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Modelling the Evolution of Traits in a Two-Sex Population, with an Application to Grandmothering

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Abstract

We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness trade-off associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price equation to include two sexes, age structure and multiple traits. We use this formula to examine the effect of grandmothering, whereby post-fertile females subsidise their daughter’s fertility by provisioning grandchildren. Grandmothering can drive a shift towards increasingly male-biased mating sex ratios due to a post-fertile life stage in females, while male fertility continues to older ages. Our fitness landscapes show a net increase in fitness for both males and females at longer lifespans, and as a result, we find that grandmothering alone provides an evolutionary trajectory to higher longevities.

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Acknowledgements

MHC and PSK were supported by the Australian Research Council, Discovery Project (DP160101597).

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    Matthew H. Chan & Peter S. Kim

  2. Department of Anthropology, University of Utah, Salt Lake City, UT, 84112, USA

    Kristen Hawkes

Authors
  1. Matthew H. Chan
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  2. Kristen Hawkes
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  3. Peter S. Kim
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Correspondence to Matthew H. Chan.

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Chan, M.H., Hawkes, K. & Kim, P.S. Modelling the Evolution of Traits in a Two-Sex Population, with an Application to Grandmothering. Bull Math Biol 79, 2132–2148 (2017). https://doi.org/10.1007/s11538-017-0323-0

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  • DOI: https://doi.org/10.1007/s11538-017-0323-0

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