Using both analytic and numerical methods, we elucidate the dynamical properties of a class of metapopulation models in which many different species/strains contend for persistence, with local extinction of subpopulations being balanced by colonization of other patches. The species/strains have a strict competitive hierarchy with a given species/strain "taking over" any patch occupied by a lower-ranking species/strain; competitively inferior species/strains compensate by having higher colonization rates and/or lower patch death rates. New species/strains keep appearing, so that we can follow the evolution of the system. Such models may be metaphors for multispecies metapopulations, or for the evolution of virulence (where the patches are hosts, who are infected with various strains of a pathogen, and then die or recover at strain-dependent rates).
Our emphasis is on a set of questions relating to the evolution of diversity. How many species/strains are present after a long time, (t) ? Asymptotically, this number continues to increase very slowly, as (\ln t) What are the relative abundances of the species/strains? Under a broad range of assumptions about the mutations which produce new species/strains, the rank-abundance distribution is roughly geometric (as is commonly observed in early succession and other "ecologically one-dimensional" situations); some of our analysis here is based in part on an interesting but unproved mathematical conjecture about a new kind of probabilistic/combinatorial problem. If the number of patches/hosts is permanently reduced--by habitat destruction or vaccination-what happens? Characteristically, there is an initial sharp loss of species/strains (with selective removal of the competitive dominants), with subsequent slow recovery as new mutants continue to partition the now-diminished "niche space" (but the pristine levels of virulence are not regained).