"Multi Strategy Eco Evolutionary Model - Stability Analysis"Bedi, Manjyot SinghEvolutionary game theory is used to model the analytical aspect of Darwinian competition. Within it are multiple approaches, with the standard method of modelling a dynamically evolving population being the replicator dynamics. Here the (per capita) rate of change of the proportion of the population playing a strategy is proportional to its fitness advantage compared to the average in the population, using a single fitness function independent of the total population size. Argasinski and Broom (2012) initiated an alternative and more realistic, detailed dynamical approach taking into account actual births and deaths within the population, quantified into separate fertility and mortality events that interacted with the population size in distinct ways. A series of models were developed, but they have currently been restricted to games involving only two strategies, such as the Hawk-Dove game. With the introduction of a third strategy, the dynamics of the game are significantly changed. We have looked at example three strategy games, including the Rock Paper Scissors game, and highlight the impact of different parameters on the dynamics of the system and also consider a more general stability analysis for the system, which will be the focus of this poster. |
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