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This paper provides evolutionary game-theoretic models for the status signaling problem in animal contests. Two stage status signaling game models are introduced and evolutionarily stable strategies and their modifications are characterized for the games. It is shown that in the stable long-run equilibria, animals must make use of signals systematically to settle the contest peacefully.
We investigate the relationship between sperm competition intensity and sperm expenditure, both across species and within a species, using a two sperm competition models. In model 1, the males cannot assess the number of competitors, and their ejaculate effort is shaped by the average number of competitors. In model 2, males can assess the number Ni of competitors at each spawning exactly. Males can vary the mass m of their sperm and the number si at a spawning. The aim is to find the evolutionarily stable strategies and hence the way that m and si vary with Ni. A continuous fertilization model in which the sperm have to swim in order to fertilize an egg is described. This is used to find simultaneous equations describing m and si. These are solved numerically.
The iterated Prisoner's Dilemma (IPD) is usually analysed by evaluating arithmetic mean pay-offs in an ESS analysis. We consider several points that the standard argument does not address. Finite population size and finite numbers of matches in the IPD game lead us to consider both pay-off variance and the sampling process in the evolutionary game. We provide a general form for the pay-off variance of the Markov strategist in the IPD game, and present a general analysis of the initial invasion process of an "all defection strategist" (ALLD) into a "tit-for-tat" (TFT) strategist population by considering stochastic processes. Finite population size, strategic error an the variances of pay-offs alter the prediction concerning the initial invasion of ALLD compared with the standard Evolutionarily Stable Strategy (ESS) analysis. Even though TFT gets the larger arithmetic mean, the variance of its pay-off is also larger when the expected iterations of the game are sufficiently large. Therefore, the boundary of the parameter of the probability of game continuity, w, above which ALLD does not have advantage to invade into the TFT population, becomes a bit larger than predicted by the deterministic model.
The choices made by juveniles, in territorial species, between dispersing and remaining in the natal territory, can be modelled as a simple multi-player evolutionary game, related to the well-known War of Attrition [Maynard Smith, J. (1974) J. theor. Biol. 47, 209-221; Haigh J. & Cannings, C. (1989) Acta Applicandae Mathematicae 14, 59-74]. The game is shown to have a unique evolutionarily stable strategy, involving a random choice between dispersing early in the game and staying indefinitely. An example is given, involving badgers (Meles meles), in which the key factor affecting the pay-off in the game is the possibility of inheriting the territory on the death of the current holders. The example indicates the sensitivity of the size of the group occupying the territory to the mortality rate among dispersers.
In most previous work on the yellow dung fly Scathophaga stercoraria (L.), as on other species, adaptive explanations have been sought for male behaviour whereas female behaviour has not been examined in similar detail. Here, the arrival of females at the mating site, fresh cattle droppings, is investigated. While almost all males are present shortly after pat deposition females arrive at a low, decreasing rate over an interval of about 5 hours. We propose that the distribution of female arrival times represents a mixed Evolutionarily Stable Strategy (ESS), formed by different trade-offs between costs and benefits of early and late arrival. Early arrival could be favoured by advantages due to better conditions for oviposition, faster egg development of reduced larval competition. Late arrival could be favoured by negative effects on females of male-male competition being weaker later after deposition. Computer simulations with distributions of arrival times deviating from the natural one were performed to "measure" the costs for females arriving at different times. These costs were compared with estimated benefits corresponding to the females' arrival times. This procedure revealed that females coming to the pat later in a population of females arriving shortly after deposition would be favoured. In a population arriving according to a uniform distribution, early females would have fitness advantages. Thus, evolution should lead to an intermediate distribution of arrival times, as in nature, i.e. female arrival behaviour is probably adaptive. The simulations also revealed that the intensity of sexual selection though male-male competition is highest with the natural pattern of female arrival. Therefore, natural selection generating this pattern amplifies the intensity of male-male interaction as a by-product. Copyright 1998 Academic Press
The population dynamics of two types of organisms in a lattice-structured habitat are studied and the evolutionarily stable allocation between short- and long-range disperser is calculated. Offsprings of short-range dispersal stay in the vicinity of their parent and cause local competition. Using pair approximation, I derive a closed system of ordinary differential equations of global and local densities (or mean crowding), and calculate the condition for one type to invade the population dominated by the other type. The evolutionarily stable strategy (ESS) of resource allocation is derived for the case in which there is a linear trade-off between short- and long-range dispersers. The maximum equilibrium abundance of the population may be achieved by a mixture of both types of dispersers, but it is in general different from the ESS resource allocation calculated from the invasibility condition. For the same parameter values, the ESS invests a larger fraction of resources to short-range disperser than the optimal allocation which maximizes the equilibrium population density. This difference can be explained by the fact that long-range disperser is more effective in the preoccupation of space than short-range disperser. The predictions are confirmed by the direct computer simulations of the lattice stochastic models. Copyright 1999 Academic Press.
The hawk-dove game has proved to be an important tool for understanding the role of aggression in social interactions. Here, the game is presented in a more general form (GHD) to facilitate analyses of interactions between individuals that may differ in "size", where size is interpreted as a surrogate for resource holding power. Three different situations are considered, based on the availability and use of information that interacting individuals have about their sizes: the classical symmetric case, in which no information about sizes is used, the asymmetric case, in which the individuals know their relative sizes and thus their chances of prevailing in combat, and a mixed-symmetry case, in which each individual only knows its own size (or only knows its opponent's size). I describe and use some recently developed methods for multitype games-evolutionary games involving two or more categories of players. With these methods and others, the evolutionarily stable strategies (ESSs) that emerge for the three different cases are identified and compared. A proof of the form and uniqueness of the ESS for the mixed-symmetry case is presented. In this situation, one size category at most can play a mixed strategy; larger individuals are aggressive and smaller individuals are not. As the number of size categories approaches infinity and the size distribution becomes continuous, there is a threshold size, above which all individuals are aggressive, and below which they are not.
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.
The classical static concept of an evolutionarily stable strategy (ESS) for a single species gives rise to two new notions when there are more than two species (called an N-species ESS and RL-stability). The paper relates these to the dynamic stability of monomorphic and polymorphic evolutionary systems. It is shown that RL-stability implies the global asymptotic stability of either system with or without mutations. However, the N-species ESS only implies stability of the monomorphic system.
We use population models that are based on dynamic energy budget models for individuals in order to study the evolution of offspring size and its relationship to the evolution of population dynamics. We show the existence of alternative evolutionarily stable strategies for offspring investment strategy resulting from a trade off between offspring number and time-to-maturity. The model predicts egg energy in Daphnia magna well, and suggests that the observed egg energy in D. magna is the result of selection for minimal egg investment constrained by minimum viable egg energy, combined with selection for a juvenile energy reserve. The selection for minimal egg size pushes populations toward chaotic dynamics. However, the minimum viable egg size combined with low efficiency of conversion of energy to new biomass is sufficient to keep population dynamics out of chaos.
Evolutionarily stable strategies or ESSs of games among kin have been calculated in the literature by both "personal-fitness" and "inclusive-fitness" methods. These methods were compared by Hines and Maynard Smith (1979) for games with bilinear payoffs. Although Hines and Maynard Smith regarded the first method as correct, they regarded the second method as useful because the inclusive-fitness conditions for an ESS gave necessary conditions for a personal-fitness ESS in the class of games they considered. In general, however, satisfying the inclusive-fitness conditions is neither necessary nor sufficient for satisfying the inclusive-fitness conditions, although the two methods may often yield identical ESSs. This result is established by reformulating the classic war-of-attrition model to allow variation in energy reserves, assumed to have a Gamma distribution. For this game, the two methods may disagree for intermediate values of relatedness. By the correct method, if the coefficient of variation in energy reserves is sufficiently high, then the game has a unique ESS in pure strategies at which populations with higher coefficients of variation or relatedness display for shorter times. Unrelated contestants are prepared to expend at least half of their reserves. For populations with lower variation coefficients, the ESS exists only if the cost of displaying per unit time is low compared to the rate at which remaining reserves translate into expected future reproductive success for the victor. The critical variation coefficient, below which the ESS exists regardless of cost, decreases from 0.52 to 0 as the coefficient of relatedness increases from 0 to 1. Although there is no assessment, contests are always won by the animal with greater energy reserves in a population at the ESS.
Stochastic matrix projection models are widely used to model age- or stage-structured populations with vital rates that fluctuate randomly over time. Practical applications of these models rest on qualitative properties such as the existence of a long term population growth rate, asymptotic log-normality of total population size, and weak ergodicity of population structure. We show here that these properties are shared by a general stochastic integral projection model, by using results in (Eveson in D. Phil. Thesis, University of Sussex, 1991, Eveson in Proc. Lond. Math. Soc. 70, 411-440, 1993) to extend the approach in (Lange and Holmes in J. Appl. Prob. 18, 325-344, 1981). Integral projection models allow individuals to be cross-classified by multiple attributes, either discrete or continuous, and allow the classification to change during the life cycle. These features are present in plant populations with size and age as important predictors of individual fate, populations with a persistent bank of dormant seeds or eggs, and animal species with complex life cycles. We also present a case-study based on a 6-year field study of the Illyrian thistle, Onopordum illyricum, to demonstrate how easily a stochastic integral model can be parameterized from field data and then applied using familiar matrix software and methods. Thistle demography is affected by multiple traits (size, age and a latent "quality" variable), which would be difficult to accommodate in a classical matrix model. We use the model to explore the evolution of size- and age-dependent flowering using an evolutionarily stable strategy (ESS) approach. We find close agreement between the observed flowering behavior and the predicted ESS from the stochastic model, whereas the ESS predicted from a deterministic version of the model is very different from observed flowering behavior. These results strongly suggest that the flowering strategy in O. illyricum is an adaptation to random between-year variation in vital rates.
In principle there are two approaches to modelling a trade-off between the positive and negative outcomes of a behavior: after suitably defining a value for the behavior in the absence of any trade-off, one can either multiply that value by an appropriate discount or subtract an appropriate cost. In a prospective analysis of sperm competition, Parker (Proc. Roy. Soc. Lond. B (1990) 242, 120-126) adopted the multiplicative approach to model the trade-off between the value of a mating and the cost of its acquisition. He obtained two paradoxical results. First, if two males 'know' whether they are first or second to mate, but these roles are assigned randomly, then sperm numbers should be the same for both males whether the 'raffle' for fertilization is fair or unfair. Second, if mating order is constant, then a favored male should expend less on sperm. His results are puzzling not only in terms of intuition about nature, but also in terms of his model's consistency. In other words, they present both an external and an internal paradox. Parker assumed the fairness of the raffle to a disfavored male to be independent of how much sperm a favored male deposits. This article both generalizes Parker's analysis by allowing fairness to decrease with sperm expenditure by the favored male and compares Parker's results to those obtained by the additive approach. In many respects, results are similar. Nevertheless, if the costs of mating are assumed to increase with sperm expenditure but not to depend on the role in which sperm is expended, as Parker assumed, then the additive approach is more fundamentally correct. In particular, Parker's constant-role paradox is an artifact of his approach. His random-role paradox is internally rationalized in terms of standard microeconomic theory. When fairness decreases, however slightly, with sperm expenditure by the favored male, both models demonstrate that the evolutionarily stable strategy is for more sperm to be deposited during a favored mating than during a disfavored mating. The lower the costs, the greater the divergence. Thus a possible resolution of the external paradox is that fairness is not constant in nature.
We study an evolutionary language game that describes how signals become associated with meaning. In our context, a language, L, is described by two matrices: the P matrix contains the probabilities that for a speaker certain objects are associated with certain signals, while the Q matrix contains the probabilities that for a listener certain signals are associated with certain objects. We define the payoff in our evolutionary language game as the total amount of information exchanged between two individuals. We give a formal classification of all languages, L(P, Q), describing the conditions for Nash equilibria and evolutionarily stable strategies (ESS). We describe an algorithm for generating all languages that are Nash equilibria. Finally, we show that starting from any random language, there exists an evolutionary trajectory using selection and neutral drift that ends up with a strategy that is a strict Nash equilibrium (or very close to a strict Nash equilibrium).
We investigate the equilibrium structure for an evolutionary genetic model in discrete time involving two monoecious populations subject to intraspecific and interspecific random pairwise interactions. A characterization for local stability of an equilibrium is found, related to the proximity of this equilibrium with evolutionarily stable strategies (ESS). This extends to a multi-population framework a principle initially proposed for single populations, which states that the mean population strategy at a locally stable equilibrium is as close as possible to an ESS.
Helminths are the most prevalent parasitic infections and malaria is the deadliest parasitic disease. Helminths have been reported to be protective against the severe forms of malaria but they were also possibly linked to increased malaria-incidence and gametocyte carriage. Connecting the dots between observations suggests that statistical regularities throughout the evolution of worms and malaria parasites in the same hosts, may have led to the emergence of non-zero interactions as observed in iterated prisoners dilemma games. Thus by protecting the host, helminths protect themselves and their reproductive potential, but also favor the dissemination and reproduction of Plasmodium falciparum. The proximate causes of this evolutionarily stable strategy might be mediated by IgE and the CD23/NO pathway, the protective role of IL10 in helminth-infected patients, and possibly the hematological consequences of worms. The chronic activation of the CD23/NO pathway might be instrumental in downregulating the expression of cytoadherence receptors thus reducing sequestration of parasitized red blood cells in the deep organs. Mild anemia in helminth-infected patients might favor gametocytogenesis and send attractive cues to the vector. This framework leads to numerous testable hypotheses and could explain certain singularities regarding the double edged role of IgE and NO. Among these hypotheses, there are 2 practical ones: the impact of helminths on malaria vaccine candidates, and the theoretical risk of increasing the severity of malaria after anthelmintics. The capacity for increased IgE responses could thus have been vital in our ancestor's wormy and malarious past. Allergies may be what remains of it in the modern world.
Theoretical models for Trivers (1974) concept of parent-offspring conflict are examined for species in which the effects of the conflict are felt by full sibs. A rare conflictor gene will spread if (f(m) greater than 1/2(m + 1), where f(m) is the fitness gained by a conflictor relative to a non-conflictor offspring (f(m) greater than 1), and m is the amount of parental investment taken by a conflictor relative to m = 1 for a non-conflictor. The range of m alleles which can spread against the parent optimum decreases as the cost to the parent increases until a point is reached where there is no conflict of evolutionary interests. There would be no polymorphism for conflictor: non-conflictor alleles unless special conditions prevail. The conflictor allele which spreads most rapidly as a rare mutant against the parental optimum is not an evolutionarily stable strategy (ESS). The ESS for parent-offspring conflict in monogamous species has mo = f(mo)/2[df(mo)/dmo]. The analytical solutions are confirmed throughout by simulations.
A structural stability approach to population-genetic systems and to dynamic evolutionary games is attempted in order to examine the theoretical significance of sociobiological selection models. A criterion of weak selection is derived that is not restricted to differential reproduction in polymorphic systems but describes possible directions of evolutionary change in time scales governed by genetic mutation rates. The criterion applies to the problems of how the initial mutational basis of an adaptive trait may be established and how this may happen, for analogous traits, independently in different species. Two basic sociobiological concepts are reconsidered with reference to the criterion. It is shown that W. D. Hamilton's condition of increases in inclusive fitness due to altruistic interactions among kin expresses the structural instability of populations against the evolution of altruistic behavior. Using the dynamic approach to evolutionary game theory, it is demonstrated that if a behavioral phenotype is an evolutionarily stable strategy, it is structurally stable against perturbations of the fitness payoffs, provided selection is weak. These results are applied to material problems of the evolution of animal social behavior.