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Title: Stochastically induced extinction, coexistence, and alternative stable states

Abstract: In nature, environmental factors such as temperature, precipitation, and resource availability fluctuate stochastically over time. As survival, growth, and reproduction of organisms depend on these environmental factors, stochastic environmental fluctuations lead to stochastic fluctuations in population densities and genotypic frequencies. In this talk, I will discuss recent mathematical advances in the analysis of stochastic difference equations to identify when these stochastic fluctuations drive populations extinct, mediate coexistence between competing genotypes or species, or generate alternative stable states within communities. Empirically based applications will be given.