Total biomass of a single population in two-patch environments

For the two-patch logistic model, we study the effect of dispersal intensity and dispersal asymmetry on the total population abundance and its distribution. Two complete classifications of the model parameter space are given: one concerning when dispersal causes smaller or larger total biomass than no dispersal, and the other addressing how the total biomass changes with dispersal intensity and dispersal asymmetry. The dependencies of the population abundance of each individual patch on dispersal intensity and dispersal asymmetry are also fully characterized. In addition, the maximal and minimal total population sizes induced by dispersal are determined for the logistic model with an arbitrary number of patches, and a weak order-preserving result correlated the local population abundances with and without dispersal is established.