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Environmentally induced dispersal under heterogeneous logistic growth
Víctor Padrón1, María Cristina Trevisan
1School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street S.E., Minneapolis, MN 55455, USA.
Mathematical Biosciences
|January 24, 2006
Summary
Environmental heterogeneity drives asymmetric migration in species populations. This evolutionarily stable strategy balances dispersal, optimizing population distribution across habitats with varying carrying capacities.
Area of Science:
- Ecology
- Population Dynamics
- Mathematical Biology
Background:
- Single-species models with logistic growth and linear migration rates are common.
- Non-homogeneous carrying capacity in spatially varying environments creates unbalanced population distributions with purely diffusive migration.
- Existing models often assume symmetric migration, which is unrealistic in heterogeneous environments.
Purpose of the Study:
- To investigate the evolutionarily stable strategy (ESS) for dispersal in a single-species model with logistic growth and heterogeneous carrying capacity.
- To determine if asymmetric migration mechanisms are selected under environmental non-homogeneity.
- To analyze how ESS dispersal balances population distribution and maximizes/minimizes ecological quantities.
Main Methods:
- Development of a single-species population model with multiple habitats, logistic growth, and linear migration rates.
- Introduction of a spatially varying carrying capacity to simulate environmental heterogeneity.
- Application of the evolutionarily stable strategy (ESS) approach to analyze dispersal mechanisms.
- Mathematical analysis to identify conditions for balanced dispersal and ideal free distribution.
Main Results:
- Purely diffusive (symmetric) migration leads to unbalanced population distributions in heterogeneous environments.
- An asymmetric migration mechanism, driven by environmental carrying capacity, is evolutionarily selected.
- The selected ESS ensures balanced dispersal within each habitat and aligns spatial distribution with carrying capacity variations.
- Several ecological quantities are shown to be maximized or minimized by the ESS dispersal strategy.
Conclusions:
- Environmental heterogeneity is a key driver for the evolution of asymmetric migration strategies.
- The evolutionarily stable dispersal strategy promotes population balance and optimizes resource utilization across diverse habitats.
- This model provides insights into the ideal free distribution and balanced dispersal in ecological systems.
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