"Growing up and feeling like a loser. Impact of maturation delay on the eco-evolutionary game dynamics in changing environment."Argasinski, KrzysztofThe talk will present the results from two unpublished papers, continuing the previous work on demographic evolutionary games by Argasinski and Broom (2018a, 2018b). The demographic approach assumes that, instead of a single payoff function describing Darwinian fitness, there are two payoff functions describing births and deaths. This approach allows for the introduction of different forms of density-dependent population size regulation, such as juvenile recruitment survival probability. We will begin by presenting the updated demographic payoff functions, taking into account the explicit probabilities of winning/losing during conflicts with a particular strategy. The updated structure of the payoff functions is more suitable for describing games with indivisible rewards than the approach from previous papers. Additionally, the existing conditions for eco-evolutionary stability will be completed by introducing so-called subnullclines – surfaces connecting stable and unstable rest points, attracting trajectories before they reach the stable rest point. Next, we will extend the modeling framework by adding a maturation delay for newborns. This implies the application of delay differential equations. The resulting models are very sensitive to the influence of external factors, as demonstrated by adding the seasonal mortality factor or explicit predator pressure modeled by a simple Lotka-Volterra system. Numerical simulations of the obtained models exhibit very complex behavior, including complex oscillations and cycles or even chaos. One of the surprising results is that in some cases, the impact of the delay vanishes in the neighborhood of subnullclines. Keywords: evolutionary game theory, delay differential equations, eco-evolutionary models, non-linear dynamics, demographic games, population dynamics. |
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