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THE IMPLICATIONS OF SCALINGAPPROACHES FOR UNDERSTANDINGRESILIENCE AND REORGANIZATIONIN ECOSYSTEMS
Date: 29th September
Erica Xie
Email: [email protected]
OUTLINE OF PAPER
1. Variability of biological and ecological at multiple scales
2. Scaling Law in Regularities E.g. Scaling of human settlement size, human fertility, distribution of forest
3. Ecological scaling indicates particular structuring processes or perturbation of ecosystem
4. Scaling provide a powerful tool for understanding resilience in Ecology
BACKGROUND: STATE OF TODAY
Increasing ecological impacts brings by human beings compel people to manage the dynamic of ecosystem
Resilience of ecosystem maintains a sustainable human population and human well beings.
Understanding resilience means identifying relevant driving variables that reinforce alternative states of the system of interest, and the spatial and temporal scales over which those variables operate
Primary impediments to developing a generalized ecological theory, is the range of scales encompassed by ecological phenomena
BACKGROUND: STATE OF TODAY
Driving
State of system
Spatial and Temporal Scale
Understanding resilience means identifying relevant driving variables that reinforce alternative states of the system of interest, and the spatial and temporal scales over which those variables operate
Primary impediments to developing a generalized ecological theory, is the range of scales encompassed by ecological phenomena
BACKGROUND: STATE OF TODAY
AMAZING SCALE
Mass of a redwood / a bacterium is
approximately 1021
biosphere,
landscapes,
ecosystems,
communities,
populations,
organisms,
Cell
CHANGES IN VIEWING OF SCALES
cells
organisms
biosphere
populations
communities
ecosystems
landscapes
WHAT IS ALLOMETRIC SCALING LAW?
Scaling laws are simply empirical generalizations describing how some property of a system changes along one of the fundamental dimensions of the system.
Allometric scaling is common in nature, both when comparing two animals of different sizes and when comparing the same animal at two different sizes (i.e., growth).
Allo = different; Metric = measure When an animal (or organ or tissue) changes shape in response to size changesdoes not maintain geometric similarity, we say that it scales allometrically.
WHAT IS ALLOMETRIC SCALING LAW?
WHAT IS ALLOMETRIC SCALING LAW?
Y=Y0Mb
Property of interest e.g., metabolic rate,species richness
Scaling exponent and coefficient
Size of the observed entity(e.g., organism body mass, islandor patch area
Normally used
between species
SCALING OF SINGLE LEVEL V.S. DIFFERENT DIMENSION
Ecological scaling relationships relate to entities at a single level of organization, the measured variables are static, steady-state, or time averaged, rather than dynamical.
However, the dimensions of the variables are context independent, continuous, and quantitative.
HOW SCALING AND RESILIENCE RELATED
Similar: Both highlight the importance of scale in the development of generalized, predictive ecological theory
Difference:
Resilience ScalingDynamic Steady State
Unpredictability Predictability
Treat scale in a discrete, hierarchical fashion
Treat scale more continuously
HOW SCALING AND RESILIENCE RELATED
HOW SCALING AND RESILIENCE RELATED
Common interest: They share a common interest in ecological theory and a common recognition that scale is a critical consideration for understanding ecological systems.
POWER LAW1: ECOLOGICALSCALING IN HUMAN SYSTEMS
The number of firms of size S falling off as a negative power of their size NS = n0S–α
Between firm size and environmental impact, where IS is the impact of a firm of size S
IS =i0Sβ
Multiples these two NS IS = n0i0Sβ–α
If β>α, the environmental impact increasesmore steeply with firm size
POWER LAW2: HUMAN FERTILITY AND ENERGY USE
Fertility of human societies is plotted as a function of per capita power consumption
F = a*B –1/3
(F, births per female per year) (B, watts [W])
UTILITY IN ADAPTIVE MANAGEMENT
Calder (2000) illustrates the use of scaling laws to derive surrogate values in the face of uncertainty as a powerful tool for adaptive management in species conservation.
Involving three-step process: (1) derivation of the broadest possible scaling relationships from empirical data, (2) prediction from the empirical relationships (3) fine-tuning predictions on the basis of departures from scaling
ADJUST OF POWER LAW IN HUMAN FERTILITY AND ENERGY USE
Scaling of fertility with energy use provides a baseline for understanding variation in human demography
Incorporating analyses of residual (energy-adjusted) fertility and other economic or social indicators (e.g., literacy, immigration, emigration rates and other indicators of human well-being) could enable better understanding of changing human life histories in a rapidly industrializing and urbanizing world.
POWER LAW3:PLANT POPULATION AND COMMUNITIES
Self thinning explanation: All individuals share a common allometry of
resource use, which is proportional to metabolic
rate (B), where B is proportional to (∝) mass
raised to the 3/4 power (M3/4); All individuals in the population compete for
limiting resources, in steady state, the rate of
resource use approximates resource supply (R). It follows that the maximum number of
individuals, Nmax , that can be supported per unit
area is related to the average whole plant size as
Nmax R(M∝ -3/4)
POWER LAW3:PLANT POPULATION AND COMMUNITIES
Multiple the above two Laws: Total energy consumed by a species per unit
area is invariant with body size
NB M∝ -3/4*M3/4 M∝ ,
consistent with the EER
WHAT IS EER
In short, the EER is a type of size-density relationship that states that total population energy-fluxes by different species should be equivalent, regardless of their respective body masses
EER IN FOREST COMMINITIES
Tree size generally refers to stem diameter (D). The plant allometric theory predicts, and empirical data broadly document, that plant mass is proportional to the 8/3 power of diameter. Thus, the EER size distribution becomes N ∝ D–2
Explanation: Multiple the law of number before with biomass law above:
N (M∝ -3/4), M D∝ 3/8
Thus, N ∝ D–2
Size distribution exponents for 226 0.1-hectare forest plots
Examined data for the mean tree size (D) and total stem density for disturbed and undisturbed plots of lowland forests in Nicaragua
EER IN FOREST COMMINITIES
EER distribution appears to provide a reasonable upper boundary for the data
Forests from both locales support the hypothesis that disturbance is manifested in the scaling properties of forest size structure.
VIDEO TIME!
Geoffrey West: The surprising math of cities and corporations
DISAGREEMENT IN RESEARCH OF MUNN, A.,ET.AL RESEARCH OF AUSTRALIAN MARSUPIALS
Firstly, EER may not be a general ecological ‘rule’, and as such it is not universal or predictive.
Alternatively, the EER may indeed be causal, but for reasons that are not yet clear it is not operating at the continental scale for Australian marsupials.
IMPLICATION FOR RESILIENCE OF ECOSYSTEM
The author generated three open questions for us to think for future work:
1. If community-level scaling relationships do represent structural attractors to the system, what determines the speed and direction of approach?
2. How can studies of scaling and resilience address variability, which is of critical concern for understanding ecological change? Many scaling studies deal only with the equilibrium, average state of the system of interest; what can they say about variance and covariance?
IMPLICATION FOR RESILIENCE OF ECOSYSTEM
3. If all of these different communities converge toward a similar structural state, what is the implication for biodiversity? Does scaling offer any insights on the role that species’ ecologies play in the resilience of ecosystems?
IMPLICATION FOR RESILIENCE OF ECOSYSTEM
Because resilience is related to the degree of perturbation that is in some sense tolerable to a system, modeling the expected levels of ecological variance is critical.
Taylor’s power law, which describes the scaling relationship between mean abundance (m) and its temporal (or spatial) variance (v) across populations: v = amb.
IMPLICATION FOR RESILIENCE OF ECOSYSTEM
The value of the exponent is of particular interest, because when b < 2, relative variability (as indexed by the coefficient of variation) decreases with increasing mean; conversely, when b > 2, it increases.
Across a wide variety of animal and plant taxa, mean-variance scaling exponents generally range between approximately 1 and 2
DISCUSSION AND SUM UP
Many of the ecological scaling relationships we have discussed, from community size distributions to the scaling of population seed output, appear relatively insensitive to the diversity and taxonomic composition of the systems described.
On the surface, it appears that ecological scaling may have little to say about the role of individual species in ecosystems.
On the contrary, we argue that the generality of many scaling relationships provides an indispensable baseline for determining what is possible and predictable in ecological systems.
WORK CITED Kurt Andrew Grimm drkurtgrimm.com Munn, A. J., Dunne, C., Müller, D. W., &
Clauss, M. (2013). Energy In-Equivalence in Australian Marsupials: Evidence for Disruption of the Continent’s Mammal Assemblage, or Are Rules Meant to Be Broken?. PloS one, 8(2), e57449.
Kerkhoff, A. J., & Enquist, B. J. (2007). The implications of scaling approaches for understanding resilience and reorganization in ecosystems.Bioscience, 57(6), 489-499.
Pictures are located in the remarks parts of this slices
Video: https://www.youtube.com/watch?v=BAwEQf_VR64
https://www.youtube.com/watch?v=XyCY6mjWOPc
ADDITIONAL RESOURCES Allometry is the study of the relationship of body size
to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892
Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body.
Arguing that there are a number of analogous concepts and mechanisms between cities and biological entities, Bettencourt et al. showed a number of scaling relationships between observable properties of a city and the city size. GDP, "supercreative" employment, number of inventors, crime, spread of disease,[19] and even pedestrian walking speeds[32] scale with city population.
