Analytical solution of metapopulation dynamics in a stochastic environment.

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Metapopulation models are crucial for understanding species persistence and distribution.
• Discrete stochastic matrix models are often complex and primarily studied numerically.
• Risk spreading by dispersal is a key factor influencing population stability.

Purpose of the Study:

• To analytically investigate the effect of risk spreading by dispersion in a discrete stochastic linear metapopulation model.
• To determine the stable population distribution across different habitats.
• To provide robust predictions for metapopulation dynamics under environmental stochasticity.

Main Methods:

• Development and analysis of a discrete stochastic linear metapopulation model.
• Analytical calculation of the stable population distribution.
• Examination of the self-similar structure of simultaneous population distributions.

Main Results:

• The population in each individual habitat follows a log-normal distribution.
• The simultaneous distribution of populations across habitats exhibits a complex self-similar structure.
• Analytical predictions demonstrate robustness across a wide range of model parameters.

Conclusions:

• Environmental stochasticity consistently promotes dispersal in metapopulation systems.
• The findings are expected to hold for systems with multiple habitats.
• Analytical insights offer a valuable alternative to purely numerical approaches for these models.