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Mathematics of Planet Earth pp 225–264Cite as

The Mathematics of Extinction Across Scales: From Populations to the Biosphere

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Part of the book series: Mathematics of Planet Earth ((MPE,volume 5))

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 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 a new example using data on Spix’s macaw, the “rarest bird in the world,” to demonstrate the challenges associated with extinction date research.

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Authors and Affiliations

  1. Department of Environmental Science, Policy and Management, University of California Berkeley, Berkeley, CA, USA

    Colin J. Carlson & Wayne M. Getz

  2. Department of Ecology & Evolutionary Biology, University of Connecticut, Storrs, CT, USA

    Kevin R. Burgio

  3. Department of Environmental Science and Policy, University of California Davis, Davis, CA, USA

    Tad A. Dallas

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  1. Colin J. Carlson
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  2. Kevin R. Burgio
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  3. Tad A. Dallas
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  4. Wayne M. Getz
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Correspondence to Wayne M. Getz .

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  1. Mathematics and Statistics, Georgetown University, Washington, DC, USA

    Hans G. Kaper

  2. DIMACS Center, Rutgers University, Piscataway, NJ, USA

    Fred S. Roberts

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Carlson, C.J., Burgio, K.R., Dallas, T.A., Getz, W.M. (2019). The Mathematics of Extinction Across Scales: From Populations to the Biosphere. In: Kaper, H., Roberts, F. (eds) Mathematics of Planet Earth. Mathematics of Planet Earth, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-22044-0_9

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