  Bacteria and their viruses ("bacteriophages") coexist in natural environments
forming complex infection networks. Recent empirical findings suggest that
phage-bacteria infection networks often possess a nested structure such that
there is a hierarchical relationship among who can infect whom. Here we
consider how nested infection networks may affect phage and bacteria dynamics
using a multi-type Lotka-Volterra framework with cross-infection. Analysis of
similar models have, in the past, assumed simpler interaction structures as a
first step towards tractability. We solve the proposed model, finding trade-off
conditions on the life-history traits of both bacteria and viruses that allow
coexistence in communities with nested infection networks. First, we find that
bacterial growth rate should decrease with increasing defense against
infection. Second, we find that the efficiency of viral infection should
decrease with host range. Next, we establish a relationship between relative
densities and the curvature of life history trade-offs. We compare and contrast
the current findings to the "Kill-the-Winner" model of multi-species
phage-bacteria communities. Finally, we discuss a suite of testable hypotheses
stemming from the current model concerning relationships between infection
range, life history traits and coexistence in complex phage-bacteria
communities.
