The mathematics of extinction across scales: from populations to the biosphere
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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.
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2018. The mathematics of extinction across scales: from populations to the biosphere. PeerJ Preprints 6:e3367v2 https://doi.org/10.7287/peerj.preprints.3367v2Author comment
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Competing Interests
The authors declare that they have no competing interests.
Author Contributions
Colin Carlson analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the paper, approved the final draft.
Kevin Burgio analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the paper, approved the final draft.
Tad Dallas prepared figures and/or tables, authored or reviewed drafts of the paper, approved the final draft.
Wayne Getz authored or reviewed drafts of the paper, approved the final draft.
Data Deposition
The following information was supplied regarding data availability:
No original code was developed for this book chapter, and the limited dataset generated is given inline in the text of the paper.
Funding
The authors received no funding for this work.
