Estimating quantitative genetic parameters in wild populations: a comparison of pedigree and genomic approaches

The estimation of quantitative genetic parameters in wild populations is generally limited by the accuracy and completeness of the available pedigree information. Using relatedness at genomewide markers can potentially remove this limitation and lead to less biased and more precise estimates. We estimated heritability, maternal genetic effects and genetic correlations for body size traits in an unmanaged long‐term study population of Soay sheep on St Kilda using three increasingly complete and accurate estimates of relatedness: (i) Pedigree 1, using observation‐derived maternal links and microsatellite‐derived paternal links; (ii) Pedigree 2, using SNP‐derived assignment of both maternity and paternity; and (iii) whole‐genome relatedness at 37 037 autosomal SNPs. In initial analyses, heritability estimates were strikingly similar for all three methods, while standard errors were systematically lower in analyses based on Pedigree 2 and genomic relatedness. Genetic correlations were generally strong, differed little between the three estimates of relatedness and the standard errors declined only very slightly with improved relatedness information. When partitioning maternal effects into separate genetic and environmental components, maternal genetic effects found in juvenile traits increased substantially across the three relatedness estimates. Heritability declined compared to parallel models where only a maternal environment effect was fitted, suggesting that maternal genetic effects are confounded with direct genetic effects and that more accurate estimates of relatedness were better able to separate maternal genetic effects from direct genetic effects. We found that the heritability captured by SNP markers asymptoted at about half the SNPs available, suggesting that denser marker panels are not necessarily required for precise and unbiased heritability estimates. Finally, we present guidelines for the use of genomic relatedness in future quantitative genetics studies in natural populations.     

Inheritance of an oviposition behavior by an egg parasitoid

A quantitative genetic study revealed genetic and environmental sources of variance in percentage parasitism of European corn borer egg masses and secondary sex ratios by Trichogramma nubilale. Full and half-sib groups of T. nubilale were obtained from a nested mating design, which permitted the partitioning of the variance of T. nubilale parasitism of European corn borer egg masses into additive genetic variance, maternal/dominant variance and environmental variance. A mother-daughter regression of the percentage of an egg mass parasitized allowed a determination of the direction of a potential response to selection in the event of maternal effects. No or very little additive genetic effects were associated with the percentage of eggs within a mass parasitized and secondary sex ratios, but a significant amount of the variance for both traits had a maternal and/or dominant genetic source. The relationship between mothers and daughters in egg mass parasitism was positive, and 55.4% of the progeny of a given mother had behaviors that resemble their mother. Most of the variance had an environmental and/or unknown genetic source implying potentially high phenotypic plasticity associated with all these traits. The presence of maternal effects and phenotypic plasticity could have multiple and complex effects on progeny characters and potential responses to selection.     

Dosage effects on heritability and maternal effects in diploid and triploid Chinook salmon (Oncorhynchus tshawytscha)

Induced triploidy (3N) in salmon results from a blockage of maternal meiosis II, and hence provides a unique opportunity to study dosage effects on phenotypic variance. Chinook salmon families were bred using a paternal half-sib breeding design (62 females and 31 males) and half of each resulting family was treated to induce triploidy. The paired families were used to test for dosage effects (resulting from triploidy) on (1) the distribution and magnitude of phenotypic variation, (2) narrow-sense heritability and (3) maternal effects in fitness-related traits (i.e., survival, size-at-age, relative growth rate and serum lysozyme activity). Quantitative genetic analyses were performed separately for diploid and triploid family groups. Triploidization resulted in significantly higher levels of phenotypic variance and substantial differences in patterns of variance distribution for growth and survival-related traits, although the patterns were reversed for lysozyme activity. Triploids exhibited higher narrow sense heritability values relative to diploid Chinook salmon. However, maternal effects estimates were generally lower in triploids than in diploids. Thus, the dosage effects resulting from adding an extra set of chromosomes to the Chinook salmon genome are primarily additive. Somewhat counterintuitively, however, the relative magnitude of the combined effects of dominance, epistasis and maternal effects is not affected by dosage. Our results indicate that inheritance of fitness-related quantitative traits is profoundly affected by dosage effects associated with induced triploidy, and that triploidization can result in unpredictable performance and fitness outcomes.     

CONSTANCY OF POPULATION PARAMETERS FOR LIFE-HISTORY AND FLORAL TRAITS IN RAPHANUS SATIVUS L. II. EFFECTS OF PLANTING DENSITY ON PHENOTYPE AND HERITABILITY ESTIMATES

To determine the effect of growing conditions on population parameters in wild radish, (Raphanus sativus L.: Brassicaceae), we replicated maternal and paternal half-sib families of seed across three planting densities in an experimental garden. A nested breeding design performed in the greenhouse produced 1,800 F₁ seeds sown in the garden. We recorded survivorship, measured phenotypic correlations among and estimated narrow-sense and broad-sense heritabilities (h²) of: days to germination, days to flowering, petal area, ovule number/flower, pollen production/flower, and modal pollen grain volume. Survivorship declined with increasing density, but the relative abundances of surviving families did not differ significantly among densities. Seeds in high-density plots germinated significantly faster than seeds sown in medium- or low-density plots, but they flowered significantly later. Plants in high-density plots had fewer ovules per flower than those in the other treatments. Petal area and pollen characters did not differ significantly among densities. Densities differed with respect to the number and sign of significant phenotypic correlations. Analyses of variance were conducted to detect additive genetic variance (V_a) of each trait in each density. At low density, there were significant paternal effects on flowering time and modal pollen grain volume; in medium-density plots, germination time, flowering time and ovule number exhibited significant paternal effects; in high-density plots, only pollen grain volume differed among paternal sibships. The ability to detect maternal effects on progeny phenotype also depended on density. Narrow-sense h² estimates differed markedly among density treatments for germination time, flowering time, ovule number and pollen grain volume. Maternal, paternal and error variance components were estimated for each trait and density to examine the sources of variation in narrow-sense h² across densities. Variance components did not change consistently across densities; each trait behaved differently. To provide qualitative estimates of genetic correlations between characters, correlation coefficients were estimated using paternal family means; these correlations also differed among densities. These results demonstrate that: a) planting density influences the magnitude of maternal and paternal effects on progeny phenotype, and of h² estimates, b) traits differ with respect to the density in which heritability is greatest, c) density affects the variance components that comprise heritability, but each trait behaves differently, and d) the response to selection on any target trait should result in different correlated responses of other traits, depending on density.     

The genetic basis of early‐life morphological traits and their relation to alternative male reproductive tactics in Atlantic salmon

Although heritability estimates for traits potentially under natural selection are increasingly being reported, their estimation remains a challenge if we are to understand the patterns of adaptive phenotypic change in nature. Given the potentially important role of selection on the early life phenotype, and thereby on future life history events in many fish species, we conducted a common garden experiment, using the Atlantic salmon (Salmo salar L.), with two major aims. The first objective is to determine how the site of origin, the paternal sexual tactic and additive genetic effects influence phenotypic variation of several morphological traits at hatching and emergence. The second aim is to test whether a link exists between phenotypic characteristics early in life and the incidence of male alternative tactics later in life. We found no evidence of a site or paternal effect on any morphological trait at hatching or emergence, suggesting that the spatial phenotypic differences observed in the natural river system from which these fish originated are mainly environmentally driven. However, we do find significant heritabilities and maternal effects for several traits, including body size. No direct evidence was found correlating the incidence of precocious maturation with early life characteristics. We suggest that under good growing conditions, body size and other traits at early developmental stages are not reliable cues for the surpassing of the threshold values associated with male sexual development.     

Quantifying the genetic component of phenotypic variation in unpedigreed wild plants: tailoring genomic scan for within-population use

The study of adaptive genetic variation in natural populations is central to evolutionary biology. Quantitative genetics methods, however, are hardly applicable to long-lived organisms, and current knowledge on adaptive genetic variation in wild plants mostly refers to annuals and short-lived perennials. Studies on long-lived species are essential to explore possible life-history correlates of genetic variation, selection, and trait heritability. In this paper, we propose a method based on molecular markers to quantify the genetic basis of individual phenotypic differences in wild plants under natural conditions. Rather than focusing on inferring individual relatedness to estimate the heritability of phenotypic traits, we directly estimate the proportion of observed phenotypic variance that is statistically accounted for by genotypic differences between individuals. This is achieved by (i) identifying loci that are correlated across individuals with the phenotypic trait of interest by means of an amplified fragment length polymorphism (AFLP)-based explorative genomic scan, and (ii) fitting multiple regression and linear random effect models to estimate the effects of genotype, environment and genotype × environment on phenotypes. We apply this method to estimate genotypic and environmental effects on cumulative maternal fecundity in a wild population of the long-lived Viola cazorlensis monitored for 20 years. Results show that between 56–63% (depending on estimation method) of phenotypic variance in fecundity is accounted for by genotypic differences in 11 AFLP loci that are significantly related to fecundity. Genotype × environment effects accounted for 38% of fecundity variance, which may help to explain the unexpectedly high levels of genetic variance for fecundity found.     

Maternal source of variability in the embryo development of an annual killifish

Organisms inhabiting unpredictable environments often evolve diversified reproductive bet‐hedging strategies, expressed as production of multiple offspring phenotypes, thereby avoiding complete reproductive failure. To cope with unpredictable rainfall, African annual killifish from temporary savannah pools lay drought‐resistant eggs that vary widely in the duration of embryo development. We examined the sources of variability in the duration of individual embryo development, egg production and fertilization rate in Nothobranchius furzeri. Using a quantitative genetics approach (North Carolina type II design), we found support for maternal effects rather than polyandrous mating as the primary source of the variability in the duration of embryo development. The number of previously laid eggs appeared to serve as an internal physiological cue initiating a shift from rapid‐to‐slow embryo developmental mode. In annual killifish, extensive phenotypic variability in progeny traits is adaptive, as the conditions experienced by parents have limited relevance to the offspring generation. In contrast to genetic control, with high phenotypic expression and heritability, maternal control of traits under natural selection prevents standing genetic diversity from potentially detrimental effects of selection in fluctuating environments.     

Consistency between marker- and genealogy-based heritability estimates in an experimental stand of Prosopis alba (Leguminosae)

Prosopis represents a valuable forest resource in arid and semiarid regions. Management of promising species requires information about genetic parameters, mainly the heritability (h(2)) of quantitative profitable traits. This parameter is traditionally estimated from progeny tests or half-sib analysis conducted in experimental stands. Such an approach estimates h(2) from the ratio of between-family/total phenotypic variance. These analyses are difficult to apply to natural populations of species with a long life cycle, overlapping generations, and a mixed mating system, without genealogical information. A promising alternative is the use of molecular marker information to infer relatedness between individuals and to estimate h(2) from the regression of phenotypic similarity on inferred relatedness. In the current study we compared h(2) of 13 quantitative traits estimated by these two methods in an experimental stand of P. alba, where genealogical information was available. We inferred pairwise relatedness by Ritland's method using six microsatellite loci. Relatedness and heritability estimates from molecular information were highly correlated to the values obtained from genealogical data. Although Ritland's method yields lower h(2) estimates and tends to overestimate genetic correlations between traits, this approach is useful to predict the expected relative gain of different quantitative traits under selection without genealogical information.     

VARIATION IN SEED CHARACTERS IN NEMOPHILA MENZIESII: EVIDENCE OF A GENETIC BASIS FOR MATERNAL EFFECT

A growing body of evidence indicates that phenotypic selection on juvenile traits of both plants and animals may be considerable. Because juvenile traits are typically subject to maternal effects and often have low heritabilities, adaptive responses to natural selection on these traits may seem unlikely. To determine the potential for evolutionary response to selection on juvenile traits of Nemophila menziesii (Hydrophyllaceae), we conducted two quantitative genetic studies. A reciprocal factorial cross, involving 16 parents and 1960 progeny, demonstrated a significant maternal component of variance in seed mass and additive genetic component of variance in germination time. This experiment also suggested that interaction between parents, though small, provides highly significant contributions to the variance of both traits. Such a parental interaction could arise by diverse mechanisms, including dependence of nuclear gene expression on cytoplasmic genotype, but the design of this experiment could not distinguish this from other possible causes, such as effects on progeny phenotype of interaction between the environmental conditions of both parents. The second experiment, spanning three generations with over 11,000 observations, was designed for investigation of the additive genetic variance in maternal effect, assessment of paternal effects, as well as further partitioning of the parental interaction identified in the reciprocal factorial experiment. It yielded no consistent evidence of paternal effects on seed mass, nor of parental interactions. Our inference of such interaction effects from the first experiment was evidently an artifact of failing to account for the substantial variance among fruits within crosses. The maternal effect was found to have a large additive genetic component, accounting for at least 20% of the variation in individual seed mass. This result suggests that there is appreciable potential for response to selection on seed mass through evolution of the maternal effect. We discuss aspects that may nevertheless limit response to individual selection on seed mass, including trade-offs between the size of individual seeds and germination time and between the number of seeds a maternal plant can mature and their mean size.     

Quantitative genetic parameters for wild stream‐living brown trout: heritability and parental effects

Adaptability depends on the presence of additive genetic variance for important traits. Yet few estimates of additive genetic variance and heritability are available for wild populations, particularly so for fishes. Here, we estimate heritability of length‐at‐age for wild‐living brown trout (Salmo trutta), based on long‐term mark‐recapture data and pedigree reconstruction based on large‐scale genotyping at 15 microsatellite loci. We also tested for the presence of maternal and paternal effects using a Bayesian version of the Animal model. Heritability varied between 0.16 and 0.31, with reasonable narrow confidence bands, and the total phenotypic variance increased with age. When introducing dam as an additional random effect (accounting for c. 7% of total phenotypic variance), the level of additive genetic variance and heritability decreased (0.12–0.21). Parental size (both for sires and for dams) positively influenced length‐at‐age for juvenile trout – either through direct parental effects or through genotype‐environment correlations. Length‐at‐age is a complex trait reflecting the effects of a number of physiological, behavioural and ecological processes. Our data show that fitness‐related traits such as length‐at‐age can retain high levels of additive genetic variance even when total phenotypic variance is high.     

PARENTAL EFFECTS ON SEED DEVELOPMENT AND SEED YIELD IN RAPHANUS RAPHANISTRUM: IMPLICATIONS FOR NATURAL AND SEXUAL SELECTION

The possibility that sexual selection operates in angiosperms to effect evolutionary change in polygenic traits affecting male reproductive success requires that there is additive genetic variance for these traits. I applied a half-sib breeding design to individuals of the annual, hermaphroditic angiosperm, wild radish (Raphanus raphanistrum: Brassicaceae), to estimate paternal genetic effects on, or, when possible, the narrow-sense heritability of several quantitative traits influencing male reproductive success. In spite of significant differences among pollen donors with respect to in vitro pollen tube growth rates, I detected no significant additive genetic variance in male performance with respect to the proportion of ovules fertilized, early ovule growth, the number of seeds per fruit, or mean individual seed weight per fruit. In all cases, differences among maternal plants in these traits far exceeded differences among pollen donors. Abortion rates of pollinated flowers and fertilized ovules also differed more among individuals as maternal plants than as pollen donors, suggesting strong maternal control over these processes. Significant maternal phenotypic effects in the absence of paternal genetic or phenotypic effects on reproductive traits may be due to maternal environmental effects, to non-nuclear or non-additive maternal genetic effects, or to additive genetic variance in maternal control over offspring development, independent of offspring genotype. While I could not distinguish among these alternatives, it is clear that, in wild radish, the opportunity for natural or sexual selection to effect change in seed weight or seed number per fruit appears to be greater through differences in female performance than through differences in male performance.     

QUANTITATIVE GENETICS OF SIZE AND PHENOLOGY OF LIFE-HISTORY TRAITS IN CHAMAECRISTA FASCICULATA

Despite numerous adaptive scenarios concerning the evolution of plant life-history phenologies few studies have examined the heritable basis for and genetic correlations among these phenologies. Documentation of genetic variation for and covariation among reproductive phenologies is important because it is this variation/covariation that will determine the potential for response to evolutionary forces. To address this problem, I conducted a breeding experiment to determine narrow-sense heritabilities for and genetic correlations among the phenologies of life-history events and plant size in Chamaecristafasciculata, a temperate summer annual plant species. Paternal families showed no evidence of heritable variation for two estimates of plant size, six measures of reproductive phenology or two fitness components. Similarly, paternal estimates of genetic correlations among these traits were low or zero. In contrast, maternal estimates of heritability suggested the influence of maternal parent on one estimate of plant size and four phenological traits. Likewise, maternal effects influenced maternal estimates of genetic correlations. These maternal effects can arise from three sources: endosperm nuclear, cytoplasmic genetic and/or maternal phenotypic. The degree to which the phenology of one life-history trait acts as a constraint on the evolution of other phenological traits depends on the source of the maternal influence in this species.     

Genetic parameters for direct and maternal effects on body weights of Draa goats

Genetic parameters and (co)variance components were estimated for weights at birth and at 30, 90 and 180 days of age for Draa goat maintained at Ouarzazate station over a period of 18 years (1988–2005). Records of 1498 kids, the progeny of 46 sires and 404 dams were used in the study. Analyses were carried out by restricted maximum likelihood. Six different animal models including or ignoring maternal genetic or permanent environmental effects were fitted for all traits. The Model 2 with only permanent environmental maternal effects seemed most suitable. Estimates of direct heritability from this model were 0.16 for birth weight and 0.07, 0.11 and 0.11 for weights at 30, 90 and 180 days, respectively. Maternal heritability estimates varied from 0.00 to 0.24 for all traits according to the model used (Models 4–6). Bivariate analysis by Model 2 was also used to estimate genetic correlations between traits. The estimates of genetic and phenotypic correlations among weights were positive and intermediate to high in value. Despite the low estimated heritabilities of body weight traits of Draa goat, there is a small genetic variability that may be exploited to improve growth performance.     

Pedigree-Free Estimates of Heritability in the Wild: Promising Prospects for Selfing Populations

Estimating the genetic variance available for traits informs us about a population’s ability to evolve in response to novel selective challenges. In selfing species, theory predicts a loss of genetic diversity that could lead to an evolutionary dead-end, but empirical support remains scarce. Genetic variability in a trait is estimated by correlating the phenotypic resemblance with the proportion of the genome that two relatives share identical by descent (‘realized relatedness’). The latter is traditionally predicted from pedigrees (Φ_A: expected value) but can also be estimated using molecular markers (average number of alleles shared). Nevertheless, evolutionary biologists, unlike animal breeders, remain cautious about using marker-based relatedness coefficients to study complex phenotypic traits in populations. In this paper, we review published results comparing five different pedigree-free methods and use simulations to test individual-based models (hereafter called animal models) using marker-based relatedness coefficients, with a special focus on the influence of mating systems. Our literature review confirms that Ritland’s regression method is unreliable, but suggests that animal models with marker-based estimates of relatedness and genomic selection are promising and that more testing is required. Our simulations show that using molecular markers instead of pedigrees in animal models seriously worsens the estimation of heritability in outcrossing populations, unless a very large number of loci is available. In selfing populations the results are less biased. More generally, populations with high identity disequilibrium (consanguineous or bottlenecked populations) could be propitious for using marker-based animal models, but are also more likely to deviate from the standard assumptions of quantitative genetics models (non-additive variance).     

Estimation of quantitative genetic parameters using marker-inferred relatedness in Japanese flounder: a case study of upward bias

Marker-based methods for estimating heritability have been proposed as an effective means to study quantitative traits in long-lived organisms and natural populations. However, practical examinations to evaluate the usefulness and robustness of a regression method are limited. Using several quantitative traits of Japanese flounder Paralichthys olivaceus, the present study examined the influence of relatedness estimator and population structure on the estimation of heritability and genetic correlation under a regression method with 7 microsatellite loci. Significant heritability and genetic correlation were detected for several quantitative traits in 2 laboratory populations but not in a natural population. In the laboratory populations, upward bias in heritability appeared depending on the relatedness estimators and the populations. Upward bias in heritability increased with decreasing the actual variance of relatedness, suggesting that the estimates of heritability under the regression method tend to be overestimated due to the underestimation of the actual variance of relatedness. Therefore, relationship structure and precise estimation of relatedness are critical for applying this method.     

Iterative kriging for removing spatial autocorrelation in analysis of forest genetic trials

Conventional analysis of spatially correlated data in inadequately blocked field genetic trials may give erroneous results that would seriously affect breeding decisions. Forest genetic trials are commonly very large and strongly heterogeneous, so adjustments for micro-environmental heterogeneity become indispensable. This study explores the use of geostatistics to account for the spatial autocorrelation in four Pinus pinaster Ait. progeny trials established on hilly and irregular terrains with a randomized complete block design and large blocks. Data of five different traits assessed at age 8 were adjusted using an iterative method based on semivariograms and kriging, and the effects on estimates of variance components, heritability, and family effects were evaluated in relation to conventional analysis. Almost all studied traits showed nonrandom spatial structures. Therefore, after the adjustments for spatial autocorrelation, the block and family × block variance components, which were extremely high in the conventional analysis, almost disappeared. The reduction of the interaction variance was recovered by the family variance component, resulting in higher heritability estimates. The removal of the spatial autocorrelation also affected the estimation of family effects, resulting in important changes in family ranks after the spatial adjustments. Comparison among families was also greatly improved due to higher accuracy of the family effect estimations. The analysis improvement was larger for growth traits, which showed the strongest spatial heterogeneity, but was also evident for other traits such as straightness or number of whorls. The present paper demonstrates how spatial autocorrelation can drastically affect the analysis of forest genetic trials with large blocks. The iterative kriging procedure presented in this paper is a promising tool to account for this spatial heterogeneity.     

Heritability and genetic correlations of personality traits in a wild population of yellow‐bellied marmots (Marmota flaviventris)

Describing and quantifying animal personality is now an integral part of behavioural studies because individually distinctive behaviours have ecological and evolutionary consequences. Yet, to fully understand how personality traits may respond to selection, one must understand the underlying heritability and genetic correlations between traits. Previous studies have reported a moderate degree of heritability of personality traits, but few of these studies have either been conducted in the wild or estimated the genetic correlations between personality traits. Estimating the additive genetic variance and covariance in the wild is crucial to understand the evolutionary potential of behavioural traits. Enhanced environmental variation could reduce heritability and genetic correlations, thus leading to different evolutionary predictions. We estimated the additive genetic variance and covariance of docility in the trap, sociability (mirror image stimulation), and exploration and activity in two different contexts (open‐field and mirror image simulation experiments) in a wild population of yellow‐bellied marmots (Marmota flaviventris). We estimated both heritability of behaviours and of personality traits and found nonzero additive genetic variance in these traits. We also found nonzero maternal, permanent environment and year effects. Finally, we found four phenotypic correlations between traits, and one positive genetic correlation between activity in the open‐field test and sociability. We also found permanent environment correlations between activity in both tests and docility and exploration in the MIS test. This is one of a handful of studies to adopt a quantitative genetic approach to explain variation in personality traits in the wild and, thus, provides important insights into the potential variance available for selection.     

Real-time patterns of pollen flow in the wild-service tree, Sorbus torminalis (Rosaceae). III. Mating patterns and the ecological maternal neighborhood

Understanding the role of mother plants as pollen recipients in shaping mating patterns is essential for understanding the evolution of populations and in particular to predict the consequence of habitat fragmentation. Here, we investigated variation in mating patterns due to maternal phenotypic traits, phenological variance, and landscape features in Sorbus torminalis, a hermaphroditic, insect-pollinated and low-density, European temperate forest tree. The diversity and composition of pollen clouds received by maternal trees in S. torminalis were mainly determined by their conspecific neighborhood: isolated individuals sample more diversity through more even paternal contributions, low relatedness among paternal genes, and high rates of long-distance pollen dispersal within their progenies. Maternal phenotypic traits related to pollinator attractiveness also had an effect, but only when competition was strong: in this case, larger mother trees with more flowers sampled more diversity. The floral architecture of S. torminalis, with multiple-seeded fruit, strongly shaped mating patterns, with higher levels of correlated paternity among seeds belonging to the same fruit (30% full sibs) than among seeds belonging to different fruits (14% full sibs). Finally, flowering phenology affected the distribution of diversity among maternal pollen clouds, but the earliest and latest mother trees did not receive less diversity of pollen than the others.     

Evolution of Adaptation and Mate Choice: Parental Relatedness Affects Expression of Phenotypic Variance in a Natural Population

Mating between relatives generally results in reduced offspring viability or quality, suggesting that selection should favor behaviors that minimize inbreeding. However, in natural populations where searching is costly or variation among potential mates is limited, inbreeding is often common and may have important consequences for both offspring fitness and phenotypic variation. In particular, offspring morphological variation often increases with greater parental relatedness, yet the source of this variation, and thus its evolutionary significance, are poorly understood. One proposed explanation is that inbreeding influences a developing organism’s sensitivity to its environment and therefore the increased phenotypic variation observed in inbred progeny is due to greater inputs from environmental and maternal sources. Alternatively, changes in phenotypic variation with inbreeding may be due to additive genetic effects alone when heterozygotes are phenotypically intermediate to homozygotes, or effects of inbreeding depression on condition, which can itself affect sensitivity to environmental variation. Here we examine the effect of parental relatedness (as inferred from neutral genetic markers) on heritable and nonheritable components of developmental variation in a wild bird population in which mate choice is often constrained, thereby leading to inbreeding. We found greater morphological variation and distinct contributions of variance components in offspring from highly related parents: inbred offspring tended to have greater environmental and lesser additive genetic variance compared to outbred progeny. The magnitude of this difference was greatest in late-maturing traits, implicating the accumulation of environmental variation as the underlying mechanism. Further, parental relatedness influenced the effect of an important maternal trait (egg size) on offspring development. These results support the hypothesis that inbreeding leads to greater sensitivity of development to environmental variation and maternal effects, suggesting that the evolutionary response to selection will depend strongly on mate choice patterns and population structure.     

Genomic best linear unbiased prediction method including imprinting effects for genomic evaluation

Background

Genomic best linear unbiased prediction (GBLUP) is a statistical method used to predict breeding values using single nucleotide polymorphisms for selection in animal and plant breeding. Genetic effects are often modeled as additively acting marker allele effects. However, the actual mode of biological action can differ from this assumption. Many livestock traits exhibit genomic imprinting, which may substantially contribute to the total genetic variation of quantitative traits. Here, we present two statistical models of GBLUP including imprinting effects (GBLUP-I) on the basis of genotypic values (GBLUP-I1) and gametic values (GBLUP-I2). The performance of these models for the estimation of variance components and prediction of genetic values across a range of genetic variations was evaluated in simulations.

Results

Estimates of total genetic variances and residual variances with GBLUP-I1 and GBLUP-I2 were close to the true values and the regression coefficients of total genetic values on their estimates were close to 1. Accuracies of estimated total genetic values in both GBLUP-I methods increased with increasing degree of imprinting and broad-sense heritability. When the imprinting variances were equal to 1.4% to 6.0% of the phenotypic variances, the accuracies of estimated total genetic values with GBLUP-I1 exceeded those with GBLUP by 1.4% to 7.8%. In comparison with GBLUP-I1, the superiority of GBLUP-I2 over GBLUP depended strongly on degree of imprinting and difference in genetic values between paternal and maternal alleles. When paternal and maternal alleles were predicted (phasing accuracy was equal to 0.979), accuracies of the estimated total genetic values in GBLUP-I1 and GBLUP-I2 were 1.7% and 1.2% lower than when paternal and maternal alleles were known.

Conclusions

This simulation study shows that GBLUP-I1 and GBLUP-I2 can accurately estimate total genetic variance and perform well for the prediction of total genetic values. GBLUP-I1 is preferred for genomic evaluation, while GBLUP-I2 is preferred when the imprinting effects are large, and the genetic effects differ substantially between sexes.