Joint Math Biology/Stochastics Seminar

Steve Krone
Department of Mathematics, University of Idaho

Continuous Branching Diffusions and Evolutionary Mitigation

Friday, August 22 , 2016, at 3:00pm
LCB 219

Species survival is determined to a large extent by combined demographic and evolutionary responses to environmental change. A species that is in decline and headed for extinction must adapt or it will be lost. Natural history is littered with many species that failed to adapt sufficiently, and yet there are others that have successfully made the transition. "Evolutionary rescue" refers to a declining population that is saved from extinction because of adaptive evolution, and this has been the subject of a growing number of theoretical and empirical studies. Our work takes a different point of view than evolutionary rescue. We seek to understand how abundance and genetic diversity in fitness impact longevity of populations that necessarily are headed to extinction without positing the beneficial mutants that are required in an evolutionary rescue study. We refer to this as "evolutionary mitigation." We base our analyses on a continuous branching diffusion model that allows for calculation of extinction time probability distributions and various percentiles that reveal the relative importance of a population's abundance and variation on its duration. (Joint work with Dick Gomulkiewicz and Chris Remien.)