Natural selection under limited population growth. Replicator dynamics and eco-evolutionary feedback

Last modified: 2014-06-09

#### Abstract

In this talk we discuss a new approach to the derivation of population dynamic models called “event based modelling,” which

relies on the assumption that the trajectory of the process is the aggregated outcome of individual interactions (i.e. “atomic”

events) occurring with respective rates. Thus, the methodology resembles that of chemical kinetics where the interaction rate is

the analogue of the reaction rate. In this approach, instead single abstract ﬁtness function, describing growth rate, there are two

separate mortality and fertility payoff functions. An important aspect of the presented framework is the explicit incorporation of

growth limitations. The regulation of the population size acts through feedback driven by density dependent juvenile mortality.

It was shown that at the population size equilibrium, newborns form a pool of candidates from which survivors who will

replace dead adults at their nest sites will be drawn. Thus fertility payoffs can be interpreted as the entries of a nest site lottery

mechanism. The new approach emphasizes the role of the turnover of individuals. In this case the stable population size is

a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary ﬁxed carrying capacity. This

mechanism can be regarded as an example of eco-evolutionary feedback. This seriously alters the predictions of game-theoretic

models in comparison to models with unlimited growth. In this case there can be for example two stable manifolds: one for the

frequency dynamics and a second for the population size. The global stationary points are intersections of those manifolds. For

example in the Hawk-Dove Game, a pure Hawk population can become evolutionarily stable in addition to the stable mixed

equilibrium known from the classical theory. This is caused by the fact that the payoff structure is not constant. The most

intriguing result is that under the impact of eco-evolutionary feedback, an apparently unstable invasion barrier between two

pure-strategy stable equilibria can become stable at the intersection with the stable density manifold.

ARGASINSKI, K.; BROOM, M. Ecological theatre and the evolutionary game: how environmental and demographic factors

determine payoffs in evolutionary games. Journal of Mathematical Biology, 2012, 1-28.

ARGASINSKI, K.; BROOM, M. The nest site lottery: how selectively neutral density dependent growth suppression induces

frequency dependent selection .Theoretical Population Biology 90 82-90, 2013

relies on the assumption that the trajectory of the process is the aggregated outcome of individual interactions (i.e. “atomic”

events) occurring with respective rates. Thus, the methodology resembles that of chemical kinetics where the interaction rate is

the analogue of the reaction rate. In this approach, instead single abstract ﬁtness function, describing growth rate, there are two

separate mortality and fertility payoff functions. An important aspect of the presented framework is the explicit incorporation of

growth limitations. The regulation of the population size acts through feedback driven by density dependent juvenile mortality.

It was shown that at the population size equilibrium, newborns form a pool of candidates from which survivors who will

replace dead adults at their nest sites will be drawn. Thus fertility payoffs can be interpreted as the entries of a nest site lottery

mechanism. The new approach emphasizes the role of the turnover of individuals. In this case the stable population size is

a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary ﬁxed carrying capacity. This

mechanism can be regarded as an example of eco-evolutionary feedback. This seriously alters the predictions of game-theoretic

models in comparison to models with unlimited growth. In this case there can be for example two stable manifolds: one for the

frequency dynamics and a second for the population size. The global stationary points are intersections of those manifolds. For

example in the Hawk-Dove Game, a pure Hawk population can become evolutionarily stable in addition to the stable mixed

equilibrium known from the classical theory. This is caused by the fact that the payoff structure is not constant. The most

intriguing result is that under the impact of eco-evolutionary feedback, an apparently unstable invasion barrier between two

pure-strategy stable equilibria can become stable at the intersection with the stable density manifold.

ARGASINSKI, K.; BROOM, M. Ecological theatre and the evolutionary game: how environmental and demographic factors

determine payoffs in evolutionary games. Journal of Mathematical Biology, 2012, 1-28.

ARGASINSKI, K.; BROOM, M. The nest site lottery: how selectively neutral density dependent growth suppression induces

frequency dependent selection .Theoretical Population Biology 90 82-90, 2013