Impact of maturation delays on the eco-evolutionary dynamics of Hawk-Dove game

In the talk the eco-evolutionary dynamics of the demographic version (expressed in expliciit mortality and fertility payoffs) of Hawk-Dove game will be analyzed. We will show that the trajectories are attracted by so called subnullcines (manifolds placed between frequency and density nullcline) before convergence to the stable rest point. Then the initial system is extended by addition of the external factors such as environmental seasonality and the predator pressure (modelled as the Lotka-Volterra system). This leads to the complex cycling behaviour around the rest point of the initial system. Then we will add the delay in fertility payoffs and the updated version of replicator dynamics will be derived. Then the trajectories of the delayed model will be compared with trajectories of the initial model without delays.