Sebastian Schreiber

• 
  When do factors promoting genetic diversity in stochastic environments also promote population persistence? A demographic perspective on Gillespie's SAS-CFF model
  Sebastian Schreiber

  Classical stochasticity demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, J.H. Gillespie demonstrated with his SAS-CFF model that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to account for demography, I examine the simultaneous effects of environmental stochasticity on genetic diversity and population persistence. Explicit expressions for the per-capita growth rates of rare alleles and the population at low-density are derived. These expressions determine when genetic diversity is maintained and the population persists i.e. allelic frequencies and population densities tend to stay away from zero almost-surely and in probability. Using these results, I will discuss (i) how mechanisms promoting population persistence may be at odds with mechanisms promoting genetic diversity, and (ii) provide conditions under which population persistence in stochastic environments relies on existing standing genetic variation.

• 
  Population persistence in the face of demographic and environmental uncertainty
  Sebastian Schreiber
  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 extinct populations are able to persist 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, briefly, the relationship between attractors of deterministic models and quasi-stationary distributions of their stochastic, finite population counterpoints i.e. models accounting for demographic stochasticity. These results shed some insight into when persistence should be observed over long time frames despite extinction being inevitable.
  
  For the second part of the talk, I will discuss results on stochastic persistence and boundedness for stochastic models accounting for environmental (but not demographic) noise. Stochastic boundedness asserts that asymptotically the population process tends to remain in compact sets. In contrast, stochastic persistence requires that the population process tends to be "repelled" by some "extinction set." Using these results, I will illustrate how environmental noise can facilitate coexistence of competing species and how dispersal in stochastic environments can rescue locally extinction prone populations. Empirical demonstrations from Kansas prairies, acorn woodpecker populations, and microcosm experiments will be discussed.
• 
  Persistence, coexistence and spatial spread in a fluctuating environment
  Sebastian Schreiber
  All populations experience stochastic
  uctuations in abiotic factors such as temperature, nutrient avail-
  ability, precipitation. This environmental stochasticity in conjunction with biotic interactions can facilitate
  or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic
  forces is the construction and analysis of stochastic dierence equations and stochastic dierential equations.
  Many theoretical biologists are interested in whether the models are stochastically bounded and persis-
  tent. Stochastic boundedness asserts that asymptotically the population process tends to remain in compact
  sets. In contrast, stochastic persistence requires that the population process tends to be epelled" by some
  "extinction set". Here, I will review recent results on both of these proprieties are reviewed for models
  of multi-species interactions and spatially-structured populations. Basic results about random products of
  matrices, Lyapunov exponents, stationary distributions, and small-noise approximations will be discussed.
  Applications include bet-hedging, coexistence via the storage eect, and evolutionary games in stochastic
  environments.