Maximizing Metapopulation Growth Rate and Biomass in Stream Networks

TL;DR

This paper investigates optimal resource distribution in stream network models to maximize population persistence, revealing different strategies for biomass and growth rate depending on diffusion rates and network structure.

Contribution

It provides a theoretical analysis of resource allocation strategies in stream networks to optimize metapopulation persistence metrics, generalizing results to any number of patches.

Findings

Maximizing biomass involves concentrating resources upstream.

Maximizing growth rate involves concentrating resources downstream when diffusion is small.

Results are generalized to arbitrary stream network sizes.

Abstract

We consider the logistic metapopulation model over a stream network and use the metapopulation growth rate and the total biomass (of the positive equilibrium) as metrics for different aspects of population persistence. Our objective is to find distributions of resources that maximize these persistence measures. We begin our study by considering stream networks consisting of three nodes and prove that the strategy to maximize the total biomass is to concentrate all the resources in the most upstream locations. In contrast, when the diffusion rates are sufficiently small, the metapopulation growth rate is maximized when all resources are concentrated in one of the most downstream locations. These two main results are generalized to stream networks with any number of patches.