyses were.
A final point of consideration is that because of the relationships between graph theory and circuit theory, both on a theoretical level and in the inputs required, circuit-theory analyses could easily be performed on portions of this study area in the future, to provide visualizations or local analyses of the intervening matrix between patches (Carroll et al., 2012; McRae et al., 2008; Rayfield et al., 2015). This would not have been the case for options such as individual-based models, which in addition to their more intensive parameterization and processing requirements, are less compatible with other approaches (McRae et al., 2008).
Below, I describe the primary inputs required to conduct graph-theoretic analyses of connectivity, and key considerations for developing these. In particular, I highlight some limitations of commonly used graph-theoretic methods, and opportunities to improve upon these.
Habitat Patches There are two major pieces to any graph: nodes and links. For this model to function, it must be possible to identify the nodes, as discrete habitat patches (Urban & Keitt, 2001). As described by Theobald (2006), the conception of a landscape as being a mix of habitat patches and corridors, surrounded by matrix, goes back to work by Forman and Godron (1986), developing the idea of island biogeography by
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Wilson and MacArthur (1967). Accordingly, this conception works well for areas with actual islands (Paquet et al., 2006) or for island-like systems, such as breeding ponds for amphibians, surrounded by forest (Wang et al., 2009). In the case of forest-dwelling C. oenanthe, a species that rarely leaves the canopy (DeLuycker, 2007) and is found almost exclusively in relatively isolated forest fragments (Bóveda-Penalba et al., 2009; DeLuycker, 2006), the patch/non-patch classification is a reasonable simplification.
That said, the actual methods for identifying patches accurately are important for this process: missing or incorrect patches can have major effects on model predictions (Beier et al., 2008; Moilanen & Hanski, 2006; Theobald, 2006). Even when there are no errors, dividing a landscape into patches and non-patches can result in oversimplifications of complex landscapes, which may be misleading to decision-makers (Cushman et al., 2006; Moilanen, 2011). While one can define a patch simply as “a surface area differing from its surrounding in nature or appearance,’’ (Wiens, 1976), the locations of patches will depend upon the perceptions and scale of the species of interest (Girvetz & Greco, 2007; Wiens, 1976). Identifying patches requires making decisions on which cells count as habitat, how large an area must be to be considered a patch, how to aggregate habitat, and whether any edge effects apply (Beier et al., 2008; Moilanen, 2011; Philibert et al., 2008).
Habitat Links The second major input of any graph analysis is the set of links (or edges) that identify which habitat patches are connected, for dispersing individuals of the species under consideration. Technically, the term ‘edge’ is the more general one: links are any edges that do not loop back to their starting node (Bondy & Murty, 1976). Because individuals that leave their source patch and immediately return do not affect most analyses of species dispersal, these terms can generally be used interchangeably. I use the term ‘link,’ to avoid confusion regarding the word ‘edge’ later in this report, where I discuss individuals leaving the edge of one patch, and reaching different points along the edge of a destination patch.
Depending on the dispersal distance threshold selected, different patches will be connected in the graph (that is, if individuals can travel farther, more patches will be reachable). The dispersal distance may be selected based on results from previous studies (e.g. Minor et al. (2009)), or by identifying a critical threshold after which graph connectivity plateaus or declines (Bunn et al., 2000; Keitt et al., 1997). Thresholding graphs inevitably means that some information will be lost, which could potentially oversimplify the landscape being studied (Moilanen, 2011). It is therefore valuable to test different thresholds, and to communicate the effects of this threshold, when discussing the results of these analyses with decision-makers.
Link length is most commonly calculated using Euclidean distance or cost-weighted distance (Cushman et al., 2009; Sawyer et al., 2011). Euclidean distance is the simplest possible approach, just the straight-line distance between each pair of patches within some designated dispersal distance (e.g. Coulon et al. (2004)). While Euclidean distance may work well within homogenous landscapes, it is inherently limited (Miller & Wentz, 2003). Euclidean distance does not perform well when barriers (such as rivers or roads) are present, or when heterogeneity in the landscape affects species movement or mortality, as is generally the case (Bunn et al., 2000; McRae, 2006).
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Because of these limitations, cost-weighted (also called effective or least-cost) distance, calculated using least-cost paths between two patches, has become the most common method for analyzing connectivity (Sawyer et al., 2011; Theobald, 2006). This works first by generating a cost surface (described in more detail below), representing the cost of crossing each cell, in energy or increased risk, then using this to calculate the cumulative cost of crossing each additional cell from a starting point (Adriaensen et al., 2003; Theobald et al., 2012). Thus, the value for any given cell will represent the total cost for an individual to reach that cell from the edge of its starting habitat patch (Theobald, 2006). Once cost distance values have been calculated, least-cost paths can be generated, identifying a path that follows the lowest cost values between a pair of habitat patches (Theobald, 2006). Studies using genetic data have shown least-cost distances to be more correlated with genetic distance than Euclidean distance is (Coulon et al., 2004; Michels et al., 2001; Spear et al., 2005; Stevens et al., 2006).
Some have criticized the apparent implications of this approach: that an omniscient animal carefully plans the most optimal route in advance (Baguette & Van Dyck, 2007; Fahrig, 2007; Matisziw et al., 2015; Palmer et al., 2011). However, the use of least-cost paths does not imply that such a route is actually the path an individual would follow between two patches; instead, this is meant to give the minimum biologically realistic cost-adjusted distance between two patches when the intervening landscape is taken into account (Adriaensen et al., 2003; Bunn et al., 2000; Singleton & McRae, 2013; Theobald, 2006). Thus, one habitat patch is considered to be closer than another if it has a lower-cost route available for a dispersing animal. While some have used least-cost paths to develop spatially explicit conservation plans (prioritizing these routes for habitat protection), this approach is of limited utility since the path is only 1 cell wide (Kautz et al., 2006; Rudnick et al., 2012; Sawyer et al., 2011; Singleton & McRae, 2013).
When a route between two patches is desired for conservation planning, a better strategy is to identify corridors by summing the cost distance surfaces from two patches, then taking slices of the lowest cost regions, to identify the areas that can be reached at the lowest cost from both habitat patches (also referred to as the conditional minimum transit cost method) (Cushman et al., 2013; Loro et al., 2015; Pinto & Keitt, 2009; Poor et al., 2012; Spencer et al., 2010; Theobald, 2006). However, this can be problematic for complex landscapes, where identifying separate corridors between every pair of patches may not be the optimal conservation strategy. Others have developed corridors by buffering a least-cost path (Sawyer et al., 2011; Singleton & McRae, 2013), or by smoothing least-cost paths using a kernel density function (Cushman et al., 2009).
Multiple Low-cost Paths The obvious drawback to least-cost path analyses is that they can only represent a single path between two habitat patches, which means that they do not provide any information on the number or configuration of alternate routes (Loro et al., 2015; Sawyer et al., 2011; Urban et al., 2009). From the perspective of least-cost paths, a patch that is 99 cost units away, with a single route to it, is more connected than a patch that is 100 cost units away, but with a thousand different routes. Similarly, least-cost paths do not account for the influence of patch shape on dispersal (Paquet et al., 2006): particularly between long patches with a long strip of intervening lands, many different routes may be possible (Theobald, 2006). Finally, by only reporting the shortest possible route, researchers are likely to underestimate the true distance traveled (Theobald, 2006).
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One solution to this problem would be to identify multiple low-cost connections between patches. This would allow managers to evaluate redundancy as an indicator of resilience: if one pair of patches is joined by a single route, and another is joined by a thousand, the second pair might be a better place to allocate resources, since it would be more likely to remain connected after further landscape impacts (Schick & Lindley, 2007; Theobald, 2006; Urban et al., 2009; Zetterberg et al., 2010). Alternately, barely connected patches might represent a better option for restoration initiatives, to improve connections between these patches. Identifying and analyzing multiple possible routes between patches can assist with either of these strategies, to prioritize lands for conservation actions (Urban et al., 2009).
Identifying many plausible routes between patches, rather than just the best route, would resolve the main issues with least-cost paths, and would provide a more detailed perspective on landscape connectivity: the question is, how can these be generated? Theoretical work at identifying multiple low-cost paths is challenging to implement in practice for conservation purposes (Eppstein, 1998; Liu & Ramakrishnan, 2001). One approach is a factorial analysis of least-cost paths, which involves identifying large numbers of paths between random or uniform points throughout the habitat patches (Landguth et al., 2012; Rudnick et al., 2012). The problem with this approach is that capturing the contours of connectivity between complex polygons requires large numbers of paths (e.g. 1000 paths between each pair of patches, in Compton et al. (2016)). This can be intensive in time and processing power, even with attempts to improve computational efficiency (Landguth et al., 2012). Another implementation, by Pinto and Keitt (2009), iteratively calculates least-cost paths 100 times from the same start and end points, but with a semi-randomly constrained cost surface to push paths in different directions. Implementing this is more complicated, and again requires that least-cost paths be identified many times for each pair of habitat patches, which can be computationally intensive.
The best approach I have found was developed by Theobald (2006), which identifies the allocation boundary (the line demarcating the portion of the cost surface closest in cost units to one patch from the portion closest to the second). The author then uses this line to extract cost values, to capture a range of possible cost distance values for crossing from one patch to another. This is a very useful approach; however, it is likely to run into challenges in realistically representing connectivity for more complex landscapes, where there are large numbers of patches with complicated allocation boundaries.
For this reason, my goal in this project was to develop an alternate method of identifying multiple low-cost paths, one that would work well for large numbers of patches and complex landscapes, and that would do so in an ecologically realistic and computationally feasible way.
Resistance Surfaces Regardless of whether single or multiple paths are identified, in order to calculate cost distances, a key step is the development of an appropriate cost surface (or resistance surface, used interchangeably) (Beier et al., 2008). Cost values can indicate reluctance or inability to move through a land cover type, and can incorporate energetic costs, physical stresses, risks to mortality, or losses in reproductive fitness (Adriaensen et al., 2003; Rayfield et al., 2010; Sawyer et al., 2011). This may also be related to habitat suitability: individuals will be more likely to move into land cover types that offer greater protection and resources (Fahrig, 2007; Sawyer et al., 2011).
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There are inherent limits on the level of detail that can be included in a cost surface: dispersal is both a species-level and an individual-level behavior, influenced by seasonality, weather events, individual health and movement behavior, habitat selectivity, population density, and other factors that would be difficult to incorporate into a resistance surface (Baguette & Van Dyck, 2007; DiBacco et al., 2006; Fahrig, 2007). As a further complication, individuals can respond to less favorable habitat types by avoiding these – or by traveling rapidly in a straight line to cross this land type quickly (Tracey, 2006). This second possibility could actually increase connectivity across unfavorable habitat types in some circumstances (Tracey, 2006).
All of these factors need to somehow be synthesized into a single value, for each cell in a cost surface. Typically the resistance value of ideal habitat is set to 1 (Adriaensen et al., 2003), but the range in possible values varies wildly between studies. In a literature review by Rayfield et al. (2010), they found that resistance values ranged from 1.7-3.5 (O’Brien et al., 2006) to 1-100,000 (Verbeylen et al., 2003). The greater the range in relative values, the more a path can diverge from the straight-line route (Adriaensen et al., 2003).
A variety of approaches can be used to develop cost surfaces. In a review by Zeller et al. (2012) of almost 100 different studies, the most common method by far was expert opinion (e.g. Graham (2001)), used in 80% of all studies, and the sole data source for 43% of studies. Sawyer et al. (2011) found that expert opinion and literature review remain the most common methods for developing cost surfaces, that only 9 of 24 studies used some form of model validation, and that only 2 succeeded in validating their results based on species behavior.
Expert opinion-based cost surfaces have attracted a great deal of criticism. Clevenger et al. (2002) found that a model based on expert opinion performed worse than either an empirical or a literature-based model. In one case, expert-derived resistance surfaces actually performed worse than the null model, where all resistances were set to 1 (Charney, 2012). Even when these methods perform well, it is generally not obvious why particular costs are set for particular habitat types, and it is difficult for experts to decide how to evaluate the cost of one feature type against others (Spear et al., 2010). Experts can be biased in their ideas of what landscape features are relevant to the species of interest, and at what scale (Cushman et al., 2006; Sawyer et al., 2011). Finally, experts tend to overestimate their own certainty (Beier et al., 2009). According to Cushman et al. (2013), the use of expert opinion, without any validation, has been one of greatest shortcomings of previous work to develop resistance surfaces.
Many recommend that empirical data be used to create or validate resistance surfaces (Adriaensen et al., 2003; Sawyer et al., 2011; Seoane et al., 2005). Actually doing this, however, can be difficult. Some researchers have used empirically derived habitat suitability maps to develop resistance layers (e.g. Chetkiewicz and Boyce (2009)), but this assumes that habitat quality directly corresponds to species movement (Cushman et al., 2013). In the case of this project, habitat suitability maps were created at a much lower resolution than would be useful for a connectivity analysis of this species.
When they are available, empirically measured mobility rates can be used, but these alone will not capture differences in dispersal behaviors, evolved responses to feature boundaries, or responses to habitat fragmentation (Baguette & Van Dyck, 2007; Fahrig, 2007). Other empirically based methods use telemetry (Kautz et al., 2006; O’Brien et al., 2006), genetic data (Cushman et al., 2006; Richardson, 2012; Spear et al., 2010; Wang et al., 2009), mark-recapture studies (Harrison & Bjorndal, 2006), detailed observational data (Stevens et al., 2006), stable isotopes (Marra et al., 2006), or a combination of these
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(for general information on different approaches for using empirical data to develop resistance surfaces, see Beier et al. (2008), Cushman et al. (2013), Sawyer et al. (2011), and Zeller et al. (2012)). All of these approaches present their own complications – and in any case, none of the datasets they rely upon were available for this species or study area.
This is a common problem. Zeller et al. (2012) points out that while expert opinion may be less rigorous than empirical data, it allows many types of information to be synthesized, and it is frequently the only method available, particular in conservation contexts where urgent action is needed. Additionally, while it may not be as accurate as good empirical data, research by Murray et al. (2009) found that expert opinion nonetheless provided valuable input, so long as experts were questioned on their own geographic area of expertise. While Baguette and Van Dyck (2007) recommend that “collecting comprehensive dispersal data on the population-landscape study system should be the first step” in conducting a connectivity analysis, this is not always possible. As Schaffer-Smith et al. (2016) point out, rare species, which are of greater conservation concern, are also more difficult to study because of their rarity. Datasets that are readily available for common species can be much more difficult to acquire for rare species. For example, in the case of the San Martin titi monkey, foreigners are not allowed to access species genetic data, because of concerns over unethical practices related to ethnobotany; this makes landscape genetic analyses more difficult for foreign scientists (Bóveda-Penalba, 2017).
Thus, while expert opinion is not the preferred option for developing cost surfaces, in many cases it is the only option. This presents a quandary, though: how do we make use of a method we know could be inaccurate? In addition to biases or oversights by experts, there may be actual errors in the data, such as misclassified cells in remotely sensed data (Zeller et al., 2012). Small errors in the resistance surface (for example, a gap in the lines for highways or rivers) can lead to major differences in the cost distance rasters produced (Adriaensen et al., 2003; Moilanen, 2011; Singleton & McRae, 2013). Likewise, incorrect estimates of patch locations, areas, quality, or consistency can all affect evaluations of connectivity (Moilanen & Hanski, 2006).
Uncertainty Analyses In order to deal with the uncertainty introduced by all these sources, many have called for some form of uncertainty analysis, to better account for errors and random variation when performing connectivity analyses (Beier et al., 2009; Beier et al., 2008; De Genst et al., 2001; Rudnick et al., 2012; Zeller et al., 2012). These approaches allow researchers to better evaluate parameter sensitivity (that is, how much a small change in the parameters changes the result) and parameter uncertainty (that is, given the range of uncertainty we have about the input parameters, what is the range of uncertainty in the output values?) (Urban et al., 2009). Separate reviews by Sawyer et al. (2011) and Zeller et al. (2012) found that only one third of studies performed sensitivity or uncertainty analyses on their resistance surfaces. These analyses are not a perfect solution: Beier et al. (2008) point out that for any connectivity analysis, there are too many different decision points to test them all thoroughly (though see Shirk et al. (2010) and Zeller et al. (2016) for possible ways of dealing with this).
However, in the absence of perfect data, such analyses can help decision-makers to better evaluate the benefits that would be provided from further data collection, weighing the costs of action against the costs of inaction (De Genst et al., 2001; Starfield, 1997). Beier et al. (2008) strongly advocate for the use
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of uncertainty analysis when designating corridors, to help stakeholders and managers understand the effect of uncertainty on management recommendations. Such analyses can be done either by selecting a variety of different resistance values somewhat arbitrarily (Chardon et al., 2003), or by using empirical data to calculate upper and lower bounds for the resistances (O’Brien et al., 2006). Others have taken the approach of building multivariate resistance surfaces by permuting different combinations of single-variable surfaces, with different cost values (Amaral et al., 2016; Cushman, Chase, et al., 2010).
As an example of how such an uncertainty analysis could be performed, Beier et al. (2009) evaluated corridors developed for 8 different species with 13 different resistance surfaces, premised on the idea that while it was reasonable to expect that the rank order of cost values for different land classes was correct, the actual cost values could be completely mistaken. They wished to test the effect that such mistakes could have on the resulting corridors, by testing values from the extreme edges of what could be considered plausible (Beier et al., 2009). Based on this, Beier et al. (2009) found that all species either had closely aligned corridors between cost surfaces, or had different corridors but similar total resistance values. They concluded that as long as the same rank order of cost values was kept for different land cover classes, the models were robust to differences in values (Beier et al., 2009).
Similarly, Ziółkowska et al. (2014) found that while using different types of cost surfaces altered the evaluation of connectivity metrics and the exact placement of corridors, they only had a minor effect on the prioritization of patches for connectivity. Rayfield et al. (2010) found that while most of the studies they reviewed showed some effect of changing the resistance surface, in about half of these studies the effect was minor (e.g. Schadt et al. (2002)). Chardon et al. (2003) and Verbeylen et al. (2003) found that all resistance surfaces they tested performed significantly better than Euclidean distance. While very large changes in resistance values can still have an effect (Gonzales & Gergel, 2007; Larkin et al., 2004), Rayfield et al. (2010) concluded that as long as the cost values used were within a plausible range, the exact values used should not affect many connectivity metrics, particularly in cases where a precise spatial prediction is not required. On the other hand, Rayfield et al. (2010) and Gonzales and Gergel (2007) both found that the specific resistance values selected mattered more in highly fragmented landscapes – which the San Martín department definitely is.
Therefore, we should not assume that the exact values do not matter; we should assume that they do matter, and attempt to assess how much they matter. Rae et al. (2007), makes the point that some managers, when dealing with uncertainty, either make the mistake of ignoring it completely, or make the opposite mistake of letting uncertainty paralyze them. Instead, uncertainty should be acknowledged, communicated to managers, and incorporated into planning processes (Rae et al., 2007).
There was a problem, however, with almost all the examples of uncertainty analyses that I found, testing different resistance surfaces. These were designed to test differences in cost values across the entire landscape: testing the effect of a cost of 20 for all agricultural lands across the landscape, compared with a cost of 5, or 50. What these did not do was test local uncertainty: the idea that there could be numerous factors effecting cost at a local level, which are not captured in a few land cover categories. This is important because while a global change in cost could result in more or less connectivity across the entire landscape, local changes could shift connectivity patterns from one portion of the landscape to another, potentially having a much larger effect on the overall conservation priorities. Testing for this, therefore, should be an essential part of the uncertainty analysis workflow, and it is one that has not been considered by previous studies.
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One general approach for testing such local effects involves the use of neutral landscape models. These work by applying some simple constraints, then allowing a set of random processes to build many statistically similar landscapes within those constraints (Rayfield et al., 2010; With & King, 1997). Random landscapes range from those that are entirely random (Deblauwe et al., 2012; Dilkina et al., 2013; Keitt, 2000) to landscape simulators incorporating detailed environmental processes (such as those of Urban (2005)) (Gardner & Urban, 2007). At an intermediate level are neutral models that incorporate information from a real landscape: for example, rearranging real values at random (Southworth et al., 2006; van Strien, Slager, et al., 2016; Wagner & Dray, 2015), setting land type proportions from real-world landscapes and scenarios (Rayfield et al., 2010), building landscapes outward from existing landscape features (Gardner & Urban, 2007), or simulating land use change on existing landscapes (Hagen-Zanker & Lajoie, 2008).
As with the other approaches described above, these methods allow researchers to evaluate uncertainty by testing plausible alternative landscapes, and analyzing the effects of this. However, they allow uncertainty to be incorporated at a local level, making them well suited to the development of new approaches in uncertainty analysis.
Evaluating Connectivity I have described above two potential opportunities to advance the science of connectivity analysis. First, I offer a new approach for identifying multiple low-cost paths in an ecologically meaningful and computationally feasible way. This will allow more information on landscape connectivity to be incorporated into decision-making on conservation priorities. Secondly, I develop methods to incorporate uncertainty at a local scale, when generating cost surfaces, in order to test the effect of such changes on the resulting prioritization.
Completing these two steps will result in the creation of a set of multigraphs (one for each cost surface), each far more complex than a typical graph. However, after these graphs have been created, the next step is to analyze them, either at a landscape or a patch scale (Moilanen & Hanski, 2001). There are a very large number of graph analysis methods available, taking into account the distances between patches, the amounts of reachable habitat, the probability of dispersal, and other factors (Kindlmann & Burel, 2008; Pascual-Hortal & Saura, 2006; Theobald, 2006). New graph metrics are steadily being added, to evaluate specific graph features and processes, or to report the results in a different way (Newman, 2005; Saura et al., 2011); in their review, Galpern et al. (2011) found more than 40 different graph analysis metrics.
Which metric is selected is an important decision: Ziółkowska et al. (2014) found a larger effect from metric type and parameterization than from the resistance surface they used. Different networks may experience different types of disturbances, or may respond to these differently, and particular metrics may be better suited to evaluating each of these (Melián & Bascompte, 2002; Minor & Urban, 2008; Pascual-Hortal & Saura, 2006). Some metrics may suggest higher connectivity in more heavily fragmented landscapes (Tischendorf & Fahrig, 2000), which is not an ideal result. Kareiva (2006) recommends considering carefully why greater connectivity is desired in a particular region, then selecting the appropriate metric to evaluate this.
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Baranyi et al. (2011) reviewed 13 frequently used graph metrics and evaluated the extent to which each provided unique information, missing from the other metrics. They found that these metrics could be placed into four major groups: the role of the patch as a stepping stone while accounting for redundancy (the impact on connectivity if that patch were lost); its role as a stepping stone without accounting for redundancy; how well connected a patch is (in terms of the number of connections, or the number of migrants expected to arrive or depart the patch), while considering patch size; and patch connectedness without consideration of patch size. Based on the analysis by Baranyi et al. (2011) and others, I selected three metrics to analyze my network, from three out of four of these groups.
First, degree is the number of links possessed by the analyzed patch (Jordán et al., 2003); this can also be calculated as normalized degree, the proportion of the potential links in the landscape held by the analyzed patch (Borgatti & Everett, 1997).This metric evaluates the patch’s connectedness, without accounting for area (Baranyi et al., 2011).
Secondly, landscape coincidence probability (dLCP) is the probability that two randomly placed points will be in connected patches, denoted as:
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = � �𝑐𝑐𝑖𝑖𝐴𝐴𝐿𝐿�2𝑁𝑁𝐶𝐶
𝑖𝑖=1
where NC is the number of components, ci is the sum of the areas for all connected patches, and AL is the total area of the landscape (Devi et al., 2013). This evaluates connectedness, while accounting for area: of the evaluated patch, of all connected patches, and of all habitat (Baranyi et al., 2011; Pascual-Hortal & Saura, 2006). dLCP changes with the total amount of habitat in the landscape, and declines as fragmentation increases (Laita et al., 2011). This is a relatively robust metric, and performs better than a variety of other connectivity metrics in many situations (Pascual-Hortal & Saura, 2006, 2007).
Thirdly, betweenness is the fraction of shortest paths between all pairs of patches that go through the analyzed patch (Bodin & Norberg, 2007; Borgatti, 2005), denoted as
𝐵𝐵𝑑𝑑(𝑘𝑘) = ��𝜌𝜌( 𝑖𝑖,𝑘𝑘, 𝑗𝑗)𝜌𝜌( 𝑖𝑖, 𝑗𝑗)
𝑗𝑗𝑖𝑖
where i ≠ j ≠ k, where ρ(i, j) is the number of shortest paths between i and j, and where ρ(i, k, j) is the number of those shortest paths passing through k (E. Estrada & Bodin, 2008). This metric evaluates the patch’s role as a stepping stone without accounting for redundancy (Baranyi et al., 2011). As with degree, this metric can be normalized to the number of paths in the graph. Unlike many other centrality measures, this metric can evaluate connectivity not just between nearby sites, but between distant ones as well (E. Estrada & Bodin, 2008). Sites with a high betweenness value may form a backbone to a network, through which more animals will move (Bodin & Norberg, 2007). For this reason, this metric may work well as a proxy for genetic diversity, since it prioritizes locations with relatively direct connections to many other locations, where diverse populations likely exist (Zetterberg et al., 2010). However, this metric does not take area into account, meaning that evaluations of betweenness may prioritize stepping stones between many small patches over those between two very large patches (Saura & Rubio, 2010).
The fourth group identified by Baranyi et al. (2011), which tests the patch’s role as a stepping stone, while accounting for patch redundancy, can be evaluated using the stepping stone connectivity
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components of the integral index of connectivity (dIIC) and probability of connectivity (dPC) metrics (Baranyi et al., 2011), both of which have been positively rated in other studies (Pascual-Hortal & Saura, 2006; Saura & Pascual-Hortal, 2007; Saura & Rubio, 2010), but were prohibitively slow to calculate for large and complex networks, and for this reason could not be included in this analysis.
Other Considerations There are several other issues that are worth bearing in mind when developing methods to evaluate habitat connectivity. First, it is important to note that while connectivity conservation is often identified with the goal of helping to preserve or restore routes of continuous habitat from patch to patch, this is not a requirement. Once high-connectivity patches have been identified, conservationists can work to preserve these as high quality stepping stones between other patches. They can improve the quality of the surrounding landscape matrix to make it easier for individuals to travel between patches (Noss & Daly, 2006); or they can improve connectivity through engineering solutions, such as constructing canopy bridges over roads (Teixeira et al., 2013). The purpose of this work may even be to identify sites for the translocation of wild or captive individuals, to maintain populations artificially (Noss & Daly, 2006).
Next, scale is an important aspect of this work: different species perceive habitat patches and their connectedness at different scales (Galpern et al., 2012; Girvetz & Greco, 2007), and different approaches can be used depending on whether conservationists are interested in improving the connectivity to local patches, or throughout an entire landscape (Beier et al., 2011; Zetterberg et al., 2010). Changes in scale can imply changes to dataset extent and grain, units (individuals, populations, metapopulations), ecological processes and measures, and methods of spatial analysis (Fortin et al., 2012; Singleton & McRae, 2013). Ecologically, analysis scale is affected by patch size, and by species characteristics such as body size, range of perception, movement patterns and habitat uses over space and time (Anderson et al., 2010; Awade et al., 2012; Baguette & Van Dyck, 2007; Rudnick et al., 2012; Singleton & McRae, 2013; Talley et al., 2006; Zetterberg et al., 2010).
Conservationists should also remember that connectivity is a dynamic property: flows can be unidirectional or bidirectional (e.g. Schick and Lindley (2007)), can include feedback effects, and can be influenced by other biotic or abiotic factors (Talley et al., 2006; Taylor et al., 2006). Connectivity can change over time in response to succession or land use changes, seasonal fluxes, climate change, and shifts in other species distributions (Taylor et al., 2006). Plans must be made while anticipating that changes in climate, technology, or other factors will occur, and taking a precautionary approach (Soulé et al., 2006). Additionally, connectivity is an issue affecting not just particular species, but ecological processes and communities; conservationists should integrate thinking of biological and socio-political issues, and land managers should incorporate connectivity into larger strategic planning efforts (Bennett et al., 2006). Finally, attention on connectivity between habitat patches should not lead conservationists to ignore the critical issues of habitat area and quality (Hodgson et al., 2011).
My intentions when developing this analytical approach were therefore to create methods that would be flexible, to allow the incorporation of other types of information, to allow analyses to be performed at different scales, and that would provide results that would be usable for different conservation purposes. The preceding sections have described the background for this project: the study area and
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species of interest, the threats facing these, and conservation actions being taken to protect them. I have described why habitat connectivity matters, what general approaches I explored, what the components were of the approach I selected, and what considerations I needed to take into account when developing my methods. Next, I describe the methods I developed, and how these offer an improved way to analyze habitat connectivity.
In particular, in developing these methods I sought to account for multiple low-cost paths (rather than just least-cost paths), and to analyze these in a multigraph framework. This approach allows researchers to evaluate the redundancy of connections, and thus their resilience to habitat loss or other impacts to connectivity. While circuit theoretic approaches can visualize alternative connections, they cannot analyze these separately, and do not provide easy methods for evaluating the effects on habitat prioritization following the loss of particular links. Finally, I wished to better account for uncertainty in the cost surfaces I used to analyze connectivity, by incorporating fine-scale spatial variation in cost values, when developing these surfaces. Although these methods were developed to assist in the conservation of a threatened primate species in Peru, they should be generally applicable to other species and landscapes threatened by habitat loss and fragmentation.
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Methods In this analysis of connectivity for the San Martin titi monkey, I offer two major innovations. First, I present a new method for creating multigraphs, to better evaluate the redundancy (and thus resilience) of connections between habitat patches. Secondly, I introduce a new method for performing an uncertainty analysis on these results, by incorporating local spatial variation into the resistance surfaces. The Methods section of this report is divided into three major steps: 1) developing input data (including the initial land cover dataset, then the habitat patches and cost surfaces based on this), 2) creating a multigraph using a multiple low-cost path analysis, and 3) analyzing the resulting graph using several different approaches, ending with one possible prioritization of habitat patches for conservation.
Data Land Cover The first step in this analysis was to develop a land cover dataset. I am basing this dataset on one created by Schaffer-Smith et al. (2016) and Ernest (2015) using satellite imagery from the Landsat 5 (1987), Landsat 8 (2013), and Aster (2010, 2012) collections. These datasets had initial grain sizes of 15 m (Aster), and 30 m (Landsat), and are mostly cloud-free (Schaffer-Smith et al., 2016). Rasters are from June, September, and December, but being a humid tropical region, the different months were not a major concern for the land classification (Schaffer-Smith et al., 2016). Schaffer-Smith et al. (2016) and Ernest (2015) orthorectified and radiometrically corrected these images, then classified these using an unsupervised classification with visible and near infrared bands, as well slope, elevation, and aspect from a 90-m DEM (Jarvis, 2006). Finally, they cleaned up these results using a majority filter, to eliminate isolated pixels.
Schaffer-Smith et al. (2016) and Ernest (2015) then field-validated their resulting land classes using 760 sampling locations. They estimated their classification to be 87.1% accurate, with user accuracy (errors of commission) ranging from 67 to 97%, depending on land cover type; producer accuracy (errors of omission) ranged from 72 to 96% (Ernest, 2015). In particular, clouds and shadows were a source of error in some of the high-altitude portions of the species range (Schaffer-Smith et al., 2016); there were also artifacts at the edges of the image tiles used in this analysis. Additionally, there were time lags between different satellite images (taken between 2010 and 3013), and between satellite image dates and the dates of field validation (2013 and 2014); it is not known how many changes occurred in these lands over that time.
This dataset was created using an extent based on the species’ modeled range, with a size of 178 by 201 km (Schaffer-Smith et al., 2016). I removed smaller disconnected areas from this extent (7.05% of the area), to retain only the contiguous portion of the species range; this simplifies the analysis, and excludes extremely isolated areas, which would be less likely to contain viable populations. These and the other spatial analyses were performed using ArcMap (Esri, 2015a, 2015b). Several studies had recommended that connectivity analysis extent be set to well outside the dispersal range for the species (Adriaensen et al., 2003; Anderson et al., 2010; Beier et al., 2011). Because the land cover dataset I used was clipped to the predicted species range (Schaffer-Smith et al., 2016), I was unable to do this for my analysis. The edges of the species range, given as No Data, were treated as absolute barriers when cost distances are calculated (Adriaensen et al., 2003).
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Next, I resampled the original land cover raster from a grain size of 14.25 m to 57 m, to allow for a series of comparatively rapid analyses over the full study area. I made this decision with reluctance, given the effect that such a change can have on analysis results. Finer grains are generally preferable (Stokes & Morrison, 2003); Rae et al. (2007) found that changing raster resolution had a larger effect than changing the patch delineation procedure or introducing errors into the resistance surface. However, preliminary tests indicated that performing this analysis over the original 176 million cells using 13,500 habitat patches (180 million pairwise connections) would be computationally unfeasible. I tested resolutions of one-half, one-fourth, and one-eighth the original cell dimensions, and selected one-fourth as the highest resolution that would work in my timeframe, given the number of analyses I planned to perform.
The necessity of lowering analysis resolution is a common one, particularly for graph-theoretic analyses, where least-cost path or other link evaluations need to be repeated pairwise, for all connected habitat patches; in fact, this was one of the major complaints by Moilanen (2011) in his critique of graph theory. As to the correct resolution to use, according to Zeller et al. (2012), methods do exist for empirically selecting a grain size (Thompson & McGarigal, 2002), when the correct data are available, but these have rarely been applied. Anderson et al. (2010) point out that when grain sizes are too small, the information contained in the raster may be redundant, while if they are too large, habitat patches and other features in the landscape may be overly smooth. They recommend using a grain size smaller than the dispersal distance; in this case, I am using a grain size that is less than one-tenth of the species’ daily travel movement (DeLuycker, 2007). A review by Zeller et al. (2012) found analyses with grains ranging from sub-meter to over 5 km; roughly half were between 11 and 100 m, suggesting that 57 m is a reasonable choice for this type of analysis.
The base form of this land cover dataset includes six classes: primary forest, secondary forest (cleared in 1987, reforested by 2010-2013), mixed primary forest and agriculture, mixed secondary forest and agriculture, recent agriculture (forested in 1987, agriculture by 2010-2013), and cleared (older agriculture: both 1987 and 2010-2013) (Schaffer-Smith et al., 2016). However, it is important to use land classes that are directly relevant to how the species experiences the landscape (Adriaensen et al., 2003). Cushman and Landguth (2010) found that changing the thematic resolution (that is, the number and types of land cover classes) of an analysis had a greater effect than changing the spatial grain.
To ensure that I was using an appropriate set of land classes, I solicited input from a set of six species experts, all published authors on this species: Anneke DeLuycker (Assistant Professor of Conservation Studies, George Mason University), Carolina García Suikkanen (Research Officer, Proyecto Mono Tocón), Rosario Huashuayo Llamocca (former Research Officer, Proyecto Mono Tocón), Danica Schaffer-Smith (PhD Candidate, Duke University), Silvy van Kuijk (PhD student, University of Texas at Austin), and Jan Vermeer (Zoological Director, Parc Animalier de Sainte Croix). My goal was to identify which additional land cover classes would both be useful additions to the original classes, and would be feasible to incorporate based on available datasets. Based on this expert input, I identified six additional classes that were relevant to the species ecology: small rivers (forested), small rivers (unforested), large rivers, major roads (forested), major roads (unforested), and urban areas (DeLuycker et al., 2016).
Roads can impact connectivity directly, by removing habitat or by blocking movement across high-traffic roads, and by deterring individuals from crossing into areas with food, mates, or high-quality habitat (Clevenger & Wierzchowski, 2006). Indirectly, road noise and disturbance can also reduce the quality of
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surrounding habitat (Clevenger & Wierzchowski, 2006). I am classifying roads and small rivers by whether or not they are forested: the idea here is that monkeys may be able to cross a road or a small river if there are overhanging branches, even if this is not their preferred habitat (DeLuycker et al., 2016). Without overhanging branches, crossing will be more difficult (DeLuycker et al., 2016), so costs should be higher in these cases.
I converted small rivers, roads, and urban areas to rasters; for the large river polygons, I created a raster from all cells these polygons intersected (Gobierno Regional San Martín, 2013), to prevent gaps from appearing in the rivers when they were rasterized (following Adriaensen et al. (2003). I then evaluated whether the river and road cells overlapped areas classified as primary or secondary forest in the original dataset, in order to create separate categories for forested/unforested roads and rivers. I modified the original raster to include the additional land cover classes, overwriting the original values. It is not possible, given the limitations of the remote sensing data, to actually identify points along roads or small rivers that have sufficiently dense overhanging branches to allow for easy crossing. However, it seems reasonable to assume that roads passing through cells identified as forested are more likely to have such crossings than roads crossing through unforested cells.
Habitat Patches I then identified habitat patches using areas of contiguous primary or secondary forest, with a size of at least 10 ha. Other methods exist for defining habitat patches, which allow for more detailed patch parameters when the species-specific data are available (for example, species rules on allowable sizes of gaps, or minimum habitat density: e.g. Girvetz and Greco (2007) and Theobald et al. (2006)). However, defining patches based on contiguity rules is the approach that is the most straightforward to implement, and that is most commonly used (Girvetz & Greco, 2007). Such rules are most commonly defined using a ‘4-cell rule’ or an ‘8-cell rule,’ depending on whether diagonal cells are considered to be contiguous (Girvetz & Greco, 2007).
I used the patch creation tool in the ArcGIS toolbox GeoHAT, which contains a variety of habitat and connectivity analyses tools (Fay & Urban, 2012). I modified this to separate patches using a 4-neighbor rule rather than the default 8-neighbor rule, in order to better break apart large convoluted patches. Unless otherwise specified, all Python scripts were written or modified the PythonWin integrated development environment (Esri, 2014; Hammond, 2008; Python Software Foundation, 2015).
The 10-ha patch habitat threshold I selected is larger than the estimated home range for this species (1.7 ha, according to DeLuycker (2007)), and larger also than the 2.5 ha threshold used by Schaffer-Smith et al. (2016). This prevents the smallest of potential habitat patches from being evaluated as source patches in this analysis, but it is unlikely that a small 2.5 ha patch would be a top priority for conservation work in any case, given the reduced ecological value of such small patches (Benchimol & Peres, 2013; Laurance et al., 2002) and the challenges of land protection in Peru (N. Shanee et al., 2016). Decreasing the number of patches from 14,944 (at a 2.5 ha threshold) to 4,340 (at a 10-ha threshold) decreases the number of pairwise combinations geometrically, which results in a major improvement in processing time.
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Resistance Surfaces To develop a resistance surface, I consulted again with six species experts, and from each I requested their estimates of low and high resistance values for each of the 12 land classes, on a scale of 1 to 100, based on their knowledge of the species behavior and ecology. Because empirical data do not exist to build such surfaces, I am relying on experts to develop ranges of values that seem reasonable (the ‘plausibility standard’) (Lima & Zollner, 1996; Tracey, 2006). As with Clevenger et al. (2002), the expert consultation proceeded in two phases, first identifying the important classes, then setting the cost values for each. Unlike the work by Clevenger et al. (2002), most of these communications needed to be done over email, not in person (as Pierik et al. (2016) recommended).
While researchers could use expert opinion to create a single resistance surface for their connectivity analysis, that approach does not account for uncertainty in the expert evaluations. According to Pierik et al. (2016) there are three types of uncertainty that can be created by the use of expert opinion: epistemic uncertainty, related to the limits in knowledge by the experts and the empirical data available; aleatory uncertainty, the inherent randomness of any process; and linguistic uncertainty, related to failures in communication between different parties. All three of these were a concern; linguistic uncertainty was increased by the fact that English was not the first language of several of my experts (DeLuycker et al., 2016).
Following the recommendation of Beier et al. (2009), I solicited input from multiple experts, which should reduce the uncertainty involved in this analysis (e.g. NPR (2015)). There are a variety of methods for consolidating expert opinions, which include taking the average of values provided by several experts, calculating a trimmed average by removing the highest and lowest values (Charney, 2012; Compton et al., 2007), and using decision-making trees (the analytical hierarchy process) (Zeller et al., 2012). I am following an approach similar to that of Beier et al. (2009), using experts’ estimates of low and high values to bracket the range of plausible costs. To do this, I averaged together the six low values, then the six high values, from all the experts, to create an average resistance range for each land cover class. This generates a possibility space for the land cover costs that depends upon the degree of certainty the group of experts felt about each land class. I then used these ranges for three different approaches to creating resistance surfaces.
First, I created absolute minimum and maximum rasters, as outer bounds for the analyses of connectivity. That is, if patches are not connected using the lowest possible values for resistance, based on the expert ranges, we can reasonably conclude that these habitats are not connected for this species, at least given the assumptions we have made about species presence and movement preferences, patch size, cell size, etc. Likewise, if patches remain connected even under the highest possible values of resistance, we can reasonably categorize these as connected habitats for this species. In other words, if the other assumptions are correct, we can evaluate connectivity based upon the absolute highest and lowest values that seemed reasonable to the group of species experts. This method does not incorporate other class-specific rules (see below), which impose additional constraints on the possible cost values.
The first approach identified only the lowest and highest possible values. For the second, I wished to identify reasonable low, medium, and high values, based on a random sampling of the expert-provided possibility space. To do this, I first created 50 resistance rasters with randomly selected values, bounded by the following additional parameters, created in consultation with species experts: 1) either primary
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or secondary forest can have a lower resistance value, but the lowest value should be set to 1, so that higher values will scale correctly; 2) recent agriculture must have a higher resistance than ‘mixed primary forest and agriculture’ or ‘mixed secondary forest and agriculture’ (whichever is higher), and 3) cleared must have a higher resistance value than recent agriculture, since it was assumed that recently established agricultural lands are more likely to have some remaining trees (DeLuycker et al., 2016). The bounded resampling was performed in the software package R (R Core Team, 2015), then the cost surfaces were created by reclassifying the original surface in ArcMap. Once I had created 50 reasonable cost surfaces, the next step was to choose three of these for further analysis, representing low, medium, and high values.
To do this, I used GeoHAT to build graphs for each of these 50 resistance rasters, using least-cost paths, with a threshold of 6600 units. This represents ten times the estimated daily movement for this species (660 m, from DeLuycker (2007)) in optimal habitat (resistance value of 1), but less than one day of travel through all cells with a resistance value greater than 10 out of 100. In earlier experiments, I used the graph summary tool in GeoHAT (programmed based on Urban and Keitt (2001)) to analyze the graph peak (following Urban and Keitt (2001), Bunn et al. (2000), and Keitt et al. (1997)). The peak varied widely depending on the resistance values used, but visual inspection suggested that the proposed 6600 threshold was sufficient to capture the plateaus for many sets of resistance values, and the areas of steepest rise for the others.
After building these graphs, I calculated the total connected area for each patch, using a modified version of the connectivity attribute tool in GeoHAT. I then calculated the mean connected area per patch for all 50 different resistance surfaces, and used this information to select a low, medium, and high raster in R. Specifically, out of the 50 surfaces, I identified the raster producing per-patch connected area values closest to the mean, the raster producing the highest values above the mean, and the raster with values lowest below the mean.
Both of these approaches have been based on the assumption that there is a true resistance value for San Martin titi monkeys in each cover type, and that it is somewhere within the ranges provided by species experts: the true number may be in the low end of the expert range, or in the high end, but there is just a single correct value for each land class. After completing the analyses above, I have created cost surfaces representing very low, low, medium, high, and very high portions of the expert ranges.
The third approach I used is based on a completely different assumption. Here, I assume that every cell of primary forest has a resistance value somewhere within the expert range, but one cell may have higher resistance within that range than another. Perhaps, for example, cost values should be higher in one area because of disturbance from a nearby town, or perhaps there are simply finer scale habitat differences than can be captured in a few land categories, with 57 m cells. The method I developed here assumes that there are spatial differences in the resistance values for each land class, but that we lack sufficient data to precisely quantify the real resistance value for each cell. While we do not know exactly which cells should have higher values than others of the same class, we can simulate this spatial variation to evaluate how much such changes could affect our results. Further, I am assuming that these spatial differences are autocorrelated (that is, whatever unknown factors are influencing cost values, they are more likely to similarly affect nearby cells than distant cells) (De Genst et al., 2001).
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In order to test the effects of the assumption described above, I generated a series of neutral landscape models, which will allow me to spatially vary the cost values of the landscape within the expert ranges. This approach is somewhat similar to a method used by De Genst et al. (2001) for a buffer-based connectivity analysis, though these authors created neutral landscapes by adding random noise based on a normal distribution, rather than using expert-provided ranges to vary their values.
The approach I am following uses what is called fractional-Brownian motion to introduce autocorrelation into random processes, an approach that more closely reproduces the types of variation introduced by environmental processes (Keitt, 2000). Specifically, I am using the midpoint displacement method, in which line segments are iteratively split at their midpoints, after which the midpoint is moved, and the lines are split again (Keitt, 2000). The result of this is a surface with patterns that are broadly similar to those of true landscapes (With & King, 1997). This method is simple, with minor artifacts and biases (Chipperfield et al., 2011; Keitt, 2000), but these do not appear to affect this application; according to Keitt (2000), this method is sufficient for most purposes.
To implement this method, I used the midpoint displacement function in the NLMpy Python package for neutral landscape model generation (Etherington et al., 2015), working in the Spyder environment on the Anaconda platform (Continuum Analytics, 2016; Esri, 2014; Raybaut & The Spyder Project Contributors, 2016; Van Der Walt et al., 2011). Because the midpoint displacement method requires square extents of certain set sizes, this tool creates a larger raster, and randomly clips it to the desired mask (in this case, the species range) (Etherington et al., 2015). I generated ten different randomized landscapes to test the influence of spatial variation on these results: that is, if in one version region A has high values and region B has low values, for the same land class, and in another version these values are reversed, how will this affect the overall analyses of connectivity within the landscape? Ten landscapes is clearly not enough to capture the full set of possible results; the purpose of this is to offer an indication of the effect of this kind of spatial uncertainty on the analysis results (De Genst et al., 2001).
I implemented this tool with an autocorrelation level of 0.75, where a value of 0.5 indicates no autocorrelation, and a value of 1.0 indicates 100% autocorrelation (Lau et al., 1995). Because I do not know what underlying factors influence finer-scale cost values, within a particular land class, I also do not know the true level of autocorrelation for these unknown factors. The value of 0.75, which was provided in the tool documentation by Etherington et al. (2015), and which indicates a medium level of autocorrelation, appears to create useful landscapes for testing. However, it should be kept in mind that greater clustering of high or low values would require larger detours by dispersing individuals to avoid or follow areas of high or low costs (De Genst et al., 2001). Therefore, I would expect different autocorrelation values to have different effects on connectivity. Further analyses could be used to test the effect of changing autocorrelation values on the connectivity results, but this is beyond the scope of the current project.
Multigraph Creation A typical least-cost distance is calculated first by generating a cost distance raster from the source patch, then finding the lowest possible cost distance value in the destination patch. This means that while an entire raster is created, only one value from this surface is used. The method I developed uses this same
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dataset, a cost distance raster, but instead of only keeping one cell, it keeps all cells along the edge of the destination patch. The idea here is that if a dispersing animal is travelling through the matrix, there are a near-infinite number of paths that it could take, but there is a single shortest route possible to each edge location in its destination patch from the source patch. By identifying the values of each of these cells, we can then build a multigraph, with a set of links representing the shortest paths to each edge cell in the destination patch, and keep only those within the species dispersal distance. In addition to graph analyses, this could allow conservationists to identify the portion of a patch that is reachable from another patch, to view a histogram of cost distances between a pair of patches, and to perform a variety of other connectivity analyses that would not be possible with a least-cost distance calculation alone.
To perform this analysis, I wrote a Python script that iterates among each of the patches, and generates cost distances from each. For each cost distance raster that is generated, all the destination patches in the resistance surface are masked out. The reason for this is that the goal is to identify the least-cost distance to each edge cell of the destination patch, for an animal travelling through the matrix; if the destination patches were not set to null, a dispersing animal could follow the least-cost route to the destination patch, then travel through the destination patch to each of its edge cells. In order to focus on the routes through the matrix, I blocked off further movement through the destination patches by removing these from the cost raster.
Next, I identified the cost distance value up to each edge cell in the destination patch. I then recorded all the cost distance values below the threshold of 6600 cost units, then repeated this for each of the destination patches. For example, patch A might have 10 edge cells within 6600 cost units of patch B, and 100 edge cells for patch C. Note that the number of cells of patch A that are reachable from patch B may be different from the number in patch B that are reachable from patch A. This will result in different graph links for each direction. The specific analyses that I am performing do not evaluate directionality (A to B and B to A are combined together for analysis purposes), but unlike in least-cost paths, the methods described above would allow for analyses with directional links (multidigraphs) (e.g. Abello and Korn (2002)), which could make novel connectivity analyses possible. This workflow and the workflow for a least-cost path analysis are compared in Figure 4; a comparison of graph and multigraph representations of a small test region is shown in Figure 5.
Analysis of Multigraphs I used the igraph library in R (Csardi & Nepusz, 2006; R Core Team, 2015, 2016; Wickham, 2011) to summarize the number of connections between each node pair (in either direction) and to identify separate subgraphs. I used Python to create ‘sticks’ from these: lines between each patch centroid and the centroids of destination patches (as in Spencer et al. (2010) and Beier et al. (2011)), for visualization purposes. I repeated this process for each of the 15 different cost surfaces I tested: minimum, maximum, low/medium/high (selected based on 50 random landscapes), and 10 spatially varying landscapes created using neutral models.
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Figure 4. Comparison of steps for least-cost path and multiple low-cost path analyses. Least-cost path analysis (left): a) develop cost surface and habitat patches, b) calculate cost distance from source patch, c) for each destination patch, find the lowest cost distance, d) use this value to add a link to the graph. Multiple low-cost path analysis (right): e) develop cost surface and patches, f) calculate cost distance, and threshold to the species dispersal distance, g) collect cost distance values to all edge cells within that distance, and h) use these values to build a multigraph.
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Figure 5. Comparison of graph and multigraph representations, for a small test region. Both contain 27 nodes, but the graph (a) contains 73 links, while the multigraph (b) contains 11,387 links.
To analyze my graph, I calculated degree and betweenness using igraph; I also used this package to produce non-spatial graph visualizations (such as those shown in Figure 5). I calculated landscape coincidence probability using the software package Conefor, run through command line in R (Saura & Torne, 2009; Torné & Saura, 2013). More information on these metrics is provided in the Background section. For all three metrics, I calculated the values based only on the shortest link in each node pair, rather than the full multigraph: for example, degree is calculated as the number of connected patches, not as the number of routes between each patch.
Next, I performed an iterative analysis, removing the shortest connection from each pair of nodes, then recalculating each metric for the new graph, and repeating. In other words, whereas a traditional cost-distance analysis only identifies the least-cost paths between each patch, and calculates connectivity metrics based on these, for this analysis the least-cost paths are analyzed at the first iteration, then the second lowest-cost paths are analyzed at the second iteration, then the third, fourth, etc., until no additional links can be removed. As these iterations are completed, patches will become disconnected, will lose their values as stepping stones, or will be connected to smaller subgraphs, and thus the values of the metrics will change as more links are removed.
This can be thought of loosely as a simulation of the effects of habitat degradation on connectivity. If we made the assumption that habitat loss removed connections between patches at an even pace across the landscape, for all pairs of connections, this evaluates which patches would remain connected longer, and which would immediately be isolated. Alternatively, this can be thought of as a correction for the assumption of omniscience on the part of dispersing animal: instead of asking what the landscape connectivity is for an individual choosing the least-cost route between each habitat patch, we can ask what the connectivity would be for an individual selecting the tenth best route. Either way, this
a. b.
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approach can help us to analyze not just connectivity but resilience, by looking at the redundancy of connections between different patches.
This analysis produces a much richer dataset than traditional analyses, with separate connectivity metrics for each iteration of link removal, for each cost surface. This allows us to identify which habitat patches are most important for different aspects of connectivity, based on different assumptions of the underlying cost surface, after different amounts of graph thinning. Note that even with all these variants, we are still exploring only a fraction of the uncertainty space for this analysis. As shown in Table 1, this analysis has nine major levers, each of which will affect the analysis results, and we are exploring only three of these in depth. A full analysis of all potential sources of uncertainty is beyond the scope of this project.
Table 1. Method parameters and the value(s) tested.
Parameter Value(s) tested Cost surface Minimum, Low, Medium, High, Maximum; ten spatially varying Metric Degree, Betweenness, Landscape Coincidence Probability Number of iterations Varies based on cost surface: until all links are removed Spatial grain 57 m (explored 14.25 m [the original resolution], 28.5 m, and 114 m in
early tests Cost distance threshold 6600 (explored up to 13,200 in early tests) Patch threshold 10 ha (explored 2.5 and 5 ha); 4-neighbor rule (explored 8-neighbor rule) Extent Species range, based on Schaffer-Smith et al. (2016) Thematic resolution 12 land classes Autocorrelation Level (for neutral landscapes)
0.75
However, even with just three parameters tested, this analysis still produces thousands of ways of evaluating every patch in the landscape. For example, conservation organizations might use the results based on the maximum resistance surface (minimum connectivity) if they wanted to prioritize the lands most likely to actually be connected, for further research and conservation. Alternately, they might use the minimum cost surface if they wanted to identify barely connected patches in order to conduct restoration work in the intervening habitat (that is, if patches only become connected when the intervening land cost values are reduced in the analysis, they could use restoration work to reduce these costs in the physical landscape as well). They could prioritize patches based on degree if they only wanted to conserve areas with many directly connected patches, betweenness if they wanted to conserve stepping stones, or landscape coincidence probability if they wished to conserve patches likely to be connected to more total habitat. Finally, they could prioritize patches based on their initial values, prior to link removal, if they wanted to develop projects based on current connectivity in the landscape, or after many iterations, if they wished to identify patches that would be more likely to remain connected after major losses in the intervening lands.
Depending on the interests and plans of the organizations performing the conservation work, different options could be selected. A full prioritization is beyond the scope of this analysis, since that would
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entail the compilation of a variety of data sources on species, ecosystems, land costs, feasibility, and other attributes, working closely with local stakeholders. Instead, I will describe several ways in which this dataset could be used to prioritize habitat patches for connectivity conservation. This is not meant to be exhaustive: new statistical methods could be developed to analyze multigraphs in new ways. However, the analysis methods described below all demonstrate the rich possibilities for using multigraphs for conservation.
First, for use in simple visualizations, I calculated the value for each metric after different numbers of links were removed: at the 1st, 10th, 25th, and 50th iteration. I converted these values to ranks (e.g. identified the patch with the greatest value for betweenness, second greatest, etc.), for comparison between different cost surfaces. For the visualizations in this report, I used the values produced by the medium cost surface, but comparative analyses could be performed using different cost surfaces.
For the second approach, I evaluated the rank of each patch for each metric, after each iteration (rather than just at several specific points in time). Thus, a patch with many redundant connections could maintain a high rank for a given metric for many iterations, while one with only a few links could rapidly drop from a very high rank to a very low rank. Ties were resolved using the minimum rank. I then calculated the average rank for all the iterations, such that a patch with a value of 1 would be the top-ranked patch for every iteration, while higher average values could indicate either consistently worse ranked patches, or patches that lost their values rapidly. Next, I calculated the mean and standard deviations of these average ranks between cost surfaces. Thus, a low mean indicates consistently good ranks, across different iterations and cost surfaces; a low standard deviation indicates a high degree of consistency between surfaces.
For the final approach, I calculated the proportion of iterations in which a patch was in the top 100 for a given metric, from the starting point until only 200 patches were left. (I stopped at this point because knowing that a patch is in the top 100 out of 101 remaining patches is not particularly useful). That is, at the first step I was identifying the top ~2% of patches (100 out of 4340 patches), and at the last step I was identifying the top 50% of patches. I then counted the number of times each patch was in the top 100, and converted this to a proportion, out of the number of iterations, such that a patch in the top 100 for every iteration would have a value of 1, and a patch that was never in the top 100 would have a value of 0. I summed these values for all 15 cost surfaces. Thus, if a patch is in the top 100 for every iteration for each of the 15 cost surfaces, it will have a value of 15; if it never is in the top 100 for any of these, it will have a value of 0. This combines an evaluation of persistence (will a patch remain important after many of its links have been severed?) with a measure of confidence (will a patch be rated as important for many different cost surfaces?). The key difference of this approach compared with the previous method (of averaging ranks) is that a patch with a medium mean rank may either have medium ranks from every iteration, or may drop from a very high rank to a very low rank when a connection is lost. This method evaluates the proportion of the time in which a patch is highly ranked, rather than just its average rank.
Other approaches I tested, not described in detail here, include taking the sum of the values from all iterations, which was less informative for degree and betweenness centrality, and did not work at all for dLCP (because this metric was normalized, as links are removed the dLCP of the remaining patches increases, which overly inflates the values of patches that remain connected for longer). I also attempted to prioritize patches by the number of links removed before the greatest drop in value for
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betweenness and dLCP, and again found that the normalization of the dLCP metric prevented this method from producing useful results. Again, the purpose here is not to present a single best method, but to present several different options, to demonstrate the utility of the multigraph approach. Empirical data (such as telemetry or genetics) could be used to evaluate which methods best capture actual dispersal across a landscape.
Next, I evaluated correlations between the 15 different cost surfaces, for the following patch values: rank of each patch at the first iteration for each metric; mean rank through all iterations and cost surfaces; and the proportion of the iterations in the top 100 for all metrics. For the first two of these, correlations were calculated using Spearman’s rank-order correlation, since these are rank values; for the last method, I calculated correlations using Pearson product-moment correlation.
Again, a comprehensive prioritization was beyond the scope of this project, but as an example of a possible approach, I took the summed proportions for each of the three metrics, as described above (e.g. maximum value of 15 indicates that patches are in the top 100 of all iterations and cost surfaces), and added these together. Thus, a high value (of 45) indicates that a patch is in the top 100 for each iteration, for each cost surface, and for each of the three metrics. A low value (of 0) indicates that a patch was never in the top 100 for any iterations, metrics, or cost surfaces. A value of 22.5 would indicate that a patch was in the top 100 exactly 50% of the time.
I then identified the top 100 patches based on this combined metric (that is, those that were in the top 100 most frequently), as a final set of recommended patches. Following Beier et al. (2011), I am reporting the final connectivity areas as an ensemble of options rather than as a ranked list of priorities, which can provoke discord among stakeholders and partners, and may imply a false degree of precision. My purpose is to identify a portfolio of high-connectivity patches that conservationists might look into further, in combination with other factors. Depending on which aspects of connectivity decision-makers value, in combination with other ecological, social, or cost attributes, they could use this dataset in different ways, to prioritize the areas that are best suited to their values and goals.
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Results Land Cover and Habitat Patches The first analysis step was to produce a modified land cover dataset, incorporating new land classes. The modifications to the original dataset seem to have been fairly seamless: what artifacts there are in the image come from satellite images taken at different dates, not from the addition of roads, rivers, and urban areas to this dataset (Figure 6). The reduction of resolution from 14.25 to 57 meter cells, both for the land cover dataset and the habitat patches, had an effect, but the proportion of the land area occupied by each land cover class was generally similar between the high and low resolution versions. The greatest differences were in the linear features (roads and rivers), which occupied a greater proportion of the land when the resolution was reduced, as the same linear feature crossed larger cells (Table 2).
There was a slight decrease in habitat patch area with the increase in resolution, at both of the tested patch size thresholds. Increasing the patch area threshold from 2.5 ha (used by Schaffer-Smith et al. (2016)) to 10 ha had a large effect on the number of patches (from 14,944 to 4,340, a 71% reduction) but had a much smaller effect on patch area (from 374,700 to 325,200 ha, only a 13% decrease). Overall, the increase in the patch size threshold did not appear to affect the distribution of patches across the landscape (Figure 7). While it removed small areas of forest as source patches, these remain in the cost surface as locations through which the species can more easily travel.
Table 2. Land classes and habitat patches. Numbers are given as the percent of total, for high resolution (14.25 m cell size) and low resolution (57 m) rasters. Habitat patches are made of contiguous primary and secondary forest areas greater than 2.5 or 10 ha.
Land Class Percent of Area High Resolution Low Resolution
Primary forest 27.5 26.5 Secondary forest 6.6 6.4 Primary forest/agriculture 30.0 29.0 Secondary forest/agriculture 7.8 7.4 Recent agriculture 16.9 15.9 Cleared 8.1 7.5 Small rivers (forested) 0.5 2.0 Small rivers (unforested) 0.2 0.7 Large rivers 1.3 1.9 Major roads (forested) 0.3 1.2 Major roads (unforested) 0.3 1.1 Urban 0.4 0.4 Patches (>2.5 ha) 29.5 28.3 Patches (>10 ha) 26.2 24.5
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Figure 6. Land cover map of the species range, including additional land cover classes recommended by species experts.
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Figure 7. Habitat patches in the species range, above 10 ha and between 2.5 and 10 ha.
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Resistance Surfaces The experts assigned a high degree of overlap to several of these classes (e.g. primary and secondary forest). In some cases, the ranges they identified were quite large (e.g. mixed secondary forest and agriculture, between 20.0 and 64.2 cost units), while other ranges were extremely small (e.g. large rivers: 99.0 to 100.0 cost units) (Figure 8).
The low, medium, and high cost surfaces (identified based on the amount of connected area calculated per patch from each of 50 randomly generated cost surfaces) provided a useful range of values. However, instead of producing a low-cost surface with the lowest value for each land class, for some land classes the low-cost surface actually had a higher cost than the high cost surface. The reason for this was that these resistance surfaces were selected based on the overall connected area, which was affected by the values for all land classes: an extremely low value for primary forest and mixed primary forest and agriculture could make up for a slightly high value in mixed secondary forest and agriculture, for example.
Given enough replicates, eventually the low-cost surface would approach the minimum values for all resistance surfaces, but the 50 surfaces generated were not sufficient to attain this. These are still useful: the purpose of the low and high surfaces was to identify reasonable variations of resistance surfaces based on the judgment of experts, who might have been on the high end for some land classes and on the low end for others. However, this could produce the surprising result that in some local areas patches may be better connected in the high cost surface than in the low. In particular, the low-cost surface will produce very different results depending on whether patches are separated by mixed primary forest/agriculture or mixed secondary forest/agriculture. Analyzing a greater variety of cost surface would provide greater differentiation between the three surfaces selected. However, as it is, these provide a wide range of possible costs, which are useful for comparison.
The spatially varying cost surfaces also included a good range of possibilities to test (two examples of these are shown in Figure 9, with the minimum and maximum cost surfaces for reference). The values for each class vary by cell between the minimum and maximum costs shown in Figure 8. The differences are more apparent over larger scales: for example, in some surfaces the entire northern portion of the range tended to have higher values than the southern areas, while the finer scale differences are more difficult to distinguish. Modifying the level of autocorrelation would affect this, providing higher or lower degrees of clumping. This autocorrelation level worked well for the current analysis, since it generates a range of multigraphs that are different at broad scales, which will affect broad-scale connectivity throughout the landscape.
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Figure 8. Ranges of resistance values for each land cover class. These ranges are based on consultation with six species experts; the minimum and maximum values for each bar are taken from the average of the low and high values, respectively, from each of the experts. The other points come from randomly generated low, medium, and high cost surfaces (note that this does not indicate low, medium, and high values for every land class, just that the cost surface as a whole tended towards low, medium, or high connected area values).
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Figure 9. Four resistance surfaces. a) The maximum cost surface possible, based on the expert-provided ranges, b) the minimum possible cost surface, c) and d) two examples of costs based on neutral landscapes, with values that vary spatially at multiple scales. Note that d) has higher costs than c) in the southern portion of the range, but lower costs in the northern areas.
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Multigraph Creation There are substantial differences in connectivity between cost surfaces, not just in which patches are connected, but in the number of connections, and the distribution of connection costs. For example, the low-cost surface produces both more links for a given patch, and more low-cost links, than the high-cost surface (Figure 10). The spatial representation of the full multigraph for a few representative cost surfaces (Figure 11), shows the influence of the cost surface on the results.
While some areas have many connections in all the cost surfaces, the differences between surfaces could have important implications for conservation planning. In this case, I prioritized areas that have high connectivity values for many different cost surfaces. However, these same results could be used to highlight other areas. For example, if patches are either strongly or weakly connected based on the resistance surface used, this may indicate opportunities for restoration: a restoration project that reduced the dispersal cost through the intervening land area could turn a weakly connected patch into a strongly connected one. Thus, while the areas of overlap in Figure 11 may indicate conservation priorities, the areas of difference could indicate priorities for restoration.
Figure 10. Effects of different resistance surfaces on connectivity. This example shows each link for a pair of patches, sorted by cost distance, based on the low, medium, and high cost surfaces.
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Figure 11. Multigraphs from four different resistance surfaces. a) The maximum cost surface possible, based on the expert-provided ranges, b) the minimum possible cost surface, c) and d) two examples of costs based on neutral landscapes, with values that vary spatially at multiple scales. The line width and color indicates the number of connections between each patch. These show only the northern portion of the species range, to provide more detail on the differences in connectivity between surfaces.
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Analysis of Multigraphs For all cost surfaces, the number of connected patches in the graph initially declined rapidly as links were removed, then the rate of decline slowed until only the largest and most highly connected patches remained (Figure 12). For individual patches, in most cases betweenness and landscape coincidence probability tended to decline more rapidly than degree. A spatial comparison of this, in Figure 13, shows that betweenness values dropped off rapidly, while the dLCP values became concentrated in a decreasing number of patches.
Plots of the changes in connectivity as links were removed are shown in Figure 14 for two example patches, both well-connected, but representing different kinds of outcomes. For both patches, degree values declined slowly and betweenness values declined rapidly, for all cost surfaces. On the other hand, for one patch the dLCP value first rose slowly then dropped off rapidly for all surfaces, while for another patch the values shifted rapidly up and down as links were removed, and there were major differences between cost surfaces. Landscape coincidence probability behaved erratically because of the normalization of this metric, which caused connected patches to see increasing dLCP values as other patches became disconnected.
Figure 12. Number of remaining patches in the graph as links are removed. This figure shows the results for all 15 cost surfaces, with the lines at the far left and right representing the maximum and minimum cost surfaces, respectively.
When calculating the top 100 patches at the first iteration, there was a substantial amount of overlap between cost surfaces. Between a theoretical minimum of 100 patches (if the same 100 patches were identified for all iterations), and a maximum of 1500 (100 different patches for each of the 15 cost surfaces), all three metrics had total numbers of patches between 250 and 350. dLCP had a higher degree of overlap (253 patches), than degree (315) or betweenness (342), both of which had more patches in the top 100 for only 1-3 of the cost surfaces (Figure 15).
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Figure 13. Values for three metrics, at different levels of connectivity. Maps indicate habitat patches as points, proportionally sized based on their values for degree, betweenness, and landscape coincidence probability, at the 1st, 10th, 25th, and 50th iteration, where at each iteration one link is removed from each node pair. These maps were created using the medium cost surface only.
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Figure 14. Examples of changing values for two different patches. The values for degree, betweenness, and landscape coincidence probability (dLCP) values are shown for each iteration, after removing another link from each node pair. Note the different behavior of dLCP between a) and b).
Figure 15. Overlap in top 100 patches, between cost surfaces. The number of surfaces for which each patch was identified is shown, based on the initial value only (before removing any links).
a. b.
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Calculating the mean rank across iterations and cost surfaces led to similar clusters of patches being identified as important for all three metrics, but betweenness highlighted more areas in the south than the other two metrics (Figure 17). The actual ranks depended on the tie evaluation method used: because I used the minimum rank in cases of ties, the mean ranks tended to be somewhat low. That is, if three patches were tied for first, all received a rank of 1, such that the 50th patch might have a rank value of 30, rather than 50. As the number of patches declined, the ranks of those patches remaining in the graph tended to improve.
This was particularly true for betweenness because of the link geometry involved: whereas a patch needed to be connected to at least one patch to have a value for degree or dLCP, it required connections to two patches to have a value for betweenness. Because of this, more patches lost all their value as stepping stones sooner, giving the remaining patches better ranks for this metric. This meant that patches tended to have better ranks for betweenness, overall, compared with the other metrics (Figure 16). Thus, while Figure 17 shows 77 and 61 patches with mean rank values better than 40 for degree and dLCP, respectively, it shows 159 for betweenness. This dynamic would need to be taken into account if this approach were used for patch prioritization.
Patch ranking was relatively stable between cost surfaces, particularly for the better ranked patches. For the top 50 patches of each metric, the average standard deviation in ranks between cost surfaces was 7.8 for degree, 7.4 for betweenness, and 6.0 for dLCP, compared with 15.6, 11.7, and 12.4, respectively, for the next 50. Thus, while patch rankings differed between cost surfaces, the highest ranked patches were fairly consistent (Figure 16).
Figure 16. Mean and variance in patch ranks, across all iterations and cost surfaces. The mean (shown as a line) and standard deviation (shaded area) between cost surfaces was calculated from the mean rank from all iterations for each cost surface. Results are shown for the first 100 patches only.
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Figure 17. Mean patch rank, for all iterations and cost surfaces, for degree, betweenness, and landscape coincidence probability values.
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Identifying patches in the top 100 for the most iterations, in the most cost surfaces, highlighted priority patches (Figure 18) that were generally similar to those identified by the previous method. Many of these patches were in the top 100 for many iterations, across a variety of different cost surfaces. Note that ‘top 100’ refers to the actual top 100, not all patches with a rank higher than 100 (which would include more than 100 patches because of ties). Overall, there was a medium to high mean correlation between cost surfaces for all of the metrics I compared (Table 3). High correlations were found even between very different cost surfaces, and these were found for very different methods of analyzing the multigraphs. Similarly high correlation results were produced when only the spatially varying cost surfaces were included, or when only the static cost surfaces were used.
For the different metrics, I got different results for the summed proportion (calculating the proportion of the iterations for a single cost surface in which patch is in the top 100, then summing for all surfaces: values range from 0 to 15). In the case of betweenness, the summed proportion of the patches in the top 100 declined very rapidly as I moved beyond the highest value patches. That is, there was a comparatively small number of patches that were identified as initially important for all surfaces, and that continued to be important as patch connections were removed. For degree and dLCP, the decline was less rapid, with 45 and 53 patches, respectively, with summed proportions greater than 10 out of 15, compared to only 22 patches for betweenness. That is, for betweenness there were only 22 patches that were in the top 100 more than two thirds of the time.
Table 3. Correlations of values for each patch, between 15 cost surfaces. Values in red show high positive pairwise correlations (>0.70), values in orange show medium correlations (>0.50), values in yellow show weak correlations (>0.30); values in blue are uncorrelated (<0.3). Correlations are given for the rank of each patch at the first iteration for each metric, for the mean rank through all iterations, and for the proportion of the iterations in the top 100. Spearman’s correlation was used for the rank values, while Pearson was used for the proportions. The overall value for the proportion in the top 100 comes from the sum of the previous three metrics for each patch; the mean rank overall is the mean of the previous three metrics.
Variable Min Mean Max Degree Rank 0.624 0.831 0.895 Betweenness Rank 0.674 0.893 0.935 dLCP Rank 0.499 0.756 0.835 Proportion of iterations in top 100: Degree 0.453 0.773 0.861 Proportion of iterations in top 100: Betweenness 0.611 0.823 0.894 Proportion of iterations in top 100: dLCP 0.549 0.804 0.866 Proportion of iterations in top 100: Overall 0.550 0.835 0.885 Mean Rank: Degree 0.269 0.678 0.769 Mean Rank: Betweenness 0.724 0.894 0.921 Mean Rank: dLCP 0.681 0.865 0.911 Mean Rank: Overall 0.707 0.879 0.922
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Figure 18. Proportion of the iterations in the top 100 patches. This was calculated for each patch from the start until 200 patches were left, then these values were summed for the 15 cost surfaces. Values range from 0 to 15, where 15 indicates that a patch was in the top 100 for every iteration, in every cost surface, and 0 indicates that the patch was never in the top 100.
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The final prioritization, based on the combined summed proportion from the three different metrics (the proportion of the number of iterations in the top 100, summed for all cost surfaces, then summed for all metrics), is shown in Figure 19. This identifies one large cluster of patches in the northern part of the range, and several smaller clusters of patches in other areas. As Figure 20 shows, in some cases these patches are identified for their importance for all three variables, while in others a patch may never attain the top 100 for betweenness, but may consistently be in the top 100 for the other two metrics. There was a substantial amount of overlap between these metrics: the top 100 patches for each of the three metrics separately were collectively captured by just 173 patches (out of a potential range of 100-300, for complete overlap to no overlap).
For the top patches betweenness took a smaller share of the overall values than the other two metrics, because there were fewer patches with consistently high values. Overall for these 100 patches, 28.2% of the value came from the summed proportion for betweenness, compared with 34.8% and 37.0%, respectively, for degree and dLCP (that is, if one stacked all the bars from Figure 20 for each of the three colors, the betweenness bar would be somewhat shorter than the other two bars).
The reason for this is that the betweenness values were spread out among more patches: where for degree or dLCP the same patch might be in the top 100 every time, for betweenness a patch might be in the top 100 one time, then in the bottom 100 for the next iteration, as its connection to the rest of the graph was severed. Only 53.6% of the total summed proportion for betweenness was taken by the first 100 patches. To put this another way, if there were 1000 iterations, and 15 cost surfaces, and we identified the top 100 patches from each of those 15,000 graphs, on average each of the patches in the top 100 overall would be in the top 100 for 53.6% of those individual graphs. In contrast, though, for degree and dLCP, the same 100 patches are identified for 66.2% and 70.4%, respectively, of the iterations.
Overall, when the summed proportions of degree, betweenness, and dLCP are added together, the top 100 patches accounted for 63.4% of the total value. In other words, if there were 1000 iterations each for 15 cost surfaces and 3 metrics, for 45,000 total graphs, the same 100 patches would be flagged in an average of 67% of those individual graphs. Moreover, there was a high degree of overlap between these 100 patches, and the top 100 identified through the previous method (calculating the mean rank for all iterations, metrics, and cost surfaces). 79 patches were in the top 100 for both methods; of the remaining 21 patches, 17 were in the top 100 for the first method and the top 200 for the second. This high degree of overlap between methods, cost surfaces, metrics, and iterations, suggests that these top 100 patches should be high priorities for connectivity conservation of the San Martin titi monkey.
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Figure 19. Top patches, for combined metrics. The proportion of the iterations in the top 100 was calculated for each patch, for each metric and cost surface, then these values were summed, and ranked, to identify the top conservation priorities for connectivity overall.
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Figure 20. Proportion of iterations in the top 100, summed for all cost surfaces. Results were calculated for three metrics (degree, betweenness, landscape coincidence probability), and are shown for the top 100 patches only. This indicates, for the top 100 patches overall, how much of their summed value comes from each of the three metrics. The best patches were consistently in the top 100 for all three metrics, while lower values could either be evenly divided between the three metrics, or might indicate a very low value for one metric, but very high values for the other two.
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Discussion The methods presented in this report offer several major improvements over standard approaches to connectivity analysis. First, using multiple low-cost paths instead of least-cost paths allows conservationists to better identify habitat patches with robust connections to other patches. Instead of merely identifying one patch with a single narrow route to another, planners can identify a patch that has many different routes available to neighboring habitat areas, and that are therefore more resilient to future land use changes. Alternately, by targeting patches that are just barely connected, planners can identify priorities for restoration, to increase the resilience of the connections in the landscapes. These possibilities are not available to planners relying on a standard least-cost path approach, and are a major improvement over this method.
The second major innovation, the addition of a spatial component to uncertainty analyses of cost surface analyses, also offers major enhancements over traditional methods. Standard uncertainty analysis methods account for one aspect of uncertainty: that when experts estimate the movement cost to be one value, it may in fact be another value. I performed this analysis, but also analyzed a second aspect of uncertainty: that when experts estimate the movement cost to be one value, there may in fact be spatial differences in values, with higher costs in some areas and lower costs in others. Including a spatial component in the uncertainty analysis recognizes that there are many local factors we do not have data on, and explores the effect of such local considerations on the connectivity results. This is important because, while changing the cost value across a landscape can increase or decrease connectivity overall, changing these values spatially may increase connectivity in one part of the landscape, and decrease it in others. This could potentially have a larger effect on patch prioritization, and it is therefore important that researchers test this possibility.
There are several main conclusions that can be drawn from these results. First, different metrics are better suited to answering different kinds of questions. Degree, the simplest of the metrics, behaves the most predictably as the graph is trimmed. Betweenness, which depends upon the connections to more distant parts of the landscape, loses value most rapidly as the graph is thinned. Finally, landscape coincidence probability worked well at identifying important areas, taking patch area into account, at the initial stages. However, because this metric was normalized, as more connections were removed, some patches saw large spikes in values, followed by large drops. These differences in behavior should be kept in mind when using these metrics as part of prioritization analysis. For a true prioritization, decision-makers would need to decide how much weight they placed on each of these metrics, as well as other attributes they cared about.
Depending on how the multigraph was analyzed, different patches were identified as important. For example, if only the initial patch value is used (essentially just treating the multigraph as a simple graph), the redundancy of habitat connections cannot be analyzed. If particular numbers of iterations are analyzed (e.g. after 10, 25, or 50 iterations of link removal), which iteration is selected will affect the results greatly. Both the mean rank and the summed proportion of iterations in the top 100 patches seemed like more useful approaches for most purposes, incorporating more information from the full multigraph. The second of these was better at identifying patches that were highly valued given many different levels of connectivity and for different cost surfaces. Mean rank has the advantage that it does not depend upon the setting of some arbitrary threshold (e.g. top 100 patches), and can provide useful
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information for comparing very low ranked patches, which would all be treated as equivalent by the summed proportion method.
Many of the top 100 patches I selected had high values for all three metrics, meaning that these patches could provide strong benefits from a number of different perspectives. That is, in many cases these top patches were good stepping stones, and had large amounts of connected area, and many different low-cost routes to other patches. These might be good candidates for conservation now, as well as strong candidates for future conservation, assuming some level of habitat loss. Finally, these patches tended to retain high values for a variety of different cost surfaces, and using different analysis methods. All of this suggests that the top 100 patches identified are a good initial cut, for identifying high priorities for connectivity conservation. Many other kinds of attributes could be incorporated into these decisions, but the methods described in this report have incorporated substantially more information about patch and route configurations than a typical least-cost path analysis, and therefore offer a major step forward for connectivity analyses.
Limitations and Extensions There are some clear limitations to this work. The types of analyses I was able to perform were limited by the available data. More detailed information on San Martin titi monkey populations, densities, and movement patterns would assist in management planning and prioritization (DeLuycker, 2006; S. Shanee et al., 2013). In particular, research into areas of marginal habitat, areas with more intact forests, and different habitat types would help in better understanding this species (S. Shanee et al., 2013). Genetic research could further illuminate the species differences between different areas in its range (S. Shanee et al., 2013), and could help evaluate whether species translocations are necessary to preserve genetic diversity of this species.
The cost surfaces I used were based on expert opinion. I consulted with six different experts, which should mitigate for individual biases. Interestingly, though, while the resistance surfaces were meant to capture the full range of possible values, one category (primary forest mixed with agriculture) did not include the value estimated by species experts separately, for an analysis of the same species by Schaffer-Smith et al. (2016). While three of six of the expert ranges that were averaged together did include the value from Schaffer-Smith et al. (2016), other experts placed a higher minimum value for this class, citing the high mortality that C. oenanthe would face in this habitat, despite their relative ease of movement (DeLuycker et al., 2016).
The initial land classification that defined the patches was validated (Schaffer-Smith et al., 2016), but of the subsequent steps, from revising the land cover datasets, to setting dispersal cost values for these different land costs, to calculating connectivity and prioritizing results, none have been verified empirically. Cost values could be evaluated empirically (e.g. Chetkiewicz and Boyce (2009)), more sophisticated methods could be used to elicit expert input (e.g. Hsu and Sandford (2007)), and the results of these analyses could be evaluated through site occupancy data or interviews with local people (Zeller et al., 2011). Such work would be valuable not just in itself, for conservation of this species, but would also allow for improved learning from experience (Bennett et al., 2006).
In particular, while least-cost paths predicted genetic connectivity better than Euclidean distances (Coulon et al., 2004; Michels et al., 2001; Spear et al., 2005; Stevens et al., 2006), it would be interesting
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to compare genetic connectivity with multiple low-cost paths. Because this approach provides information not just on how close two patches are, but on how many routes there are between them, these results may be better correlated with the level of gene transfer between areas. Likewise, other data sources (telemetry, detailed observational data, etc.) might provide support for this approach, if more individuals are observed crossing between patches that have more routes between them.
The specific results I found depended upon the choices of several key parameters; adjusting these levers would change the results to an unknown degree. These levers include changing the spatial and thematic resolution, the extent, the autocorrelation level for the neutral landscapes, and the thresholds for the patch sizes and dispersal distance (De Genst et al., 2001; Moilanen, 2011; Rae et al., 2007). While I attempted to explore several sources of uncertainty (expert evaluations of cost; metrics selected; the effect of removing links from the multigraph), I was not able to fully explore all sources of uncertainty in this analysis, and this should be kept in mind when interpreting these results.
As with graph theory analyses based on least-cost paths, metrics that only evaluate the number of connections between patches (such as degree), will show more connections as a landscape becomes more fragmented; a landscape with a single contiguous forest will not have any links, while an extremely fragmented landscape may have many thousands of connections. Other metrics, such as landscape coincidence probability, do take area into account when making their calculations. To the well-known philosophical question regarding whether a single large or several small protected areas are superior, different metrics will therefore give different answers (Saura & Rubio, 2010). The metrics I chose were selected to evaluate three different perspectives on connectivity, but other metrics could have been chosen to answer specific connectivity questions.
Moreover, the best metric to choose, to answer any particular question, may be different using the multigraph approach. With least-cost paths, there will only be a single route possible between any two patches. With the multiple low-cost path approach, large patches (and in particular, large patches with long shared borders with other patches) will have many connections. As a result, this method will tend to emphasize larger patches, rather than strings of small stepping-stone patches. While this is generally a desirable result, planners should keep this in mind; if ‘patch area’ were included as a separate attribute, the use of this method might over-weight patch size, over other attributes. Additionally, with this method, more fragmented areas will lose connectivity more rapidly as links are removed: a patch connected to ten small patches will lose ten links in one iteration, while a patch connected to a single large patch will only lose one link per iteration. This will cause the ranks of more fragmented habitat to fall away more quickly than less fragmented habitat. However, further side-by-side comparisons between least-cost paths and multiple low-cost path analyses would need to be done to fully understand the effects of this on each of the metrics used, to explore in more detail the consequences of the multigraph approach, and to identify optimal metrics to deal with multigraph analyses.
In all these analyses, one link was removed from each pair of nodes in each iteration. This provides a very rough approximation for the effects of habitat loss on connectivity (as habitat is lost, more connections will be removed). The multigraph approach could be combined with more detailed models of habitat loss, to improve upon these results: instead of removing all links at a constant rate, links could be removed preferentially in different locations based on forecasts of future habitat loss. This would allow planners to more realistically model future connectivity losses, based on different development scenarios.
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It needs to be noted that all of the work completed for this project only performs the first step in a connectivity conservation project, that of identifying priority habitat patches for connectivity. Even if other important landscape attributes were accounted for (such as biodiversity, human impacts, land costs, etc.), actually implementing conservation on the ground would require many more steps, which are beyond the scope of the current project. First, like Theobald (2006)’s work, but unlike that of others (e.g. Pinto and Keitt (2009) and Landguth et al. (2012)), this method of identifying multiple low-cost paths does not draw actual routes upon a map. Thus, if the purpose of the connectivity analysis is not just to identify priority habitat patches for connectivity conservation, but to assist with parcel-level decisions on land purchases or easements between patches, this method will not immediately serve that end. These kinds of specific corridor-routing recommendations could be created by calculating least cost paths between all pairs of connected edge cells in a small set of patches. Alternately, other tools such as Circuitscape or conditional minimum transit cost corridors could be used to create visualizations of connectivity between pairs of patches, and prioritize land parcels for conservation. Such an analysis did not fit into this particular project, but any of these approaches could be easily implemented at a later stage for priority habitat patches, if Proyecto Mono Tocón or other conservation organizations needed these for their work.
Next, even if these additional analyses were conducted, using this information to implement corridors requires many more steps (for examples, see Alagador and Cerdeira (2007), Beier et al. (2006), Moilanen et al. (2011), or Noss and Daly (2006)). The design of a connectivity network depends on three key elements, according to Sanderson et al. (2006): first, the conservation of protected areas containing the habitats, species, and ecosystem services of interest; second, the corridors connecting these areas; and third, the surrounding matrix, where conservationists can encourage compatible land uses, such as shade-grown coffee. In some cases, the matrix may include hard barriers to movement, or may be associated with high mortality rates (Soulé et al., 2006). However, in others it may help to increase the viability of species, even on lands that do not form long-term habitat (Soulé et al., 2006). “Managing the matrix” is therefore an important consideration: improving connectivity is not just a matter of designating protected lands, but of implementing practices to reduce the negative effects of the surrounding areas (Taylor et al., 2006; Wiens, 2006). In all cases, applied conservation work should rely as much as possible both on theoretical work (including graph theory, metapopulation theory, population genetics, etc.), and on empirical research on how species move through the landscape (K. R. Crooks & Sanjayan, 2006).
Connectivity benefits can be provided in different ways in different parts of the landscape. Carroll (2006) points out that there may be additional opportunities for conservation in locations where the landscape is just beginning to fragment. On the other hand, for highly fragmented areas, others have shown that corridors do not themselves need to be high quality habitat, or to support resident populations, in order to improve connectivity; they just need to be higher quality than the surrounding matrix (Haddad & Tewksbury, 2005; Richard Walker & Craighead, 1997). Both of these factors mean that there may be additional opportunities for the conservation of connectivity, in a variety of different types of landscapes.
Implementation of connectivity conservation plans depends upon consideration of a long list of other socioeconomic factors, including governance, property rights, engagement with communities and other stakeholders, local buy-in, financing, capacity-building in government or other institutions, zoning, legal mechanisms, incentives, and enforcement (Brodie et al., 2015; Sanderson et al., 2006). In particular, it is
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important that conservationists work to raise awareness of the importance of connectivity (Soulé et al., 2006), and to better communicate the results of scientific analyses with decision-makers (Singleton & McRae, 2013). Decision-makers, meanwhile, can do a better job of integrating connectivity considerations into strategic planning (Bennett et al., 2006). Finally, it is important to remember that no matter what is done to improve connectivity, this is not by itself sufficient to protect a species, if strong anthropogenic pressures such as hunting continue to impact the species at high levels (Benchimol & Peres, 2013). Fragmentation and other direct and indirect human impacts should be dealt with holistically, to account for feedbacks between related threats (Brook et al., 2008). The work that has been done in this analysis only scratches the surface, of all that might be done to provide improved connectivity for the San Martin titi monkey and other species in this area.
Conclusion Habitat connectivity is a major priority for conservation work, particularly for endangered species in rapidly fragmenting areas, such as the San Martin titi monkey. The analysis described in this paper provides several major advantages over traditional connectivity analyses. First, by identifying multiple low-cost paths, instead of just the least-cost paths, it allows conservationists to better take into account the shapes of habitat patches and the configuration of routes between them. Decision-makers can prioritize patches with many connections for land protection, or areas with only a few connections for restoration work. Furthermore, while we do not know where habitat degradation will occur in the future, by simulating connectivity losses, we can identify priority patches at different levels of connectivity.
Secondly, by incorporating different land cost surfaces into our connectivity models, we can better evaluate the uncertainty that comes from the inherently subjective process of assigning land costs. By adjusting these costs spatially we better simulate actual uncertainty in the landscape. Instead of assigning all cells for a land class to a higher or lower value, we can generate higher or lower values on a cell-by-cell basis, allowing for some spatial autocorrelation, to generate realistically varying cost surfaces. By incorporating uncertainty spatially, we can test for the effects of unknown local and regional differences on habitat connectivity. This allows us to perform a prioritization that is robust to many of the uncertainties inherent in remote sensing-based analysis over large scales. Finally, by combining a variety of cost surfaces with different connectivity metrics and with analyses at different levels of connectivity loss, we can generate rich datasets that can be analyzed in a variety of ways, to highlight different sites for conservation depending on the priorities of the land manager or conservation organization.
All of this does not obviate the need for continued data collection: better empirical data can allow for improved analyses, the evaluation of different analytical approaches, and better prioritization of habitat for conservation. However, in the absence of such data, the methods described in this paper allow for improved prioritization of lands for conservation, restoration, or for future research. Because they offer more detailed results without requiring more intensive data collection, these methods should be well-suited to studies of other species facing rapid habitat losses, or species about which little is known. This approach offers a major step forward for connectivity conservation, and should be broadly applicable to other regions, ecosystems, and species.
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Acknowledgements This project would not have been possible without the generous help and support of a large number of people. In particular, I would like to thank:
• My advisors Dr. Jennifer Swenson and Dr. Dean Urban, as well as Danica Schaffer-Smith, all of whom provided essential advice and support as I was developing this project;
• Dr. Anneke DeLuycker, Rosario Huashuayo Llamocca, Danica Schaffer-Smith, Dr. Carolina García Suikkanen, Silvy Van Kuijk, and Jan Vermeer for providing habitat cost ranges for the titi monkey;
• the staff of Proyecto Mono Tocón, who helped me not only by providing me with valuable advice, but for showing me such incredible hospitality as I spent my summer in a foreign country;
• Maggie Ernest, who wrote her master’s project on connectivity analyses of the San Martin titi monkey in 2015, and who was immensely helpful as I was beginning this project;
• the Nicholas School International Internship Fund, the Center for Latin American and Caribbean Studies, and the Environmental Internship Fund for their generous financial assistance;
• and, finally, my parents, for their love and support, and for putting up with me spending my winter break working on this project.
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