Bulletin of Mathematical Biology

, Volume 79, Issue 8, pp 1907–1922 | Cite as

Further Mathematical Modelling of Mating Sex Ratios & Male Strategies with Special Relevance to Human Life History

  • Sara L. LooEmail author
  • Matthew H. Chan
  • Kristen Hawkes
  • Peter S. Kim
Original Article


Influential models of male reproductive strategies have often ignored the importance of mate guarding, focusing instead on trade-offs between fitness gained through care for dependants in a pair bond versus fitness from continued competition for additional mates. Here we follow suggestions that mate guarding is a distinct alternative strategy that plays a crucial role, with special relevance to the evolution of our own lineage. Human pair bonding may have evolved in concert with the evolution of our grandmothering life history, which entails a shift to male-biased sex ratios in the fertile ages. As that sex ratio becomes more male biased, payoffs for mate-guarding increase due to partner scarcity. We present an ordinary differential equation model of mutually exclusive strategies (dependant care, multiple mating, and mate guarding), calculate steady-state frequencies and perform bifurcation analysis on parameters of care and guarding efficiency. Mate guarding triumphs over alternate strategies when populations are male biased, and guarding is fully efficient. When guarding does not ensure complete certainty of paternity, and multiple maters are able to gain some paternity from guarders, multiple mating can coexist with guarding. At female-biased sex ratios, multiple mating takes over, unless the benefit of care to the number of surviving offspring produced by the mates of carers is large.


Mate guarding Paternal care Multiple mating Sex ratio Difference equations Ordinary differential equations 



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


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  • Sara L. Loo
    • 1
    Email author
  • Matthew H. Chan
    • 1
  • Kristen Hawkes
    • 2
  • Peter S. Kim
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  2. 2.Department of AnthropologyUniversity of UtahSalt Lake CityUSA

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