Stabilization of fine-scale host-pathogen diversity by spatiotemporal chaos

DNA sequencing studies have increasingly found that within microbial species, fine-scale genetic diversity coexists. A major open question is how such diversity can develop and be maintained under pervasive selection when the subtypes all compete locally. Host-pathogen interactions are often cited as a cause of diversity. But the behavior with large numbers of closely related (but distinct) types is not understood. We analyze a generalized Lotka-Volterra model of host-pathogen interactions. The set of pathogens are all similar, as are the hosts: we thus assume no explicit specificity and approximate the variations in the host-pathogen interactions as being random. The negative effect of a pathogen on a host is correlated with the positive-effect of that host on the pathogen: thus the full matrix of interactions has antisymmetric correlations. With purely antisymmetric interactions, there is a stable chaotic phase with many types surviving but the population of each type fluctuating wildly. Deviations from this special case cause runaway extinctions. We show that the addition of spatial structure can stabilize the chaos: there are local extinctions, but repopulations from other islands prevent a substantial fraction of the types from going globally extinct.