CRB: Demographic and Genetic Factors in Extinction

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WPCD 2 B V P Z Courier 10cpi ? x x x , x 6 X @ 8 ; X @ HP DeskJet 500 HPDES500.PRS x @ x X , , 0 FX @ #| x 2 B 9225127 Lande The goals of this project are to formulate and analyze mathematical models of demographic and genetic factors and their interactions affecting the risk of population extinction. Demographic factors to be investigated include random catastrophes and their interaction with fluctuating environments, local extinction and colonization in spatially distributed "metapopulations", and harvesting of populations in a fluctuating environment. Genetic factors to be investigated include inbreeding in small populations, deleterious mutation, random genetic drift, and adaptive evolution in changing environments. Methods from dynamical system theory and stochastic process theory will be employed, e.g. modeling fluctuating environments and random genetic drift as diffusion processes, and random catastrophes as a jump process. The main quantities of interest are times and probabilities of extinction, especially the mean time to extinction. Using suitable approximations, simple formulas will be derive that elucidate the extinction risks associated with each factor and their interactions. Analytical results will be checked by computer simulation where feasible. %%% The results will help to establish a stronger theoretical foundation for the science of conservation biology. A better understanding of factors causing extinction, particularly in small populations, will have immediate applications in viability analysis, and in conservation and restoration plans for threatened and endangered species. ***