  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.
