Abstract

An elementary mathematical theory based on a “selectivity-variability” principle is proposed to address a question raised by Charles Darwin, namely, how one sex of a sexually dimorphic species might tend to evolve with greater variability than the other sex. Two mathematical models of the principle are presented: a discrete-time one-step probabilistic model of the short-term behavior of the subpopulations of a given sex, with an example using normally distributed perceived fitness values; and a continuous-time deterministic coupled ODE model for the long-term asymptotic behavior of the expected sizes of the subpopulations, with an example using exponentially distributed fitness levels.

Disciplines

Mathematics

Number of Pages

23

Publisher Statement

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Interdisciplinary Mathematics on July 22020, available online: https://www.tandfonline.com/doi/abs/10.1080/09720502.2020.1769827

Available for download on Tuesday, July 13, 2021

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Mathematics Commons

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URL: https://digitalcommons.calpoly.edu/rgp_rsr/89