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Individual optimization efforts and population dynamics: a mathematical model for the evolution of resource allocation strategies, with applications to reproductive and mating systems

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Abstract

We develop a formal framework for the optimal allocation of limited resources that includes and clarifies the interplay between individual optimization and the resulting effects at the population level. As an example, in regard to the evolution of sexual recombination, the paradox of the twofold cost of sex is avoided by distinguishing between the evolution of recombination and the subsequent emergence and stability of different mating types as a result of individual optimization within a population that benefits from recombination.

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Notes

  1. As an alternative to differential calculus and as a way to relax some of these assumptions, one may instead choose the framework and methods of convex optimisation. This, however, requires certain convexity assumptions that may interfere more seriously with our biological applications.

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Acknowledgments

The authors thank the Santa Fe Institute for the stimulating atmosphere in which this work was started.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103, Leipzig, Germany

    Jürgen Jost

  2. Department of Ecology and Evolutionary Biology, University of Arizona, Biosciences West, 1041 E.Lovell, Tucson, AZ, 85721-0088, USA

    John Pepper

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  1. Jürgen Jost
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  2. John Pepper
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Correspondence to Jürgen Jost.

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Jost, J., Pepper, J. Individual optimization efforts and population dynamics: a mathematical model for the evolution of resource allocation strategies, with applications to reproductive and mating systems. Theory Biosci. 127, 31–43 (2008). https://doi.org/10.1007/s12064-007-0021-9

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  • DOI: https://doi.org/10.1007/s12064-007-0021-9

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