Mathematical Models for Habitat Contributions of Migrating Species on a Network, Part II

Understanding the influence of specific habitats on the survival of a migratory species is an essential part of making successful management decisions. Migration is a complicated process, and mathematical models of migratory networks offer a way to understand the importance of different parts of an organism’s annual cycle. The National Institute for Mathematical and Biological Symbiosis (NIMBioS) “Habitat for Migratory Species” working group has developed several approaches to study this problem. We will present three different approaches. The first method yields a per-capita metric for the number of individuals produced or surviving during a one-year time step for any habitat, transition, or pathway in the migratory network. This metric ranks areas from the number of individuals produced or surviving during a one year time step. Next, we will introduce a generalized network framework to demonstrate how perturbation analysis can be used to determine the relative importance of habitats and movement pathways. Then we will present an extension of the network modeling approach: a continuous model that links energy resources, at the nodes and along the paths, to the movement and survival of the migrating species. All three frameworks are intended to be general, not species specific, so that they can be applied in a standard way to a wide range of species with different migration patterns