4 Presentations

• 
  08:30 AM - 08:55 AM

  Evolutionary models of kleptoparasitism with time delays

  • Mark Broom, presenter, City University London
  • Robert Spencer, University of Middlesex

  In this talk we discuss evolutionary models of food stealing behaviour, kleptoparasitism, which centre on potentially lengthy contests between individuals. Individuals must choose whether it is worth challenging for, or defending, food items, and this will depend upon various population parameters such as food availability, probability of success and length of contest. We discuss a series of models developed by Broom and co-workers, and in particular focus on a recent model relating to a real population of urban gulls. For this population extensive data was collected, and the model in general fitted the data well, but with one significant limitation, which we shall discuss. This in turn points to interesting future model developments.

• 
  08:55 AM - 09:20 AM

  Evolutionary games over the day and the year

  • Zoltan Barta, presenter, MTA-DE Behavioural Ecoloy Research Group

  Because of Earth's movements, the environment of most organisms is periodical. As a consequences of these regular changes organisms must consider time of day and year when deciding about their behaviour, that is, they have to optimise their timing of behaviour. Periodicity is, however, rarely considered in evolutionary games where interactions between individuals are explicitly taken into account. In this talk I investigate how individuals should time their behaviour in two game theoretical settings. First, I concentrate on social foraging and study time dependent behaviour of exploitation of others search effort. I shortly discuss how time dependency alter exploitation and its consequences for resource use. Second, I focus on optimal annual routine of moult and reproduction where the interaction between individuals is mediated through competition for food. These examples show that time dependency can significantly alter the evolutionarily stable behaviour.

• 
  09:20 AM - 09:45 AM

  Monomorphic evolutionary stability for matrix games under time constrains

  • József Garay, presenter, Eötvös Lorand University

  Monomorphic evolutionary stability for matrix games under time constrains

  József Garay
  MTA Centre for Ecological Research, Evolutionary Systems Research Group., Klebelsberg Kuno utca 3, Tihany, 8237, Hungary.

  We introduce a matrix game under time constraints, where each pairwise interaction has two consequences: both players receive a payoff and they cannot play the next game for a specified time duration. Thus our model is defined by two matrices: a payoff matrix and an average time duration matrix. Maynard Smith’s concept of monomorphic evolutionary stability is extended to this class of games.
  We illustrate the effect of time constraints by the prisoner’s dilemma game, where additional time constraints can ensure the existence of unique evolutionary stable strategies (ESS), both pure and mixed, or the coexistence of two pure ESS.

• 
  09:45 AM - 10:10 AM

  Static characterizations of ESS under time constraints and strong stability for two dimensional strategies

  • Tamas Varga, presenter,
  • Tamás Móri F., Eötvös Loránd University
  • József Garay, Eötvös Lorand University

  A strategy p is a (monomophic) ESS if the population of individuals of p phenotypes resists against any other
  phenotype q distinct from p. This means mathematically that the fitness of a p individual is higher than that of a mutant phenotype if the proportion of the mutants is small enough. For classical matrix games, it is known that p is ESS if and only if the payoff of a focal p strategist against a mutant is higher than that of a focal mutant against another mutant provided the mutant strategy is close enough to p in the strategy space. This characterization eliminates the proportion of the mutants from the definition simplifying the investigation of the relationship between the monomorh ESS and the stable state of a polymorph population. Our result is that an analogue characterization also exists under time constraints. Moreover, for two dimensional strategies, a dynamical characterization analogues with the strong stability concept for classical matrix games can also be established.