Evol Ecol Res 11: 141-151 (2009)     Full PDF if your library subscribes.

Using stage-structured evolutionary game theory to model the experimentally observed evolution of a genetic polymorphism

R.C. Rael1, R.F. Costantino2, J.M. Cushing1,3 and T.L. Vincent4

1Program in Applied Mathematics,  2Department of Ecology and Evolutionary Biology, 3Department of Mathematics and  4Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA

Correspondence: R.C. Rael, Program in Applied Mathematics, University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721, USA.
e-mail: rrael@math.arizona.edu


Aim: Our aim is to show the utility of evolutionary game theory (EGT) methods in describing and predicting the outcome of experiments for which genetic data are available in the absence of phenotypic data. As an example we use experimental data from genetically perturbed cultures of the flour beetle Tribolium castaneum. Using natural selection, the theory provides a theoretical basis for the observed population dynamics and evolution of a polymorphism of wild-type and corn oil sensitive alleles.

Method of analysis: We derive an EGT version of a well-validated model for the population dynamics of Tribolium (the LPA model) using a version of EGT developed for stage-structured populations given by Vincent and Brown (2005). We use the wild-type allele frequency as the strategy in this model. We estimate model parameters and conduct simulations using the parameterized model.

Experimental data: We use population and genetic data from an experiment conducted by Desharnais (1979). Cultures of T. castaneum homozygous for corn oil sensitivity are perturbed by adding homozygous wild-type individuals. The data include population densities of larvae, pupae, and adults as well as allele frequencies obtained from genetically perturbed cultures.

Conclusions: The parameterized EGT version of the LPA model fits reasonably accurately the population and genetic data in both the control and genetically perturbed treatments. For both treatments, the model predicts an oscillatory 2-cycle asymptotic attractor. The predicted oscillations match well with the oscillations observed in the population data, even capturing observed increases in amplitude and population densities in the genetically perturbed treatment. Interestingly, the model also predicts a periodic oscillation in allele frequency, although the amplitude is too small to be detected in the data. We conclude that the EGT-predicted evolution of a polymorphism by natural selection is obtained in agreement with the experimental data. Our results illustrate two points concerning EGT: first, the theory can be successful in application to real data and, second, it can be applied in a context that allows a connection to classical population genetics theory.

Keywords: allele frequency, evolutionary game theory, genetic polymorphism, LPA stage-structured model, Tribolium.

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