Extrapair paternity, migration, and breeding synchrony in birds

To understand interspecific patterns in the strength of sexualselection, variation in the costs and benefits of exercisingmate choice needs to be evaluated. One manifestation of sexualselection in birds is the occurrence of greatly variable levelsof extrapair paternity (EPP). A proposed general explanationfor this variation is that the benefits to females in seekingextrapair copulations vary in a predictable manner accordingto the degree of breeding synchrony because females are betterable to assess potential extrapair partners when males are simultaneouslyin breeding condition. This hypothesis predicts a latitudinaltrend in EPP because birds tend to breed more synchronouslyaway from the equator. Expanding on previous geographicallyand taxonomically restricted tropical/temperate comparisons,we used phylogenetically independent standardized linear contraststo show that this positive relationship persists when all birdspecies for which EPP estimates currently exist are considered.However, if a third factor covaries with latitude in the sameway as breeding synchrony and EPP, this relationship need notbe causal. Migration could also account for latitudinal variationin the benefits to females of pursuing EPP, if migration isassociated with (1) hasty or (2) inaccurate mate choice, (3)facilitated assessment of male quality through the condition-dependenceof arrival time, or (4) increased genetic variance in male quality.We show that migration distance is positively related to theproportion of EPP and that migration can statistically explainthe latitudinal trend in EPP, even when confounding factorsare simultaneously controlled. Hence, alternative explanationsfor latitudinal variation in EPP may be feasible, and carefulintraspecific tests are needed to assess their relative importanceand their implications for geographical variation in life-historyevolution.     

Sexual dimorphism and synchrony of breeding: variation in polygyny potential among populations in the common brushtail possum, Trichosurus vulpecula

Male-biased sexual dimorphism in both size and body mass isa common characteristic of many polygynous mammals and is oftenattributed to sexual selection favoring large males. The degreeof dimorphism is thought to be related to the potential forsome males to monopolize access to estrous females, which isin turn related to the distribution of receptive females inspace and time. In the present study, we investigated the relationshipbetween the temporal distribution of breeding females and thedegree of mass dimorphism among 11 populations of the commonbrushtail possum from northern Australia. Breeding patternsvaried from complete aseasonality in some populations to a seasonalconcentration of births within 2 or 3 months in others. We predictedthat in populations in which mating opportunities were distributedthroughout the year, dominant males would be able to monopolizeaccess to larger numbers of estrous females than in populationsin which matings were more seasonal, and in such populations,large body size in males would be favored. We found that dimorphismwas related to seasonality of breeding, being greatest in populationswith a more aseasonal pattern. Mean body mass of male possumsalso decreased with increasing population density. Populationdensity may influence the degree of breeding synchrony withinpopulations, particularly in locations with a more seasonalclimate. The present study is the first to demonstrate plasticityin mass dimorphism in response to local variation in the synchronyof breeding in a mammal species.     

Effects of breeding density, synchrony, and experience on extrapair paternity in tree swallows

Breeding density, synchrony, and experience are expected toinfluence the frequency of extrapair paternity in birds. UsingDNA fingerprinting, we examined the effect of these factorson tree swallows nesting at relatively high (grids of nest-boxes)and low (solitary boxes at least 100 m from the nearest neighbor)densities and in relatively synchronous (Alberta) and asynchronous(Ontario) populations in Canada. The mean percentage of extrapairoffspring per nest did not differ significantly between birdsnesting in grids (43%, n = 22 families) and solitary boxes (57%,n = 12 families). Similarly, there was no significant differencein the mean percentage of extrapair offspring per nest betweenrelatively synchronous (60%, n = 12 Alberta families) and asynchronous(41%, n = 22 Ontario families) populations. We also found noconsistent pattern between extrapair paternity and breedingexperience among seven males and seven females examined overtwo to three breeding seasons. Female tree swallows can influencethe fertilization success of extrapair males by active selectionand rejection of copulation partners. We suggest that this abilitylimits the predicted effect of various ecological factors onthe frequency of extrapair paternity     

Experimental manipulation of timing of breeding suggests laying order instead of breeding synchrony affects extra-pair paternity in house sparrows

The timing of breeding may not only affect breeding patterns such as the overlap of chick rearing period with the peak in food availability but also the opportunity for extra-pair mating. A negative relationship has been predicted between extra-pair paternity and breeding synchrony, assuming that male extra-pair activity is traded against mate guarding and parenting duties. In contrast, if female ability to assess male quality is temporally constrained, sperm competition might be a positive function of breeding synchrony. Here we manipulated the progress of nesting by nest material exchange within nesting aggregations to see whether the timing of breeding affects extra-pair paternity in house sparrows. We found that late broods within nesting clusters contained extra-pair young more often than early broods, but breeding synchrony did not turn out to be a significant predictor of extra-pair paternity. Our study indicates that temporal constraints of male extra-pair activity may account for extra-pair paternity levels, but it is also possible that late-breeding females may accept extra-pair copulations to ensure egg fertilization.     

Multiple ornamentation, female breeding synchrony, and extra-pair mating success of golden whistlers (Pachycephala pectoralis)

Considerable variation exists in rates of extra-pair paternity between species, and across and within populations of the same species. Explanations for this variation include ecological (e.g. breeding synchrony), morphological (e.g. ornamentation), and genetic (e.g. relatedness) factors, but it is rare for studies to simultaneously explore these factors within a single population. This is especially true for highly ornamented species, where mate choice based on ornamentation may be more complex than in less-adorned species. We conducted such a study in a migratory population of the highly ornamented golden whistler (Pachycephala pectoralis). We quantified male genetic reproductive success and related it to a range of factors putatively involved in determining extra-pair mating success. We found no effects of genetic factors (male heterozygosity and relatedness) on extra-pair success, nor of territory size, male age, or incubation effort. Instead, males possessing yellower breast plumage and large song repertoires enjoyed higher reproductive success. Additionally, we found a negative relationship between local breeding synchrony and male extra-pair mating success. This may be a consequence of mate guarding during the female fertile period and an inability of males to simultaneously mate-guard and pursue extra-pair fertilisations. In this species, the opportunity for extra-pair matings appears to vary temporally with an ecological variable (local breeding synchrony), while fine-scale, inter-male differences in mating success may be influenced by individual attributes (male ornamentation). The migratory nature of the study population and its lack of natal philopatry may mean that relatedness and inbreeding avoidance are less important considerations in mate choice.     

Cross entropy minimization in uninvadable states of complex populations

Selection is often. viewed as a process that maximizes the average fitness of a population. However, there are often constraints even on the phenotypic level which may prevent fitness optimization. Consequently, in evolutionary game theory, models of frequency dependent selection are investigated, which focus on equilibrium states that are characterized by stability (or uninvadability) rather than by optimality. The aim of this article is to show that nevertheless there is a biologically meaningful quantity, namely cross (fitness) entropy, which is optimized during the course of evolution: a dynamical model adapted to evolutionary games is presented which has the property that relative entropy decreases monotonically, if the state of a (complex) population is close to an uninvadable state. This result may be interpreted as if evolution has an order stabilizing effect.     

Breeding synchrony and extrapair fertilizations in two populations of red-winged blackbirds

We tested the relationship between synchrony of breeding andthe frequency of extrapair fertilizations (EPFs) in two populationsof red-winged blackbirds known to differ in female extrapairbehavior. We found no association between the number of simultaneouslyfertilizable females (temporal neighbors) and EPF rate in eitherpopulation, although a significant difference between populationsin the direction of this relationship (positive where femalesinitiated extrapair copulations and negative where males initiatedthem) suggested a modest difference in the influence of synchrony.Males losing offspring to EPFs tended to have more fertilizablefemales at that time than the actual sires in some analysesbut not in others. We also tested several assumptions underlyingtwo competing hypotheses for the effects of synchrony. We foundno evidence that females pursued extrapair copulations moreoften when other females were synchronous. Rather, females weremore likely to gain EFFs with exirapatr males whose social mateswere not yet building their nests. Synchrony also did not consistentlyaffect male pursuit of exirapair copulations or achievementof EPFs. These results suggest that timing of breeding has someeffects on extrapair activity, but that those effects are bothrelatively weak and influenced by other factors that vary betweenyears or populations.     

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.     

Extrapair paternity is influenced by breeding synchrony and density in the common yellowthroat

The effects of breeding synchrony and density on levels of extrapair paternity in birds are controversial. We used multilocus DNAfingerprinting and microsatellite analysis to examine the effectsof breeding synchrony and density on levels of extrapair paternityin the common yellowthroat (Geothlypis trichas). As in manyNeotropical migrants, breeding synchrony was greatest at thebeginning of the breeding season. Levels of extrapair paternitywere higher after the peak in synchrony, leading to an overallnegative relationship between extrapair paternity and breeding synchrony. However, there was a significant interaction betweenbreeding synchrony and density, as levels of extrapair paternitywere higher only for males breeding when both synchrony anddensity were low. We discuss several possible explanationsfor this interaction, including lower quality males or territoriesin low density areas and greater demands on mate guarding among males with larger territories. Most studies have not consideredsimultaneously the effects of breeding synchrony and densityon extrapair paternity. Our results suggest that ecologicalcorrelates of paternity may be revealed only after testingfor interactions in multivariate analyses.     

Male rank, female breeding synchrony, and patterns of paternity in the boat-tailed grackle

Species in which males directly defend groups of breeding femalesoftenhave extreme skew in observed male mating success. Inonly a few species,however, has a corresponding skew in fertilizationsuccess been confirmed.Furthermore, the ecological and socialfactors contributing to variation infertilization success needinvestigation. This study examined competition formates andpaternity in the boat-tailed grackle (Quiscalus major).Observationsat colonies of nesting females revealed that the toprankingoralpha males performed more than 70% of the copulations. DNAfingerprintingindicated that alpha males sired less than 40%of nestlings. Nevertheless,analysis of band-sharing scoresamong nestlings from different nests suggestedthat alpha malessired more than three times as many offspring as any otherindividualmale. Because few nestlings were sired by the nonalpha malesthatassociated with colonies, females must have mated withother males while ontrips away from colonies. Analysis of paternitywithin broods revealed that atleast half of all females hadtheir brood fertilized by more than one male.Alpha males' successat fertilizing eggs did not vary with the number ofsimultaneouslyreceptive females within a colony. Our results suggest thatmaleand female behavior in female-defense polygyny results fromcomplexcoevolution of the sexes.     

Emergence and resilience of cooperation in the spatial prisoner's dilemma via a reward mechanism

We study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May [1992. Evolutionary games and spatial chaos. Nature 415, 424-426] showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost-benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanism is turned off. We discuss analytically the case of the invasion by a single cooperator and present agent-based simulations for small initial fractions of cooperators. Large cooperation levels, in the sustainability range, are found. In the conclusions we discuss possible applications of this model as well as its connections with other mechanisms proposed to promote the emergence of cooperation.     

Evolutionary stability and quasi-stationary strategy in stochastic evolutionary game dynamics

Stochastic evolutionary game dynamics for finite populations has recently been widely explored in the study of evolutionary game theory. It is known from the work of Traulsen et al. [2005. Phys. Rev. Lett. 95, 238701] that the stochastic evolutionary dynamics approaches the deterministic replicator dynamics in the limit of large population size. However, sometimes the limiting behavior predicted by the stochastic evolutionary dynamics is not quite in agreement with the steady-state behavior of the replicator dynamics. This paradox inspired us to give reasonable explanations of the traditional concept of evolutionarily stable strategy (ESS) in the context of finite populations. A quasi-stationary analysis of the stochastic evolutionary game dynamics is put forward in this study and we present a new concept of quasi-stationary strategy (QSS) for large but finite populations. It is shown that the consistency between the QSS and the ESS implies that the long-term behavior of the replicator dynamics can be predicted by the quasi-stationary behavior of the stochastic dynamics. We relate the paradox to the time scales and find that the contradiction occurs only when the fixation time scale is much longer than the quasi-stationary time scale. Our work may shed light on understanding the relationship between the deterministic and stochastic methods of modeling evolutionary game dynamics.     

The different limits of weak selection and the evolutionary dynamics of finite populations

Evolutionary theory often resorts to weak selection, where different individuals have very similar fitness. Here, we relate two ways to introduce weak selection. The first considers evolutionary games described by payoff matrices with similar entries. This approach has recently attracted a lot of interest in the context of evolutionary game dynamics in finite populations. The second way to introduce weak selection is based on small distances in phenotype space and is a standard approach in kin-selection theory. Whereas both frameworks are interchangeable for constant fitness, frequency-dependent selection shows significant differences between them. We point out the difference between both limits of weak selection and discuss the condition under which the differences vanish. It turns out that this condition is fulfilled by the popular parametrization of the prisoner's dilemma in benefits and costs. However, for general payoff matrices differences between the two frameworks prevail.     

Parental selection,number of breeding populations,and size of each population in inbred development

Some breeders select inbreds from many F₂ or backcross breeding populations, each with relatively few progenies. Other breeders select inbreds from only a few breeding populations, each with many progenies. My objectives were to: (1) determine the relative importance of parental selection, number of breeding populations, and size of each population, and (2) find optimum combinations between number and size of breeding populations. I assumed that a breeder has resources to test a total of 2,000 recombinant inbreds for a quantitative trait that was controlled by 100 additive loci and had a heritability of 0.20, 0.60, or 1.0. The parental inbreds had an inherent pedigree structure due to advanced cycle breeding. The parental inbreds were ranked according to their mean performance, and breeding populations were made among all parents, the top 25% of parents, and the top 10% of parents. I found that the issue of number versus size of breeding populations was only secondary compared with the ability to identify, prior to making the crosses, the breeding populations with the highest mean performance. For a given level of effectiveness of parental selection, the selection response was largest when the maximum number of breeding populations was used. The effect of the number of breeding populations was minor, however, when selection was practiced among the parents or when heritability was less than 1.0. The results suggested that, in practice, large selection responses could be obtained with a wide range of combinations between number and size of breeding populations.Communicated by H.C. Becker     

Population trends and spatial synchrony in peripheral populations of the endangered Lesser grey shrike in response to environmental change

Regional synchronization in species dynamics as well as particular ecological and demographic characteristics of peripheral populations poses special challenges for conservation purposes, particularly under the current scenario of global climate change. Here, we study the population trend and spatial synchrony of several peripheral populations of the endangered Lesser grey shrike Lanius minor at the western limit of its breeding range (southern France and northeast Spain). In an attempt to ascertain the effect of environmental change on the decline of the species we also look for evidence of climate changes in the breeding and wintering area of this shrike and related effects on vegetation by using the normalized difference vegetation index (NDVI). We found that the interannual fluctuations of the peripheral populations in France and Spain are strongly correlated, therefore suggesting that their decline can be under the influence of a common factor. We obtained clear evidence of climatic change (an increased thermal oscillation) in one peripheral population that could have resulted in a decrease of the NDVI index in the area. Our study finds correlational evidence that climatic variables in the breeding area may account for fluctuations in abundances of some populations and that environmental conditions experimented by some population could influence the fate of the neighboring populations. Our results indicate that the studied peripheral populations are spatially synchronized, so that conservation efforts should be applied at a large-scale encompassing all the isolated populations at the western border of the range of the species in the Mediterranean area.     

John Maynard Smith and the importance of consistency in evolutionary game theory

John Maynard Smith was the founder of evolutionary game theory. He has also been the major influence on the direction of this field, which now pervades behavioural ecology and evolutionary biology. In its original formulation the theory had three components: a set of strategies, a payoff structure, and a concept of evolutionary stability. These three key components are still the basis of the theory, but what is assumed about each component is often different to the original assumptions. We review modern approaches to these components. We emphasis that if a game is considered in isolation, and arbitrary payoffs are assumed, then the payoffs may not be consistent with other components of the system which are not modelled. Modelling the whole system, including not only the focal game, but also the future behaviour of the players and the behaviour of other population members, allows a consistent model to be constructed. We illustrate this in the case of two models of parental care, showing how linking a focal game to other aspects of the system alters what is predicted.     

Stochastic fluctuations in frequency-dependent selection: a one-locus, two-allele and two-phenotype model

Stochastic fluctuations in a simple frequency-dependent selection model with one-locus, two-alleles and two-phenotypes are investigated. The steady-state statistics of allele frequencies for an interior stable phenotypic equilibrium are shown to be similar to the stochastic fluctuations in standard evolutionary game dynamics [Tao, Y., Cressman, R., 2007. Stochastic fluctuations through intrinsic noise in evolutionary game dynamics. Bull. Math. Biol. 69, 1377-1399]. On the other hand, for an interior stable phenotypic or genotypic equilibrium, our main results show that the deterministic model cannot be used to predict the expectation of phenotypic frequency. The variance of phenotypic frequency for an interior stable genotypic equilibrium is more sensitive to the expected population size than for an interior stable phenotypic equilibrium. Furthermore, the stochastic fluctuations of allele frequency and phenotypic frequency can be considered approximately independent of each other for these genotypic equilibria, but not for phenotypic.