Strong evolutionary equilibrium and the war of attrition

In developing the concept of an evolutionarily stable strategy, Maynard Smith proposed formal conditions for stability. These conditions have since been shown to be neither necessary nor sufficient for evolutionary stability in finite populations. This paper provides a strong stability condition which is sensitive to the population size. It is then demonstrated that in the war of attrition with uncertain rewards there is a unique “strong evolutionary equilibrium” strategy. As the population becomes large this is shown to approach the solution strategy proposed by Bishop, Cannings and Maynard Smith.The analysis is then extended to wars of attrition between different populations. It is concluded that for such contests there is a whole family of potential strong evolutionary equilibria.     

Cellular functions of a cell in a metastable equilibrium state

A unifying hypothesis which might replace some of the many ion pumps which are invoked to describe distribution of ions across living cell membranes is developed quantitatively. Resting cells are assumed to be in a metastable state such that ions are in equilibrium between an extracellular aqueous phase, in which water has the properties of the bulk liquid, and an intracellular aqueous phase in which water has enhanced structure and strongly modified solvent properties. Partition coefficients or medium effects for Na⁺, K⁺ and Cl⁻ are calculated for several cell types. It is shown that in such a hypothetical cell, possessing no ion pumps there is an amplified Donnan potential between the two phases, its sign determined by the net charge on intracellular proteins, and its magnitude increased by a separation of ions induced by the difference in solvent properties of the water in the two phases. It is shown that a cell in such a metastable state is excitable and can generate an action potential with an inward surge of Na+ followed by an outward surge of K+. An explanation is offered for the transient release of Caa+ from the sarcoplasmic reticulum following excitation of a muscle fibre. Regulation of cellular volume is shown to be a necessary result of the presence in the extracellular solution of a high concentration of Na+, an ion with a very low affinity for intracellular water. It is concluded that the principal cellular functions that are commonly attributed to the sodium pump are also a feature of a cell in a metastable equilibrium state.     

Differences in dynamics between discrete strategies and continuous strategies in a multi-player game with a linear payoff structure

A deductive analysis concerning replicator dynamics proved that a continuous strategy game (in which a player chooses an arbitrary real number between [0, 1] as a cooperative fraction) has the same equilibrium as a discrete strategy game (in which a player chooses only C or D), which has the same linear payoff structure as a continuous strategy game. The deduction is shown for two-player and multi-player games.     

Coordination strategies of chimpanzees and human children in a Stag Hunt game

Much of human cooperation takes place in mutualistic contexts in which the main challenge for individuals is how to coordinate decisions. In the current studies, we compared the abilities of chimpanzees and young children to coordinate with a partner in two versions of a Stag Hunt game. When risks were low (the hare was of low value) and information was cheap (the partner''s behaviour was readily observable), partners of both species were able to successfully coordinate on the higher value stag more than 90% of the time. By contrast, when the risks were raised and observing the partner was more difficult, the chimpanzees became less successful, whereas the children compensated, and so remained highly successful, by communicating more often and more specifically. This pattern of results is consistent with the hypothesis that humans evolved unique skills of coordination and communication in the context of especially risky coordination problems.     

Minimax strategies for a predator—Prey game

Suppose prey are distributed in patches. The predator knows the fraction of patches containing 0, 1, 2,… prey, but not how many prey a particular patch contains. It searches each patch randomly, at constant speed. It leaves a patch when the intercapture times satisfy a formula designed to maximize the number of prey eaten per unit time. We show that, if the prey distribution is Poisson, the predator should stay in each patch for the same time, regardless of what happens there. Accordingly, the prey can minimize the predator's maximum intake by choosing the Poisson distribution, and the predator can maximize its minimum intake (against a “smart” prey) by choosing the constant-time strategy.     

Mating strategies in primates: a game theoretical approach to infanticide

Infanticide by newly immigrated or newly dominant males is reported among a variety of taxa, such as birds, rodents, carnivores and primates. Here we present a game theoretical model to explain the presence and prevalence of infanticide in primate groups. We have formulated a three-player game involving two males and one female and show that the strategies of infanticide on the males' part and polyandrous mating on the females' part emerge as Nash equilibria that are stable under certain conditions. Moreover, we have identified all the Nash equilibria of the game and arranged them in a novel hierarchical scheme. Only in the subspace spanned by the males are the Nash equilibria found to be strict, and hence evolutionarily stable. We have therefore proposed a selection mechanism informed by adaptive dynamics to permit the females to transition to, and remain in, optimal equilibria after successive generations. Our model concludes that polyandrous mating by females is an optimal strategy for the females that minimizes infanticide and that infanticide confers advantage to the males only in certain regions of parameter space. We have shown that infanticide occurs during turbulent changes accompanying male immigration into the group. For changes in the dominance hierarchy within the group, we have shown that infanticide occurs only in primate groups where the chance for the killer to sire the next infant is high. These conclusions are confirmed by observations in the wild. This model thus has enabled us to pinpoint the fundamental processes behind the reproductive decisions of the players involved, which was not possible using earlier theoretical studies.     

Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.     

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

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

Mutation-selection equilibrium in games with multiple strategies

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.     

The evolution of pattern camouflage strategies in waterfowl and game birds

Visual patterns are common in animals. A broad survey of the literature has revealed that different patterns have distinct functions. Irregular patterns (e.g., stipples) typically function in static camouflage, whereas regular patterns (e.g., stripes) have a dual function in both motion camouflage and communication. Moreover, irregular and regular patterns located on different body regions (“bimodal” patterning) can provide an effective compromise between camouflage and communication and/or enhanced concealment via both static and motion camouflage. Here, we compared the frequency of these three pattern types and traced their evolutionary history using Bayesian comparative modeling in aquatic waterfowl (Anseriformes: 118 spp.), which typically escape predators by flight, and terrestrial game birds (Galliformes: 170 spp.), which mainly use a “sit and hide” strategy to avoid predation. Given these life histories, we predicted that selection would favor regular patterning in Anseriformes and irregular or bimodal patterning in Galliformes and that pattern function complexity should increase over the course of evolution. Regular patterns were predominant in Anseriformes whereas regular and bimodal patterns were most frequent in Galliformes, suggesting that patterns with multiple functions are broadly favored by selection over patterns with a single function in static camouflage. We found that the first patterns to evolve were either regular or bimodal in Anseriformes and either irregular or regular in Galliformes. In both orders, irregular patterns could evolve into regular patterns but not the reverse. Our hypothesis of increasing complexity in pattern camouflage function was supported in Galliformes but not in Anseriformes. These results reveal a trajectory of pattern evolution linked to increasing function complexity in Galliformes although not in Anseriformes, suggesting that both ecology and function complexity can have a profound influence on pattern evolution.     

Multi-behavioral strategies in a predator–prey game: an evolutionary algorithm analysis

Behavioral games between predators and prey often involve two sub-games: 'pre-encounter' games affecting the rate of encounter between predators and prey (e.g. predator–prey space games, Sih 2005 ), and 'post-encounter' games that influence the outcome of encounters (e.g. waiting games at prey refugia, Hugie 2003 , and games of vigilance, Brown et al. 1999 ). Most models, however, focus on only one or the other of these two sub-games.
I investigated a multi-behavioral game between predators and prey that integrated both pre-encounter and post-encounter behaviors. These behaviors included landscape-scale movements by predators and prey, a type of prey vigilance that increases immediately after an encounter and then decays over time ('ratcheting vigilance'), and predator management of prey vigilance. I analyzed the game using a computer-based evolutionary algorithm. This algorithm embedded an individual-based model of ecological interactions within a dynamic adaptive process of mutation and selection. I investigated how evolutionarily stable strategies (ESS) varied with the predators' learning ability, killing efficiency, density and rate of movement. I found that when predators learn prey location, random prey movement can be an ESS. Increased predator killing efficiency reduced prey movement, but only if the rate of predator movement was low. Predators countered ratcheting vigilance by delaying their follow-up attacks; however, this delay was reduced in the presence of additional predators. The interdependence of pre-and post-encounter behaviors revealed by the evolutionary algorithm suggests an intricate co-evolution of multi-behavioral predator–prey behavioral strategies.     

Evolutionary stable strategies and game dynamics for n-person games

This note contains a generalization of the definition of an evolutionary stable strategy and of the corresponding game dynamics from 2-person to n-person games. This broader framework also allows modelling of several interacting populations or of populations containing different types of individuals, for example males and females.     

It takes two: sexual strategies and game theory

David Buss’s Sexual Strategies Theory is one of the major evolutionary psychological research programmes, but, as I try to show in this paper, its theoretical and empirical foundations cannot yet be seen to be fully compelling. This lack of cogency comes about due to Buss’s failure to attend to the interactive nature of his subject matter, which leads him to overlook two classic and well known issues of game theoretic and evolutionary biological analysis. Firstly, Buss pays insufficient attention to the fact that, since mate choice is a cooperative decision, what is adaptive for the two sexes individually is irrelevant to the evolutionary explanation of our sexual strategies; instead, all that matters is what is adaptive given the choices made by the other sex. Secondly, Buss does not pay enough attention to the difference between polymorphic and monomorphic evolutionarily stable states in his attempt to empirically confirm his theory. Because of this, the data he presents and analyses are unable to show that natural selection is the most important element in the explanation of the origins of our sexual strategies. In this way, I try to make clear that, at least as things stand now, Buss has failed to provide compelling grounds for thinking that Sexual Strategies Theory can make a major contribution to human psychology.     

The grand game of metazoan phylogeny: rules and strategies

Many cladistic analyses of animal phylogeny have been published by authors arguing that their results are well supported. Comparison of these analyses indicates that there can be as yet no general consensus about the evolution of the animal phyla. We show that the various cladistic studies published to date differ significantly in methods of character selection, character coding, scoring and weighting, ground-pattern reconstructions, and taxa selection. These methodological differences are seldom made explicit, which hinders comparison of different studies and makes it impossible to assess a particular phylogeny outside its own scope. The effects of these methodological differences must be considered before we can hope to reach a morphological reference framework needed for effective comparison and combination with the evidence obtained from molecular and developmental genetic studies.     

Stable isotope evidence of diverse species-specific and individual wintering strategies in seabirds

Although there is increasing evidence that climatic variations during the non-breeding season shape population dynamics of seabirds, most aspects of their winter distribution and ecology remain essentially unknown. We used stable isotope signatures in feathers to infer and compare the moulting (wintering) habitat of subantarctic petrels breeding at two distant localities (South Georgia and Kerguelen). Petrels showed species-specific wintering habitat preferences, with a similar pattern of latitudinal segregation for all but one taxon. At both localities, delta13C values indicated that blue petrels (Halobaena caerulea) moult in Antarctic waters, South Georgian diving petrels (Pelecanoides georgicus) in the vicinity of the archipelagos and/or in the Polar Frontal Zone and Antarctic prions (Pachyptila desolata) in warmer waters. In contrast, common diving petrels (Pelecanoides urinatrix) showed divergent strategies, with low and high intrapopulation variation at South Georgia and Kerguelen, respectively. Birds from Kerguelen dispersed over a much wider range of habitats, from coastal to oceanic waters and from Antarctica to the subtropics, whereas those from South Georgia wintered mainly in waters around the archipelago. This study is the first to show such striking between-population heterogeneity in individual wintering strategies, which could have important implications for likely demographic responses to environmental perturbation.     

Stable, stoichiometric delivery of diverse protein functions

As contemporary "genomics" steadily reveals an increasing number of novel gene sequences, the need for efficient methodologies to functionally characterize these genes in vivo increases significantly. Reliable coupling of target gene expression to a variety of surrogate reporter functions is critical to properly assay novel gene function in complex cell populations. Ideally, independent target and reporter proteins would be derived from a single open reading frame creating a stoichiometric relationship without obscuring subcellular localization. We report here effective strategies for assaying gene function through the stable production of chimeric polyproteins, processed intracellularly by inclusion of an intervening 19-amino-acid sequence from the 2A region of the Foot and Mouth Disease virus. Using drug-resistance and flow cytometry-based assay systems, we demonstrate that diverse protein functions are effectively delivered to various cell types by retroviral constructs as single 2A-cleaved polyproteins. For example, cells infected with a retrovirus encoding a nuclear cell cycle regulator, linked via the 2A-motif to a marker membrane protein, showed a direct correlation between cell cycle arrest and surface marker level. This demonstrates the utility of this methodology for stable and stoichiometric delivery of distinctly localized protein functionalities. In particular, the ability to exploit multiple cellular functions will serve to accelerate the functional characterization of gene products and facilitate novel gene therapy approaches.     

Brain training game improves executive functions and processing speed in the elderly: a randomized controlled trial

Background

The beneficial effects of brain training games are expected to transfer to other cognitive functions, but these beneficial effects are poorly understood. Here we investigate the impact of the brain training game (Brain Age) on cognitive functions in the elderly.

Methods and Results

Thirty-two elderly volunteers were recruited through an advertisement in the local newspaper and randomly assigned to either of two game groups (Brain Age, Tetris). This study was completed by 14 of the 16 members in the Brain Age group and 14 of the 16 members in the Tetris group. To maximize the benefit of the interventions, all participants were non-gamers who reported playing less than one hour of video games per week over the past 2 years. Participants in both the Brain Age and the Tetris groups played their game for about 15 minutes per day, at least 5 days per week, for 4 weeks. Each group played for a total of about 20 days. Measures of the cognitive functions were conducted before and after training. Measures of the cognitive functions fell into four categories (global cognitive status, executive functions, attention, and processing speed). Results showed that the effects of the brain training game were transferred to executive functions and to processing speed. However, the brain training game showed no transfer effect on any global cognitive status nor attention.

Conclusions

Our results showed that playing Brain Age for 4 weeks could lead to improve cognitive functions (executive functions and processing speed) in the elderly. This result indicated that there is a possibility which the elderly could improve executive functions and processing speed in short term training. The results need replication in large samples. Long-term effects and relevance for every-day functioning remain uncertain as yet.

Trial Registration

UMIN Clinical Trial Registry 000002825     

Multiple signaling functions of song in a polymorphic species with alternative reproductive strategies

Vocal traits can be sexually selected to reflect male quality, but may also evolve to serve additional signaling functions. We used a long‐term dataset to examine the signaling potential of song in dimorphic white‐throated sparrows (Zonotrichia albicollis). We investigated whether song conveys multifaceted information about the vocalizing individual, including fitness, species identity, individual identity, and morph. We also evaluated whether song traits correlate differently with fitness in the two morphs, as the more promiscuous strategy of white, relative to tan, morph males might impose stronger sexual selection. Males with high song rates achieved higher lifetime reproductive success, and this pattern was driven by white morph males. In addition, males that sang songs with many notes survived longer, but this pattern was less robust. Thus, song traits reflect differences in fitness and may more strongly affect fitness in the white morph. Song frequency was unrelated to fitness, body size, or morph, but was individual specific and could signal individual identity. Songs of the two morphs displayed similar frequency ratios and bandwidths. However, tan morph males sang songs with longer first notes, fewer notes, and higher variability. Thus, song could be used in morph discrimination. Variation in frequency ratios between notes was low and could function in conspecific recognition, but pitch change dynamics did differ between four different song types observed. Our results support a multiple messages model for white‐throated sparrow song, in which different song traits communicate discrete information about the vocalizing individual.