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Is there a "Wainer's rule"? Testing which sex varies most as an example analysis using GueSDat, the free Guenon Skull Database


Abstract


The distinguished statistician Howard Wainer claimed that larger phenotypic variance in males might be a general occurrence in mammals. We called this putative pattern "Wainer’s rule" and employed a dataset of more than 1300 specimens, each measured using 86 anatomical landmarks on skulls, to test this hypothesis using size and shape data in a group of Old World monkeys, the guenons. Our study is one example of an application that takes advantage of this large set of data (named "GueSDat"), made freely available to the research community. The analysis showed that large samples are crucial to estimate variances, and, in this respect, estimates of univariate size may require even larger samples than estimates of the magnitude of shape variance. Despite limited statistical power in species with smaller samples, results consistently suggest larger variance in male skull size but not in shape. Size could be more plastic and thus respond more directly to the environment. As males are larger than females, the costs of becoming bigger can be sustained only when conditions are optimal, thus making size strongly condition dependant and therefore more variable in the bigger sex. However, it is not only overall size and shape that may behave differently in terms of whether they follow "Wainer’s rule": preliminary analyses suggest that, as in insects, different traits (e.g., different cranial regions) may vary in how similar or different their phenotypic variance is. The example study shows the potentially wide applications of data in GueSDat and suggests that, besides the most common comparison of mean differences in females and males, the study of differences between sexes in phenotypic variance offers a promising avenue for future research in mammals.
Indeed, as exemplified by our work, testing "Wainer’s rule" in mammals and other animals could become an active field of investigation in a variety of disciplines (from morphological to behavioural studies), and one that will hopefully elucidate whether this trend might be so common to be considered as a "rule" in evolutionary biology.

Keywords


allometry; anatomical landmarks; bootstrap; geometric morphometrics; Procrustes; sampling error; shape; size

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DOI: http://dx.doi.org/10.4404/hystrix-28.2-12139

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Copyright (c) 2017 Andrea Cardini, Sarah Elton

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Hystrix, the Italian Journal of Mammalogy ISSN 1825-5272 (electronic version) 0394-1914 (printed version) Impact Factor (2016) 1.479, CiteScore (2016) 3.51.
Published by Associazione Teriologica Italiana
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Creative Commons LicenseWorks published in Hystrix are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.