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Viability of small populations experiencing recurring catastrophes

Journal article
Authors Peter Jagers
Karin C. Harding
Published in Math. Pop Studies
Volume 16
Issue 3
Pages 177-198
ISSN 0889-8490
Publication year 2009
Published at Linnaeus Centre for Marine Evolutionary Biology (CEMEB)
Department of Mathematical Sciences, Mathematical Statistics
Department of Marine Ecology
Pages 177-198
Language en
Keywords branching processes; carrying capacity; density dependent catastrophes; survival time
Subject categories Mathematical statistics, Biological Sciences

Abstract

Some small populations are characterized by periods of exponential growth, interrupted by sudden declines in population number. These declines may be linked to the population size itself, for example through overexploitation of local resources. We estimate the long term population extinction risk and the time to extinction for thistype of repeatedly collapsing populations. Our method is based on general branching processes, allowing realistic modelling of reproduction patterns, litter (or brood or clutch) sizes, and life span distributions, as long as individuals reproduce freely and density effects are absent. But as the population grows, two extrinsic factors enter: habitat carrying capacity and severity of decline after hitting the carrying capacity. The reproductive behaviour of individuals during periods when the population is not experiencing any density effects also has a fundamental impact on the development. In particular, this concerns the population's potential for recovery, as mirrored by the intrinsic rate of increase as well as the extinction probability of separate family lines of unhampered populations. Thus, the details of life history which shape demographic stochasticity and determine both rate of increase and extinction probability of freely growing populations,can have a strong effect on overall population extinction risk. We are interested in consequences for evolution of life history strategies in this type of systems. We compare time to extinction of a single large system (high carrying capacity) with that of a population distributed over several small patches, and find that for non-migrating systems a single large is preferable to several small habitats.

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