Asynchronous snowdrift game with synergistic effect as a model of cooperation

The snowdrift (or chicken) game emerges as a new paradigm inthe study of nonkin cooperation in animals. Many situations,for example, cooperative hunting, group foraging, territorialdefense, predator watching, or parental care, can be adequatelydescribed as a snowdrift game. In this paper, we investigatethe asynchronous version of the game in which, contrary to therather unrealistic assumption of simultaneous moves, one ofthe players acts first and the other responds by knowing itsdecision. Players are assigned to be first or second moversrandomly and with the same probability. We found that both asynergistic effect of cooperation (i.e., cooperative effortis better than the sum of the individual efforts) and populationstructure (low dispersal, spatial confinement, or group formation)are crucial for mutual cooperation to emerge. Otherwise, onlyone of the players will carry the burden of cooperation.     

Simulating natural selection as a culling mechanism on finite populations with the hawk-dove game

The behaviors of individuals and species are often explained in terms of evolutionary stable strategies (ESSs). The analysis of ESSs determines which, if any, combinations of behaviors cannot be invaded by alternative strategies. Two assumptions required to generate an ESS (i.e., an infinite population and payoffs described only on the average) do not hold under natural conditions. Previous experiments indicated that under more realistic conditions of finite populations and stochastic payoffs, populations may evolve in trajectories that are unrelated to an ESS, even in very simple games. The simulations offered here extend earlier research by employing truncation selection with random parental selection in a hawk-dove game. Payoffs are determined in pairwise contests using either the expected outcome, or the result of a random variable. In each case, however, the mean fraction of hawks over many generations and across many independent trials does not conform to the expected ESS. Implications of these results and philosophical underpinnings of ESS theory are offered.     

Learning in a game context: strategy choice by some keeps learning from evolving in others

Behavioural decisions in a social context commonly have frequency-dependent outcomes and so require analysis using evolutionary game theory. Learning provides a mechanism for tracking changing conditions and it has frequently been predicted to supplant fixed behaviour in shifting environments; yet few studies have examined the evolution of learning specifically in a game-theoretic context. We present a model that examines the evolution of learning in a frequency-dependent context created by a producer–scrounger game, where producers search for their own resources and scroungers usurp the discoveries of producers. We ask whether a learning mutant that can optimize its use of producer and scrounger to local conditions can invade a population of non-learning individuals that play producer and scrounger with fixed probabilities. We find that learning provides an initial advantage but never evolves to fixation. Once a stable equilibrium is attained, the population is always made up of a majority of fixed players and a minority of learning individuals. This result is robust to variation in the initial proportion of fixed individuals, the rate of within- and between-generation environmental change, and population size. Such learning polymorphisms will manifest themselves in a wide range of contexts, providing an important element leading to behavioural syndromes.     

Parental investment with a superior alien in the brood

When a parent's parentage differs across breeding attempts, established theory predicts that the parent should invest more in a brood when perceived parentage is high. We present a model of parental investment in which offspring unrelated to the parent have a competitive advantage over the parent's own offspring and take a larger share of investment. We show that this can weaken or, if the competitive advantage is great, reverse the predicted relationship between perceived parentage and parental investment. A moderate competitive advantage of extra-pair young over within-pair young could partly explain the lack of any clear relationship between paternal care and paternity in many studies, and could easily arise if females choose extra-pair partners for good genes. Our results are also relevant to interspecific avian brood parasitism. As parasites reared together with host offspring are often superior competitors, their hosts could benefit from increasing investment in response to suspected parasitism.     

Evolutionary game dynamics in a Wright-Fisher process

Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.     

Using blocks of linked single nucleotide polymorphisms as highly polymorphic genetic markers for parentage analysis

Single nucleotide polymorphisms (SNPs) are plentiful in most genomes and amenable to high throughput genotyping, but they are not yet popular for parentage or paternity analysis. The markers are bi-allelic, so individually they contain little information about parentage, and in nonmodel organisms the process of identifying large numbers of unlinked SNPs can be daunting. We explore the possibility of using blocks of between three and 26 linked SNPs as highly polymorphic molecular markers for reconstructing male genotypes in polyandrous organisms with moderate (five offspring) to large (25 offspring) clutches of offspring. Haplotypes are inferred for each block of linked SNPs using the programs Haplore and Phase 2.1. Each multi-SNP haplotype is then treated as a separate allele, producing a highly polymorphic, 'microsatellite-like' marker. A simulation study is performed using haplotype frequencies derived from empirical data sets from Drosophila melanogaster and Mus musculus populations. We find that the markers produced are competitive with microsatellite loci in terms of single parent exclusion probabilities, particularly when using six or more linked SNPs to form a haplotype. These markers contain only modest rates of missing data and genotyping or phasing errors and thus should be seriously considered as molecular markers for parentage analysis, particularly when the study is interested in the functional significance of polymorphisms across the genome.     

Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations

Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak, et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy α is greater than that of strategy β when α has a frequency , strategy α fixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.     

A resource-sharing model based on a repeated game in fog computing

With the rapid development of cloud computing techniques, the number of users is undergoing exponential growth. It is difficult for traditional data centers to perform many tasks in real time because of the limited bandwidth of resources. The concept of fog computing is proposed to support traditional cloud computing and to provide cloud services. In fog computing, the resource pool is composed of sporadic distributed resources that are more flexible and movable than a traditional data center. In this paper, we propose a fog computing structure and present a crowd-funding algorithm to integrate spare resources in the network. Furthermore, to encourage more resource owners to share their resources with the resource pool and to supervise the resource supporters as they actively perform their tasks, we propose an incentive mechanism in our algorithm. Simulation results show that our proposed incentive mechanism can effectively reduce the SLA violation rate and accelerate the completion of tasks.     

Sex-ratio distortion in Drosophila simulans: co-occurence of a meiotic drive and a suppressor of drive

A sex-ratio distortion factor was found at high frequency in D. simulans strains from Seychelles and New Caledonia. This factor is poorly or not expressed within those strains which are resistant to it. Its presence was detected by crossing females from New Caledonia or the Seychelles with males from a different geographic origin. Most of the F1 males obtained produced an excess of females (up to 99%) in their progeny. The two strains are infected with Wolbachia, but these micro-organisms are not involved in the sex-ratio distortion. The sex-ratio factor is shown to be an X-linked meiotic driver; nuclear resistance factor(s) act by suppressing the drive. It is likely that the same X-located driver invaded the two populations, which subsequently developed resistance factor(s) against it.     

Confidence of paternity and paternal care by eastern bluebirds

Male birds are often faced with low confidence of paternityin their mates' offspring, raising the question of how paternalcare covaries with confidence of paternity. We tested the hypothesisthat male eastern bluebirds (Sialia sialis) reduce care of nestlingsin response to experimentally decreased confidence of paternity.Actual paternity, as assessed by DNA fingerprinting, had noeffect on male feeding rates, nor did males reduce care whenconfidence of paternity was experimentally decreased. Malesthat had been removed for 2 days while their mate was fertile(experimental group) fed nestlings at absolute rates similarto those of control males. The proportion of feeding trips providedby males was also similar for control and experimental nests.We found no difference in fledging success and nestling growthbetween experimental and control broods. Seven original residentmales were displaced by previously unbanded males. Althoughthese replacement males appeared to feed nestlings at normalrates, the nests attended by replacement males suffered reducedfledging success compared to control and experimental nests.Overall, we found no evidence that males reduce feeding effortwhen confidence of paternity is experimentally decreased. Malesmay tolerate some reduction in confidence of paternity withoutreducing care if paternal care is crucial to nestling survival.Alternatively, males may assess paternity within a brood usingcues other than their ability to guard their fertile mates.     

Evolution of learned strategy choice in a frequency-dependent game

In frequency-dependent games, strategy choice may be innate or learned. While experimental evidence in the producer-scrounger game suggests that learned strategy choice may be common, a recent theoretical analysis demonstrated that learning by only some individuals prevents learning from evolving in others. Here, however, we model learning explicitly, and demonstrate that learning can easily evolve in the whole population. We used an agent-based evolutionary simulation of the producer-scrounger game to test the success of two general learning rules for strategy choice. We found that learning was eventually acquired by all individuals under a sufficient degree of environmental fluctuation, and when players were phenotypically asymmetric. In the absence of sufficient environmental change or phenotypic asymmetries, the correct target for learning seems to be confounded by game dynamics, and innate strategy choice is likely to be fixed in the population. The results demonstrate that under biologically plausible conditions, learning can easily evolve in the whole population and that phenotypic asymmetry is important for the evolution of learned strategy choice, especially in a stable or mildly changing environment.     

When should cuckolded males care for extra-pair offspring?

In socially monogamous species with bi-parental care, males suffer reduced reproductive success if their mate engages in extra-pair copulations (EPCs). One might therefore expect that males should refuse to care for a brood if they can detect that an EPC has occurred. Here, we use a game-theory model to study male brood care in the face of EPCs in a cooperatively breeding species in which offspring help to raise their (half-) siblings in their parents' next breeding attempt. We show that under certain conditions males are selected to care even for broods completely unrelated to themselves. This counterintuitive result arises through a form of pseudo-reciprocity, whereby surviving extra-pair offspring, when helping to rear their younger half-siblings, can more than compensate for the cost incurred by the male that raised them. We argue that similar effects may not be limited to cooperative breeders, but may arise in various contexts in which cooperation between (half-) siblings occurs.     

Fairness evolution in the ultimatum game is a function of reward size

I formulate a simple model of the ultimatum game, in which a proposer and a responder can receive a reward if they agree on how to divide this reward between them. The model is easy to analyse and shows that strong tendencies to fair division are expected when evolution of strategy frequencies follow the traditional gradient dynamics assumed in evolutionary models. The mean stable offer is typically around 20-40% although this depends on the maximum payoff and if rejection thresholds can evolve independently from proposals. The stable proportion offered at evolutionary equilibrium increases with the maximum payoff, if proposal and acceptance thresholds are dictated by the same strategy and cannot evolve independently. If proposal and acceptance evolve independently, the stable proportion instead decreases with the maximum payoff. The stable outcome may also show substantial variation.     

纯种犬在15个STR基因座上的遗传多态性

目的:指导纯种犬的繁育及建立一套简便的犬个体识别和亲权鉴定方法。方法:通过设计引物进行PCR扩增及PAGE检测的方法,分析了88头纯种犬在15个STR基因座上的遗传学多态性。结果:15个STR基因座的累积非父排除率(CPE)和累积个体识别率(TDP)分别为0.999678和0.999999999997,而平均杂合度和平均多态信息含量分别为0.607和0.640。12个STR基因座(PEZ1、PEZ2、PEZ3、PEZ5、PEZ6、PEZ8、PEZ12、FHC2010、FHC2054、FHC2087UbF、HC2132、FHC2611)的多态信息含量(PIC)和杂合度(H)大于0.5,它们的TDP和CPE值分别为0.999999999963和0.999334,能有效用于犬的个体识别和亲权鉴定。结论:这15个STR基因座可以用于指导犬的繁育,其中12个STR基因座能有效用于犬的个体识别和亲权鉴定。     

Cloning of highly polymorphic microsatellites in the horse

We have isolated equine microsatellites by screening a genomic library with (TG)n and (TC)n probes. TG microsatellites were found to be more abundant than TC repeats, with an estimated frequency of one per 100,000bp. Sequence analysis of eight TG-positive clones revealed varying structures of the repeat regions; perfect stretches of TG repeats, imperfect stretches of TG repeats and compound regions of TG and TC repeats. Five loci were analysed by PCR and showed extensive polymorphism; three to seven alleles and heterozygosities of 0.40-0.76 were observed when screening 20-30 unrelated individuals. The high degree of polymorphism, their abundance and the possibility of automating the typing procedure make these loci ideal for standardized paternity testing in the horse. Furthermore, we demonstrate that single hairs can be used as starting material for the PCR analysis.     

Evolutionary game dynamics with non-uniform interaction rates

The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to non-linear fitness functions. We show that a strict Nash equilibrium remains uninvadable for non-uniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of non-uniform interaction rates can lead to a pair of interior equilibria. For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators.