Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal

Area of Science:

• Ecology
• Evolutionary Biology
• Mathematical Biology

Background:

• Dispersal is crucial for species survival and distribution.
• Previous models (Hastings, 1993) explored random dispersal in resource gradients.
• Conditional dispersal strategies can influence competitive outcomes.

Purpose of the Study:

• To investigate the evolution of conditional dispersal strategies in competing species.
• To analyze the stability of dispersal strategies under environmental gradients.
• To determine optimal habitat selection strategies balancing random and directed movement.

Main Methods:

• Development of a mathematical model for two competing species.
• Analysis of dispersal strategies involving random movement and biased movement along a resource gradient.
• Application of evolutionary stability theory (local and convergent stability).

Main Results:

• In the absence of directed movement, lower random dispersal rates favor invasion.
• A small amount of directed movement (advection) can lead to a stable, positive random dispersal rate.
• The model identifies conditions where a combination of random and biased dispersal is evolutionarily advantageous.

Conclusions:

• Conditional dispersal, balancing random and directed movement, can be a superior habitat selection strategy.
• Environmental gradients and advection significantly alter the evolution of dispersal.
• Optimal population strategies may involve a nuanced combination of movement types.