Evolutionarily stable strategies in dynamic population models with applications to bird migration

Dynamic state variable models have been widely used to understand individual animal behaviors.¹ However, when a population is studied, frequency-dependence and density-dependence often provide incentives to switch strategies, which are not captured in traditional dynamic models. In the discrete states and discrete time problem, we have a coupled forward-backward system, solution of which gives the evolutionarily stable policies determining the strategies for a given state. With the recent development of mean field game theory², we can find general ecological conditions under which evolutionarily stable policies exist, and can be numerically found. We will also apply the results to understand various strategies during bird migration, such as choice of intermediate sites, foraging rates, and timing of arrival.

References:
1. Clark, C. W., & Mangel, M. (2000). Dynamic state variable models in ecology: methods and applications. Oxford University Press on Demand.

2. Guéant, O., Lasry, J. M., & Lions, P. L. (2011). Mean field games and applications. In Paris-Princeton lectures on mathematical finance 2010 (pp. 205-266). Springer, Berlin, Heidelberg.