Mate choice for non-additive genetic benefits: a resolution to the lek paradox

In promiscuous mating systems, females often show a consistent preference to mate with one or a few males, presumably to acquire heritable genetic benefits for their offspring. However, strong directional selection should deplete additive genetic variation in fitness and consequently any benefit to expressing the preference by females (referred to as the lek paradox). Here, we provide a novel resolution that examines non-additive genetic benefits, such as overdominance or inbreeding, as a source of genetic variation. Focusing on the inbreeding coefficient f and overdominance effects, we use dynamic models to show that (1) f can be inherited from sire to offspring, (2) populations with females that express a mating preferences for outbred males (low f) maintain higher genetic variation than populations with females that mate randomly, and (3) preference alleles for outbred males can invade populations even when the alleles are associated with a fecundity cost. We show that non-additive genetic variation due to overdominance can be converted to additive genetic variation and becomes “heritable” when the frequencies of alternative homozygous genotypes at fitness loci deviate from equality. Unlike previous models that assume an infinite population size, we now show that genetic drift in finite populations can lead to the necessary deviations in the frequencies of homozygous genotypes. We also show that the “heritability of f,” and hence the benefit to a mating preference for non-additive genetic benefits, is highest in small populations and populations in which a smaller number of loci contribute to fitness via overdominance. Our model contributes to the solution of the lek paradox.     

Genetic benefits of extreme sequential polyandry in a terrestrial‐breeding frog

Sequential polyandry may evolve as an insurance mechanism to reduce the risk of females choosing mates who are genetically inferior (intrinsic male quality hypothesis) or genetically incompatible (genetic incompatibility hypothesis). The prevalence of such indirect benefits remains controversial, however, because studies estimating the contributions of additive and nonadditive sources of genetic variation to offspring fitness have been limited to a small number of taxonomic groups. Here, we used artificial fertilization techniques combined with a crossclassified breeding design (North Carolina Type II) to simultaneously test the “good genes hypothesis” and the “genetic incompatibility hypothesis” in the brown toadlet (Pseudophryne bibronii); a terrestrial‐breeding species with extreme sequential polyandry. Our results revealed no significant additive or nonadditive genetic effects on fertilization success. Moreover, they revealed no significant additive genetic effects, but highly significant nonadditive genetic effects (sire by dam interaction effects), on hatching success and larval survival to initial and complete metamorphosis. Taken together, these results indicate that offspring viability is significantly influenced by the combination of parental genotypes, and that negative interactions between parental genetic elements manifest during embryonic and larval development. More broadly, our findings provide quantitative genetic evidence that insurance against genetic incompatibility favors the evolution and maintenance of sequential polyandry.     

Additive genetic variation and the distribution of QTN effects among sites

Early quantitative genetic theories emphasize the distribution of gene effects at individual loci or the distribution of mutant effects in maintaining quantitative genetic variation, but infrequently stress the distribution of gene effects among loci. In this study, we analyse the effects of the distribution of quantitative trait nucleotides (QTN) effects among sites under artificial and stabilizing selection. Wright's formula is applied to describing the density distribution of allele frequencies of multiple diallelic QTN at the equilibrium of mutation-drift-selection. Our results demonstrate that the distribution of QTN effects among sites can affect additive genetic variation in terms of total additive variance, average gene diversity, per-class contribution of QTN effects and per-QTN contribution. When the distribution of QTN effects among sites is changed from L-shaped to bell-shaped or to be a flatter, both the total additive variance and the average gene diversity are changed. Per-class and per-QTN contributions exhibit different distribution patterns. The L-shaped distribution indicates the predominant role of the aggregative effects from the QTN of small finite effects. The bell-shaped or flatter distributions indicate the predominance of the QTN of intermediate and large effects. These predictions highlight the significance of the distribution of QTN effects among sites in interpreting the maintenance of quantitative genetic variation at the fine genome scale.     

Age-specific genetic and maternal effects in fecundity of preindustrial Finnish women

A population's potential for evolutionary change depends on the amount of genetic variability expressed in traits under selection. Studies attempting to measure this variability typically do so over the life span of individuals, but theory suggests that the amount of additive genetic variance can change during the course of individuals' lives. Here we use pedigree data from historical Finns and a quantitative genetic framework to investigate how female fecundity, throughout an individual's reproductive life, is influenced by "maternal" versus additive genetic effects. We show that although maternal effects explain variation in female fecundity early in life, these effects wane with female age. Moreover, this decline in maternal effects is associated with a concomitant increase in additive genetic variance with age. Our results thus highlight that single over-lifetime estimates of trait heritability may give a misleading view of a trait's potential to respond to changing selection pressures.     

Males influence maternal effects that promote sexual selection: a quantitative genetic experiment with dung beetles Onthophagus taurus

Recently, doubt has been cast on studies supporting good genes sexual selection by the suggestion that observed genetic benefits for offspring may be confounded by differential maternal allocation. In traditional analyses, observed genetic sire effects on offspring phenotype may result from females allocating more resources to the offspring of attractive males. However, maternal effects such as differential allocation may represent a mechanism promoting genetic sire effects, rather than an alternative to them. Here we report results from an experiment on the horned dung beetle Onthophagus taurus, in which we directly compare genetic sire effects with maternal effects that are dependent on sire phenotype. We found strong evidence that mothers provide more resources to offspring when mated with large-horned males. There were significant heritabilities for both horn length and body size, but when differential maternal effects were controlled, the observed estimates of genetic variance were greatly reduced. Our experiment provides evidence that differential maternal effects may amplify genetic effects on offspring traits that are closely related to fitness. Thus, our results may partly explain the relatively high coefficients of additive genetic variation observed in fitness-related traits and provide empirical support for the theoretical argument that maternal effects can play an important role in evolution.     

Paternal Genetic Effects on Offspring Swimming Performance Vary with Age of Juvenile Chinook Salmon, Oncorhynchus tshawytscha

While fish swimming behaviour has been extensively studied, the parental genetic basis of this critical behaviour has been rarely examined, especially past the earliest stages of development. We used a quantitative genetic breeding design to measure the critical swimming speed (U-crit) of offspring (15 and 18 weeks post-hatch) from 36 families of Chinook salmon (Oncorhynchus tshawytscha), a species with a nonresource-based mating system. We investigated the roles of dam, sire, and dam × sire on offspring U-crit, and estimated contributions of additive and nonadditive genetic effects and maternal effects to phenotypic variation in U-crit at both ages. We also used existing ‘high-survival’ and ‘low-survival’ lines of Chinook to determine if these two lines show differences in U-crit. At 15 weeks, there were no significant genetic effects, but at 18 weeks there were significant sire effects. Furthermore, additive genetic effects increased from 26 to 100 % from 15 to 18 weeks post-hatch. The two survival lines also showed differences in U-crit at 18 weeks post-hatch, with higher U-crit associated with “high-survival” sires. Collectively, the present study provides evidence for increasing importance of paternal identity (additive genetic variation) on swimming as juvenile offspring age. Given that mortality is high in young Pacific salmon and swimming ability is crucial, the sire effects could potentially shape survival though subsequent developmental stages. The change in the magnitude of effects in the present study indicates that future research should investigate genetic effects across multiple stages for better understanding of how phenotypic traits could respond to selection.     

THE GENETIC ARCHITECTURE OF WING SIZE DIVERGENCE AT VARYING SPATIAL SCALES ALONG A BODY SIZE CLINE IN DROSOPHILA MELANOGASTER

Latitudinal clines in quantitative traits are common, but surprisingly little is known about the genetic bases of these divergences and how they vary within and between clines. Here, we use line‐cross analysis to investigate the genetic architecture of wing size divergences at varying spatial scales along a body size cline in Drosophila melanogaster. Our results revealed that divergences in wing size along the cline were due to strong additive effects. Significant nonadditive genetic effects, including epistasis and maternal effects, were also detected, but they were relatively minor in comparison to the additive effects and none were common to all crosses. There was no evidence of increased epistasis in crosses between more geographically distant populations and, unlike in previous studies, we found no significant dominance effects on wing size in any cross. Our results suggest there is little variation in the genetic control of wing size along the length of the Australian cline. They also highlight marked inconsistencies in the magnitude of dominance effects across studies, which may reflect different opportunities for mutation accumulation while lines are in laboratory culture.     

Context-dependent genetic benefits of polyandry in a marine hermaphrodite

Numerous studies emphasize the potential indirect (genetic) benefits of polyandry in animals with resource-free mating systems. In this paper, we examine the potential for these benefits to fuel sexual selection and polyandry in the hermaphroditic ascidian Pyura stolonifera. Individuals were designated either sire (sperm producers) or dam (egg producers) at random and crossed in a North Carolina II breeding design to produce both paternal and maternal half siblings for our quantitative genetic analysis. We then partitioned the phenotypic variance in fertilization and hatching rates into additive and non-additive variance components. We found significant additive variance attributable to sire and dam effects at fertilization and hatching, suggesting the potential for selection to favour individuals carrying intrinsically 'good genes' for these traits. In separate analyses involving monandrous and polyandrous clutches, we found that both traits were elevated under polyandry, but the difference in hatching rates was due entirely to the difference in fertilization rates between treatments. When the hatching rates were standardized to account for variance at fertilization, there was no overall net benefit of polyandry for this trait. Despite this, we found that hatching success declined with increasing embryo densities, and that the slope of this decline was significantly greater in monandrous than polyandrous clutches. Hence, selection on embryo viability may still favour polyandry under restricted environmental conditions. Nevertheless, our results caution against interpreting elevated hatching success as an indirect genetic benefit of polyandry when variance in fertilization is not controlled.     

Genetic correlation between resting metabolic rate and exploratory behaviour in deer mice (Peromyscus maniculatus)

According to the 'pace-of-life' syndrome hypothesis, differences in resting metabolic rate (RMR) should be genetically associated with exploratory behaviour. A large number of studies reported significant heritability for both RMR and exploratory behaviour, but the genetic correlation between the two has yet to be documented. We used a quantitative genetic approach to decompose the phenotypic (co)variance of several metabolic and behavioural measures into components of additive genetic, common environment and permanent environment variance in captive deer mice. We found significant additive genetic variance for two mass-independent metabolic measures (RMR and the average metabolic rate throughout the respirometry run) and two behavioural measures (time spent in centre and distance moved in a novel environment). We also detected positive additive genetic correlation between mass-independent RMR and distance moved (r(A) = 0.78 ± 0.23). Our results suggest that RMR and exploratory behaviour are functionally integrated traits in deer mice, providing empirical support for one of the connections within the pace-of-life syndrome hypothesis.     

Comparing Evolvability and Variability of Quantitative Traits

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.     

COMPARING STRENGTHS OF DIRECTIONAL SELECTION: HOW STRONG IS STRONG?

The fundamental equation in evolutionary quantitative genetics, the Lande equation, describes the response to directional selection as a product of the additive genetic variance and the selection gradient of trait value on relative fitness. Comparisons of both genetic variances and selection gradients across traits or populations require standardization, as both are scale dependent. The Lande equation can be standardized in two ways. Standardizing by the variance of the selected trait yields the response in units of standard deviation as the product of the heritability and the variance-standardized selection gradient. This standardization conflates selection and variation because the phenotypic variance is a function of the genetic variance. Alternatively, one can standardize the Lande equation using the trait mean, yielding the proportional response to selection as the product of the squared coefficient of additive genetic variance and the mean-standardized selection gradient. Mean-standardized selection gradients are particularly useful for summarizing the strength of selection because the mean-standardized gradient for fitness itself is one, a convenient benchmark for strong selection. We review published estimates of directional selection in natural populations using mean-standardized selection gradients. Only 38 published studies provided all the necessary information for calculation of mean-standardized gradients. The median absolute value of multivariate mean-standardized gradients shows that selection is on average 54% as strong as selection on fitness. Correcting for the upward bias introduced by taking absolute values lowers the median to 31%, still very strong selection. Such large estimates clearly cannot be representative of selection on all traits. Some possible sources of overestimation of the strength of selection include confounding environmental and genotypic effects on fitness, the use of fitness components as proxies for fitness, and biases in publication or choice of traits to study.     

DIRECT AND INDIRECT SEXUAL SELECTION AND QUANTITATIVE GENETICS OF MALE TRAITS IN GUPPIES (POECILIA RETICULATA)

Abstract.— The ornamentation and displays on which sexual attractiveness and thus mating success are based may be complex and comprise several traits. Predicting the outcome of sexual selection on such complex phenotypes requires an understanding of both the direct operation of selection on each trait and the indirect consequences of selection operating directly on genetically correlated traits. Here we report the results of a quantitative genetic analysis of the ornamentation, sexual attractiveness, and mating success of male guppies (Poecilia reticulata). We analyze male ornamentation both from the point of view of single ornamental traits (e.g., the area of each color) and of composite measures of the way the entire pattern is likely to be perceived by females (e.g., the mean and contrast in chroma). We demonstrate that there is substantial additive genetic variation in almost all measures of male ornamentation and that much of this variation may be Y linked. Attractiveness and mating success are positively correlated at the phenotypic and genetic level. Orange area and chroma, the area of a male's tail, and the color contrast of his pattern overall are positively correlated with attractiveness and/or mating success at the phenotypic and genetic levels. Using attractiveness and mating success as measures of fitness, we estimate gradients of linear directional sexual selection operating on each male trait and use equations of multivariate evolutionary change to predict the response of male ornamentation to this sexual selection. From these analyses, we predict that indirect selection may have important effects on the evolution of male guppy color patterns.     

A genetic model involving fetal effects on traits of the dam

The genetic fetal effects model shows that the usual sire effect is composed of one-half the direct additive genetic value and one-fourth of the fetal additive genetic value of the sire. The usual sire component of variance is actually the variance of that function. Genetic covariances between records of relatives influenced by fetuses of related sires can easily be written. If the magnitude of fetal sire effects is such that nonrandom use of fetal sires on daughters of sires being evaluated on daughter performance results in bias, the bias can be eliminated (Henderson 1975) by considering the fetal sire effects to be fixed effects. Some reduction in prediction error variance is likely by including fetal sire in the sire evaluation model.     

Quantitative genetic analysis of skin reflectance: a multivariate approach.

Skin color is a polygenically determined quantitative trait. Although it has been used extensively in studies of between-population variation, there have been relatively few studies of the inheritance of skin color. In this article we use measurements on 359 members of the Jirel population of eastern Nepal to assess the heritabilities and additive genetic correlations of three skin reflectance measures. Skin color was measured at the upper inner arm site at three wavelengths. A maximum likelihood approach was used to estimate sex and age effects on skin reflectance, heritabilities, and phenotypic variances at each wavelength and both additive genetic and environmental correlations between wavelengths. This technique incorporated information from 36 pedigrees with 2-25 members and 173 independent individuals. Likelihood ratio tests were used to assess the significance of specific variance/covariance components. The results indicate that skin reflectances are moderately heritable at all three wavelengths. The pairwise phenotypic correlations ranged from 0.76 to 0.88. The observed additive genetic correlations were not significantly different from 1.00, suggesting that the same loci influence variation at each wavelength. This evidence for relatively complete pleiotropy implies that measurements at multiple wavelengths yield little additional genetic information, although they may be useful for reducing measurement error. Based on estimates of the genetic and phenotypic covariance matrices, we determined that skin reflectance measurements are expected to provide only as much information for assessing local between-population genetic variation as a single two-allele polymorphic marker. Therefore microevolutionary studies based on skin color variation should be viewed with caution.     

Strong habitat and weak genetic effects shape the lifetime reproductive success in a wild clownfish population

The relative contributions of environmental, maternal and additive genetic factors to the Lifetime reproductive success (LRS) determine whether species can adapt to rapid environmental change. Yet to date, studies quantifying LRS across multiple generations in marine species in the wild are non‐existent. Here we used 10‐year pedigrees resolved for a wild orange clownfish population from Kimbe Island (PNG) and a quantitative genetic linear mixed model approach to quantify the additive genetic, maternal and environmental contributions to variation in LRS for the self‐recruiting portion of the population. We found that the habitat of the breeder, including the anemone species and geographic location, made the greatest contribution to LRS. There were low to negligible contributions of genetic and maternal factors equating with low heritability and evolvability. Our findings imply that our population will be susceptible to short‐term, small‐scale changes in habitat structure and may have limited capacity to adapt to these changes.     

Genetic quality and offspring performance in Chinook salmon: implications for supportive breeding

Each year salmon and other fishes are caught and used for supportive breeding programs that attempt to augment natural populations that are threatened with extinction. These programs typically mate individuals randomly and as such they overlook the importance of genetic quality to offspring fitness and ultimately to ensuring population health. Here, we use Chinook salmon (Oncorhynchus tshawytscha) and a fully crossed quantitative genetic breeding design to partition genetic variance in offspring performance (growth and survival) to additive and non-additive genetic effects as well as maternal effects. We show that these three effects contribute about equally to the variation in survival, but only non-additive genetic and maternal effects contribute to variation in growth. Some of the genetic effects could be assigned to variation at the class IIB locus of the major histocompatibility complex, but the maternal effects were not associated with egg size and we found no relationship between dam phenotypic measures and offspring survival or growth. We also found no relationship between sire sexually selected characters and offspring survival or growth, which is inconsistent with a “good genes” hypothesis. Finally, we show that incorporation of genetic quality into supportive breeding programs can increase offspring growth or survival by between 3% and 19% during the endogenous feeding stage alone, and projections to adulthood suggest that survivorship could be over four fold higher. Electronic Supplementary Material  Supplementary material is available in the online version of this article at and is accessible for authorised users.     

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.     

Parental effects on embryonic viability and growth in Arctic charr Salvelinus alpinus at two incubation temperatures

The parental influences on three progeny traits (survival to eyed‐embryo stage, post‐hatching body length and yolk‐sac volume) of Arctic charr Salvelinus alpinus were studied under two thermal conditions (2 and 7° C) using a factorial mating design. The higher temperature resulted in elevated mortality rates and less advanced development at hatching. Survival was mostly attributable to maternal effects at both temperatures, but the variation among families was dependent on egg size only at the low temperature. No additive genetic variation (or pure sire effect) could be observed, whereas the non‐additive genetic effects (parental combination) contributed to offspring viability at 2° C. In contrast, any observable genetic variance in survival was lost at 7° C, most likely due to the increased environmental variance. Irrespective of temperature, dam and sire–dam interaction contributed significantly to the phenotypic variation in both larval length and yolk size. A significant proportion of the variation in larval length was also due to the sire effect at 2° C. Maternal effects were mediated partly through egg size, but as a whole, they decreased in importance at the high temperature, enabling a concomitant increase in non‐additive genetic effects. For larval length, however, the additive component, like maternal effects, decreased at 7° C. The present results suggest that an exposure to thermal stress during incubation can modify the genetic architecture of early developmental traits in S. alpinus and presumably constrain their short‐term adaptive potential and evolvability by increasing the amount of environmentally induced variation.     

GWAPower: a statistical power calculation software for genome-wide association studies with quantitative traits

Background

In designing genome-wide association (GWA) studies it is important to calculate statistical power. General statistical power calculation procedures for quantitative measures often require information concerning summary statistics of distributions such as mean and variance. However, with genetic studies, the effect size of quantitative traits is traditionally expressed as heritability, a quantity defined as the amount of phenotypic variation in the population that can be ascribed to the genetic variants among individuals. Heritability is hard to transform into summary statistics. Therefore, general power calculation procedures cannot be used directly in GWA studies. The development of appropriate statistical methods and a user-friendly software package to address this problem would be welcomed.

Results

This paper presents GWAPower, a statistical software package of power calculation designed for GWA studies with quantitative traits, where genetic effect is defined as heritability. Based on several popular one-degree-of-freedom genetic models, this method avoids the need to specify the non-centrality parameter of the F-distribution under the alternative hypothesis. Therefore, it can use heritability information directly without approximation. In GWAPower, the power calculation can be easily adjusted for adding covariates and linkage disequilibrium information. An example is provided to illustrate GWAPower, followed by discussions.

Conclusions

GWAPower is a user-friendly free software package for calculating statistical power based on heritability in GWA studies with quantitative traits. The software is freely available at: http://dl.dropbox.com/u/10502931/GWAPower.zip     

Costs of resistance: genetic correlations and potential trade-offs in an insect immune system

Theory predicts that natural selection will erode additive genetic variation in fitness-related traits. However, numerous studies have found considerable heritable variation in traits related to immune function, which should be closely linked to fitness. This could be due to trade-offs maintaining variation in these traits. We used the Egyptian cotton leafworm, Spodoptera littoralis, as a model system to examine the quantitative genetics of insect immune function. We estimated the heritabilities of several different measures of innate immunity and the genetic correlations between these immune traits and a number of life history traits. Our results provide the first evidence for a potential genetic trade-off within the insect immune system, with antibacterial activity (lysozyme-like) exhibiting a significant negative genetic correlation with haemocyte density, which itself is positively genetically correlated with both haemolymph phenoloxidase activity and cuticular melanization. We speculate on a potential trade-off between defence against parasites and predators, mediated by larval colour, and its role in maintaining genetic variation in traits under natural selection.