4 Presentations

• 
  04:10 PM - 04:35 PM

  Replicator dynamics for age structured populations

  • Argasinski Krzysztof, presenter, Institute of Mathematics, Polish Academy of Sciences
  • Mark Broom, City University of London

  In the talk will be presented the new modelling framework combining the replicator dynamics (which is the standard model of the frequency dependent selection) with the Leslie Matrix model of the age-structured population. Firstly the continuous version of the discrete Leslie Matrix model will be derived. We will show that the Euler-Lotka equation is satisfied when new model reaches the steady state (ie. stable related frequencies between the age classes). The methodology of the multipopulation games will be used for derivation of two, mutually equivalent systems of equations. First contains equations describing the evolution of the strategy frequencies in the whole population completed by subsystems of equations describing the evolution of the age structure for each strategy. Second system contains equations describing the changes of the age structure of the general population, completed with subsystems of equations describing the selection of the strategies within each age class. The proposed modelling framework can be used to extend the standard evolutionary game structure to the age structured case with assumption that the modelled game is played within specific age classes only. Results will be illustrated by age structured sex ratio model with different intervals of sexual activity within life cycle for both sexes.

• 
  04:35 PM - 05:00 PM

  Incompetence in evolutionary games

  • Maria Kleshnina, presenter, University of Queensland
  • Jerzy Filar, University of Queensland
  • Vladimir Ejov, Flinders University
  • McKerral Jody, Flinders University

  The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species. We introduce an incompetence parameter into a learning function in a single-population game and analyze its effect on the outcome of the replicator dynamics. Incompetence can change the outcome of the game and its dynamics, indicating its significance within what are inherently imperfect natural systems.

• 
  05:00 PM - 05:25 PM

  Reflective Evolution under Strategic Uncertainty

  • Arnaud Dragicevic, presenter, Laboratory of Forest Economics, Agro ParisTech

  We consider population dynamics of agents who can both play the cooperative strategy and the competition strategy but ignore whether the game to come will be cooperative or non-cooperative. For that purpose, we propose an evolutionary model, built upon replicator(-mutator) dynamics under strategic uncertainty, and study the impact of update decay. In replicator-mutator dynamics, we find that the strategy replication under certain mutation in an unstructured population is equivalent to a negative strategy replication in a structured population. Likewise, in replicator-mutator dynamics with decay, the strategy replication under certain mutation in a structured population is equivalent to a negative replication issued from an unstructured population. Our theoretical statements are supported by numerical simulations performed on bifurcation diagrams.

• 
  05:25 PM - 05:50 PM

  Entropic Equilibria Selection of Stationary Extrema in Finite Populations

  • Dashiell Fryer, presenter, San Jose State University
  • Marc Harper, Google

  We propose the entropy of random Markov trajectories originating and terminating at a state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation and show that variations in population size, mutation rate, and strength of selection all affect the stability of the stationary extrema.