The mathematics of extinction across scales: from populations to the biosphere

, , ,
1 Department of Environmental Science, Policy, and Management, University of California, Berkeley, Berkeley, California, United States
2 Department of Ecology & Evolutionary Biology, University of Connecticut, Storrs, Connecticut, United States
3 Department of Environmental Science and Policy, University of California, Davis, Davis, California, United States
DOI
10.7287/peerj.preprints.3367v2
Published
Accepted
Subject Areas
Conservation Biology, Ecology, Mathematical Biology, Statistics, Climate Change Biology
Keywords
extinction rates, extinction date estimation, species area relationship, population viability analysis, extinction risk, Spix's macaw, population modeling, metapopulation modeling
Copyright
© 2018 Carlson et al.
Licence
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
Cite this article
Carlson C, Burgio K, Dallas T, Getz W. 2018. The mathematics of extinction across scales: from populations to the biosphere. PeerJ Preprints 6:e3367v2

Abstract

The sixth mass extinction poses an unparalleled quantitative challenge to conservation biologists. Mathematicians and ecologists alike face the problem of developing models that can scale predictions of extinction rates from populations to the level of a species, or even to an entire ecosystem. We review some of the most basic stochastic and analytical methods of calculating extinction risk at different scales, including population viability analysis, stochastic metapopulation occupancy models, and the species area relationship. We also consider two major extensions of theory: the possibility of evolutionary rescue from extinction in a changing environment, and the posthumous assignment of an extinction date from sighting records. In the case of the latter, we provide an example using data on Spix's macaw (Cyanopsitta spixii), the "rarest bird in the world," to demonstrate the challenges associated with extinction date research.

Author Comment

Small tweaks to the content.