Population dynamics in spatially heterogeneous systems with drift: The generalized contact process

Area of Science:

• Mathematical Biology
• Statistical Physics
• Ecology

Background:

• Stochastic population models are crucial for understanding ecological dynamics.
• Spatial heterogeneity and external forces like drift significantly impact population distributions.
• Previous deterministic models offer insights into population behavior in convective heterogeneous media.

Purpose of the Study:

• To investigate the time evolution and stationary states of a stochastic population model.
• To analyze the effects of spatial heterogeneity (oasis/desert) and imposed drift (wind) on population dynamics.
• To compare results with deterministic models and map phase diagrams.

Main Methods:

• Computer simulations of a spatially discrete contact process in 1D and 2D.
• Modeling space divided into regions with differing death rates (oasis and desert).
• Analysis of population states (zero, localized, delocalized) under varying drift parameters.

Main Results:

• The population's quasi-stationary state can be extinct, localized, or delocalized.
• These states are determined by the interplay of drift strength and other model parameters.
• A phase diagram emerges, showing distinct regions for each population state.

Conclusions:

• Stochastic population models with drift and heterogeneity exhibit complex behaviors.
• The phase diagram of this stochastic model closely resembles that of deterministic models.
• Environmental factors like wind and habitat type critically influence population persistence and distribution.