The nest site lottery: How selectively neutral density dependent growth suppression induces frequency dependent selection

Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary fixed carrying capacity. The latest replicator dynamics models assume that regulation of the population size acts through feedback driven by density dependent juvenile mortality. Here, we consider a simplified model to extract the properties of this approach. We show that at the stable population size, the structure of the frequency dependent evolutionary game emerges. Turnover of individuals induces a lottery mechanism where for each nest site released by a dead adult individual a single newborn is drawn from the pool of newborn candidates. This frequency dependent selection leads toward the strategy maximizing the number of newborns per adult death. However, multiple strategies can maximize this value. Among them, the strategy with the greatest mortality (which implies the greatest instantaneous growth rate) is selected. This result is important for the discussion about universal fitness measures and which parameters are maximized by natural selection. This is related to the fitness measures R0 and r, because the number of newborns per single dead individual equals lifetime production of newborn R0 in models without ageing. We thus have a two-stage procedure, instead of a single fitness measure, which is a combination of R0 and r. According to the nest site lottery mechanism, at stable population size, selection favours strategies with the greatest r, i.e. those with the highest turnover, from those with the greatest R0

Evolutionary stability under limited population growth: Eco-evolutionary feedbacks and replicator dynamics

This paper further develops a new way of modelling evolutionary game models with an emphasis on ecological realism, concerned with how ecological factors determine payoffs in evolutionary games. Our paper is focused on the impact of strategically neutral growth limiting factors and background fitness components on game dynamics and the form of the stability conditions for the rest points constituted by the intersections of the frequency and density nullclines. It is shown that for the density dependent case, that at the stationary state, the turnover coefficients (numbers of newborns per single dead adult) are equal for all strategies. In addition, the paper contains a derivation of the EESS (eco-evolutionarily stable states) conditions, describing evolutionary stability under limited population growth. We show that evolutionary stability depends on the local geometry (slopes) of the intersecting nullclines. The paper contains examples showing that density dependence induces behaviour which is not compatible with purely frequency dependent static game theoretic ESS stability conditions. We show that with the addition of density dependence, stable states can become unstable and unstable states can be stabilised. The stability or instability of the rest points can be explained by a mechanism of eco-evolutionary feedback

Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk–Dove example

Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games

In the standard approach to evolutionary games and replicator dynamics, differences in fitness can be interpreted as an excess from the mean Malthusian growth rate in the population. In the underlying reasoning, related to an analysis of "costs" and "benefits", there is a silent assumption that fitness can be described in some type of units. However, in most cases these units of measure are not explicitly specified. Then the question arises: are these theories testable? How can we measure "benefit" or "cost"? A natural language, useful for describing and justifying comparisons of strategic "cost" versus "benefits", is the terminology of demography, because the basic events that shape the outcome of natural selection are births and deaths. In this paper, we present the consequences of an explicit analysis of births and deaths in an evolutionary game theoretic framework. We will investigate different types of mortality pressures, their combinations and the possibility of trade-offs between mortality and fertility. We will show that within this new approach it is possible to model how strictly ecological factors such as density dependence and additive background fitness, which seem neutral in classical theory, can affect the outcomes of the game. We consider the example of the Hawk-Dove game, and show that when reformulated in terms of our new approach new details and new biological predictions are produced

Towards a replicator dynamics model of age structured populations

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

Asymmetric Games in Monomorphic and Polymorphic Populations

Evolutionary game theory is an increasingly important way to model the evolution of biological populations. Many early models were in the form of matrix games, or bi-matrix games in asymmetric situations when individuals occupy distinct roles within the contest, where rewards are accrued through independent contests against random members of the population. More recent models have not had the simple linear properties of matrix games, and more general analysis has been required. In this paper we carry out a general analysis of asymmetric games, comparing monomorphic and polymorphic populations. We are particularly interested in situations where the strategies that individuals play influence which role that they occupy, for example in a more realistic variant of the classical Owner-Intruder game. We both prove general results and consider specific examples to illustrate the difficulties of these more complex games

2013)The nest site lottery: how selectively neutral density dependent growth suppression induces frequency dependent selection, arXiv:1303.0564 [q-bio.PE

h i g h l i g h t s • We analyze the population dynamics model. • We assume selectively neutral density dependent growth suppression. • At equilibrium size the frequency dependent selection is induced. • This mechanism can be called nest site lottery. • Our result suggests existence of the new fitness measure. Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary fixed carrying capacity. The latest replicator dynamics models assume that regulation of the population size acts through feedback driven by density dependent juvenile mortality. Here, we consider a simplified model to extract the properties of this approach. We show that at the stable population size, the structure of the frequency dependent evolutionary game emerges. Turnover of individuals induces a lottery mechanism where for each nest site released by a dead adult individual a single newborn is drawn from the pool of newborn candidates. This frequency dependent selection leads towards the strategy maximizing the number of newborns per adult death. However, multiple strategies can maximize this value. Among them, the strategy with the greatest mortality (which implies the greatest instantaneous growth rate) is selected. This result is important for the discussion about universal fitness measures and which parameters are maximized by natural selection. This is related to the fitness measures R 0 and r, because the number of newborns per single dead individual equals the lifetime production of newborn R 0 in models without aging. We thus have a two-stage procedure, instead of a single fitness measure, which is a combination of R 0 and r. According to the nest site lottery mechanism, at stable population size, selection favors strategies with the greatest r, i.e. those with the highest turnover, from those with the greatest R 0 . a r t i c l e i n f