Prior fitness and the evolutionarily stable strategy for intraspecific conflict.
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Animals↗
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Results for “evolutionarily stable strategy”
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A note on evolutionarily stable strategies in asymmetric animal conflicts.
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Animals↗
Required parental investment and mating patterns: a quantitative analysis in the context of evolutionarily stable strategies.
Much social psychological research has been dedicated to understanding mating strategies from the standpoint of genetic-fitness payout (e.g., Simpson and Gangestad, 2000). The current work is designed to provide a coherent, quantitative model for predicting different classes of mating strategies in both males and females. Specifically, the framework developed in this paper is an elaboration of Dawkins' (1989) quantitative assessment of different male and female mating strategies. Dawkins suggests that the prevalence of different strategies employed should be predictable in terms of evolutionary stable strategies. In the current work, a quantitative analysis predicting the prevalence of different mating strategies within each sex was conducted. The mathematical functions derived suggest that variability in the costs associated with raising offspring affects the expected prevalence of mating strategies differently for males and females. According to the present model, variability in female strategies should be less affected by changes in parental investment (PI) than variability in male strategies. Important predictions regarding male and female mating strategies across cultures are discussed.
Biological Evolution↗
The parental investment conflict in continuous time: St. Peter's fish as an example.
The parental investment conflict considers the question of how much each sex should invest in each brood, thereby characterizing different animal species. Each species usually adopts a certain parental care pattern: female-care only, male-care only, biparental care, or even no parental care at all. The differences in care patterns are usually explained by the different costs and benefits arising from caring for the offspring in each animal species. This paper proposes a game-theoretical model to the parental investment conflict based on the parental behavior of St. Peter's fish. St. Peter's fish exhibit different parental care patterns, allowing the examination of the factors which determine the particular behavior in each mating. We present a continuous time, two-stage, asymmetric game, with two types of players: male and female. According to the model's results, three parental care patterns: male-only care, female-only care and biparental care, are possible evolutionarily stable strategies. The evolutionarily stable parental care pattern in a certain mating depends on a parent's increase in mortality due to parental care, and on its advantage from biparental care. These results may explain the different parental care patterns observed in a variety of animal species, including those found in the St. Peter's fish.
Animals↗
Evolutionarily [corrected] stable strategies: a review of basic theory.
Widely successful in applied population biology, the Evolutionarily Stable Strategy concept remains controversial because of the severe restrictions present in its original formulation. We review theory which explores and relaxes these restrictions, finding the concept to be quite robust and adaptable, incorporating considerations such as genetics, population diversity, environmental variability, and mutation.
Animals↗
An explicit approach to evolutionarily stable dispersal strategies: no cost of dispersal.
The evolution of dispersal is examined by looking at evolutionarily stable strategies (ESS) for dispersal parameters in discrete time multisite models without any cost of dispersal. ESS are investigated analytically, based on explicit results on sensitivity analysis of matrix models. The basic model considers an arbitrary number of sites and a single age class. An ESS for dispersal parameters is obtained when the spatial reproductive values, calculated at the density-dependent population equilibrium, are equal across sites. From this basic formulation, one derives equivalently that all local populations should be at equilibrium in the absence of migration, and that dispersal between sites should be balanced, i.e., the numbers of individuals arriving to and leaving a site are equal. These results are then generalized to a model with several age classes. Equal age-specific reproductive values do not however imply balanced dispersal in this case. Our results generalize to any number of sites and age classes those available ¿M. Doebeli, Dispersal and dynamics, Theoret. Popul. 47 (1995) 82 for two sites and one age class.
Age Distribution↗
Evolutionarily Stable Reproductive Strategies in Sexual Organisms: III. The Effects of Lottery Density Dependence and Pollen Limitation
This paper extends our previous work on modelling, within a single framework, the allocation of resources to reproduction vs. survival and the male vs. female components of reproduction in perennial plants. We derive the evolutionarily stable strategy (ESS) results under pollen limitation for both hermaphroditic and dioecious plant populations held stable through density-dependent juvenile recruitment. Pollen limitation affects female reproductive allocation in our model because there is post-flowering provisioning of offspring. We find that pollen limitation is unimportant to the ESS reproductive allocation and sex allocation so long as there are enough seeds to fill the empty sites left by the death of adults. To the extent that the relationships between gamete output and resource investment are linear for both sexes or sex functions, the separate treatment of reproductive and sex allocation in modern life-history and sex-allocation theories is adequate. In such cases, the ESS sex allocation is exactly what is found in traditional sex allocation theory, and the ESS reproductive allocation of hermaphrodites or females in a dioecious species maximizes the amount of resources allocated to reproduction during an average lifespan, an analogue of the usual maximization principle in life-history theory modified to include the possibility of pollen limitation and extended seed maturation. The ESS reproductive allocation of males in a dioecious species maximizes lifetime pollen production, independent of pollen limitation and the female's resource allocation. Copyright 1997 Academic Press Limited
Journal Article↗
No strategy is evolutionarily stable in the repeated prisoner's dilemma.
Following the influential work of Axelrod, the repeated Prisoner's Dilemma game has become the theoretical gold standard for understanding the evolution of co-operative behavior among unrelated individuals. Using the game, several authors have found that a reciprocal strategy known as Tit for Tat (TFT) has done quite well in a wide range of environments. TFT strategists start out co-operating and then do what the other player did on the previous move. Despite the success of TFT and similar strategies in experimental studies of the game, Boyd & Lorberbaum (1987, Nature, Lond. 327, 58) have shown that no pure strategy, including TFT, is evolutionarily stable in the sense that each can be invaded by the joint effect of two invading strategies when long-term interaction occurs in the repeated game and future moves are discounted. Farrell & Ware (1989, Theor. Popul. Biol. 36, 161) have since extended these results to include finite mixes of pure strategies as well. Here, it is proven that no strategy is evolutionarily stable when long-term relationships are maintained in the repeated Prisoner's Dilemma and future moves are discounted. Namely, it is shown each completely probabilistic strategy (i.e. one that both co-operates and defects with positive probability after every sequence of behavior) may be invaded by a single deviant strategy. This completes the proof started by Boyd and Lorberbaum and extended by Farrell and Ware. This paper goes on to prove that no reactive strategy with a memory restricted to the opponent's preceding move is evolutionarily stable when there is no discounting of future moves. This is true despite the success of a more forgiving variant of TFT called GTFT in a recent tournament among reactive strategies conducted by Nowak & Sigmund (1992, Nature 355, 250) where future moves were not discounted. GTFT, for example, may be invaded by a pair of reactive mutants. Since no strategy is evolutionarily stable when future moves are discounted in the repeated game, the restriction of strategy types to those actually maintained by mutation and phenotypic and environmental variability in natural populations may be the key to understanding the evolution of co-operation. However, the result presented here that the somewhat realistic reactive strategies are also not evolutionarily stable at least in the non-discounted game suggests something else may be going on. For one, the proof that no reactive strategy is evolutionarily stable ironically shows the robustness of TFT-like strategies.(ABSTRACT TRUNCATED AT 400 WORDS)
Animals↗
Types of evolutionary stability and the problem of cooperation.
The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.
Journal Article↗
Evolutionarily Stable Reproductive Strategies in Sexual Organisms: IV. Parent-Offspring Conflict and Selection of Seed Size in Perennial Plants.
The provisioning of offspring in sexually reproducing organisms provides an arena in which genetic conflict of interests between parents and their offspring may be expressed. While most existing models of parent-offspring-conflict consider the case of a parent that rears one offspring a year, this paper is concerned with perennial plants that produce many seeds at one time. Parent-offspring conflict is examined in the context of an integrated analysis of reproductive allocation, sex allocation, and the amount of resources invested in each offspring. I derive the evolutionarily stable strategy (ESS) results for the allocation of resources when the mother plant is in control as well as when the offspring are in control taking into account both density-independent and density-dependent population growth. To the extent that the relationships between gamete output and resource investment are linear for both sex functions, the separate treatment of reproductive effort, sex allocation, and offspring size-number compromise in modern life-history theories is justified, regardless of which side, parents or offspring, wins the conflict. In such cases, the ESS sex allocation is exactly what is found in traditional sex allocation theory, and the ESS reproductive effort maximizes the rate of population growth in density-independent populations, or the amount of resources allocated to reproduction during an average lifespan in density-dependent populations. In contrast to the previous theoretical conclusions based on the analyses of single-offspring cases, the ESS reproductive effort under the offspring's control of allocation to individual offspring is found to be lower than that when mothers are in control. This paradoxical result occurs because a mother producing fewer ovules fares better if she knows that each of her seed offspring will get more resources than the amount she is selected to give. The evolutionarily stable offspring size in both density-independent and density-dependent populations does not depend on mother's reproductive effort and investment-independent mortality, just as traditional models of offspring size-number trade-offs would predict.Copyright 1998 Academic Press Limited
Journal Article↗
Sperm competition I: basic model, ESS and dynamics.
We examine models of sperm competition to determine which strategies are evolutionarily stable according to game theory. Games are considered in which the males of a species must divide a fixed amount of sperm between a fixed number of rounds in competition over fertilization of a given set of eggs. Sperm success with a single female is allocated using the raffle principle". A two round model is formulated and we show that the evolutionarily stable strategy (ESS) is a pure strategy in which a male should use at least half his sperm in the first round if given the opportunity to mate. The ESS is unique and globally stable, in contrast to most classical ESSs which are only locally stable. The model is extended to include the effects of sperm replenishment and egg oviposition between rounds. Both serve to increase the ESS amount of sperm inseminated in round one.
Animals↗
Host-parasite dynamics and the evolution of host immunity and parasite fecundity strategies.
We explore evolutionarily stable co-evolution of host-macroparasite++ interactions in a discrete-time two-species population dynamics model, in which the dynamics may be stable, cyclic or chaotic. The macroparasites are assumed to harm host individuals through decreased reproductive output. Hosts may develop costly immune responses to defend themselves against parasites. Parasites compete with conspecifics by adjusting their fecundities. Overall, the presence of both parasites and the immune response in hosts produces more stable dynamics and lower host population sizes than that observed in the absence of the parasites. In our evolutionary analyses, we show that maximum parasite fecundity is always an evolutionarily stable strategy (ESS), irrespective of the type of population interaction, and that maximum parasite fecundity generally induces a minimum parasite population size through over-exploitation of the host. Phenotypic polymorphisms with respect to immunity in the host species are common and expected in ESS host strategies: the benefits of immunication depend on the frequency of the immune hosts in the population. In particular, the steady-state proportions of immune hosts depend, in addition to all the parameters of the parasite dynamics only on the cost of immunity and on the virulence of parasites in susceptible hosts. The implicit ecological dynamics of the host-parasite interaction affect the proportion of immune host individuals in the population. Furthermore, when changes in certain population parameters cause the dynamics of the host-parasite interaction to move from stability to cyclicity and then to chaos, the proportion of immune hosts tend to decrease; however, we also detected counter-examples to this result. As a whole, incorporating immunological and genetic aspects, as well as life-history trade-offs, into host-macroparasite dynamics produces a rich extension to the patterns observed in the models of ecological interactions and epidemics, and deserves more attention than is currently the case.
Animals↗
Properties of a mixed ESS candidate in continuous strategy sets.
An evolutionarily stable strategy (ESS) is a strategy that if almost all members of the population adopt, then this population cannot be invaded by any mutant strategy. An ESS is not necessarily a possible end point of the evolutionary process. Moreover, there are cases where the population evolves towards a strategy that is not an ESS. This paper studies the properties of a unique mixed ESS candidate in a continuous time animal conflict. A member of a group sized three finds itself at risk and needs the assistance of another group member to be saved. In this conflict, a player's strategy is to choose the probability distribution of the interval between the beginning of the game and the moment it assists the player which is at risk. We first assume that a player is only allowed to choose an exponential distribution, and show that in this case the ESS candidate is an attracting ESS; the population will always evolve towards this strategy, and once it is adopted by most members of the population it cannot be invaded by mutant strategies. Then, we extend the strategy sets and allow a player to choose any continuous distribution. We show that although this ESS candidate may no longer be an ESS, under fairly general conditions the population will tend towards it. This is done by characterizing types of strategies that if established in the population, can be invaded by this ESS candidate, and by presenting possible paths of transition from other types of common strategies to this ESS candidate.
Animals↗
Evolutionarily stable germination strategies with time-correlated yield.
We investigate the effect of auto-correlated yield on the evolutionarily stable germination fraction of dormant seeds. By using both analytics and numerics, we first show that in a regime of small fluctuations a positive correlation reduces dormancy and a negative correlation enhances dormancy. By extending the numerical analysis we also show that in the regime of large fluctuations a more complex picture emerges where also negative correlations can reduce dormancy.
Biological Evolution↗
Models on butterfly protandry: virgin females are at risk to die.
Current models on protandry in butterflies assume that females are mated instantaneously upon eclosion. However, for most butterfly species this assumption is not realistic. In this paper a model is formulated in which the mating rate depends on both male and female density. Given the female presence curve, protandry is an evolutionarily stable strategy (ESS) for males. The evolutionarily stable amount of protandry decreases with increasing death rate and decreasing encounter rate. Given the male presence curve, protandry also is an ESS for females. However, male and female ESS are not identical; moreover, in the present model a simultaneous ESS does not exist. Protandry critically depends on the assumption that females mate only once, whereas males are capable of multiple mating. If females too are capable of multiple mating, absence of protandry is the ESS for males as well as females. The model predicts that protandry depends on population density: protandry should be more pronounced in populations with high density than in populations with low density. Protandry also depends on sex ratio. It becomes more pronounced when the proportion of males among emerging adults increases.
Animals↗
How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies.
We define a fitness concept applicable to structured metapopulations consisting of infinitely many equally coupled patches. In addition, we introduce a more easily calculated quantity Rm that relates to fitness in the same manner as R0 relates to fitness in ordinary population dynamics: the Rm of a mutant is only defined when the resident population dynamics converges to a point equilibrium and Rm is larger (smaller) than 1 if and only if mutant fitness is positive (negative). Rm corresponds to the average number of newborn dispersers resulting from the (on average less than one) local colony founded by a newborn disperser. Efficient algorithms for calculating its numerical value are provided. As an example of the usefulness of these concepts we calculate the evolutionarily stable conditional dispersal strategy for individuals that can account for the local population density in their dispersal decisions. Below a threshold density x, at which staying and leaving are equality profitable, everybody should stay and above x everybody should leave, where profitability is measured as the mean number of dispersers produced through lines of descent consisting of non-dispersers.
Algorithms↗
Some evolutionary properties of parental investment per offspring in a heterogeneous environment.
The possibility of protected polymorphisms and of monomorphic evolutionarily stable strategies for parental investment per offspring in a heterogeneous environment is theoretically analysed. A high density two-niche model of the classical soft selection kind is used, although it incorporates the possibility of rare strategies invading an empty niche the contribution of which is not constant. Protected polymorphisms can be found whether or not both strategies included produce surviving offspring in both niches. However, a monomorphic evolutionarily stable strategy exists unless offspring of the optimal size in one of the niches cannot survive in the other. The robustness of the model is graphically illustrated under a variety of circumstances, and some evolutionary consequences are briefly discussed.
Animals↗
Reproductive asynchrony increases with environmental disturbance.
While it is widely recognized that the manner in which organisms adjust their timing of reproduction reflects evolutionary strategies aimed at minimizing offspring mortality or maximizing reproductive output, the conditions under which the evolutionarily stable strategy involves synchronous or asynchronous reproduction is a matter of considerable discord. A recent theoretical model predicts that whether a population displays reproductive synchrony or asynchrony will depend on the relative scales of intrinsic regulation and environmental disturbance experienced by reproducing individuals. This model predicts that, under conditions of negligible competition and large-scale environmental perturbation, evolution of a single mixed strategy will result in asynchronous reproduction. We tested this prediction using empirical data on large-scale climatic fluctuation and the annual timing of reproduction by three species of flowering plants covering 1300-population-years and four degrees of latitude in Norway. In agreement with model predictions, within populations of all three species reproductive asynchrony increased with the magnitude of large-scale climatic perturbation, but bore no relation to the strength of local density dependence. These results suggest that mixed evolutionarily stable strategies can arise from the interplay of combinations of agents of selection and the scale at which they operate; hence it is fruitless to associate synchronous versus asynchronous timing with particular single factors like climate, competition, or predation.
Climate↗