Mathematics Colloquia and Seminars

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Populations, whether they be viral particles, bio-chemicals, plants or animals, are subject to intrinsic and extrinsic sources of stochasticity. This stochasticity in conjunction with nonlinear interactions between individuals determines to what extent populations persist and species coexist in the long-term. Understanding the precise nature of these interactive effects is a central issue in population biology from theoretical, empirical, and applied perspectives. For the first part of this talk, I will discuss the relationship between attractors of deterministic models and quasi-stationary distributions of their stochastic, finite population counterpoints i.e. models accounting for demographic stochasticity (Faure & Schreiber 2014 Ann.Appl.Probab.). These results shed some insight into the metastable behavior of stochastic modes for which extinction is inevitable. For the second part of the talk, I will discuss results on stochastic persistence and coexistence for models accounting for environmental noise (Roth & Schreiber 2014 J.Math.Biol.). Stochastic persistence requires that, asymptotically, the support of the empirical measures are bounded away from the "extinction set." Using these results, I will illustrate how environmental noise can facilitate coexistence of competing species and hinder persistence of predatory species.