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N-person games and the evolution of co-operation: a model based on predator inspection in fish.

Two N-person game theoretical models examining the evolution of co-operation during predator inspection in fish are presented. Predator inspection occurs in small shoals of fish, in which one to a few individuals, the "inspectors" (co-operators) break away from the shoal and cautiously approach a predator to obtain information on this potential danger. In the models presented here, remaining with the shoal and not inspecting is considered an act of defection. Both model I and II produce a stable internal polymorphism of inspectors and noninspectors. While the equilibrial frequency of inspectors can be low (i.e. less than 10%) at large shoal size, the proportion of shoals containing any inspectors--and therefore exhibiting the inspection behavior--is much greater. Both models presented here, and N-person games in general are equivalent to intrademic group selection models of evolution in structured populations, in which shoals are trait groups and co-operation evolves by between-shoal selection. While the results are cast in terms of predator inspection, the model itself is general and applies to any multi-group scenario where co-operators benefit entire groups at their own expense. The results presented here add to the mounting theoretical and empirical evidence that co-operation is frequently not a pure evolutionarily stable strategy, and that many metapopulations should be polymorphic for both co-operators and defectors.

Animals↗

Efficiency in evolutionary games: Darwin, Nash and the secret handshake.

This paper considers any evolutionary game possessing several evolutionarily stable strategies, or ESSs, with differing payoffs. A mutant is introduced which will "destroy" any ESS which yields a lower payoff than another. This mutant possesses a costless signal and also conditions on the presence of this signal in each opponent. The mutant then can protect itself against a population playing an inefficient ESS by matching this against these non-signalers. At the same time, the mutants can achieve the more efficient ESS against the signaling mutant population itself. This construction is illustrated by means of the simplest possible example, a co-ordination game. The one-shot prisoner's dilemma is used to illustrate how a superior outcome which is not induced by an ESS may be temporarily but not permanently attained. In the case of the repeated prisoner's dilemma, the present argument seems to render the "evolution of co-operation" ultimately inevitable.

Animals↗

ESS equations sometimes do not specify an ESS.

The equations used to find an evolutionarily stable strategy in the basic game theory model (Maynard Smith, 1974, 1982; Maynard Smith & Price, 1973), and in sexual conflict models (Maynard Smith, 1977; Parker, 1979) do not, in fact, specify an ESS when the expected number of contests entered is not the same for each strategy. This means that the conclusions of many game theory models may be incorrect. This is particularly likely to be true when the mean durations of contests for different strategies are not the same, or when the probability that an individual enters a contest is not the same for all strategies. New ESS equations are developed which incorporate the expected number of contests entered.

Animals↗

Patterns of ESS's. I.

A matrix may have several evolutionarily stable strategies (ESS's). It is thus possible for different populations of a species to adopt a different ESS even when the pay-offs for the populations are the same. The occurrence of different strategies does not imply different circumstances. However, there are constraints upon the collection of supports of the ESS's (i.e. pattern) that any matrix can have. The best-known of these is that the support of one ESS cannot be contained in that of another and this gives bounds on the number of different patterns possible for n x n matrices. Other general constraints are presented here. The enumeration of the patterns for 3 x 3 and 4 x 4 matrices is completed and considerable progress made on 5 x 5 matrices where the number of (permutationally distinct, maximal) patterns exceeds 16.

Biological Evolution↗

Spatial patterns and ESS's.

The classical idea of an evolutionarily stable strategy (ESS) does not involve any spatial dependence. An evolution equation for analyzing games in a region is suggested and the possibility of spatial patterns is investigated. It is shown that an ESS is so stable that it forbids any spatial dependence but that other equilibria may have patterns associated with them if the dispersion rates are suitably chosen.

Biological Evolution↗

Bounds on the number of ESSs of a matrix game.

It is well known that for any evolutionary game there may be more than one evolutionarily stable strategy (ESS). In general, the more ESSs there are, the more difficult it is to work out how the population will behave (unless there are no ESSs at all). If a matrix game has an ESS which allows all possible pure strategies to be played, referred to as an internal ESS, then no other ESS can exist. In fact, the number of ESSs possible is highly dependent upon how many of the pure strategies each allow to be played, their support size. It is shown that if alpha is the ratio of the mean support size to the number of pure strategies n, then as n tends to infinity the greatest number of ESSs can be represented by a continuous function f(alpha) with useful regularity properties, and bounds are found for both f(alpha) and the value alpha(*), where it attains its maximum. Thus we can obtain a limit on the complexity of any particular system as a function of its mean support size.

Animals↗

Game theory and evolution: finite size and absolute fitness measures.

This article is concerned with the characterization and existence of evolutionarily stable strategies (ESS) in Games against Nature, a class of models described by finite size populations and absolute fitness measures. We address these problems in terms of a new formalism which revolves around the concept evolutionary entropy, a measure of the diversity of options associated with a strategy pure - strategies have zero entropy, mixed strategies positive entropy. We invoke this formalism to show that ESS are characterized by extremal states of entropy. We illustrate this characterization of ESS by an analysis of the evolution of the sex ratio and the evolution of seed size.

Animals↗

Ideal free distributions when resources undergo population dynamics.

This study examines the influence of optimal patch choice by consumers on resource population dynamics and on consumer distribution in a two patch environment. The evolutionarily stable strategy which describes animal distributions across habitat patches is called the ideal free distribution (IFD) strategy. Two mechanisms that lead to the IFD are: (1) direct consumer competition such as interference, and (2) exploitative competition for resources. This article focuses on the second mechanism by assuming that resources undergo population dynamics while consumer abundance is fixed. Two models of resource growth are considered in detail: the exponential and the logistic. The corresponding consumer IFD is derived for each of these two models, assuming that consumers behave adaptively by moving to the patch which provides them with the highest fitness. This derivation does not require that resources are at an equilibrium, and it provides, for each resource density, the corresponding distribution of consumers. The article suggests that adaptive patch choice by consumers decreases between patch heterogeneity in resource levels and weakens the apparent competition between resources. The results for a single consumer population are extended for two competing consumer populations. The corresponding IFD is computed as a function of the two consumer densities. This allows for the analytical description of isolegs which are the boundary lines, in the two consumer density phase space, separating regions where qualitatively different habitat preferences are predicted.

Animals↗

Evolutionary flux of P element regulation in a Drosophila melanogaster hybrid dysgenesis cline.

Clines of P-induced hybrid dysgenesis provide a means for monitoring the evolution of transposition repression over space and time. We have studied the molecular and phenotypic profiles of flies taken from a 2900 km cline along the eastern coast of Australia, which had previously been characterized over 10 years ago as having P populations in the north, Q populations at central sites and M' populations in the south. We have found that Q and M' populations of flies have increased their range within the cline at the expense of P lines. Q populations were found to be in the north of the cline and M' populations in the south. Some of the northern Q lines transmit repression through both sexes and type I deletion elements have been isolated from them. We suggest that these elements are responsible for Q type repression. The results support our model that populations made up of Q individuals with strong biparentally transmitted repression form an evolutionarily stable strategy for the repression of hybrid dysgenesis in Drosophila melanogaster.

Animals↗

Survival with an asymmetrical brain: advantages and disadvantages of cerebral lateralization.

Recent evidence in natural and semi-natural settings has revealed a variety of left-right perceptual asymmetries among vertebrates. These include preferential use of the left or right visual hemifield during activities such as searching for food, agonistic responses, or escape from predators in animals as different as fish, amphibians, reptiles, birds, and mammals. There are obvious disadvantages in showing such directional asymmetries because relevant stimuli may be located to the animal's left or right at random; there is no a priori association between the meaning of a stimulus (e.g., its being a predator or a food item) and its being located to the animal's left or right. Moreover, other organisms (e.g., predators) could exploit the predictability of behavior that arises from population-level lateral biases. It might be argued that lateralization of function enhances cognitive capacity and efficiency of the brain, thus counteracting the ecological disadvantages of lateral biases in behavior. However, such an increase in brain efficiency could be obtained by each individual being lateralized without any need to align the direction of the asymmetry in the majority of the individuals of the population. Here we argue that the alignment of the direction of behavioral asymmetries at the population level arises as an "evolutionarily stable strategy" under "social" pressures occurring when individually asymmetrical organisms must coordinate their behavior with the behavior of other asymmetrical organisms of the same or different species.

Animals↗

Mechanisms and evolution of deceptive pollination in orchids.

The orchid family is renowned for its enormous diversity of pollination mechanisms and unusually high occurrence of non-rewarding flowers compared to other plant families. The mechanisms of deception in orchids include generalized food deception, food-deceptive floral mimicry, brood-site imitation, shelter imitation, pseudoantagonism, rendezvous attraction and sexual deception. Generalized food deception is the most common mechanism (reported in 38 genera) followed by sexual deception (18 genera). Floral deception in orchids has been intensively studied since Darwin, but the evolution of non-rewarding flowers still presents a major puzzle for evolutionary biology. The two principal hypotheses as to how deception could increase fitness in plants are (i) reallocation of resources associated with reward production to flowering and seed production, and (ii) higher levels of cross-pollination due to pollinators visiting fewer flowers on non-rewarding plants, resulting in more outcrossed progeny and more efficient pollen export. Biologists have also tried to explain why deception is overrepresented in the orchid family. These explanations include: (i) efficient removal and deposition of pollinaria from orchid flowers in a single pollinator visit, thus obviating the need for rewards to entice multiple visits from pollinators; (ii) efficient transport of orchid pollen, thus requiring less reward-induced pollinator constancy; (iii) low-density populations in many orchids, thus limiting the learning of associations of floral phenotypes and rewards by pollinators; (iv) packaging of pollen in pollinaria with limited carry-over from flower to flower, thus increasing the risks of geitonogamous self-pollination when pollinators visit many flowers on rewarding plants. All of these general and orchid-specific hypotheses are difficult to reconcile with the well-established pattern for rewardlessness to result in low pollinator visitation rates and consequently low levels of fruit production. Arguments that deception evolves because rewards are costly are particularly problematic in that small amounts of nectar are unlikely to have a significant effect on the energy budget of orchids, and because reproduction in orchids is often severely pollen-, rather than resource-limited. Several recent experimental studies have shown that deception promotes cross-pollination, but it remains unknown whether actual outcrossing rates are generally higher in deceptive orchids. Our review of the literature shows that there is currently no evidence that deceptive orchids carry higher levels of genetic load (an indirect measure of outcrossing rate) than their rewarding counterparts. Cross-pollination does, however, result in dramatic increases in seed quality in almost all orchids and has the potential to increase pollen export (by reducing pollen discounting). We suggest that floral deception is particularly beneficial, because of its promotion of outcrossing, when pollinators are abundant, but that when pollinators are consistently rare, selection may favour a nectar reward or a shift to autopollination. Given that nectar-rewardlessness is likely to have been the ancestral condition in orchids and yet is evolutionarily labile, more attention will need to be given to explanations as to why deception constitutes an 'evolutionarily stable strategy'.

Biological Evolution↗

Mate guarding as paternity insurance in Idaho ground squirrels.

Following a copulation, males in many species of vertebrates (particularly birds) and invertebrates remain near the inseminated female and repel other suitors with displays or force. Guarding males must delay resumption of competitive mate searching, but they may insure their paternity by reducing possibilities for secondary matings and sperm competition. Among mammals, post-copulatory mate guarding has been reported in rodents, mongooses, ungulates and primates, including humans, but the effects of such behaviour on male reproductive success have not been determined genetically. I report here that mate guarding by male Idaho ground squirrels (Spermophilus brunneus) enhances a male's probability of paternity. Furthermore, an analysis based on game theory shows that mate guarding is an evolutionarily stable strategy for male S. brunneus, but not male Belding's ground squirrels (S. beldingi), which resume searching once copulation is completed.

Animals↗

Population density drives the local evolution of a threshold dimorphism.

Evolution can favour more than one reproductive tactic among conspecifics of the same sex. Under the conditional evolutionarily stable strategy, individuals adopt the tactic that generates the highest fitness return for their status: large males guard females, whereas small males sneak copulations. Tactics change at the status at which fitness benefits switch from favouring one tactic to favouring the alternative. This 'switchpoint' is expressed in many species as a threshold between divergent morphologies. Environmental and demographic parameters that influence the relative fitness of male tactics are predicted to determine a population's switchpoint and consequently whether the population is monomorphic or dimorphic. Here we show threshold evolution in the forceps dimorphism of the European earwig Forficula auricularia and document the transition from completely monomorphic to classical male-dimorphic populations over a distance of only 40 km. Because the superior fighting ability of the dominant morph will be more frequently rewarded at high encounter rates, population density is likely to be a key determinant of the relative fitness of the alternative tactics, and consequently the threshold. We show that, as predicted, population density correlates strongly with the shift in threshold, and that this factor drives the local evolution of the male dimorphism in these island populations. Our data provide evidence for the origin of phenotypic diversity within populations, through the evolution of a switchpoint in a conditional strategy that has responded to local population density.

Animals↗

Local mate competition with lethal male combat: effects of competitive asymmetry and information availability on a sex ratio game.

We constructed a sex allocation model for local mate competition considering the asymmetry of competitive abilities among sons. This model assumes two females of a parasitoid wasp oviposit on the same host in sequential order. The evolutionarily stable strategy will be in either Stackelberg or Nash equilibrium, depending on whether the females can recognize their opponent's sex ratio or not, respectively. The Nash equilibrium predicts the second female produce more males than the first. If the second female is able to know and respond to the strategy of the first (a Stackelberg equilibrium), the first will decide an optimal sex ratio assuming that the second reply to it. Under such an assumption, our model predicts that not producing sons is adaptive for the second female when the sons she produces have low competitive ability. Males of parasitoid wasps Melittobia spp. are engaged in lethal male-male combat, indicating large asymmetry in mating success among sons. If females have the ability to recognize their opponent's sex ratio, our model suggests that the severe lethal male-male combat may be one factor explaining their extremely female-biased sex ratio that is unexplainable by pre-existent models.

Aggression↗

Life history consequences of mammal sibling rivalry.

Mammal life history traits relating to growth and reproduction are extremely diverse. Sibling rivalry may contribute to selection pressures influencing this diversity, because individuals that are relatively large at birth typically have an advantage in competition for milk. However, selection for increased growth rate is likely to be constrained by kin selection and physiological costs. Here, we present and test a model examining the ESS (evolutionarily stable strategy) balance between these constraints and advantages associated with increased prenatal growth in mammal sibling rivalry. Predictions of the model are supported by results of comparative analyses for the Carnivora and Insectivora, which demonstrate an increase in prenatal growth rate with increasing intensity of postnatal scramble competition, and a decrease in postnatal growth rate relative to size at birth. Because increased prenatal growth rates are predicted to select for reduced gestation length under certain conditions, our study also indicates that sibling rivalry may contribute to selection pressures influencing variation in altriciality and precociality among mammals.

Animal Nutritional Physiological Phenomena↗

Begging and sibling competition: how should offspring respond to their rivals?

Godfray's influential model of competitive begging predicted that offspring should respond to each other's behavior, displaying more intensely when competing with needier rivals. Empirical tests of this prediction have, however, yielded equivocal results. Here, I develop a series of evolutionarily stable strategy models of begging as a signal of need, which show that this prediction holds only for competitive aspects of display that influence the division of food among the brood. No such response is expected for cooperative begging (which influences the total level of provisioning by the parent), and the models even predict the opposite trend under some circumstances (where the indirect costs of extracting additional resources from the parent are high). These contrasting sets of predictions may help to explain the varying empirical results obtained by studies of sibling interaction. Cooperative (as opposed to competitive) begging is likely to be of greater significance in cases where dominant young can gain direct control of allocation (or enjoy some competitive advantage). Dominants are then predicted to parasitize the efforts of their weaker rivals and reduce their own investment in cooperative signaling while continuing to claim a disproportionately large share of the resources provided by the parent.

Animal Communication↗

Kin selection and parasite evolution: higher and lower virulence with hard and soft selection.

Conventional models predict that low genetic relatedness among parasites that coinfect the same host leads to the evolution of high parasite virulence. Such models assume adaptive responses to hard selection only. We show that if soft selection is allowed to operate, low relatedness leads instead to the evolution of low virulence. With both hard and soft selection, low relatedness increases the conflict among coinfecting parasites. Although parasites can only respond to hard selection by evolving higher virulence and overexploiting their host, they can respond to soft selection by evolving other adaptations, such as interference, that prevent overexploitation. Because interference can entail a cost, the host may actually be underexploited, and virulence will decrease as a result of soft selection. Our analysis also shows that responses to soft selection can have a much stronger effect than responses to hard selection. After hard selection has raised virulence to a level that is an evolutionarily stable strategy, the population, as expected, cannot be invaded by more virulent phenotypes that respond only to hard selection. The population remains susceptible to invasion by a less virulent phenotype that responds to soft selection, however. Thus, hard and soft selection are not just alternatives. Rather, soft selection is expected to prevail and often thwart the evolution of virulence in parasites. We review evidence from several parasite systems and find support for soft selection. Most of the examples involve interference mechanisms that indirectly prevent the evolution of higher virulence. We recognize that hard selection for virulence is more difficult to document, but we take our results to suggest that a kin selection model with soft selection may have general applicability.

Adaptation, Physiological↗

Genetic conflicts.

Self-promoting elements (also called ultraselfish genes, selfish genes, or selfish genetic elements) are vertically transmitted genetic entities that manipulate their "host" so as to promote their own spread, usually at a cost to other genes within the genome. Examples of such elements include meiotic drive genes and cytoplasmic sex ratio distorters. The spread of a self-promoting element creates the context for the spread of a suppressor acting within the same genome. We may thus say that a genetic conflict exists between different components of the same genome. Here we investigate the properties of such conflicts. First we consider the potential diversity of genomic conflicts and show that every genetic system has potential conflicts. This is followed by analysis of the logic of conflicts. Just as Evolutionarily Stable Strategy (ESS) terminology provides a short cut for discussion of much in behavioral ecology, so the language of modifier analysis provides a useful terminology on which to base discussions of conflicts. After defining genetic conflict, we provide a general analysis of the conflicting parties, and note a distinction between competing and conflicting genes. We then provide a taxonomy of possible short- and long-term outcomes of conflicts, noting that potential conflict in an unconstrained system can never be removed, and that the course of evolution owing to conflict is often unpredictable. The latter is most particularly true for strong conflicts in which suppressors may take surprising forms. The possibility of extended conflicts in the form of "arms races" between element and suppressor is illustrated. The peculiar redundancy of these systems is one possible trace of conflict, and others are discussed. That homologous conflicts may find highly different expression is discussed by referring to the mechanistic differences that are thought to underlie the action of the two best-described meiotic drive genes, and by the multiplicity of forms of cytoplasmic sex ratio distorters. The theoretical analysis establishes a logical basis for thinking about conflicts, but fails to establish the importance of conflict in evolution. We illustrate this contentious issue through consideration of some phenomena for whose evolution conflict has been proposed as an important force: the evolution of sex, sex determination, species, recombination, and uniparental inheritance of cytoplasmic genes. In general, it is proposed that conflict may be a central force in the evolution of genetic systems. We conclude that an analysis of conflict and its general importance in evolution is greatly aided by application of the concept of genetic power. We consider the possible components of genetic power and ask whether and how power evolves.

Animals↗