Evolutionarily stable stealing: game theory applied to kleptoparasitism

We present an individual-based model of a group of foraginganimals. Individuals can obtain food either by discovering itthemselves or by stealing it from others (kleptoparasitism).Given that challenging another individual for a discovered fooditem costs time (which could otherwise be spent searching foran undiscovered item), attempting to steal from another maynot always be efficient We show that there is generally a uniquestrategy that maximizes uptake rate—always or never challengingothers. For any combination of parameter values, we can identifywhich strategy is appropraite. As a corollary to this, we predictthat small changes in ecolgical conditions can, under some circumstances,cause a dramatic change in the aggressive behavior of individuals.Further, we investigate situations where searching for undiscoveredfood and searching for potential opportunities for stealingare mutually exclusive activities (i.e., success at one canonly be improved at the expense of the other). Using game theory,we are able to find the evolutionarily stable strategy for investmentin these two activities in terms of the ecological parametersof the model.     

An evolutionarily stable strategy for aggressiveness in feeding groups

Animals searching for food in groups display highly variabledegrees of aggressiveness. In this paper I present an individual-basedgame theoretical model of how gregarious animals should adjusttheir level of aggressiveness to their environmental conditions.In accordance with behavioral observations, the predicted levelof aggressiveness increases progressively with decreasing foodavailability and increasing animal density. The proposed modelalso predicts a positive influence of food energy value andhandling time on the level of aggressiveness within the group.In addition, the model provides information about the influenceof aggressive behavior on individual foraging success, interference,and population dynamics. Adaptive behavioral rules for aggressivenessin consumers are predicted to respond to both competitors andfood density in a way that contributes to stabilization of thedynamics of population systems.     

Biological auctions with multiple rewards

The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.     

Why do some nectar foragers perch and others hover while probing flowers?

Diurnal hawkmoths, Hemaris fuciformis, and bumblebees, Bombus pasquorum, were observed foraging for nectar in flowers of Viscaria vulgaris. The hawkmoths hovered in front of the flowers, while the bees perched on them. The hawkmoths had a faster probing rate than the bees, and consequently also had higher gross and net rates of energy gain. A model is presented that shows that hovering only yields a higher net rate of energy gain (NREG) than perching when nectar volumes are high due to low competition for the resource. The difference in NREG of perchers and hoverers decreases with an increase of competition, and eventually perching yields the highest NREG. This is an effect of the higher cost of hovering. The results suggest that hovering can only evolve as a pure evolutionarily stable strategy (ESS) if competition is reduced, for example by co-evolutionary specializations with plants. The possibility that it has evolved as a mixed ESS (i.e. individuals can both hover and perch depending on the resource level) is discussed. The evolution of optimal foraging strategies is discussed, and it is pointed out that the rate of gain of an animal is independent of the strategy used when all competing foragers use the same strategy, but competitively superior strategies will nevertheless evolve because they are ESSs. Competition between strategies with different energy costs are special, because resource availability determines which strategy is competitively superior. A high-cost strategy can only evolve as a pure ESS at high resource levels, or as a mixed ESS at intermediate levels.     

Negotiation may lead selfish individuals to cooperate: the example of the collective vigilance game

Game-theoretical models have been highly influential in behavioural ecology. However, these models generally assume that animals choose their action before observing the behaviour of their opponents while, in many natural situations, individuals in fact continuously react to the actions of others. A negotiation process then takes place and this may fundamentally influence the individual attitudes and the tendency to cooperate. Here, I use the classical model system of vigilance behaviour to demonstrate the consequences of such behavioural negotiation among selfish individuals, by predicting patterns of vigilance in a pair of animals foraging under threat of predation. I show that the game played by the animals and the resulting vigilance strategies take radically different forms, according to the way predation risk is shared in the pair. In particular, if predators choose their target at random, the prey respond by displaying moderate vigilance and taking turns scanning. By contrast, if the individual that takes flight later in an attack endures a higher risk of being targeted, vigilance increases and there is always at least one sentinel in the pair. Finally, when lagging behind its companion in fleeing from an attacker becomes extremely risky, vigilance decreases again and the animals scan simultaneously.     

The risks of parenthood II. Parent-offspring conflict

Summary Previous work has demonstrated the value of dynamic programming models for the analysis of parental decision making. In the present paper we extend this approach to analyse conflicts between parents and their offspring, and develop a dynamic ESS model of feeding and fledging of nestling birds. In order to simplify the formulation and solution of the dynamic ESS model, we adopt an assumption of alternating decisions: in each time period the parent first decides whether to continue provisioning the nestling, after which the nestling decides whether to leave the nest. The model takes into account numerous tradeoffs involved in parent-offspring decisions, including differential growth and mortality rates for offspring in and out of the nest, risk of fledging, relation between long-term survival and post-breeding mass of offspring, and parental mortality risk associated with provisioning of offspring. Depending on assumed parameter values, the model is capable of predicting a wide range of feeding-fledging behaviour. The model is applied specifically to the juvenile life history of dovekies (Alle alle), and provides a behavioural explanation for the phenomenon of pre-fledging mass recession in this species.     

War of attrition with implicit time cost

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the strategies of the whole population. We identify and analyse the underlying mechanisms responsible for the implicit time cost. Each player participates in a series of games, where those prepared to wait longer win with higher certainty but play less frequently. The model is characterized by the ratio of the winner's score to the loser's score, in a single game. The fitness of a player is determined by the accumulated score from the games played during a generation. We derive the stationary distribution of strategies under the replicator dynamics. When the score ratio is high, we find that the stationary distribution is unstable, with respect to both evolutionary and dynamical stability, and the dynamics converge to a limit cycle. When the ratio is low, the dynamics converge to the stationary distribution. For an intermediate interval of the ratio, the distribution is dynamically but not evolutionarily stable. Finally, the implications of our results for previous models based on the war of attrition are discussed.     

Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction

It has recently been demonstrated that ecological feedback mechanisms can facilitate the emergence and maintenance of cooperation in public goods interactions: the replicator dynamics of defectors and cooperators can result, for example, in the ecological coexistence of cooperators and defectors. Here we show that these results change dramatically if cooperation strategy is not fixed but instead is a continuously varying trait under natural selection. For low values of the factor with which the value of resources is multiplied before they are shared among all participants, evolution will always favour lower cooperation strategies until the population falls below an Allee threshold and goes extinct, thus evolutionary suicide occurs. For higher values of the factor, there exists a unique evolutionarily singular strategy, which is convergence stable. Because the fitness function is linear with respect to the strategy of the mutant, this singular strategy is neutral against mutant invasions. This neutrality disappears if a nonlinear functional response in receiving benefits is assumed. For strictly concave functional responses, singular strategies become uninvadable. Evolutionary branching, which could result in the evolutionary emergence of cooperators and defectors, can occur only with locally convex functional responses, but we illustrate that it can also result in coevolutionary extinction.     

Evolution of airborne infectious diseases according to changes in characteristics of the host population

The authors predicted evolutionary changes in airborne infectious diseases according to changes in the characteristics of the host population. The predictions were based upon a mathematical model of infectious diseases and the validity of the predictions was verified against the history of man and pathogens. The feature of this model is that it involves a density of pathogens in the environment as an additional variable which can be regarded as more suitable to airborne infectious diseases. In spite of this modification, this study reached a similar conclusion to the threshold density theory: that is, susceptible host density in the absence of the pathogen must be larger than that in the presence of the pathogen, for the pathogen to be persistent. Moreover the authors concluded that one type of pathogen cannot be replaced by another type of pathogen as long as the susceptible host density of the former type is the mininum one. The predictions were considered to be valid for a wide range of infectous diseases. Making use of these principles, the authors predicted that the variety of infectious diseases should increase as host density increases and that pathogens should evolve to be less virulent as the host life-span increases. The finalidea discussed is whether or nor the history of man and pathogen can be verified by the predictions.     

Evolution of virulence when transmission occurs before disease

Most models of virulence evolution assume that transmission and virulence are constant during an infection. In many viral (HIV and influenza), bacterial (TB) and prion (BSE and CWD) systems, disease-induced mortality occurs long after the host becomes infectious. Therefore, we constructed a model with two infected classes that differ in transmission rate and virulence in order to understand how the evolutionarily stable strategy (ESS) depends on the relative difference in transmission and virulence between classes, on the transition rate between classes and on the recovery rate from the second class. We find that ESS virulence decreases when expressed early in the infection or when transmission occurs late in an infection. When virulence occurred relatively equally in each class and there was disease recovery, ESS virulence increased with increased transition rate. In contrast, ESS virulence first increased and then decreased with transition rate when there was little virulence early in the infection and a rapid recovery rate. This model predicts that ESS virulence is highly dependent on the timing of transmission and pathology after infection; thus, pathogen evolution may either increase or decrease virulence after emergence in a new host.     

THE QUICK AND THE DEAD? SPERM COMPETITION AND SEXUAL CONFLICT IN SEA

Our view of sperm competition is largely shaped by game-theoretic models based on external fertilizers. External fertilization is of particular interest as it is the ancestral mode of reproduction and as such, relevant to the evolution and maintenance of anisogamy (i.e., large eggs and tiny, numerous sperm). Current game-theoretic models have been invaluable in generating predictions of male responses to sperm competition in a range of internal fertilizers but these models are less relevant to marine broadcast spawners, the most common and archetypal external fertilizers. Broadcast spawners typically have incomplete fertilization due to sperm limitation and/or polyspermy (too many sperm), but the effects of incomplete (<100% fertilization rates) fertilization on game-theoretic predictions are unclear particular with regards to polyspermy. We show that incorporating the effects of sperm concentration on fertilization success changes the predictions of a classic game-theoretic model, dramatically reversing the relationship between sperm competition and the evolutionarily stable sperm release strategy. Furthermore, our results suggest that male and female broadcast spawners are likely to be in conflict at both ends of the sperm environment continuum rather than only in conditions of excess sperm as previously thought. Across the majority of the parameter space we explored, males release either too little to too much sperm for females to achieve complete fertilization. This conflict could result in a coevolutionary race that may have led to the evolution of internal fertilization in marine organisms.     

Why Darwin would have loved evolutionary game theory

Humans have marvelled at the fit of form and function, the way organisms'' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin''s arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so.     

Patch leaving strategies and superparasitism: an asymmetric generalized war of attrition

When several competitors deplete a patch, it can be advantageous for each of them to stay provided that others leave, whereas, on the other hand, staying longer decreases the expected payoff for everyone. This situation can be considered as a generalized war of attrition. Previous studies have shown that optimal patch leaving strategies become stochastic and the expected leaving time is much larger than predicted by the marginal value theorem when competitors interfere. The possibility of superparasitism, as occurs for example in parasitoids, induces such interference. In addition, it gives several complications. First, the payoff of females that have left the patch is affected by the ovipositions of the remaining individuals. Second, differences in the arrival time of females cause payoff-relevant asymmetries, since females that arrived early on have parasitized more hosts in a patch at the moment superparasitism starts than those that arrived later. We show that this can be modelled as an asymmetric generalized war of attrition, and derive global characteristics of the ESS for simultaneous decisions on when to start superparasitism and when to leave a patch.     

Evolution of unstable and stable biparental care

Evolutionarily stable strategy models suggest that biparentalcare will be stable when parents partially compensate for changesin care by the other parent. Previous work has emphasized therelationship between parental expenditure and the current componentof fitness (e. g., offspring survival and fecundity) in causingpartial compensation. This study shows that partial compensationdepends critically on the effect of current parental expenditureon a parent's future fitness (e. g., survival to and fecundityin subsequent breeding seasons). Partial compensation is favoredand biparental care is stable when future fitness is a concave-downfunction of expenditure (i. e., each increment of expenditureis more costly than the previous). However, when future fitnessis a convex-down function of expenditure (i. e., each incrementof expenditure is less costly) biparental care is unstable.(BehavEcol 7: 490–493(1996)]     

Evolution of the distribution of dispersal distance under distance‐dependent cost of dispersal

Abstract We analyse the evolution of the distribution of dispersal distances in a stable and homogeneous environment in one‐ and two‐dimensional habitats. In this model, dispersal evolves to avoid the competition between relatives although some cost might be associated with this behaviour. The evolutionarily stable dispersal distribution is characterized by an equilibration of the fitness gains among all the different dispersal distances. This cost‐benefit argument has heuristic value and facilitates the comprehension of results obtained numerically. In particular, it explains why some minimal or maximal probability of dispersal may evolve at intermediate distances when the cost of dispersal function is an increasing function of distance. We also show that kin selection may favour long range dispersal even if the survival cost of dispersal is very high, provided the survival probability does not vanish at long distances.     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.