Towards a replicator dynamics model of age structured populations

Abstract We present a new modelling framework combining replicator dynamics, the standard model of frequency dependent selection, with an age-structured population model. The allows for populations consisting competing strategies carried by individuals who change across their life cycle. Firstly discretization McKendrick von Foerster is derived. show that Euler–Lotka equation satisfied when reaches steady state (i.e. stable frequencies between age classes). This consists unit classes where timescale chosen so only fraction play single game round. implies linear dynamics and not killed during round are moved to next class; linearity means system equivalent large Bernadelli–Lewis–Leslie matrix. Then we use methodology multipopulation games derive two, mutually systems equations. first contains equations describing evolution strategy in whole population, completed subsystems structure each strategy. second changes general population’s structure, selection within class. then obtained form mixed ODE-PDE which independent timescale, much simpler. results illustrated example sex ratio shows different mortalities sexes assumed, 0.5 but Fisher’s mechanism, driven reproductive value sexes, equilibrium.