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Mathematical Physics Seminar

Daniel Fisher - Ecological Chaos and Microbial Diversity

Daniel Fisher – Stanford University

Location:  zoom
Date & time: Wednesday, 10 February 2021 at 10:45AM - 11:45AM


One of the discoveries enabled by the DNA sequencing revolution is the enormous diversity of microbes, And this extends far below the species-level down to the finest scales of genetic differences. Remarkably, extensive diversity within a single bacterial species can coexist in the same location and time. Biological diversity is conventionally explained in terms of niches and geographic separation, but this is unreasonable for large numbers of close relatives that all compete directly. Going back to Robert May, physicists have explored Lotka-Volterra (LV) models of many interacting species assuming that interactions with their own species are substantially stronger than the assumed-approximately random interactions with other species finding that the number of species that can stably coexist is nevertheless limited. But for closely related strains, their interactions with siblings are not expected to be substantially stronger than with distant cousins: this destroys stable coexistence. But what occurs instead is not known. We analyze LV models focussing on interactions with antisymmetric correlations, such as from direct one-on-one competition or for multiple strains of a pathogen interacting with multiple strains of a host. A partially exactly solvable model, a perfectly antisymmetric interaction matrix, provides the basis for a general analysis via dynamical mean-field theory. We find a robust spatio-temporally chaotic “phase” in which a large fraction of the strains coexist, each undergoing blooms and busts of their local population densities. The conditions under which such a phase could evolve and the degree of complexity of the interactions needed for it to occur will be discussed.

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