Fixation probability with multiple alleles and projected average allelic effect on selection

The first-order effect of selection on the probability of fixation of an allele, with respect to an intensity of selection s>0 in a diploid population of fixed finite size N, undergoing discrete, non-overlapping generations, is shown to be given by the sum of the average effects of that allele on the coefficient of selection in the current generation and all future generations, given the population state in the current generation. This projected average allelic effect is a weighted sum of average allelic effects in allozygous and autozygous offspring in the initial generation, with weights given in terms of expected coalescence times, under neutrality, for the lineages of two or three gametes chosen at random in the same generation. This is shown in the framework of multiple alleles at one locus, with genotypic values determining either viability or fertility differences, and with either multinomial or exchangeable reproduction schemes. In the limit of weak selection in a large population such that Ns tends to zero, the initial average allelic effects in allozygous offspring and autozygous offspring have the same weight on the fixation probability only in the domain of application of the Kingman coalescent. With frequency-dependent selection in a linear-game-theoretic context with two phenotypes determined by additive gene action, the first-order effect on the fixation probability is a combination of two effects of frequency-independent selection, one in a haploid population, the other in a diploid population. In the domain of application of the Kingman coalescent as the population size goes to infinity and Ns to zero, the first effect is three times more important than the second effect. This explains the one-third law of evolutionary dynamics in this domain, and shows how this law can be extended beyond this domain.     

Phenotypic selection and covariation in the life‐history traits of elephant seals: heavier offspring gain a double selective advantage

Early developmental conditions contribute to individual heterogeneity of both phenotypic traits and fitness components, ultimately affecting population dynamics. Although the demographic consequences of ontogenic growth are best quantified using an integrated measure of fitness, most analyses to date have instead studied individual fitness components in isolation. Here, we estimated phenotypic selection on weaning mass in female southern elephant seals Mirounga leonina by analyzing individual‐based data collected between 1986 and 2016 with capture–recapture and matrix projection models. In support of a hypothesis predicting a gradual decrease of weaning mass effects with time since weaning (the replacement hypothesis), we found that the estimated effects of weaning mass on future survival and recruitment probability was of intermediate duration (rather than transient or permanent). Heavier female offspring had improved odds of survival in early life and a higher probability to recruit at an early age. The positive link between weaning mass and recruitment age is noteworthy, considering that pre‐recruitment mortality already imposed a strong selective filter on the population, leaving only the most ‘robust’ individuals to reproduce. The selection gradient on asymptotic population growth rate, a measure of mean absolute fitness, was weaker than selection on first‐year survival and recruitment probabilities. Weaker selection on mean fitness occurs because weaning mass has little impact on adult survival, the fitness component to which the population growth of long‐lived species is most sensitive. These results highlight the need to interpret individual variation in phenotypic traits in a context that considers the demographic pathways between the trait and an inclusive proxy of individual fitness. Although variation in weaning mass do not translate to permanent survival differences among individuals in adulthood, it explains heterogeneity and positive covariation between survival and breeding in early life, which contribute to between‐individual variation in fitness.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

Hamilton's rule confronts ideal free habitat selection

If individuals occupy habitats in a way that maximizes their fitness, if they are free to occupy the habitats they choose and if fitness declines with population density, then their abundance across habitats should follow an ideal free distribution. But, if individuals are genetically related, this simple fitness-maximization mechanism breaks down. Habitat occupation should obey Hamilton's rule (natural selection favours traits causing a loss in individual fitness as long as they result in an equal or greater gain in inclusive fitness) and depends more on inclusive fitness than it does on individual fitness. We demonstrate that the resulting inclusive-fitness distribution inflates the population density in habitats of poorer inherent quality, creating pronounced source sink dynamics. We also show that density-dependent habitat selection among relatives reinforces behaviours such as group defence and interspecific territoriality, and that it explains many anomalies in dispersal and foraging.     

Sex‐biased dispersal,kin selection and the evolution of sexual conflict

There is growing interest in resolving the curious disconnect between the fields of kin selection and sexual selection. Rankin's (2011, J. Evol. Biol. 24 , 71–81) theoretical study of the impact of kin selection on the evolution of sexual conflict in viscous populations has been particularly valuable in stimulating empirical research in this area. An important goal of that study was to understand the impact of sex‐specific rates of dispersal upon the coevolution of male‐harm and female‐resistance behaviours. But the fitness functions derived in Rankin's study do not flow from his model's assumptions and, in particular, are not consistent with sex‐biased dispersal. Here, we develop new fitness functions that do logically flow from the model's assumptions, to determine the impact of sex‐specific patterns of dispersal on the evolution of sexual conflict. Although Rankin's study suggested that increasing male dispersal always promotes the evolution of male harm and that increasing female dispersal always inhibits the evolution of male harm, we find that the opposite can also be true, depending upon parameter values.     

The effect of inbreeding on natural selection in a seed‐feeding beetle

Little is known about how inbreeding alters selection on ecologically relevant traits. Inbreeding could affect selection by changing the distribution of traits and/or fitness, or by changing the causal effect of traits on fitness. Here, I test whether selection on egg size varies with the degree of inbreeding in the seed‐feeding beetle, Stator limbatus. There was strong directional selection favoring large eggs for both inbred and outbred beetles; offspring from smaller eggs had lower survivorship on a resistant host. Inbreeding treatment had no effect on the magnitude of selection on egg size; all selection coefficients were between ~0.078 and 0.096, regardless of treatment. However, inbreeding depression declined with egg size; this is because the difference in fitness between inbreds and outbreds did not change, but average fitness increased, with egg size. A consequence of this is that populations that differ in mean egg size should experience different magnitudes of inbreeding depression (all else being equal) and thus should differ in the magnitude of selection on traits that affect mating, simply as a consequence of variation in egg size. Also, maternal traits (such as egg size) that mediate stressfulness of the environment for offspring can mediate the severity of inbreeding depression.     

Reversed selection responses in small populations of the housefly (Musca domestica L.)

We compared the efficacy of artificial and natural selection processes in purging the genetic load of perpetually small populations. We subjected replicate lines of the housefly (Musca domestica L.), recently derived from the wild, to artificial selection for increased mating propensity (i.e., the proportion of male–female pairs initiating copulation within 30 min) in efforts to cull out the inbreeding depression effects of long-term small population size (as determined by a selection protocol for increased assortative mating). We also maintained parallel non-selection lines for assessing the spontaneous purge of genetic load due to inbreeding alone. We thus evaluated the fitness of artificially and ‘naturally’ purging populations held at census sizes of 40 individuals over the course of 18 generations. We found that the artificially selected lines had significant increases in mating propensity (up to 46% higher from the beginning of the protocol) followed by reversed selection responses back to the initial levels, resulting in non-significant heritabilities. Nevertheless, the ‘naturally’ selected lines had significantly lower fitness overall (a 28% reduction from the beginning of the protocol), although lower effective population sizes could have contributed to this effect. We conclude that artificial selection bolstered fitness, but only in the short-term, because the inadvertent fixation of extant genetic load later resulted in pleiotropic fitness declines. Still, the short-term advantage of the selection protocol likely contributed to the success of the speciation experiment since our recently-derived housefly populations are particularly vulnerable to inbreeding depression effects on mating behavior.     

Inbreeding reveals mode of past selection on male reproductive characters in Drosophila melanogaster

Directional dominance is a prerequisite of inbreeding depression. Directionality arises when selection drives alleles that increase fitness to fixation and eliminates dominant deleterious alleles, while deleterious recessives are hidden from it and maintained at low frequencies. Traits under directional selection (i.e., fitness traits) are expected to show directional dominance and therefore an increased susceptibility to inbreeding depression. In contrast, traits under stabilizing selection or weakly linked to fitness are predicted to exhibit little‐to‐no inbreeding depression. Here, we quantify the extent of inbreeding depression in a range of male reproductive characters and then infer the mode of past selection on them. The use of transgenic populations of Drosophila melanogaster with red or green fluorescent‐tagged sperm heads permitted in vivo discrimination of sperm from competing males and quantification of characteristics of ejaculate composition, performance, and fate. We found that male attractiveness (mating latency) and competitive fertilization success (P₂) both show some inbreeding depression, suggesting they may have been under directional selection, whereas sperm length showed no inbreeding depression suggesting a history of stabilizing selection. However, despite having measured several sperm quality and quantity traits, our data did not allow us to discern the mechanism underlying the lowered competitive fertilization success of inbred (f = 0.50) males.     

Heterosis is common and inbreeding depression absent in natural populations of Arabidopsis thaliana

The importance of genetic drift in shaping patterns of adaptive genetic variation in nature is poorly known. Genetic drift should drive partially recessive deleterious mutations to high frequency, and inter‐population crosses may therefore exhibit heterosis (increased fitness relative to intra‐population crosses). Low genetic diversity and greater genetic distance between populations should increase the magnitude of heterosis. Moreover, drift and selection should remove strongly deleterious recessive alleles from individual populations, resulting in reduced inbreeding depression. To estimate heterosis, we crossed 90 independent line pairs of Arabidopsis thaliana from 15 pairs of natural populations sampled across Fennoscandia and crossed an additional 41 line pairs from a subset of four of these populations to estimate inbreeding depression. We measured lifetime fitness of crosses relative to parents in a large outdoor common garden (8,448 plants in total) in central Sweden. To examine the effects of genetic diversity and genetic distance on heterosis, we genotyped parental lines for 869 SNPs. Overall, genetic variation within populations was low (median expected heterozygosity = 0.02), and genetic differentiation was high (median F_ST = 0.82). Crosses between 10 of 15 population pairs exhibited significant heterosis, with magnitudes of heterosis as high as 117%. We found no significant inbreeding depression, suggesting that the observed heterosis is due to fixation of mildly deleterious alleles within populations. Widespread and substantial heterosis indicates an important role for drift in shaping genetic variation, but there was no significant relationship between fitness of crosses relative to parents and genetic diversity or genetic distance between populations.     

Evidence for overdominant selection maintaining X-linked fitness variation in Drosophila melanogaster

The role of balancing selection in maintaining genetic variation for fitness is largely unresolved. This reflects the inherent difficulty in distinguishing between models of recurrent mutation versus selection, which produce similar patterns of inbreeding depression, as well as the limitations of testing such hypotheses when fitness variation is averaged across the genome. Signatures of X-linked overdominant selection are less likely to be obscured by mutational variation because X-linked mutations are rapidly eliminated by purifying selection in males. Although models maintaining genetic variation for fitness are not necessarily mutually exclusive, a series of predictions for identifying X-linked overdominant selection can be used to separate its contribution from other underlying processes. We consider the role of overdominant selection in maintaining fitness variation in a sample of 12 X chromosomes from a population of Drosophila melanogaster. Substantial variation was observed for male reproductive success and female fecundity, with heterozygous-X genotypes exhibiting the greatest degree of variance, a finding that agrees well with predictions of the overdominance model. The importance of X-linked overdominant selection is discussed along with models of recurrent mutation and sexually antagonistic selection.     

A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal

The analysis of kin selection in subdivided populations has been hampered by the lack of well‐defined measures of genealogical relatedness in the presence of localized dispersal. Furthermore, the usual arguments underlying the definition of game‐theoretical measures of inclusive fitness are not exact under localized dispersal. We define such measures to give the first‐order effects of selection on the probability of fixation of an allele. The derived measures of kin selection and relatedness are valid in finite populations and under localized dispersal. For the infinite island model, the resulting measure of kin selection is equivalent to a previously used measure. In other cases its definition is based on definitions of relatedness which are different from the usual ones. To illustrate the approach, we reanalyse a model with localized dispersal. We consider sex ratio evolution under sex‐specific dispersal behaviour, and the results confirm the earlier conclusion that the sex ratio is biased towards the sex with the dispersal rate closer to the optimal dispersal rate in the absence of sex‐specific dispersal behaviour.     

Effective sizes of livestock populations to prevent a decline in fitness

In livestock populations, fitness may decrease due to inbreeding depression or as a negatively correlated response to artificial selection. On the other hand, fitness may increase due to natural selection. In the absence of a correlated response due to artificial selection, the critical population size at which the increase due to natural selection and the decrease due to inbreeding depression balance each other is approximately D/2_wa ², where D=the inbreeding depression of fitness with complete inbreeding, and _wa ²=the additive genetic variance of fitness. This simple expression agrees well with results from transmission probability matrix methods. If fitness declines as a correlated negative response to artificial selection, then a large increase in the critical effective population size is needed. However, if the negative response is larger than the response to natural selection, a reduction in fitness cannot be prevented. From these results it is concluded that a negative correlation between artificial and natural selection should be avoided. Effective sizes to prevent a decline in fitness are usually larger than those which maximize genetic gain of overall efficiency, i.e., the former is a more stringent restriction on effective size. In the examples presented, effective sizes ranged from 31 to 250 animals per generation.     

Assortative mating for relatedness in a large naturally occurring population of Drosophila melanogaster

New theoretical work on kin selection and inclusive fitness benefits predicts that individuals will sometimes choose close or intermediate relatives as mates to maximize their fitness. However, empirical examples supporting such predictions are rare. In this study, we look for such evidence in a natural population of Drosophila melanogaster. We compared mating and nonmating individuals to test whether mating was nonrandom with respect to relatedness. Consistent with optimal inbreeding, males were more closely related to their mate than to randomly sampled females. However, all individuals collected mating showed higher relatedness and males were not significantly more related to their mate than to other mating females. We also found a negative relationship between relatedness and fecundity. Our results are consistent with the hypothesis that inclusive fitness benefits may drive inbreeding tolerance despite direct costs to fitness; however, an experimental approach is needed to investigate the link between mate preference and relatedness.     

Sib‐mating in the ant Plagiolepis pygmaea: adaptative inbreeding?

Multiple functional queens in a colony (polygyny) and multiple mating by queens (polyandry) in social insects challenge kin selection, because they dilute inclusive fitness benefits from helping. Colonies of the ant Plagiolepis pygmaea brash contain several hundreds of multiply mated queens. Yet, within‐colony relatedness remains unexpectedly high. This stems from low male dispersal, extensive mating among relatives and adoption of young queens in the natal colony. We investigated whether inbreeding results from workers expelling foreign males, and/or from preferential mating between related partners. Our data show that workers actively repel unrelated males entering their colony, and that queens preferentially mate with related males. These results are consistent with inclusive fitness being a driving force for inbreeding: by preventing outbreeding, workers reduce erosion of relatedness within colonies due to polygyny and polyandry. That virgin queens mate preferentially with related males could result from a long history of inbreeding, which is expected to reduce depression in species with regular sibmating.     

Quantifying selection on standard metabolic rate and body mass in Drosophila melanogaster

Standard metabolic rate (SMR), defined as the minimal energy expenditure required for self‐maintenance, is a key physiological trait. Few studies have estimated its relationship with fitness, most notably in insects. This is presumably due to the difficulty of measuring SMR in a large number of very small individuals. Using high‐throughput flow‐through respirometry and a Drosophila melanogaster laboratory population adapted to a life cycle that facilitates fitness measures, we quantified SMR, body mass, and fitness in 515 female and 522 male adults. We used a novel multivariate approach to estimate linear and nonlinear selection differentials and gradients from the variance‐covariance matrix of fitness, SMR, and body mass, allowing traits specific covariates to be accommodated within a single model. In males, linear selection differentials for mass and SMR were positive and individually significant. Selection gradients were also positive but, despite substantial sample sizes, were nonsignificant due to increased uncertainty given strong SMR‐mass collinearity. In females, only nonlinear selection was detected and it appeared to act primarily on body size, although the individual gradients were again nonsignificant. Selection did not differ significantly between sexes although differences in the fitness surfaces suggest sex‐specific selection as an important topic for further study.     

Resolving the conundrum of inbreeding depression but no inbreeding avoidance: Estimating sex‐specific selection on inbreeding by song sparrows (Melospiza melodia)

Inbreeding avoidance among interacting females and males is not always observed despite inbreeding depression in offspring fitness, creating an apparent “inbreeding paradox.” This paradox could be resolved if selection against inbreeding was in fact weak, despite inbreeding depression. However, the net magnitude and direction of selection on the degree to which females and males inbreed by pairing with relatives has not been explicitly estimated. We used long‐term pedigree data to estimate phenotypic selection gradients on the degree of inbreeding that female and male song sparrows (Melospiza melodia) expressed by forming socially persistent breeding pairs with relatives. Fitness was measured as the total numbers of offspring and grand offspring contributed to the population, and as corresponding expected numbers of identical‐by‐descent allele copies, thereby accounting for variation in offspring survival, reproduction, and relatedness associated with variation in parental inbreeding. Estimated selection gradients on the degree to which individuals paired with relatives were weakly positive in females, but negative in males that formed at least one socially persistent pairing. However, males that paired had higher mean fitness than males that remained socially unpaired. These analyses suggest that net selection against inbreeding may be weak in both sexes despite strong inbreeding depression, thereby resolving the “inbreeding paradox.”     

Response to selection on cold tolerance is constrained by inbreeding

The evolutionary potential of any given population is of fundamental importance for its longer term prospects. Modern land-use practices often result in small and isolated populations, increasing the risk of extinction through reduced genetic diversity as a consequence of inbreeding or drift. Such genetic erosion may also interfere with a population's evolutionary potential. In this study, we investigate the consequences of inbreeding on evolutionary potential (the ability to increase cold resistance) in a laboratory population of the tropical butterfly Bicyclus anynana. To explore constraints on evolution, we applied artificial selection to chill-coma recovery time, starting from three levels of inbreeding (outbred control, one or two full-sibling matings). Ten generations of selection produced highly divergent phenotypes, with the lines selected for increased cold tolerance showing about 28% shorter recovery times after cold exposure relative to unselected controls. Correlated responses to selection in 10 different life-history and stress-resistance traits were essentially absent. Inbred lines showed a weaker response to selection, indicating reduced evolutionary potential and thereby constraints on evolution. Inbreeding depression was still measurable in some traits after the course of selection. Traits more closely related to fitness showed a clear fitness rebound, suggesting a trait-specific impact of purging. Our findings have important implications for the longer term survival of small populations in fragmented landscapes.     

No evidence for divergence in male harmfulness or female resistance in response to changes in the opportunity for dispersal

The outcome of sexual conflict can depend on the social environment, as males respond to changes in the inclusive fitness payoffs of harmfulness and harm females less when they compete with familiar relatives. Theoretical models also predict that if limited male dispersal predictably enhances local relatedness while maintaining global competition, kin selection can produce evolutionary divergences in male harmfulness among populations. Experimental tests of these predictions, however, are rare. We assessed rates of dispersal in female and male seed beetles Callosobruchus maculatus, a model species for studies of sexual conflict, in an experimental setting. Females dispersed significantly more often than males, but dispersing males travelled just as far as dispersing females. Next, we used experimental evolution to test whether limiting dispersal allowed the action of kin selection to affect divergence in male harmfulness and female resistance. Populations of C. maculatus were evolved for 20 and 25 generations under one of three dispersal regimens: completely free dispersal, limited dispersal and no dispersal. There was no divergence among treatments in female reproductive tract scarring, ejaculate size, mating behaviour, fitness of experimental females mated to stock males or fitness of stock females mated to experimental males. We suggest that this is likely due to insufficient strength of kin selection rather than a lack of genetic variation or time for selection. Limited dispersal alone is therefore not sufficient for kin selection to reduce male harmfulness in this species, consistent with general predictions that limited dispersal will only allow kin selection if local relatedness is independent of the intensity of competition among kin.     

Inbreeding reveals stronger net selection on Drosophila melanogaster males: implications for mutation load and the fitness of sexual females

Stronger selection on males has the potential to lower the deleterious mutation load of females, reducing the cost of sex. However, few studies have directly quantified the strength of selection for both sexes. As the magnitude of inbreeding depression (ID) is related to the strength of selection, we measured the cost of inbreeding for both males and females in a laboratory population of Drosophila melanogaster. Using a novel technique for inbreeding, we found significant ID for both juvenile viability and adult fitness in both sexes. The genetic variation responsible for this depression in fitness appeared to be recessive for adult fitness (h=0.11) and partially additive for juvenile viability (h=0.29). ID was identical across the sexes in terms of juvenile viability but was significantly more deleterious for males than females as adults, even though female X-chromosome homogamety should predispose them to a higher inbreeding load. We estimated the strength of selection on adult males to be 1.24 greater than on adult females, and this appears to be a consequence of selection arising from competition for mates. Combined with the generally positive intersexual genetic correlation for inbred lines, our results suggest that the mutation load of sexual females could be meaningfully reduced by stronger selection acting on males.     

Riding across the selection landscape: fitness consequences of annual variation in reproductive characteristics

Evolutionary models estimating phenotypic selection in character size usually assume that the character is invariant across reproductive bouts. We show that variation in the size of reproductive traits may be large over multiple events and can influence fitness in organisms where these traits are produced anew each season. With data from populations of two orchid species, Caladenia valida and Tolumnia variegata, we used Bayesian statistics to investigate the effect on the distribution in fitness of individuals when the fitness landscape is not flat and when characters vary across reproductive bouts. Inconsistency in character size across reproductive periods within an individual increases the uncertainty of mean fitness and, consequently, the uncertainty in individual fitness. The trajectory of selection is likely to be muddled as a consequence of variation in morphology of individuals across reproductive bouts. The frequency and amplitude of such changes will certainly affect the dynamics between selection and genetic drift.