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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

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

    Sara L. Loo, Matthew H. Chan & Peter S. Kim

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

    Kristen Hawkes

Authors
  1. Sara L. Loo
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  2. Matthew H. Chan
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  3. Kristen Hawkes
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  4. Peter S. Kim
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Corresponding author

Correspondence to Sara L. Loo.

Appendix A

Appendix A

1.1 Female-Biased Steady-State Solutions

Example steady states given the parameter values in Table 3 can be calculated using the analytic expressions of the steady states presented in Sect. 3.1.1. The steady states, the corresponding eigenvalues, and the subsequent stability at each solution given these parameter values are:

Table 3 Summary of parameters used for female-biased population simulations of stability and equilibrium
Full size table

1.2 Male-Biased Steady-State Solutions

Similarly, steady-state solutions for a male-biased sex ratio with other parameter values as summarised in Table 3 can be numerically determined. While analytic solutions for male-biased populations cannot be determined, we find that numerical simulations show the existence of one equilibrium point at a large P value of 0.74 and another stable state corresponding to extinction out of the paternal care strategy. Three numerical solutions of the three steady states are given below in Eq. 7. Numerical simulation of these solutions and bifurcations is conducted in AUTO07.

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Loo, S.L., Chan, M.H., Hawkes, K. et al. Further Mathematical Modelling of Mating Sex Ratios & Male Strategies with Special Relevance to Human Life History. Bull Math Biol 79, 1907–1922 (2017). https://doi.org/10.1007/s11538-017-0313-2

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