Evolutionarily stable strategies with complex life cycles.
Moll, Jason*,1, Brown, Joel1, 1 University of Illinois at Chicago, Chicago, IL, USA
ABSTRACT- Adaptive dynamics provide a useful framework for studying evolution in ecological communities. We investigate how ontogenetic niche shifts and complex life cycles affect evolutionarily stable strategies (ESS) using the G-function approach. This approach consists of both an inner game in which the players get payoffs from their choice of strategy (similar to traditional evolutionary game theory), and an outer game, where the frequencies of strategies change as a result of those payoffs. Our model expands on previous single-stage model of Lotka-Volterra competition in which strategies determine the carrying capacity and also the strength of competition between different strategies. In the single-stage model, the ESS can consist of either a single strategy or a coalition of multiple strategies, depending on the choice of parameters. In the two-stage model, the strategies in different stages can either be evolutionarily linked or able to evolve independently from one another. In all cases, it is again possible to get an ESS of either a single strategy or a coalition of strategies. If the stages can evolve independently, an ESS can contain a different number of strategies in different stages. When the two stages are linked, however, it is difficult to get a different number of ESS strategies in each stage. These results suggest that the effect of complex life cycles on diversity may depend on how strongly stages are tied together evolutionarily.
Key words: adaptive dynamics, evolutionary game theory, evolutionary simulation
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