Species coexistence in the face of demographic and environmental uncertainty: Part I

主讲人：Professor Sebastian Schreiber，University of California, Davis

时间：2019年6月19日14：30

地点：3号楼332报告厅

举办单位：数理学院

内容介绍：A long standing, fundamental question in biology is what are the minimal  conditions to ensure the long-term persistence of a population, or to ensure the  long-term coexistence of interacting species? The answers to this question are  essential for identifying mechanisms that maintain biodiversity and guiding  conservation efforts. Mathematical models play an important role in identifying  potential mechanisms and, when coupled with empirical work, can determine  whether or not a given mechanism is operating in a specific population or  community. For over a century, nonlinear difference and differential equations  have been used to identify mechanisms for population persistence and species  coexistence. These models, however, fail to account for intrinsic and extrinsic  random fluctuations experienced by all populations. In this talk, I discuss  recent mathematical results about persistence and coexistence for models  accounting for demographic and environmental stochasticity. Demographic  stochasticity stems from populations consisting of a finite number of  interacting individuals. These dynamics can be represented by Markov chains on a  countable state space. For closed populations in a bounded world, extinction in  these models occurs in finite time, but may be preceded by long-term transients.  Quasi-stationary distributions (QSDs) of these Markov chains characterize this  meta-stable behavior. These QSDs correspond to an eigenvector of the transition  operator restricted to non-extinction states, and the associated eigenvalue  determines the mean time to extinction when the Markov chain is in the  quasi-stationary state. I will discuss under what conditions (i) this mean time  to extinction increases exponentially with habitat size and (ii) the QSDs  concentrate on attractors of the mean field model of the Markov chain. These  results will be illustrated with models of competing California annual plant  species, and a classical model of host-pathogen interactions.