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Stochastic population growth in spatially heterogeneous environments
Steven N Evans1, Peter L Ralph, Sebastian J Schreiber
1Department of Statistics #3860, University of California, 367 Evans Hall, Berkeley, CA 94720-3860, USA.
Journal of Mathematical Biology
|March 20, 2012
Summary
Environmental stochasticity and spatial heterogeneity impact population growth. This study models these factors, revealing how dispersal strategies influence long-term population growth rates and persistence in variable environments.
Area of Science:
- Population Ecology
- Mathematical Biology
- Conservation Biology
Background:
- Environmental stochasticity typically increases extinction risk by reducing population growth rates.
- Classical models often assume homogeneous environments, neglecting spatial heterogeneity and dispersal effects.
- Understanding interactive effects of environmental variability, spatial structure, and dispersal is crucial for population dynamics.
Purpose of the Study:
- To develop and analyze a mathematical model for population growth in spatially extended, temporally variable environments.
- To characterize the long-term stochastic growth rate considering environmental stochasticity, spatial heterogeneity, and dispersal.
- To investigate the influence of dispersal strategies on population persistence and growth rate optimization.
Main Methods:
- Utilized stochastic differential equations to model population dynamics in multiple patches.
- Derived expressions for the stochastic growth rate based on average per-capita growth and temporal variation.
- Employed analytical and group-theoretic techniques to approximate growth rates for different dispersal scenarios and landscape structures.
Main Results:
- The stochastic growth rate is determined by the space-time average per-capita growth rate and temporal variation.
- Explicit expressions for two-patch systems and approximations for dispersal-limited and multi-scale populations were derived.
- Ideal-free dispersers occupy multiple patches in heterogeneous environments under strong, weakly correlated fluctuations.
Conclusions:
- Dispersal strategies significantly influence population persistence and growth rates in variable, heterogeneous environments.
- Intermediate dispersal rates can maximize stochastic growth rates in certain conditions, while ideal-free movement promotes patch occupancy.
- Findings offer insights into population persistence, evolution of dispersal, and conservation strategies like the SLOSS debate.
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