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

Models of kleptoparasitism on networks: the effect of population structure on food stealing behaviour

The behaviour of populations consisting of animals that interact with each other for their survival and reproduction is usually investigated assuming homogeneity amongst the animals. However, real populations are non-homogeneous. We focus on an established model of kleptoparasitism and investigate whether and how much population heterogeneities can affect the behaviour of kleptoparasitic populations. We consider a situation where animals can either discover food items by themselves or attempt to steal the food already discovered by other animals through aggressive interactions. Representing the likely interactions between animals by a network, we develop pairwise and individual-based models to describe heterogeneities in both the population structure and other individual characteristics, including searching and fighting abilities. For each of the models developed we derive analytic solutions at the steady state. The high accuracy of the solutions is shown in various examples of populations with different degrees of heterogeneity. We observe that highly heterogeneous structures can significantly affect the food intake rate and therefore the fitness of animals. In particular, the more highly connected animals engage in more conflicts, and have a reduced food consumption rate compared to poorly connected animals. Further, for equivalent average level of connectedness, the average consumption rate of a population with heterogeneous structure can be higher

The effect of very low-calorie diets on renal and hepatic outcomes : a systematic review

Peer reviewedPublisher PD

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

A study of the dynamics of multi-player games on small networks using territorial interactions.

Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection

Detection of cold pain, cold allodynia and cold hyperalgesia in freely behaving rats

BACKGROUND: Pain is elicited by cold, and a major feature of many neuropathic pain states is that normally innocuous cool stimuli begin to produce pain (cold allodynia). To expand our understanding of cold induced pain states we have studied cold pain behaviors over a range of temperatures in several animal models of chronic pain. RESULTS: We demonstrate that a Peltier-cooled cold plate with ± 1°C sensitivity enables quantitative measurement of a detection withdrawal response to cold stimuli in unrestrained rats. In naïve rats the threshold for eliciting cold pain behavior is 5°C. The withdrawal threshold for cold allodynia is 15°C in both the spared nerve injury and spinal nerve ligation models of neuropathic pain. Cold hyperalgesia is present in the spared nerve injury model animals, manifesting as a reduced latency of withdrawal response threshold at temperatures that elicit cold pain in naïve rats. We also show that following the peripheral inflammation produced by intraplantar injection of complete Freund's adjuvant, a hypersensitivity to cold occurs. CONCLUSION: The peltier-cooled provides an effective means of assaying cold sensitivity in unrestrained rats. Behavioral testing of cold allodynia, hyperalgesia and pain will greatly facilitate the study of the neurobiological mechanisms involved in cold/cool sensations and enable measurement of the efficacy of pharmacological treatments to reduce these symptoms

The effect of fight cost structure on fighting behaviour involving simultaneous decisions and variable investment levels

In the “producer–scrounger” model, a producer discovers a resource and is in turn discovered by a second individual, the scrounger, who attempts to steal it. This resource can be food or a territory, and in some situations, potentially divisible. In a previous paper we considered a producer and scrounger competing for an indivisible resource, where each individual could choose the level of energy that they would invest in the contest. The higher the investment, the higher the probability of success, but also the higher the costs incurred in the contest. In that paper decisions were sequential with the scrounger choosing their strategy before the producer. In this paper we consider a version of the game where decisions are made simultaneously. For the same cost functions as before, we analyse this case in detail, and then make comparisons between the two cases. Finally we discuss some real examples with potentially variable and asymmetric energetic investments, including intraspecific contests amongst spiders and amongst parasitoid wasps. In the case of the spiders, detailed estimates of energetic expenditure are available which demonstrate the asymmetric values assumed in our models. For the wasps the value of the resource can affect the probabilities of success of the defender and attacker, and differential energetic investment can be inferred. In general for real populations energy usage varies markedly depending upon crucial parameters extrinsic to the individual such as resource value and intrinsic ones such as age, and is thus an important factor to consider when modelling

Evolutionary Dynamics on Small-Order Graphs

Abstract. We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312-316]. We consider all possible connected undirected graphs of orders three through eight. For each graph, using the Monte Carlo Markov Chain simulations, we determine the fixation probability of a mutant introduced at every possible vertex. We show that the fixation probability depends on the vertex and on the graph. A randomly placed mutant has the highest chances of fixation in a star graph, closely followed by star-like graphs. The fixation probability was lowest for regular and almost regular graphs. We also find that within a fixed graph, the fixation probability of a mutant has a negative correlation with the degree of the starting vertex. 1