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On the Evolution of Polygamy: A Theoretical Examination of the Polygamy Threshold Model


  • Susan Ptak
  • Michael Lachmann


The polygamy threshold model states that if costs incurred are less than the benefits gained from a polygamous relationship in terms of male or habitat quality, then polygamy is favored and could evolve. Here we construct mathematical models and computer simulations to evaluate this hypothesis theoretically. In the basic model, there is a single locus with two alleles, where this locus regulates whether or not the female is receptive to polygamy. There are two habitats of different quality for which females vie, and on which males randomly assort themselves. This basic model is extended mathematically to include cost to the initial female of a polygamously mated male and again to include gene expression in males. The computer simulations extend the basic model to multiple loci and alleles, and to multiple habitats. The results presented here suggest that the polygamy threshold model is valid in a population genetic context -- in all cases in which the fitness of females that actually mated polygamously is greater than the fitness of monogamous females on poorer habitats, polygamy evolved. However, using this approach revealed interesting dynamics not apparent from the original verbal model. If the trait is expressed in males and females, then polygamy can evolve even if females mating polygamously have a lower fitness than females mating monogamously. In the multiple habitat model, the polygamy allele increases to some equilibrium value above which it experiences no selection. Surprisingly, as the cost to polygamy increases, the equilibrium value of the polygamy allele also increases.

Suggested Citation

  • Susan Ptak & Michael Lachmann, 2001. "On the Evolution of Polygamy: A Theoretical Examination of the Polygamy Threshold Model," Working Papers 01-01-001, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-01-001

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    References listed on IDEAS

    1. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    2. Dean Foster & H Peyton Young, 1999. "On the Impossibility of Predicting the Behavior of Rational Agents," Economics Working Paper Archive 423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
    3. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
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