Impact of network connectivity on the dynamics of populations in stream environments

We consider the impact of network connectivity on the dynamics of a population in a stream environment. The population is modeled using a graph theoretical framework, with habitats represented by isolated patches. We introduce a change in connectivity into the model through the addition of a bi-directional or one-directional edge between two patches and examine the impact of this edge modification on the metapopulation growth rate and the network biomass. Our main results indicate that adding a bi-directional edge often decreases both measures, while the effect of adding an one-directional edge is more intricate and dependent on the model parameters. We establish complete analytical results for stream networks of three patches, and provide some generalizations and conjectures for more general stream networks of $n$ patches. These conjectures are supported with numerical simulations.