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

  • Colin J. Carlson
  • Kevin R. Burgio
  • Tad A. Dallas
  • Wayne M. GetzEmail author
Part of the Mathematics of Planet Earth book series (MPE, volume 5)


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.


Mean time to extinction Sighting records Sixth mass extinction Species–area relationship Population viability analysis 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Colin J. Carlson
    • 1
  • Kevin R. Burgio
    • 2
  • Tad A. Dallas
    • 3
  • Wayne M. Getz
    • 1
    Email author
  1. 1.Department of Environmental Science, Policy and ManagementUniversity of California BerkeleyBerkeleyUSA
  2. 2.Department of Ecology & Evolutionary BiologyUniversity of ConnecticutStorrsUSA
  3. 3.Department of Environmental Science and PolicyUniversity of California DavisDavisUSA

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