Models of Character Displacement and the Theoretical Robustness of Taxon Cycles

The appropriateness of the techniques used in modeling character displacement has been the focus of vigorous debate. In this paper, the three competing methods (the coevolutionarily stable community (CSC), the evolutionarily stable strategy (ESS), and quantitative genetic recursion (QGR)) are compared in models using a common ecological setting. Specific predictions of the CSC model have been used to understand features of character displacement among Cnemidophorous lizards on islands off Mexico, Anolis lizards in the Lesser Antilles and Galapagos finches. Nonetheless, the validity of the approach has been repeatedly questioned. Conceptually the three formalisms vary in the degree to which within species variability is allowed in the models. The predictions of the CSC are found not to be robust to even small violation of its fundamental assumption of absolute species monomorphy. We show by simulation and analytical observations that the CSC is not valid under frequency dependent selection, and that the ESS is the limiting case of QGR as intraspecific phenotypic variation goes to zero. Thus the ESS and the QGR models agree closely when the between-phenotype component (BPC) of the niche width is small. However, as the BPC increases, quantitative discrepancies between ESS and QGR predictions increase, although model behavior remains qualitatively similar. A fourth approach, termed "Quantitative Genetic Optimization" (QGO) analysis, is suggested, combining advantages of both the ESS and QGR. Although all approaches support the possibility of taxon cycles, the cycle patterns predicted are qualitatively different and strongly model dependent.