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The effect of fight cost structure on fighting behaviour

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Abstract

A common feature of animal populations is the stealing by animals of resources such as food from other animals. This has previously been the subject of a range of modelling approaches, one of which is the so called “producer-scrounger” model. In this model a producer finds a resource that takes some time to be consumed, and some time later a (generally) conspecific scrounger discovers the producer with its resource and potentially attempts to steal it. In this paper we consider a variant of this scenario where each individual can choose to invest an amount of energy into this contest, and the level of investment of each individual determines the probability of it winning the contest, but also the additional cost it has to bear. We analyse the model for a specific set of cost functions and maximum investment levels and show how the evolutionarily stable behaviour depends upon them. In particular we see that for high levels of maximum investment, the producer keeps the resource without a fight for concave cost functions, but for convex functions the scrounger obtains the resource (albeit at some cost).

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Acknowledgments

The research has been supported by grant GAČR 201/11/0345 (Michal Johanis) and the Simons Foundation grant #245400 (Jan Rychtář).

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Authors and Affiliations

  1. Department of Mathematics, City University London, Northampton Square, London, EC1V 0HB, UK

    Mark Broom

  2. Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 , Praha 8, Czech Republic

    Michal Johanis

  3. Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, 27412, USA

    Jan Rychtář

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  1. Mark Broom
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  2. Michal Johanis
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Correspondence to Jan Rychtář.

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Broom, M., Johanis, M. & Rychtář, J. The effect of fight cost structure on fighting behaviour. J. Math. Biol. 71, 979–996 (2015). https://doi.org/10.1007/s00285-014-0848-x

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  • DOI: https://doi.org/10.1007/s00285-014-0848-x

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