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 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

The evolution of cooperation in a mobile population on random networks: Network topology matters only for low-degree networks

We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from complete, circle, and star graphs to various random networks to further investigate the effect of network topology on the evolution of cooperation. We discover that the network topology affects the outcomes of the evolutionary process only for networks of small average degree. Once the degree becomes sufficiently high, the outcomes match those for the complete graph. The actual value of the degree when this happens is much smaller than that of the complete graph, and the threshold value depends on other network characteristics

An acute bout of cycling does not induce compensatory responses in pre-menopausal women not using hormonal contraceptives

There is a clear need to improve understanding of the effects of physical activity and exercise on appetite control. Therefore, the acute and short-term effects (three days) of a single bout of cycling on energy intake and energy expenditure were examined in women not using hormonal contraceptives. Sixteen active (n = 8) and inactive (n = 8) healthy pre-menopausal women completed a randomised crossover design study with two conditions (exercise and control). The exercise day involved cycling for 1 h (50% of maximum oxygen uptake) and resting for 2 h, whilst the control day comprised 3 h of rest. On each experimental day participants arrived at the laboratory fasted, consumed a standardised breakfast and an ad libitum pasta lunch. Food diaries and combined heart rate-accelerometer monitors were used to assess free-living food intake and energy expenditure, respectively, over the subsequent three days. There were no main effects or condition (exercise vs control) by group (active vs inactive) interaction for absolute energy intake (P > 0.05) at the ad libitum laboratory lunch meal, but there was a condition effect for relative energy intake (P = 0.004, ηp2 = 0.46) that was lower in the exercise condition (1417 ± 926 kJ vs. 2120 ± 923 kJ). Furthermore, post-breakfast satiety was higher in the active than in the inactive group (P = 0.005, ηp2 = 0.44). There were no main effects or interactions (P > 0.05) for mean daily energy intake, but both active and inactive groups consumed less energy from protein (14 ± 3% vs. 16 ± 4%, P = 0.016, ηp2 = 0.37) and more from carbohydrate (53 ± 5% vs. 49 ± 7%, P = 0.031, ηp2 = 0.31) following the exercise condition. This study suggests that an acute bout of cycling does not induce compensatory responses in active and inactive women not using hormonal contraceptives, while the stronger satiety response to the standardised breakfast meal in active individuals adds to the growing literature that physical activity helps improve the sensitivity of short-term appetite control

Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations

Evolutionary models are used to study the self-organisation of collective action, often incorporating population structure due to its ubiquitous presence and long-known impact on emerging phenomena. We investigate the evolution of multiplayer cooperation in mobile structured populations, where individuals move strategically on networks and interact with those they meet in groups of variable size. We find that the evolution of multiplayer cooperation primarily depends on the network topology and movement cost while using different stochastic update rules seldom influences evolutionary outcomes. Cooperation robustly co-evolves with movement on complete networks and structure has a partially detrimental effect on it. These findings contrast an established wisdom in evolutionary graph theory that cooperation can only emerge under some update rules and if the average degree is low. We find that group-dependent movement erases the locality of interactions, suppresses the impact of evolutionary structural viscosity on the fitness of individuals, and leads to assortative behaviour that is much more powerful than viscosity in promoting cooperation. We analyse the differences remaining between update rules through a comparison of evolutionary outcomes and fixation probabilities.Comment: 26 pages, 12 figures, 1 tabl

A general framework for analysing multiplayer games in networks using territorial interactions as a case study

Recently, models of evolution have begun to incorporate structured populations, including spatial structure, through the modelling of evolutionary processes on graphs (evolutionary graph theory). One limitation of this otherwise quite general framework is that interactions are restricted to pairwise ones, through the edges connecting pairs of individuals. Yet, many animal interactions can involve many players, and theoretical models also describe such multiplayer interactions. We shall discuss a more general modelling framework of interactions of structured populations with the focus on competition between territorial animals, where each animal or animal group has a “home range” which overlaps with a number of others, and interactions between various group sizes are possible. Depending upon the behaviour concerned we can embed the results of different evolutionary games within our structure, as occurs for pairwise games such as the Prisoner's Dilemma or the Hawk–Dove game on graphs. We discuss some examples together with some important differences between this approach and evolutionary graph theory

Approximating evolutionary dynamics on networks using a Neighbourhood Configuration model

Evolutionary dynamics have been traditionally studied on homogeneously mixed and infinitely large populations. However, real populations are usually finite and characterised by complex interactions among individuals. Recent studies have shown that the outcome of the evolutionary process might be significantly affected by the population structure. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. In this paper, we adopt an approximation method which has been recently used for the modelling of infectious disease transmission, to model evolutionary game dynamics on complex networks. Comparisons of the predictions of the model constructed with the results of computer simulations reveal the effectiveness of the process and the improved accuracy that it provides when, for example, compared to well-known pair approximation methods. This modelling framework offers a flexible way to carry out a systematic analysis of evolutionary game dynamics on graphs and to establish the link between network topology and potential system behaviours. As an example, we investigate how the Hawk and Dove strategies in a Hawk-Dove game spread in a population represented by a random regular graph, a random graph and a scale-free network, and we examine the features of the graph which affect the evolution of the population in this particular game

The Four Regions in Settlement Space: A Game-Theoretical Approach to Investment Treaty Arbitration Part II: Cases

Following from Part I of this paper, which introduced the notion of decision-modelling for investor-state arbitration, Part II of the paper uses the game theoretic notions developed in Part I to explore the question of why a relatively large fraction of investor-state disputes proceed to arbitration tribunals. Likely explanations are advanced. The detailed mathematical model derived in Part I of the paper is then used to analyse 31 cases where an investor-state dispute has been judged by an arbitration tribunal. Auxiliary mathematics are developed to identify the relevant averages and variances, which are then calculated from the full data set. Three sample cases are analysed in greater detail, with the model results being compared against the actual awards. It is concluded that applying the mathematical model of the international arbitration process developed in Part I together with the data analysis laid out in Part II will provide useful insight and guidance to both parties involved or likely to be involved in a dispute between investor and state