BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marco Morandotti (Politecnico di Torino) DTSTART:20250324T144000Z DTEND:20250324T161000Z DTSTAMP:20260405T175450Z UID:NSCM/168 DESCRIPTION:Title: R eplicator dynamics as the large population limit of a discrete Moran proce ss\nby Marco Morandotti (Politecnico di Torino) as part of Nečas Semi nar on Continuum Mechanics\n\nLecture held in Room K3\, Faculty of Mathem atics and Physics\, Charles University\, Sokolovská 83 Prague 8..\n\nAbs tract\nThe replicator dynamics accomplishes the task of modelling the evol ution of strategies in a population by subjecting the probability of repro duction to their fitness: The higher the fitness\, the higher the chance o f being selected to reproduce. Yet\, the criterion followed by individual agents to select their strategies is latent in the replicator equation\, w hich describes the continuous-time evolution of the proportions of strateg ies in an averaged fashion.\n\nIn this talk\, we provide a mathematical fr amework to derive the replicator equation as a mean-field limit of a discr ete stochastic process modelling this evolutionary mechanism from the poin t of view of individual agents and their pairwise interactions. In this co ntext\, the classical Moran process is a prototypical example of discrete stochastic process that models natural selection in finite populations wit h two strategies (alleles\, in biology) competing for dominance. We study the mean-field limit of a generalised Moran process as the number of agent s diverges and we show that\, in the weak selection regime\, it converges to the replicator dynamics.\n LOCATION:https://researchseminars.org/talk/NSCM/168/ END:VEVENT END:VCALENDAR