It is shown 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 hosts have the smallest host range. This confirms earlier work of Jover, Cortez, and Weitz (2013) who raised the issue of whether nested infection networks are permanent. In addition, 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 are provided.