The use of multiplayer game theory in the modeling of biological populations

The use of game theory in modeling the natural world is widespread. However, this modeling mainly involves two player games only, or "playing the field" games where an individual plays against an entire (infinite) population. Game-theoretic models are common in economics as well, but in this case the use of multiplayer games has not been neglected. This article outlines where multiplayer games have been used in evolutionary modeling and the merits and limitations of these games. Finally, we discuss why there has been so little use of multiplayer games in the biological setting and what developments might be useful

Balancing risks and rewards: the logic of violence

Violence is widespread throughout the natural world, prominent examples being predatory violence between species, seasonal violent competition for mating rights and territories within species and food competition both within and between species. These interactions are generally between unrelated individuals with no social connection. There are, however, examples of violent behaviour which occurs within groups of individuals who otherwise cooperate to live, have significant social bonds and may also be related, and that is the primary focus of this paper. Examples are in the establishment and maintenance of dominance hierarchies, or in infanticide, where (usually) incoming males attempt to kill existing infants in a group. Such violence can seem paradoxical, but in fact is often perfectly logical for the individual perpetrating the violence, as distinct from the group as a whole. We discuss such situations from the perspective of evolutionary game theory, and also consider wider questions of interspecific violence

A game theoretic model of kleptoparasitism with strategic arrivals and departures of beetles at dung pats

Dung beetles Onthophagus taurus lay their eggs in brood balls within dung pats. The dung that is used must be sufficiently fresh, and so beetles must keep moving from pat to pat to find fresh dung. If another beetle finds a brood ball it will usually eat the egg inside and lay its own egg in the brood ball instead of constructing its own ball. Thus, beetles will often stay near their eggs to guard them. We model a population of beetles where the times of arrival and departure from pats are strategic choices, and investigate optimal strategies depending upon environmental conditions, which can be reduced to two key parameters, the cost of brood ball construction and the ease of finding balls to parasitise. We predict that beetles should follow one of three distinct behaviors; stay in patches for only short periods, arrive late and be purely parasitic, remain in pats for longer periods in order to guard their brood balls. Under different conditions populations can consist of the first of these types only, a combination of the first and second types, or a combination of all three types

The biology and culture of marine bivalve molluscs of the genus Anadara

A review of the general biology, ecology, population dynamics, reproduction and culture methods of marine bivalves of the family Arcidae, subfamily Anadarinae. These cockles are harvested on a subsistence basis in many tropical, subtropical and warm temperate areas. The important species are Anadara granosa (L.), A. subcrenata (Lischke) and A. broughtoni (Schrenk).Clam culture, Aquaculture techniques, Population dynamics, Reproduction Anadara

A game theoretical model of kleptoparasitism with incomplete information

Kleptoparasitism, the stealing of food from one animal by another, is a common natural phenomenon that has been modelled mathematically in a number of ways. The handling process of food items can take some time and the value of such items can vary depending upon how much handling an item has received. Furthermore this information may be known to the handler but not the potential challenger, so there is an asymmetry between the information possessed by the two competitors. We use game-theoretic methods to investigate the consequences of this asymmetry for continuously consumed food items, depending upon various natural parameters. A variety of solutions are found, and there are complex situations where three possible solutions can occur for the same set of parameters. It is also possible to have situations which involve members of the population exhibiting different behaviours from each other. We find that the asymmetry of information often appears to favour the challenger, despite the fact that it possesses less information than the challenged individual

The stochastic modelling of kleptoparasitism using a Markov process

Kleptoparasitism, the stealing of food items from other animals, is a common behaviour observed across a huge variety of species, and has been subjected to significant modelling effort. Most such modelling has been deterministic, effectively assuming an infinite population, although recently some important stochastic models have been developed. In particular the model of Yates and Broom (Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480–489) introduced a stochastic version following the original model of Ruxton and Moody (The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449–458), and whilst they generated results of interest, they did not solve the model explicitly. In this paper, building on methods used already by van der Meer and Smallegange (A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134–142) we give an exact solution to the distribution of the population over the states for the Yates and Broom model and investigate the effects of some key biological parameters, especially for small populations where stochastic models can be expected to differ most from their deterministic equivalents

Stochastic models of kleptoparasitism

In this paper, we consider a model of kleptoparasitism amongst a small group of individuals, where the state of the population is described by the distribution of its individuals over three specific types of behaviour (handling, searching for or fighting over, food). The model used is based upon earlier work which considered an equivalent deterministic model relating to large, effectively infinite, populations. We find explicit equations for the probability of the population being in each state. For any reasonably sized population, the number of possible states, and hence the number of equations, is large. These equations are used to find a set of equations for the means, variances, covariances and higher moments for the number of individuals performing each type of behaviour. Given the fixed population size, there are five moments of order one or two (two means, two variances and a covariance). A normal approximation is used to find a set of equations for these five principal moments. The results of our model are then analysed numerically, with the exact solutions, the normal approximation and the deterministic infinite population model compared. It is found that the original deterministic models approximate the stochastic model well in most situations, but that the normal approximations are better, proving to be good approximations to the exact distribution, which can greatly reduce computing time

A framework for modelling and analysing conspecific brood parasitism

Recently several papers that model parasitic egg-laying by birds in the nests of others of their own species have been published. Whilst these papers are concerned with answering different questions, they approach the problem in a similar way and have a lot of common features. In this paper a framework is developed which unifies these models, in the sense that they all become special cases of a more general model. This is useful for two main reasons; firstly in order to aid clarity, in that the assumptions and conclusions of each of the models are easier to compare. Secondly it provides a base for further similar models to start from. The basic assumptions for this framework are outlined and a method for finding the ESSs of such models is introduced. Some mathematical results for the general, and more specific, models are considered and their implications discussed. In addition we explore the biological consequences of the results that we have obtained and suggest possible questions which could be investigated using models within or very closely related to our framework

Evolutionary games on graphs and the speed of the evolutionary process

In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example