Dynamics of a model of microbial competition with internal nutrient storage in a flowing habitat

Competition between two microbial populations for one nutrient is examined. When nutrient is taken up, it is stored internally, and population growth is a positive function of stored nutrient. The competitors live in a flowing habitat with both advection and diffusion, where the nutrient is supplied in the upstream flow, and all constituents flow out at the downstream end. Conditions for persistence of single species populations without competition, and for competitive outcomes of exclusion and coexistence are shown to depend on principal eigenvalues of boundary value problems, similar to conditions derived for other spatial competition models. In particular, persistence without competition requires that a species consume nutrient sufficiently rapidly at the supplied concentration to allow growth that replaces its losses due to flow. Competitive exclusion and coexistence depend on the ability of a species to invade when it is rare and the other species is at its own, semitrivial equilibrium. Such invasion requires that a species consume nutrient sufficiently rapidly from the concentration distribution created by the competitor, to allow growth that replaces its losses due to flow. Conditions for persistence, competitive exclusion, and coexistence depend on the flow characteristics (advection and diffusivity). Numerical work suggests that bifurcations between these dynamical outcomes occur within a relatively narrow range of the dimensionless Peclet number characterizing flow conditions.

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