Combining Behaviour and Population Dynamics with Applications for Predicting Consequences of Habitat Loss

Combining Behaviour and Population Dynamics with Applications for Predicting Consequencesof Habitat LossAuthor(s): William J. Sutherland and Paul M. DolmanSource: Proceedings: Biological Sciences, Vol. 255, No. 1343 (Feb. 22, 1994), pp. 133-138Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/49736 .

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Combining behaviour and population dynamics with applications for predicting consequences of habitat loss

WILLIAM J. SUTHERLAND AND PAUL M. DOLMAN

School of Biological Sciences, University of East Anglia, Norwich NR4 7TJ, U.K.

SUMMARY

A population model for migratory vertebrates is developed by combining game theory models of foraging behaviour with population biology. Models of foraging behaviour which incorporate interference and resource depletion are developed to determine the density-dependent mortality occurring within sites. Population size can then be related to the strength of interference, the variance in competitive ability and the rate at which resources are depleted. The model is extended to predict evolutionarily stable migration strategies. This novel framework is then used to predict the population decline resulting from habitat loss.

1. INTRODUCTION

Current models of vertebrate populations tend to depend on descriptive parameters and do not consider the individual interactions which underlie these parameters. It is difficult to interpret how a change in habitat quality or extent will modify the parameter values in such models, limiting their ability to predict the consequences for populations. A full understanding of ecological processes at the population level requires a knowledge of how individuals interact (Hassell & May 1989; Koehl 1989; Kacelnik et al. 1992), so models based on behaviour are likely to be more useful in predicting the consequences of environmental or ecological changes for populations. However, with a few exceptions (Goss-Custard 1980; Goss-Custard & Durrell 1990), most studies of individual strategies of resource exploitation have not considered the consequences for population ecology.

In this paper we first consider the behaviour of vertebrates foraging in a heterogeneous environment. We show how mutual interference between competitors and depletion of resources can lead to density- dependent starvation. We then determine population size by combining this with density-independent mortality and density-dependent breeding productivity. Population size may then be expressed in terms of behaviour parameters. Game theory is used to show that it is possible to determine both the evolutionarily stable migration strategies and the population size of migratory populations. The decline in population resulting from habitat loss can be determined: even populations that do not use the damaged site may decline as a result of increased competition caused by displaced individuals.

2. POPULATION MODEL

(a) Density-dependent mortality derivedfrom individual foraging behaviour

Vertebrates populations often experience density-

dependent mortality through food limitation, particularly during the non-breeding season (Sinclair 1989; Goss-Custard & Durrell 1990; Grenfell et al. 1992). To model this we consider the dynamics of a consumer population foraging in a patchy environment.

Two density-dependent processes, mutual interference and depletion of resources by consumers, are important in determining the degree of competition between consumers, their intake rates and their distribution among patches of different resource density (Hassell & Varley 1969; Royama 1971; Comins & Hassell 1979; Goss-Custard 1980; Bernstein et al. 1988, 1991). Interference is defined as the reversible decline in intake resulting from the presence of other individuals due, for example, to antagonistic interactions between consumers or disturbance of prey (Hassell & Varley 1969; Goss-Custard 1980). The relative im- portance of interference and depletion depends on the species involved (Goss-Custard 1980). Interference is likely to be more important where prey are easily disturbed, or where each item is large and of sufficient value to fight over (Monaghan 1980; Goss-Custard 1980; Goss-Custard & Durell 1988).

Following Hassell & Varley (1969), interference is usually expressed by

a= Qpjm, (1)

where a' is the searching efficiency of an individual in patch i, Pi is the density of consumers in patch i, Q is the Quest constant (the value of a' achieved by a solitary individual) and m is the interference coefficient. Equation (1) assumes that all individuals are equal; however, individuals often differ in competitive ability, due to age, sex, physiological differences and other factors such as prior residency. We consider a population as consisting of a number of phenotypes which differ in competitive ability. Interference can then be incorporated by using the function

a = QpmR(sMi) (2)

Proc. R. Soc. Lond. B (1994) 255, 133-138 133 ? 1994 The Royal Society Printed in Great Britain



134 W. J. Sutherland and P. M. Dolman Modelling vertebrate populations

(a)

100

0

60

~3 20

c> ,?4 0.1

(b)

0 El 60

03 2

~ 00

20

cJ)

100 ~ ~ 00

Figure 1. Density-dependent mortality through starvation (a) Altering the strength of interference, m. All individuals are of equal competitive ability. (b) Altering variance in competitive abilities. Interference is constant, m = 0.2. (c) Altering the extent to which sites are buffered against depletion, 0, 500 equal time intervals are considered. Mortality acts within each time interval before the cal- culation of depletion Interference is constant, m = 0.2, variance = 4. Competitive ability is normally distributed over 21 phenotypes spanning ? 3 standard deviations around a mean of 10. Simulations consider 1000 consumers, feeding for 10 h per day for 150 days, in a site of five patches each of 20 ha whose initial resources density ranges from one to five items per square metre. Handling time = 20 s, quest constant, Q = 0.001 m2 s-l. Threshold intake for survival = 0.001 items s-1.

where a'si is the searching efficiency of all individuals of phenotype S in patch i, and R(s,i) is the relative competitive ability of phenotype S in patch i, expressed as the mean competitive ability of all other individuals

in patch i divided by the competitive ability of an individual of phenotype S (Parker & Sutherland 1986). Models which incorporate such individual differences are biologically more realistic than those assuming equal competitors, and their predictions agree more closely with field observations (Parker & Sutherland 1986; Sutherland & Parker 1992).

Although m has been estimated for many invertebrates, there are very few published values for vertebrates. For oystercatchers, Haematopus ostralegus, feeding on mussels, Mytilus edulis, estimated values of m in different locations ranged from 0.10+0.04 to 0.35+0.11 (Sutherland & Koene 1982). We assume the coefficient of interference is constant within a given system; however, it may vary with consumer density and resource density (Beddington 1975).

By using game theory we model the distribution and intake rates for a population of vertebrates foraging in a heterogeneous environment, consisting of distinct patches differing in resource density. Patch choice depends on a trade off between the benefits of feeding in areas of high resource density and avoidance of favoured areas where many individuals aggregate as searching efficiency will be depressed through interference (equation (1) or (2)).

Bernstein et al. (1988, 1991) showed that, if individuals are able to sample across the range of patch quality efficiently in relation to the rate of resource depletion, then an evolutionarily stable strategy (ESS) iS

attained. As many vertebrate consumers meet these conditions we assume they attain such a distribution. At this equilibrium, each individual is distributed so that it achieves the maximum intake rate it can given the distribution of all other individuals of the same and other competitive phenotypes, resulting in the phenotype-limited ESS (Parker 1982).

The effect of resource depletion can be examined by considering a range of patches which initially differ in resource density (Sutherland & Anderson 1993). In the absence of interference, consumers do not avoid high densities of competitors, so they all initially aggregate in the patch with the highest resource density. Once this patch has been depleted to the same resource density as the next-best patch, consumers feed there also, so consumer density and resource density gradually become equalized over a greater range of patches. Models using this approach have been successful in predicting the distribution of geese (Sutherland & Allport 1994). Interference and depletion have usually been studied in isolation but we combine them within a temporal depletion model.

Within each time interval the phenotype-limited ESS

is determined by game theory simulation (Parker & Sutherland 1986; Sutherland & Parker 1992). Individual intake rates are calculated from the values of a' or a' derived from equation (1) or (2), assuming a type II functional response, using Holling's disc equation (Holling 1959). Depletion is determined from the intake rates and distribution of consumers, giving the resource distribution for the next time interval.

This game theory model predicts the distribution and intake rates of the consumers. With weak interference most aggregate in the patches of highest

Proc. R. Soc. Lond. B (1994)



Modelling vertebrate populations W. J. Sutherland and P. M. Dolman 135

resource density, but if interference is strong intake rates are reduced and consumers are spread more evenly. As variance in competitive ability increases, poorer competitors are increasingly displaced to patches with lower resource densities.

In some situations growth or reproduction of resources may offset depletion (see, for example, Sutherland & Allport 1994), whereas in other situations consumers feed on a standing crop of resources with no renewal during the period of exploitation. We consider the affect of varying the extent to which sites are buffered against depletion, while still holding all foraging parameters constant. To do this we introduce the parameter 0, defined as the numerical reduction in the total resource population resulting from the removal of a single resource item. When 0 is small (0 << 1), depletion is slow; when 0 is maximal (0 = 1), the total resource population is reduced by 1 for each item consumed. If the depletion rate is high then consumers become dispersed across a greater range of patches.

The nature of density-dependent mortality can then be determined by assuming that individuals need to achieve a threshold intake rate to stay alive. If the phenotype with the lowest intake rate is below the minimum intake rate for survival then that phenotype class is assumed to have died, and the distribution and intake rate of survivors are re-calculated. This process is repeated until the intake rate of all surviving phenotypes is above the threshold. Figure 1 shows the resulting relation between mortality and density. As interference increases, or if the system is more sus- ceptible to depletion, density-dependent mortality becomes stronger and starts to act at a lower population density. The relation between mortality and population density is particularly sensitivity to changes in the strength of interference, m, when m is small. If the variance in competitive ability is increased, although density-dependent mortality again acts at a lower population density, the slope of the mortality response becomes shallower.

(b) Population size

Population size is determined by incorporating the density-dependent mortality resulting from interference and depletion in the non-breeding season with population productivity and density-independent mortality in a trans-generational model.

Breeding productivity may be density dependent (reviewed by Sinclair 1989). We model this by using Maynard Smith & Slatkin's (1973) curvilinear equation for density dependence, which is considered to give the best fit to data (Bellows 1981).

P = NF[I + (aN)b]-l (3)

where P is the productivity of the breeding population, N is the number of individuals, F is the mean fecundity, a is a scaling constant, and b is the strength of the relation between density and the loss of productivity. Some studies of breeding populations have found density dependence to be weak or negligible (b 0 )

(Sinclair 1989); however, in others regulation occurs which may approach perfectly compensating density dependence (b 1) (Newton 1986; Galbraith 1988; Baillie & Peach 1992), and may on occasions be overcompensating (b > 1) (Dobson & Poole 1994).

Figure 2 shows the relation between population size and the strength of density dependence in the breeding season for each of the combinations of interference,

8

-o 0

ez me

0R CL

0~ ~ ~~~~~~~10

- 0 -0.

Figure 2. Population size in relation to the strength of density-dependent regulation of breeding productivity, b, for the conditions shown in figure 1. Mean post-breeding population is calculated over 40 generations after allowing 160 generations for the simulation to stabilize. Population breeds in a site of 25 kin2, a = 0.25, an equal sex ratio is assumed, fecundity per female = 1.2 per annum in absence of density dependence. Density-independent mortality (0.15 per annum) acts on the post-breeding population before the winter. Winter site, foraging parameters and threshold intake rate as in figure 1.





(a) (b)

geographical scale ...... 0 500

km post breeding numbers using route scaled by arrow width 0 2000

Figure 3. (a) The evolutionarily stable migration strategies and population sizes of breeding populations where individuals have a choice of wintering sites. Site array represents a hypothetical geographical arrangement, distances between site and the size of each site are shown to scale. Line widths are scaled to show post-breeding numbers taking each route. (b) The new population sizes and modified evolutionarily stable migration strategies arising following habitat loss of 75 % of area of all patches at one wintering site of simulation a. For each winter site, in each year, available resource densities vary from one to five items per square metre in five equal-sized patches. For all breeding sites, a = 0.25, b = 0.2, fecundity as in figure 2. Migration cost = 5 x 10' items per second per 1000 km. Foraging parameters and threshold intake for winter survival are as in figure 1; m = 0.2, variance = 4, 0 = 0.01.

variance in competitive ability and depletion rate used in figure 1. When productivity is strongly density dependent then this largely determines population size. However, when density-dependent productivity is undercompensating, the overall population size depends on the interaction between density-dependent processes operating in both the wintering and breeding grounds. As would be expected from the results for density-dependent starvation (figure 1), overall population size is lower if the strength of interference is high, if there is greater variance in competitive ability, or if depletion proceeds at a high rate.

3. MIGRATION

Many vertebrates show regular seasonal migration at a range of scales, from across continents for migrant birds to across tens of metres for amphibians. The productivity and mortality components of the population model may then operate at different times and places. A further complexity is that individuals from separate breeding grounds often have a potentially common winter range such that the interference and depletion they experience will depend on the wintering distribution and size of other populations. We use game theory to determine the suite of evolutionarily stable migration strategies between a range of breeding and wintering sites.

We assume breeding populations are distinct with no interchange between them. Individuals migrate to a single wintering site and do not move between sites

during the winter. Within sites, the distribution between patches, individual intake rates and survival are determined by interference and depletion, as in figure 1. Migration costs incur an additional requirement for food intake which we assume is proportional to the length of the migration route.

The choice of wintering sites can be considered as an extension of the choice of patches within a site. Within each population, each competitive phenotype is further divided into migration phenotypes which determine the winter destination of individuals. Within each breeding population, the proportion of each competitive phenotype using each migration strategy is initially equal. It is then recalculated every generation, relative to the trade off obtained by that strategy in the preceding winter. At the evolutionarily stable migration strategies, within each population, individuals of each competitive phenotype obtain the same net intake rate and will not increase this by changing their migration strategy. Using the same approaches as before, density- dependent fecundity and starvation are combined to determine the size of each population and thus the number of individuals using each wintering site.

Wintering sites are likely to differ in size and resources. Here, for simplicity, we assume that site quality does not vary between years, however, stoch- astic variation could be incorporated. Breeding sites are also likely to differ in size and quality, which may affect both productivity in the absence of density dependence (parameter F in equation (3)) and the critical density at which density dependence starts to




Modelling vertebrate populations W. J. Sutherland and P. M. Dolman 137

operate (parameter a) (Holmes 1970; Newton 1986). Figure 3 a shows an example of the evolutionarily stable migration strategy and population sizes obtained for a set of scattered wintering and breeding sites. The size of each population (the thickness of the lines in figure 3 a) is dependent on a complex interaction of the size of the wintering area, breeding area, the length of the migratory journey and competition with other populations in the wintering grounds.

4. HABITAT LOSS

This framework may be used to assess the effect of a loss of wintering habitat on overall population size. Loss of wintering habitat may result in a higher density of consumers in the remaining habitat, which in turn results in greater interference and depletion and thus lower intake rates, leading to higher winter mortality and a lower overall population size. Figure 3 b shows that habitat loss in one wintering site may markedly reduce the size of breeding populations which primarily winter in that site, but that further knock-on effects may also occur. For example, increased competition with displaced individuals may lead to increased winter mortality, resulting in reduction in breeding populations that did not use the damaged site.

This approach may also be used to consider the consequences of piecemeal habitat loss. We illustrate this by removing wintering habitat patch by patch and recalculating the evolutionarily stable migration strategy at each state. Figure 4 shows the extremes. In one simulation, at each stage the patch is removed which contains the lowest density of wintering individuals. Initially the removal of poor-quality habitat patches has a negligible effect on population size, which then rapidly crashes as the remaining habitat is lost. In the other simulation, at each step the patch supporting the highest wintering density is removed. In

12000 0 o N ' w oo ? 00

0 ?8000 X

0 0 2 0

v~~~~~~ o

0 4000

0 0 ~~~~~~~~~~

0 20 40 60 80 100 wintering habitat lost (%)

Figure 4. Consequences of habitat loss on total population size for the migration system used in figure 3 a. Single patches within wintering sites were sequentially removed from the simulation, and the new evolutionarily stable migration strategies and population size were determined. The patch removed is either that which currently supports the highest (good habitat lost first, closed circles) or lowest (poor habitat lost first, open circles) density of consumers. Foraging parameters, migration cost, site quality and initial site area as in figure 3a.

this case, even low levels of habitat loss results in a marked population reduction.

5. DISCUSSION

This work shows that aspects of behavioural ecology and population biology may be combined to provide a model of vertebrate populations in a spatially heterogeneous environment. Although theoretical population models based on individual foraging and behavioural parameters have previously been developed for invertebrates, particularly host-parasitoid systems (Hassell & May 1989), these are inapplicable to most vertebrate systems. The framework which we present here will lead to insights into critical behavioural parameters determining population size. This may highlight areas of research needed if we are to improve further our understanding of vertebrate population dynamics. For example, predictions are sensitive to the value of m, the interference coefficient; however, few published estimates of this parameter are available for vertebrates. There is also a need for an improved understanding of the proximal mechanisms of competitive ability and the magnitude of variation between individuals within different systems.

It is now recognized that migratory populations may be regulated in both the wintering and breeding grounds (Goss-Custard 1980). The results presented here explicitly show how overall population size depends on the interaction between density-dependent breeding productivity and processes in the non- breeding season such as interference and depletion.

Habitat loss in either the wintering grounds or breeding grounds is an increasing problem which affects many animal populations (Terbrogh 1989; Baillie & Peach 1992). It is far from straightforward to predict the consequences of habitat loss for a migratory species which uses a range of sites. For example, in public enquiries over the loss of inter-tidal mudflats, it is usually argued by developers that displaced birds can simply feed elsewhere, whilst conservationists usually argue that habitat loss will result in a reduced population. The situation becomes more complex where individuals from different breeding populations interact within shared wintering grounds.

This framework provides a tool which may be used to predict the likely effects of habitat loss. The predictions of the effects of habitat loss within a migratory system, shown in figures 3 and 4, assume that populations are able to alter their migration routes in response to environmental change and converge on the evolutionarily stable migration strategy. There is evidence that migration routes may change where they are largely determined by genetical factors (Berthold & Helbig 1992; Berthold et al. 1992), and also that changes occur in species where migration is culturally determined (Sutherland & Crockford 1993), but the time lag of such a response is obviously critical. We have shown that, where individuals from different migratory populations have the potential to overlap and compete in their wintering grounds, consequences of habitat loss may be amplified beyond direct effects on populations which primarily wintered in the site.





This has important implications for the conservation of separate breeding populations of migratory species.

We thank the Joint Nature Conservation Committee, Nuffield Foundation, and UEA research promotion fund for financing this work; Bob James, John Reynolds, Tom Tew and Andrew Watkinson for useful comments; and Diane Alden for drawing figure 3. We also thank three referees for useful comments.

REFERENCES

Baillie, G. & Peach, W. 1992 Population limitation in Palearctic-African migrant passerines. Ibis 13 (Suppl. 1), 120-132.

Beddington, J. R. 1975 Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44, 331-340.

Bellows, T. S. 1981 The descriptive properties of some models for density-dependence. J. Anim. Ecol. 50, 139-156.

Bernstein, C., Kacelnik, A. J. & Krebs, J. R. 1988 Indi- vidual decisions and the distribution of predators in a patchy environment. J. Anim. Ecol. 57, 1007-1026.

Bernstein, C., Kacelnik, A.J. & Krebs, J. R. 1991 Indi- vidual decisions and the distribution of predators in a patchy environment. II. The influence of travel costs and structure of the environment. J. Anim. Ecol. 60, 205-225.

Berthold, P. & Helbig, A. J. 1992 The genetics of bird migration: stimulus, timing and direction. Ibis 134 (Suppl. 1) 35-40.

Berthold, P., Helbig, A. J., Mohr, G. & Guerner, U. 1992 Rapid microevolution of migratory behaviour in a wild bird species. Nature, Lond. 360, 668-670.

Comins, H. N. & Hassell, M. P. 1979 The dynamics of optimally foraging predators and parasitoids. J. Anim. Ecol. 48, 335-351.

Dobson, A. & Poole, J. H. 1994 The population dynamics of African elephants and their response to exploitation for ivory. Conserv. Biol. (In the press.)

Galbraith, H. 1988 The effects of territorial behaviour on Lapwing populations. Ornis scand. 19, 134-138.

Goss-Custard, J. D. 1980 Competition for food and interference among waders. Ardea 68, 31-52.

Goss-Custard,J. D. & Durrell, S. E. A. Le V. Dit 1988 The effect of dominance and feeding method on the intake rates of oystercatchers Haematopus ostralegus, feeding on mussels. J. Anim. Ecol. 57, 827-844.

Goss-Custard,J. D. & Durrell, S. E. A. Le V. Dit 1990 Bird behaviour and environmental planning: approaches in the study of wader populations. Ibis 132, 272-289.

Grenfell, B. T., Price, 0. F., Albon, S. D. & Clutton-Brock, T. H. 1992 Overcompensation and population cycles in an ungulate. Nature, Lond. 355, 823-826.

Hassell, M. P. & May, R. M. 1989 The population biology of host-parasite and host-parasitoid populations. In Perspectives in ecological theory (ed. J. Roughgarden, R. M. May & G. A. Levin), pp. 319-347. Princeton University Press.

Hassell, M. P. & Varley, G. C. 1969 New inductive population model for insect parasites and its bearing on biological control. Nature, Lond. 223, 1133-1136.

Holling, C. S. 1959 Some characteristics of simple types of predation. Can. Ent. 91, 385-398.

Holmes, R. T. 1970 Differences in population density, territoriality and food supply of dunlin on arctic and subarctic tundra. In Animalpopulations in relation to theirfood resources (ed. A. Watson), pp. 303-319. Oxford: Blackwell Scientific.

Kacelnik, A., Krebs, J. R. & Bernstein, C. 1992 The ideal free distribution and predator prey populations. Trends Ecol. Evol. 7, 50-55.

Koehl, M. A. R. 1989 Discussion: from individuals to populations. In Perspectives in ecological theory (ed. J. Roughgarden, R. M. May & G. A. Levin), pp. 39-53. Princeton University Press.

Maynard Smith, J. & Slatkin, M. 1973 The stability of predator-prey systems. Ecology 54, 384-391.

Monaghan, P. 1980 Dominance and dispersal between feeding sites in the herring gull (Larus argentatus). Anim. Behav. 28, 521-527.

Newton, I. 1986 The sparrowhawk. Calton: Poyser. Parker, G. A. 1982 Phenotype limited evolutionarily stable

strategies. In Current problems in sociobiology (ed. Kings College Sociobiology Group), pp. 173-201. Cambridge University Press.

Parker, G. A. & Sutherland, W.J. 1986 Ideal free distribution when individuals differ in competitive ability: phenotype-limited ideal free models. Anim. Behav. 34, 1222-1242.

Royama, T. 1971 Evolutionary significance of predators response to local differences in prey density: a theoretical study. In Dynamics ofpopulations (ed. P. J. den Boer & G. R. Gradwell), pp. 344-357. Wageningen: Centre for Agri- cultural Publishing and Documentation.

Sinclair, A. R. E. 1989 Population regulation in animals. In Ecological concepts (ed. J. M. Cherrett), pp. 197-241. Oxford: Blackwell Scientific.

Sutherland, W. J. & Allport, G. A. 1994 A spatial depletion model of the interaction between bean geese and wigeon with the consequences for habitat management. J. Anim. Ecol. (In the press.)

Sutherland, W. J. & Anderson, C. W. 1993 Predicting the distribution of individuals and the consequences of habitat loss: the role of prey depletion. J. theor. Biol. 160, 223-230.

Sutherland, W. J. & Crockford, N. J. 1993 Factors affecting the feeding distribution of red-breasted geese Branta ruficollis wintering in Romania. Biol. Conserv. 63, 61-65.

Sutherland, W. J. & Koene, P. 1982 Field estimates of the strength of interference between oystercatchers Haematopus ostralegus. Oecologia 55, 108-109.

Sutherland, W. J. & Parker, G. A. 1992 The relationships between continuous input and interference models of ideal free distributions with unequal competitors. Anim. Behav. 44, 345-355.

Terbrogh, J. 1989 Where have all the birds gone? Princeton University Press.

Received 15 October 1993; accepted 10 November 1993




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Combining Behaviour and Population Dynamics with Applications for Predicting Consequences of Habitat Loss