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

The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology

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

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

Kleptoparasitic melees--modelling food stealing featuring contests with multiple individuals

Kleptoparasitism is the stealing of food by one animal from another. This has been modelled in various ways before, but all previous models have only allowed contests between two individuals. We investigate a model of kleptoparasitism where individuals are allowed to fight in groups of more than two, as often occurs in real populations. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable challenging strategies. We find that there is always at least one ESS, but sometimes there are two or more, and discuss the circumstances when particular ESSs occur, and when there are likely to be multiple ESSs

Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size

Evolutionary game theory is an important tool to model animal and human behaviour. A key class of games are the social dilemmas, where cooperation benefits the group but defection benefits the individual within any group. Previous works have considered which games qualify as social dilemmas, and different categories of dilemmas, but have generally concentrated on fixed sizes of interacting groups. In this paper we develop a systematic investigation of social dilemmas on all group sizes. This allows for a richer definition of social dilemmas. For example, while increasing a group size to include another defector is always bad for all existing group members, extra cooperators can be good or bad, depending upon the particular dilemma and group size. We consider a number of commonly used social dilemmas in this context, and in particular show the effect of variability in group sizes for the example of a population comprising negative binomially distributed group sizes. The most striking effect is that increasing the variability in group sizes for non-threshold public goods games is favourable for the evolution of cooperation. The situation for threshold public goods games and commons dilemmas is more complex

Evolving multiplayer networks: Modelling the evolution of cooperation in a mobile population

We consider a finite population of individuals that can move through a structured environment using our previously developed flexible evolutionary framework. In the current paper the behaviour of the individuals follows a Markov movement model where decisions about whether they should stay or leave depends upon the group of individuals they are with at present. The interaction between individuals is modelled using a public goods game. We demonstrate that cooperation can evolve when there is a cost associated with movement. Combining the movement cost with a larger population size has a positive effect on the evolution of cooperation. Moreover, increasing the exploration time, which is the amount of time an individual is allowed to explore its environment, also has a positive effect. Unusually, we find that the evolutionary dynamics used does not have a significant effect on these results

Modelling Dominance Hierarchies Under Winner and Loser Effects

Animals that live in groups commonly form themselves into dominance hierarchies which are used to allocate important resources such as access to mating opportunities and food. In this paper, we develop a model of dominance hierarchy formation based upon the concept of winner and loser effects using a simulation-based model and consider the linearity of our hierarchy using existing and new statistical measures. Two models are analysed: when each individual in a group does not know the real ability of their opponents to win a fight and when they can estimate their opponents' ability every time they fight. This estimation may be accurate or fall within an error bound. For both models, we investigate if we can achieve hierarchy linearity, and if so, when it is established. We are particularly interested in the question of how many fights are necessary to establish a dominance hierarchy

A Game-Theoretical Winner and Loser Model of Dominance Hierarchy Formation

Many animals spend large parts of their lives in groups. Within such groups, they need to find efficient ways of dividing available resources between them. This is often achieved by means of a dominance hierarchy, which in its most extreme linear form allocates a strict priority order to the individuals. Once a hierarchy is formed, it is often stable over long periods, but the formation of hierarchies among individuals with little or no knowledge of each other can involve aggressive contests. The outcome of such contests can have significant effects on later contests, with previous winners more likely to win (winner effects) and previous losers more likely to lose (loser effects). This scenario has been modelled by a number of authors, in particular by Dugatkin. In his model, individuals engage in aggressive contests if the assessment of their fighting ability relative to their opponent is above a threshold [Formula: see text]. Here we present a model where each individual can choose its own value [Formula: see text]. This enables us to address questions such as how aggressive should individuals be in order to take up one of the first places in the hierarchy? We find that a unique strategy evolves, as opposed to a mixture of strategies. Thus, in any scenario there exists a unique best level of aggression, and individuals should not switch between strategies. We find that for optimal strategy choice, the hierarchy forms quickly, after which there are no mutually aggressive contests

Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population

The classical models of evolution have been developed to incorporate structured populations using evolutionary graph theory and, more recently, a new framework has been developed to allow for more flexible population structures which potentially change through time and can accommodate multiplayer games with variable group sizes. In this paper we extend this work in three key ways. Firstly by developing a complete set of evolutionary dynamics so that the range of dynamic processes used in classical evolutionary graph theory can be applied. Secondly, by building upon previous models to allow for a general subpopulation structure, where all subpopulation members have a common movement distribution. Subpopulations can have varying levels of stability, represented by the proportion of interactions occurring between subpopulation members; in our representation of the population all subpopulation members are represented by a single vertex. In conjunction with this we extend the important concept of temperature (the temperature of a vertex is the sum of all the weights coming into that vertex; generally, the higher the temperature, the higher the rate of turnover of individuals at a vertex). Finally, we have used these new developments to consider the evolution of cooperation in a class of populations which possess this subpopulation structure using a multiplayer public goods game. We show that cooperation can evolve providing that subpopulations are sufficiently stable, with the smaller the subpopulations the easier it is for cooperation to evolve. We introduce a new concept of temperature, namely “subgroup temperature”, which can be used to explain our results