Evol Ecol Res 12: 1-22 (2010)     Full PDF with comments if your library subscribes.

The three-quarter-power scaling of extinction risk in Late Pleistocene mammals, and a new theory of the size selectivity of extinction

Leonard V. Polishchuk

Department of General Ecology, Biological Faculty, M.V. Lomonosov Moscow State University, Moscow, Russia and Department of Aquatic Ecology, Centre for Limnology, Netherlands Institute of Ecology, Nieuwersluis, Netherlands

Correspondence: L.V. Polishchuk, Department of General Ecology, Biological Faculty, M.V. Lomonosov Moscow State University, 119992 Moscow, Russia.
e-mail: leonard_polishchuk@hotmail.com


Questions: What is the pattern of body mass versus extinction risk in the Late Pleistocene extinctions of mammals, both qualitatively and quantitatively? Are there patterns that relate extinction risk to the well-known allometries of body mass with population density or population growth rate?

Theory: A simple theory to predict both qualitative pattern and quantitative parameters of the size-selectivity of extinction. First, I assume that external pressures (e.g. human impact and climate change) increased the overall risk of extinction in the Late Pleistocene in a way that does not depend on body size. Then, I assume that this overall risk is modified by a species’ biological traits and that these traits are related allometrically to the species’ body mass. Specifically, the traits are population density, N, which scales as body mass to the power of −0.75 (Damuth, 1981), and population growth rate, r, which scales as body mass to the power of −0.25 (Fenchel, 1974). I assume that extinction probability is the reciprocal of either N or r. This leads to an allometric relationship between extinction risk and body size. I assume that the external pressures during the Late Pleistocene did not change the shape (e.g. slope) of that relationship, making it possible to tease out some of its important features.

Prediction: The probability of extinction, P, is a logistic function of log-transformed body mass with slope 0.75 or 0.25. Or, equivalently, the odds of extinction, P/(1 − P), scale as body mass to the power of 0.75 and 0.25, respectively.

Test data: A comprehensive database of body masses of all mammalian species from four continents, containing all species on those continents that became extinct in the Late Pleistocene and all those that survived it (Smith et al., 2003).

Methods: Ordinary logistic regression and logistic regression with mixed effects (the latter to account for the non-independence of data that is inherent in comparative species analyses). I analysed the full data set with and without bats or pinnipeds, as well as a truncated data set containing only species whose mass is/was 5 kg or greater. I also analysed continent-specific subsets of species.

Results: For both full and truncated data sets on a worldwide scale, the probability of extinction follows a logistic curve whose slope is close to, and statistically indistinguishable from, 0.75, the value that assumes that extinction probability depends on population density. The continent-specific subsets of species, however, deviate from the worldwide pattern.

Conclusions: The Late Pleistocene extinctions, although strongly biased towards large-bodied species, are biased no more than expected from the −0.75-power population-density scaling.

Keywords: allometric scaling, body mass, extinction pattern, logistic regression.

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