  We show that a chemostat community of bacteria and bacteriophage in which
bacteria compete for a single nutrient and for which the bipartite infection
network is perfectly nested is permanent, a.k.a. uniformly persistent, provided
that bacteria that are superior competitors for nutrient devote the least to
defence against infection and the virus that are the most efficient at
infecting host have the smallest host range. This confirms earlier work of
Jover et al \cite{Jover} who raised the issue of whether nested infection
networks are permanent. In addition, we provide sufficient conditions that a
bacteria-phage community of arbitrary size with nested infection network can
arise through a succession of permanent subcommunties each with a nested
infection network by the successive addition of one new population.
