Evolutionary equilibrium strategies.

This paper re-examines the concept of evolutionary stability proposed by Maynard Smith.For any finite population it is shown that a strategy which is stable in the sense of Maynard Smith may have a lower fitness than a mutant strategy regardless of the proportion of contestants using the latter.Two alternative concepts of evolutionary stability are then proposed. A strategy is described as being strongly stable if no mutant is able to invade because of its higher fitness and weakly stable if it has a higher fitness whenever the contestants using any particular mutant strategy become sufficiently numerous.For the “war of attrition” between contestants of a given species Maynard Smith and others have argued that the evolutionarily stable strategy is for a contestant to bid (for food or territory) by attempting to wait out its opponent according to an exponential mixed strategy. This paper establishes that such a strategy is only weakly stable and that for any number n there exists a mutant strategy with a higher fitness until the number of mutants in the population exceeds n.The final section reconsiders the stability issue when a natural informational asymmetry is introduced. Each contestant is assumed to be uncertain as to the value its opponent places on the object over which they are competing. In contrast to the symmetric case it is shown that there is a strategy which is strongly stable with respect to any feasible mutant as long as the population is sufficiently large.     

Startle durations reveal visual assessment abilities during contests between convict cichlids

In animal contests, the widespread ability of contestants to assess their opponents’ resource holding potential (RHP) relative to their own, termed mutual assessment, has recently been questioned. It is possible that each contestant may only have information about its own abilities or state, incurring costs up to a particular threshold then giving up, termed self-assessment. We used a technique that provides a measure of fight motivation to discriminate between different assessment models during aggressive encounters between male convict cichlids, Amatitlania nigrofasciata. A novel stimulus was applied to cause a startle response in one contestant of an aggressively interacting, size mis-matched pair, whereby the animal temporarily stops fighting. The time taken to resume the contest has been verified to provide a measure of the motivation to fight, from which it is possible to infer if any visual information concerning opponent asymmetries has been gathered. The data showed support for two differing types of assessment. There was some support for self-assessment, with startle duration being negatively related to own size, and, in a later trial series some support for an opponent only assessment strategy, with startle duration being positively related to opponent size. These results are consistent with individuals learning to use visual information about opponents when deprived of other sensory cues. Evidence within a trial supporting visual mutual assessment was lacking and possible reasons for this are discussed.     

High Altitude Frogs (Rana kukonoris) Adopt a Diversified Bethedging Strategy in the Face of Environmental Unpredictability

Environmental unpredictability can influence strategies of maternal investment among eggs within a clutch. Models predict that breeding females should adopt a diversified bet-hedging strategy in unpredictable environments, but empirical field evidence from Asia is scarce. Here we tested this hypothesis by exploring spatial patterns in egg size along an altitudinal gradient in a frog species(Rana kukunoris) inhabiting the Tibetan Plateau. Within-clutch variability in egg size increased as the environment became variable(e.g., lower mean monthly temperature and mean monthly rainfall at higher altitudes), and populations in environments with more unpredictable rainfall produced eggs that were smaller and more variable in size. We provide support for a diversified bet-hedging strategy in high-altitude environments, which experience dynamic weather patterns and therefore are of unpredictable environmental quality. This strategy may be an adaptive response to lower environmental quality and higher unpredictable environmental variance. Such a strategy should increase the likelihood of breeding success and maximize maternal lifetime fitness by producing offspring that are adapted to current environmental conditions. We speculate that in high-altitude environments prone to physical disturbance, breeding females are unable to consistently produce the optimal egg size due to physiological constraints imposed by environmental conditions(e.g., duration of the active season, food availability). Species and populations whose breeding strategies are adapted to cope with uncertain environmental conditions by adjusting offspring size and therefore quality show a remarkable degree of ability to cope with future climatic changes.     

Divide and conquer: when and how should competitors share?

When two individuals are unwilling to fight over a valuable resource, then they may obtain it with equal probability, or they may choose to divide the resource in some way. Although both strategies have been observed in nature, modelers have so far implicitly assumed that their long-term payoffs are the same. First we show that increasing returns to size in the value of a resource favor random allocation over sharing, whereas diminishing returns favor the reverse. Next we extend our approach to understand the conditions under which sharing will evolve when contestants vary in their resource-holding potential. We show that although closely matched individuals are more likely to share, it is by no means a prerequisite when contestants have limited information about one another’s abilities. Collectively, our models support recent observations of physical sharing as a solution to conflict resolution, and elucidate the conditions under which sharing will arise.     

The logic of asymmetric contests

A theoretical analysis is made of the evolution of behavioural strategies in contest situations. It is assumed that behaviour will evolve so as to maximize individual fitness. If so, a population will evolve an ‘evolutionarily stable strategy’, or ESS, which can be defined as a strategy such that, if all members of a population adopt it, no ‘mutant’ strategy can do better. A number of simple models of contest situations are analysed from this point of view. It is concluded that in ‘symmetric’ contests the ESS is likely to be a ‘mixed’ strategy; that is, either the population will be genetically polymorphic or individuals will be behaviourally variable. Most real contests are probably asymmetric, either in pay-off to the contestants, or in size or weapons, or in some ‘uncorrelated’ fashion; i.e. in a fashion which does not substantially bias either the pay-offs or the likely outcome of an escalated contest. An example of an uncorrelated asymmetry is that between the ‘discoverer’ of a resource and a ‘late-comer’. It is shown that the ESS in asymmetric contests will usually be to permit the asymmetric cue to settle the contest without escalation. Escalated contests will, however, occur if information to the contestants about the asymmetry is imperfect.     

Imperfect assessment and limited information preclude optimal strategies in male-male fights in the orb-weaving spider Metellina mengei

Agonistic behaviour between male orb-web spiders Metellina mengei competing for access to female webs was examined in field experiments to test the major predictions of game theory. Winners of fights were significantly larger than losers, particularly with respect to the length of the first pair of legs, which are sexually dimorphic in this species and used extensively in agonistic encounters. The size of the winning male had no influence on contest intensity or duration, and neither did relative size. However, fight intensity and duration were both positively correlated with the size of the losing male. Resident males won significantly more contests than intruders. Winning intruders were significantly larger than winning residents and it was these winning intruders that tended to produce the longer fights. Female weight and hence reproductive value had a marked influence on fight intensity and duration of fights won by the intruder but not those won by the resident. This indicates that only the resident obtains information about the female. These data are discussed with reference to the discrepancy with theory and a failure of some contestants to obtain information on resource value and relative contestant size necessary to optimize fight strategy.     

Natural selection. I. Variable environments and uncertain returns on investment

Many studies have analysed how variability in reproductive success affects fitness. However, each study tends to focus on a particular problem, leaving unclear the overall structure of variability in populations. This fractured conceptual framework often causes particular applications to be incomplete or improperly analysed. In this article, I present a concise introduction to the two key aspects of the theory. First, all measures of fitness ultimately arise from the relative comparison of the reproductive success of individuals or genotypes with the average reproductive success in the population. That relative measure creates a diminishing relation between reproductive success and fitness. Diminishing returns reduce fitness in proportion to variability in reproductive success. The relative measurement of success also induces a frequency dependence that favours rare types. Second, variability in populations has a hierarchical structure. Variable success in different traits of an individual affects that individual's variation in reproduction. Correlation between different individuals' reproduction affects variation in the aggregate success of particular alleles across the population. One must consider the hierarchical structure of variability in relation to different consequences of temporal, spatial and developmental variability. Although a complete analysis of variability has many separate parts, this simple framework allows one to see the structure of the whole and to place particular problems in their proper relation to the general theory. The biological understanding of relative success and the hierarchical structure of variability in populations may also contribute to a deeper economic theory of returns under uncertainty.     

Male contest investment changes with male body size but not female quality in the spider Nephila clavipes

Animals use rules to adjust their level of investment in a contest. We evaluate male strategies during contests over females in the golden orb-web spider Nephila clavipes. We tested whether male behaviour changes with female value, and found that contests were similar in intensity and outcome whether the female was a juvenile or adult, virgin or non-virgin, or whether one male had invested sperm in the female. We found evidence that males use a self-assessment strategy when deciding to withdraw from a contest. Loser body size and contestant size difference were correlated with a higher frequency of contest escalation, and fights involving two large males were more likely to escalate than a fight in which one male was small. A multiple regression showed that loser body size had a stronger effect on contest escalation than contestant body size difference. More importantly, the size of the winning male had no effect on contest escalation, a key prediction of a self-assessment strategy. In N. clavipes, body size is the primary factor that determines the outcome of male contests, and males do not appear to assess their opponent or the quality of the resource when deciding to withdraw from the fight.     

Patterns of Parental Investment and Sexual Selection in Teleost Fishes: Do They Support Bateman's Principles?

Bateman demonstrated differences in variance for fertility andmating success between the sexes, with males usually havinga greater variance than females. Thus in general, male reproductivesuccess increases with number of mates acquired. These resultshave been referred to as "Bateman's principles" and taken togetherwith other parameters (e.g., relative parental investment) havebeen proposed to estimate a component of sexual selection. Forthis review I examine patterns of parental care and sexual selectionin teleost fishes (substrate brooding and with internal fertilization).I present data for the pumpkinseed sunfish Lepomis gibbosus,in which I estimated cost of paternal care and compared directmeasures of the intensity of selection on possible sexuallyselected traits to measures of sexual selection based on Bateman'sprinciples. Despite high levels of paternal care in substrate brooding fishes,sexual selection tends to act more strongly on males than onfemales, which suggests that maternal investment is higher thanpaternal investment and that parental care does not limit thereproductive rate for males. In pumpkinseed sunfish, selectionfavors parents with high levels of defense that may excludepredators more effectively and, as suggested by Bateman's measures,alternative reproductive strategies may decrease the opportunityfor sexual selection within the parental strategy. In teleostfishes with internal fertilization, patterns of parental investmentand intensity of sexual selection seem to support Bateman'sprinciples, but further studies using these systems and thesemeasures of selection will improve the understanding of factorsaffecting the intensity of sexual selection and its relationto mating systems.     

Effects of cognitive abilities on metapopulation connectivity

Connectivity among demes in a metapopulation depends on both the landscape's and the focal organism's properties (including its mobility and cognitive abilities). Using individual‐based simulations, we contrast the consequences of three different cognitive strategies on several measures of metapopulation connectivity. Model animals search suitable habitat patches while dispersing through a model landscape made of cells varying in size, shape, attractiveness and friction. In the blind strategy, the next cell is chosen randomly among the adjacent ones. In the near‐sighted strategy, the choice depends on the relative attractiveness of these adjacent cells. In the far‐ sighted strategy, animals may additionally target suitable patches that appear within their perceptual range. Simulations show that the blind strategy provides the best overall connectivity, and results in balanced dispersal. The near‐sighted strategy traps animals into corridors that reduce the number of potential targets, thereby fragmenting metapopulations in several local clusters of demes, and inducing sink–source dynamics. This sort of local trapping is somewhat prevented in the far‐sighted strategy. The colonization success of strategies depends highly on initial energy reserves: blind does best when energy is high, near‐sighted wins at intermediate levels, and far‐sighted outcompetes its rivals at low energy reserves. We also expect strong effects in terms of metapopulation genetics: the blind strategy generates a migrant‐pool mode of dispersal that should erase local structures. By contrast, near‐ and far‐sighted strategies generate a propagule‐pool mode of dispersal and source–sink behavior that should boost structures (high genetic variance among‐ and low variance within local clusters of demes), particularly if metapopulation dynamics is also affected by extinction–colonization processes. Our results thus point to important effects of the cognitive ability of dispersers on the connectivity, dynamics and genetics of metapopulations.     

Sexual selection in a lekking bird: the relative opportunity for selection by female choice and male competition

Leks are classic models for studies of sexual selection due to extreme variance in male reproductive success, but the relative influence of intrasexual competition and female mate choice in creating this skew is debatable. In the lekking lance-tailed manakin (Chiroxiphia lanceolata), these selective episodes are temporally separated into intrasexual competition for alpha status and female mate choice among alpha males that rarely interact. Variance in reproductive success between status classes of adult males (alpha versus non-alpha) can therefore be attributed to male-male competition whereas that within status largely reflects female mate choice. This provides an excellent opportunity for quantifying the relative contribution of each of these mechanisms of sexual selection to the overall opportunity for sexual selection on males (I males). To calculate variance in actual reproductive success, we assigned genetic paternity to 92.3% of 447 chicks sampled in seven years. Reproduction by non-alphas was rare and apparently reflected status misclassifications or opportunistic copulations en route to attaining alpha status rather than alternative mating strategies. On average 31% (range 7-44%, n=6 years) of the total I males was due to variance in reproductive success between alphas and non-alphas. Similarly, in a cohort of same-aged males followed for six years, 44-58% of the total I males was attributed to variance between males of different status. Thus, both intrasexual competition for status and female mate choice among lekking alpha males contribute substantially to the potential for sexual selection in this species.     

Prestige and reproductive success in man

The relationship between prestige and reproductive success is explored in ten human societies. Formally, the aim is to test the hypothesis that prestige and reproductive success are positively correlated in all populations. It is concluded that in societies at or slightly above the subsistence level prestige and reproductive success are congruent, but that with the accumulation of surplus wealth sources of prestige which have no relevance for reproductive success begin to appear, their development being facilitated by the law of diminishing returns as applied to parents' nonbiological investment in offspring, a point being reached where further investment can have no beneficial effect on reproductive success. As a result sociocultural success and reproductive success may separate. In some societies, where prestige depends upon the possession of real estate, population control is embraced by wealthy families in order to keep their estates intact, thus increasing the effectiveness of the law of diminishing returns by reducing the “fixed resources” (i.e., number of offspring) available for investment. In these conditions, which may spread to the less wealthy, sociocultural success often takes precedence over reproductive success.     

Aerial hunting behaviour and predation success by peregrine falcons Falco peregrinus on starling flocks Sturnus vulgaris

Predators use diverse hunting strategies to maximize hunting success, while preys adopt anti‐predator strategies to maximize escape chances, among which flocking, communal roosting, and the related collective responses are a common pattern in gregarious species. Prey‐predator interactions involving a single predator and flocks, a common situation in birds, have received little attention. We studied predation behaviour and success of peregrine falcons Falco peregrinus on starlings Sturnus vulgaris, a highly gregarious species, in proximity of two winter roosts. A total of 328 hunting sequences, with an overall success of 23.1% were recorded. They usually consisted of several attacks, predation success being higher when hunting sequences lasted less than 1.5 min, included less than 3 attacks and no other falcons were hunting simultaneously. Predation success was higher when hunts were directed on singletons than on flocks. However, most hunting sequences were directed towards flocks. Nine hunting strategies on flocks were identified. The most frequent was the ‘surprise attack’, which was also the most successful. We suggest that this strategy minimizes the amount of anti‐predator display elicited by flocks and economizes energy spent in hunting. The constant predation pressure did not seem to affect the use of roosts by starlings, consistent with the ‘dilution’ hypothesis, while falcons captured at least one prey item every evening. Communal roosting may benefit predator and prey, as both sides could have reached a mutual local equilibrium.     

Offspring size-number trade-offs in scorpions: an empirical test of the van Noordwijk and de Jong model

Abstract Life-history traits are expected to exhibit negative phenotypic trade-offs, but often do not. In a seminal paper, van Noordwijk and de Jong (1986) provided an answer to this seeming paradox. According to their model, trade-offs will be more difficult to detect if variation in resource acquisition (or investment) is high relative to variation in resource allocation to the traits under consideration. Despite its influence on subsequent life-history studies, this model has rarely been tested. I use data from 10 species of scorpion (a total of 30 datasets, including multiple populations or years for some species) to test the van Noordwijk-de Jong model as modified to examine the relationship between offspring size and number. For both the overall data and a subset, including only the species Centruroides vittatus , I found that the correlation between offspring size and number within a population was significantly negatively correlated with the ratio of allocation variance to investment variance. That is, strong trade-offs were found when the investment variance was low relative to the allocation variance. These results were robust to the particular measure of offspring size and to whether offspring data were adjusted for female size variation. My results therefore provide strong evidence in support of the van Noordwijk and de Jong model.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

Conditions for the trivers-willard hypothesis to be valid: A minimal population-genetic model

The very insightful Trivers-Willard hypothesis, proposed in the early 1970s, states that females in good physiological condition are more likely to produce male offspring when the variance of reproductive success among males is high. The hypothesis has inspired a number of studies over the last three decades aimed at its experimental verification, and many of them have found adequate supportive evidence in its favour. Theoretical investigations, on the other hand, have been few, perhaps because formulating a population-genetic model for describing the Trivers-Willard hypothesis turns out to be surprisingly complex. The present study is aimed at using a minimal population-genetic model to explore one specific scenario, namely how is the preference for a male offspring by females in good condition altered wheng, the proportion of such females in the population, changes from a low to a high value. As expected, when the proportion of such females in good condition is low in the population, i.e. for low values ofg, the Trivers-Willard (TW) strategy goes to fixation against the equal investment strategy. This holds true up to g_max, a critical value ofg, above which the two strategies coexist, but the proportion of the TW strategy steadily decreases asg increases to unity. Similarly, when the effect of well-endowed males attaining disproportionately high number of matings is more pronounced, the TW strategy is more likely to go to fixation. Interestingly, the success of the TW strategy has a complex dependence on the variance of the physiological condition of females. If the difference in the two types of conditions is not large, TW strategy is favoured, and its success is more likely as the difference increases. However, beyond a critical value of the difference, the TW strategy is found to be less and less likely to succeed as the difference becomes larger. Possible reasons for these effects are discussed. This paper is dedicated to the memory of W. D. Hamilton.     

Testing models of parental investment strategy and offspring size in ants

Parental investment strategies can be fixed or flexible. A fixed strategy predicts making all offspring a single ‘optimal’ size. Dynamic models predict flexible strategies with more than one optimal size of offspring. Patterns in the distribution of offspring sizes may thus reveal the investment strategy. Static strategies should produce normal distributions. Dynamic strategies should often result in non-normal distributions. Furthermore, variance in morphological traits should be positively correlated with the length of developmental time the traits are exposed to environmental influences. Finally, the type of deviation from normality (i.e., skewed left or right, or platykurtic) should be correlated with the average offspring size. To test the latter prediction, we used simulations to detect significant departures from normality and categorize distribution types. Data from three species of ants strongly support the predicted patterns for dynamic parental investment. Offspring size distributions are often significantly non-normal. Traits fixed earlier in development, such as head width, are less variable than final body weight. The type of distribution observed correlates with mean female dry weight. The overall support for a dynamic parental investment model has implications for life history theory. Predicted conflicts over parental effort, sex investment ratios, and reproductive skew in cooperative breeders follow from assumptions of static parental investment strategies and omnipresent resource limitations. By contrast, with flexible investment strategies such conflicts can be either absent or maladaptive. Electronic Supplementary Material Supplementary material is available for this article at     

Evolutionary branching under asymmetric competition

I investigate the evolution of a continuous trait, such as body size or arms level, which affects the outcome of competitive contests such that the contestant with the larger trait value has a higher probability of winning. I show that a polymorphism of distinctly different strategies can evolve in an initially monomorphic population even if mutations have only small phenotypic effect. In a simple Lotka-Volterra-type model of asymmetric competition, I derive the conditions under which two strategies can gradually evolve from a single ancestral strategy; the evolution of higher level polymorphisms is studied by numerical analysis and computer simulations of specific examples. High levels of polymorphism may build up during evolution. The coevolution of strategies in polymorphic populations, however, may also lead to extinction, which decreases the level of polymorphism. I discuss whether the evolution of several haploid strategies from a single initial strategy may correspond to the evolution of several sympatric species in a diploid outbreeding population.     

INTRASPECIFIC VARIATION IN SEX ALLOCATION IN A SIMULTANEOUS HERMAPHRODITE: THE EFFECT OF INDIVIDUAL SIZE

Within a population of simultaneous hermaphrodites, individuals may vary in both their current reproductive investment (biomass invested in gonads) and in how they allocate that investment between male and female function. In the chalk bass, Serranus tortugarum, estimates of both reproductive allocation and reproductive success as a male and a female can be made for individuals of different sizes. As individuals increase in size, their investment in gamete production increases, and there is a shift in allocation to a stronger female bias. Spawning frequency as a female in pair spawnings and as a male in both pair spawning and streaking (an alternative mating tactic) does not vary with individual size. As a result, larger individuals should release more sperm or eggs per spawn. Size-assortative pair spawning in this species leads to larger individuals having higher potential returns in total male reproductive success than smaller individuals, which should lead to increases in absolute levels of sperm production in larger individuals when individuals compete for fertilizations through sperm competition. However, smaller individuals contribute a smaller proportion of the sperm released in spawns with multiple spawners and thus are under more intense sperm competition than larger individuals, which should select for increases in male allocation in smaller individuals, all else equal. A local-mate-competition (LMC) model predicts that these factors select for increasing absolute male and female investment with individual size but a relative shift to more female-biased allocation as individual size increases. These predictions are supported by gonadal data. The predictions of average male allocation from the quantitative LMC model were 21.6% and 25.7%, whereas the collections averaged 21.3%. This close agreement of both the mean male allocation and its relative shift with individual size between model and data support the hypothesis that size-specific shifts in sex allocation in this species represent an adaptive response to patterns of mating success and sperm competition.     

Infanticide by male house sparrows: gaining time or manipulating females?

The killing of genetically unrelated young by males has been viewed as a strategy that forces victimized females to advance the onset of their next fertile period, thus infanticidal males gain a time advantage that may be crucial to maximize reproductive success. Among females that may raise several broods in a year, a failure occurring relatively earlier in the time-course of the previous breeding attempt may result in an increased investment in the next breeding attempt. This female strategy may be exploited by males in their own interest, and may strongly select for male infanticidal behaviour. I demonstrate that, in the house sparrow, females mated with infanticidal males re-laid earlier, initiated more breeding attempts and fledged more offspring than females mated with non-infanticidal males. These results suggest that both the time saving and the manipulation of female investment are independent mechanisms conferring advantages that may have selected for male infanticide in the studied population.