An Optimal Switching Approach for Bird Migration

TL;DR

This paper introduces an optimal switching model for bird migration, using stochastic differential equations and numerical methods to analyze strategies under perfect and partial environmental information.

Contribution

It presents a novel mathematical framework modeling bird migration as an optimal switching problem with stochastic differential equations, incorporating environmental information levels.

Findings

Optimal strategies depend on environmental information availability.

Numerical methods effectively compute expected payoffs and strategies.

Model characterizes migration behaviors under various scenarios.

Abstract

Bird migration is an adaptive behavior ultimately aiming at optimizing survival and reproductive success. We propose an optimal switching model to study bird migration, where birds' migration behaviors can be efficiently modeled as switching between different stochastic differential equations. For individuals with perfect information regarding the environment, we implement numeric methods to see the expected payoff and corresponding optimal control. For individual with only partial information of the environment, we combine the finite difference method and stochastic simulations to investigate the change of the bird's optimal strategy. Based on biological backgrounds, we characterizing the optimal strategies of birds under different scenarios and these behaviors depend on the specific assumptions of the model.