Heritability estimates from genomewide relatedness matrices in wild populations: Application to a passerine,using a small sample size

Genomic developments have empowered the investigation of heritability in wild populations directly from genomewide relatedness matrices (GRM). Such GRM‐based approaches can in particular be used to improve or substitute approaches based on social pedigree (PED‐social). However, measuring heritability from GRM in the wild has not been widely applied yet, especially using small samples and in nonmodel species. Here, we estimated heritability for four quantitative traits (tarsus length, wing length, bill length and body mass), using PED‐social, a pedigree corrected by genetic data (PED‐corrected) and a GRM from a small sample (n = 494) of blue tits from natural populations in Corsica genotyped at nearly 50,000 filtered SNPs derived from RAD‐seq. We also measured genetic correlations among traits, and we performed chromosome partitioning. Heritability estimates were slightly higher when using GRM compared to PED‐social, and PED‐corrected yielded intermediate values, suggesting a minor underestimation of heritability in PED‐social due to incorrect pedigree links, including extra‐pair paternity, and to lower information content than the GRM. Genetic correlations among traits were similar between PED‐social and GRM but credible intervals were very large in both cases, suggesting a lack of power for this small data set. Although a positive linear relationship was found between the number of genes per chromosome and the chromosome heritability for tarsus length, chromosome partitioning similarly showed a lack of power for the three other traits. We discuss the usefulness and limitations of the quantitative genetic inferences based on genomic data in small samples from wild populations.     

RAD‐sequencing for estimating genomic relatedness matrix‐based heritability in the wild: A case study in roe deer

Estimating the evolutionary potential of quantitative traits and reliably predicting responses to selection in wild populations are important challenges in evolutionary biology. The genomic revolution has opened up opportunities for measuring relatedness among individuals with precision, enabling pedigree‐free estimation of trait heritabilities in wild populations. However, until now, most quantitative genetic studies based on a genomic relatedness matrix (GRM) have focused on long‐term monitored populations for which traditional pedigrees were also available, and have often had access to knowledge of genome sequence and variability. Here, we investigated the potential of RAD‐sequencing for estimating heritability in a free‐ranging roe deer (Capreolous capreolus) population for which no prior genomic resources were available. We propose a step‐by‐step analytical framework to optimize the quality and quantity of the genomic data and explore the impact of the single nucleotide polymorphism (SNP) calling and filtering processes on the GRM structure and GRM‐based heritability estimates. As expected, our results show that sequence coverage strongly affects the number of recovered loci, the genotyping error rate and the amount of missing data. Ultimately, this had little effect on heritability estimates and their standard errors, provided that the GRM was built from a minimum number of loci (above 7,000). Genomic relatedness matrix‐based heritability estimates thus appear robust to a moderate level of genotyping errors in the SNP data set. We also showed that quality filters, such as the removal of low‐frequency variants, affect the relatedness structure of the GRM, generating lower h² estimates. Our work illustrates the huge potential of RAD‐sequencing for estimating GRM‐based heritability in virtually any natural population.     

The influence of nonrandom extra‐pair paternity on heritability estimates derived from wild pedigrees

Quantitative genetic analysis is often fundamental for understanding evolutionary processes in wild populations. Avian populations provide a model system due to the relative ease of inferring relatedness among individuals through observation. However, extra‐pair paternity (EPP) creates erroneous links within the social pedigree. Previous work has suggested this causes minor underestimation of heritability if paternal misassignment is random and hence not influenced by the trait being studied. Nevertheless, much literature suggests numerous traits are associated with EPP and the accuracy of heritability estimates for such traits remains unexplored. We show analytically how nonrandom pedigree errors can influence heritability estimates. Then, combining empirical data from a large great tit (Parus major) pedigree with simulations, we assess how heritability estimates derived from social pedigrees change depending on the mode of the relationship between EPP and the focal trait. We show that the magnitude of the underestimation is typically small (<15%). Hence, our analyses suggest that quantitative genetic inference from pedigrees derived from observations of social relationships is relatively robust; our approach also provides a widely applicable method for assessing the consequences of nonrandom EPP.     

Variance and covariance components for liability of piglet survival during different periods

Variance and covariance components for piglet survival in different periods were estimated from individual records of 133 004 Danish Landrace piglets and 89 928 Danish Yorkshire piglets, using a liability threshold model including both direct and maternal additive genetic effects. At the individual piglet level, the estimates of direct heritability in Landrace were 0.035, 0.057 and 0.027, and in Yorkshire the estimates were 0.012, 0.030 and 0.025 for liability of survival at farrowing (SVB), from birth to day 5 (SV5) and from day 6 to weaning (SVW), respectively. The estimates of maternal heritability for SVB, SV5 and SVW were, respectively, 0.057, 0.040 and 0.030 in Landrace, and 0.050, 0.038 and 0.019 in Yorkshire. Both direct and maternal genetic correlations between the three survival traits were low and not significantly different from zero, except for a moderate direct genetic correlation between SVB and SV5 and between SV5 and SVW in Landrace. Direct and maternal genetic correlations between piglet birth weight (BW) and SV5 were moderately high, but the correlations between BW and SVB and between BW and SVW were low and most of them were not significantly different from zero. These results suggest that effective genetic improvement in piglet survival before weaning by selection should be based on both direct and maternal additive genetic effects and treat survival in different periods as different traits.     

SSRs,SNPs and DArTs comparison on estimation of relatedness and genetic parameters’ precision from a small half-sib sample population of <Emphasis Type="Italic">Eucalyptus grandis</Emphasis>

Simple sequence repeats (SSR) are the most widely used molecular markers for relatedness inference due to their multi-allelic nature and high informativeness. However, there is a growing trend toward using high-throughput and inter-specific transferable single-nucleotide polymorphisms (SNP) and Diversity Arrays Technology (DArT) in forest genetics owing to their wide genome coverage. We compared the efficiency of 15 SSRs, 181 SNPs and 2816 DArTs to estimate the relatedness coefficients, and their effects on genetic parameters’ precision, in a relatively small data set of an open-pollinated progeny trial of Eucalyptus grandis (Hill ex Maiden) with limited relationship from the pedigree. Both simulations and real data of Eucalyptus grandis were used to study the statistical performance of three relatedness estimators based on co-dominant markers. Relatedness estimates in pairs of individuals belonging to the same family (related) were higher for DArTs than for SNPs and SSRs. DArTs performed better compared to SSRs and SNPs in estimated relatedness coefficients in pairs of individuals belonging to different families (unrelated) and showed higher ability to discriminate unrelated from related individuals. The likelihood-based estimator exhibited the lowest root mean squared error (RMSE); however, the differences in RMSE among the three estimators studied were small. For the growth traits, heritability estimates based on SNPs yielded, on average, smaller standard errors compared to those based on SSRs and DArTs. Estimated relatedness in the realized relationship matrix and heritabilities can be accurately inferred from co-dominant or sufficiently dense dominant markers in a relatively small E. grandis data set with shallow pedigree.     

Bayesian inference of genetic parameters for ultrasound scanning traits of Kivircik lambs

Ultrasound scanning traits have been adapted in selection programs in many countries to improve carcass traits for lean meat production. As the genetic parameters of the traits interested are important for breeding programs, the estimation of these parameters was aimed at the present investigation. The estimated parameters were direct and maternal heritability as well as genetic correlations between the studied traits. The traits were backfat thickness (BFT), skin+backfat thickness (SBFT), eye muscle depth (MD) and live weights at the day of scanning (LW). The breed investigated was Kivircik, which has a high quality of meat. Six different multi-trait animal models were fitted to determine the most suitable model for the data using Bayesian approach. Based on deviance information criterion, a model that includes direct additive genetic effects, maternal additive genetic effects, direct maternal genetic covariance and maternal permanent environmental effects revealed to be the most appropriate for the data, and therefore, inferences were built on the results of that model. The direct heritability estimates for BFT, SBFT, MD and LW were 0.26, 0.26, 0.23 and 0.09, whereas the maternal heritability estimates were 0.27, 0.27, 0.24 and 0.20, respectively. Negative genetic correlations were obtained between direct and maternal effects for BFT, SBFT and MD. Both direct and maternal genetic correlations between traits were favorable, whereas BFT–MD and SBFT–MD had negligible direct genetic correlation. The highest direct and maternal genetic correlations were between BFT and SBFT (0.39) and between MD and LW (0.48), respectively. Our results, in general, indicated that maternal effects should be accounted for in estimation of genetic parameters of ultrasound scanning traits in Kivircik lambs, and SBFT can be used as a selection criterion to improve BFT.     

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.     

ESTIMATING GENETIC CORRELATIONS FROM MEASUREMENTS OF FIELD-CAUGHT WATERSTRIDERS

Abstract Lynch (1999) proposed a method for estimation of genetic correlations from phenotypic measurements of individuals for which no pedigree information is available. This method assumes that shared environmental effects do not contribute to the similarity of relatives, and it is expected to perform best when sample sizes are large, many individuals in the sample are paired with close relatives, and heritability of the traits is high. We tested the practicality of this method for field biologists by using it to estimate genetic correlations from measurements of field‐caught waterstriders {Aquarius remigis). Results for sample sizes of less than 100 pairs were often unstable or undefined, and even with more than 500 pairs only half of those correlations that had been found to be significant in standard laboratory experiments were statistically significant in this study. Statistically removing the influence of environmental effects (shared between relatives) weakened the estimates, possibly by removing some of the genetic similarity between relatives. However, the method did generate statistically significant estimates for some genetic correlations. Lynch (1999) anticipated the problems found, and proposed another method that uses estimates of relatedness between members of pairs (from molecular marker data) to improve the estimates of genetic correlations, but that approach has yet to be tested in the field.     

Sex-specific genetic variances in life-history and morphological traits of the seed beetle Callosobruchus maculatus

Knowledge of heritability and genetic correlations are of central importance in the study of adaptive trait evolution and genetic constraints. We use a paternal half-sib-full-sib breeding design to investigate the genetic architecture of three life-history and morphological traits in the seed beetle, Callosobruchus maculatus. Heritability was significant for all traits under observation and genetic correlations between traits (r(A)) were low. Interestingly, we found substantial sex-specific genetic effects and low genetic correlations between sexes (r(MF)) in traits that are only moderately (weight at emergence) to slightly (longevity) sexually dimorphic. Furthermore, we found an increased sire ([Formula: see text]) compared to dam ([Formula: see text]) variance component within trait and sex. Our results highlight that the genetic architecture even of the same trait should not be assumed to be the same for males and females. Furthermore, it raises the issue of the presence of unnoticed environmental effects that may inflate estimates of heritability. Overall, our study stresses the fact that estimates of quantitative genetic parameters are not only population, time, environment, but also sex specific. Thus, extrapolation between sexes and studies should be treated with caution.     

Sex differences in the genetic architecture of aggressiveness in a sexually dimorphic spider

Sex differences in the genetic architecture of behavioral traits can offer critical insight into the processes of sex‐specific selection and sexual conflict dynamics. Here, we assess genetic variances and cross‐sex genetic correlations of two personality traits, aggression and activity, in a sexually size‐dimorphic spider, Nuctenea umbratica. Using a quantitative genetic approach, we show that both traits are heritable. Males have higher heritability estimates for aggressiveness compared to females, whereas the coefficient of additive genetic variation and evolvability did not differ between the sexes. Furthermore, we found sex differences in the coefficient of residual variance in aggressiveness with females exhibiting higher estimates. In contrast, the quantitative genetic estimates for activity suggest no significant differentiation between males and females. We interpret these results with caution as the estimates of additive genetic variances may be inflated by nonadditive genetic effects. The mean cross‐sex genetic correlations for aggression and activity were 0.5 and 0.6, respectively. Nonetheless, credible intervals of both estimates were broad, implying high uncertainty for these estimates. Future work using larger sample sizes would be needed to draw firmer conclusions on how sexual selection shapes sex differences in the genetic architecture of behavioral traits.     

Heritability of Quasi-Continuous Skeletal Traits in a Randombred Population of House Mice

Heritabilities of 11 quasi-continuous skeletal traits were estimated in randombred house mice of three separate ages (1, 3, and 5 months). Three separate methods—regression, maximum likelihood correlation, and Falconer's Method—were used to obtain heritabilities for each of the separate age groups. Significant differences in the incidences of seven of the skeletal traits were found among ages, but they did not affect the heritability estimates, these estimates being pooled over ages. Heritabilities calculated from female parents were consistently higher (by about 13%) than those from male parents, indicating the presence of maternal effects. Mid-parent estimates made by all three methods gave very similar mean levels (0.17 — 0.20). Although low, this level compared favorably with that expected on the basis of previously estimated rates of accumulation of genetic variance. Maternal effects estimated from full sib correlations averaged 0.08.     

Marker-Based Estimation of Heritability in Immortal Populations

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within- and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.     

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.     

Estimating genetic correlations in natural populations

Information on the genetic correlation between traits provides fundamental insight into the constraints on the evolutionary process. Estimates of such correlations are conventionally obtained by raising individuals of known relatedness in artificial environments. However, many species are not readily amenable to controlled breeding programmes, and considerable uncertainty exists over the extent to which estimates derived under benign laboratory conditions reflect the properties of populations in natural settings. Here, non-invasive methods that allow the estimation of genetic correlations from phenotypic measurements derived from individuals of unknown relatedness are introduced. Like the conventional approach, these methods demand large sample sizes in order to yield reasonably precise estimates, and special precautions need to be taken to eliminate bias from shared environmental effects. Provided the sample consists of at least 20% or so relatives, informative estimates of the genetic correlation are obtainable with sample sizes of several hundred individuals, particularly if supplemental information on relatedness is available from polymorphic molecular markers.     

Inheritance of size and shape in a natural population of collared flycatchers,Ficedula albicollis

Four external skeletal and three feather dimensions were measured on adult collared flycatchers (Ficedula albicollis) and their adult offspring. By using mid-offspring-midparent regressions, all traits were found to be heritable with an arithmetic mean heritability of 0.46. Heritability estimates from full-sib analyses were about 1.5 times higher (mean 0.67), indicating that variation in traits was affected by shared nest environment among full-sibs. The overall body size as measured by principal component one (PC1) was found to be heritable (h² = 0.40). However, this multivariate measure of heritability was not significant in offspring-father comparison, while highly so in offspring-mother comparison (h² = 0.60). Low offspring-father resemblance was evident also in univariate estimates of heritability. Possible causes of this (extra-pair copulations, maternal effects, sex-linked variance) are discussed. Genetic correlations among seven traits were estimated to be low (mean 0.22), and of similar magnitude or higher than phenotypic correlations (mean 0.18). All genetic correlations were positive. Genetic and phenotypic correlations as well as covariances were fairly similar to each other (r = 0.85 and r = 0.87, respectively). Environmental correlations did not follow the pattern of genetic correlations (r = 0.11), but were more similar to phenotypic correlations (r = 0.60). Given the low genetic correlations and moderate heritabilities, the overall conclusion is that the external morphology of collared flycatchers is largely under additive genetic control and that there is a strong potential for evolutionary change in morphology even under complex multivariate selection.     

Exploration of relationships between production and fertility traits in dairy cattle via association studies of SNPs within candidate genes derived by expression profiling

The objective of this work was to integrate findings from functional genomics studies with genome-wide association studies for fertility and production traits in dairy cattle. Association analyses of production and fertility traits with SNPs located within or close to 170 candidate genes derived from two gene expression studies and from the literature were performed. Data from 2294 Holstein bulls genotyped for 39557 SNPs were used. A total of 111 SNPs were located on chromosomal segments covered by a candidate gene. Allele substitution effects for each SNP were estimated using a mixed model with a fixed effect of marker and a random polygenic effect. Assumed covariance was derived either from marker or from pedigree information. Results from the analysis with the kinship matrix built from marker genotypes were more conservative than from the analysis with the pedigree-derived relationship matrix. From sixteen SNPs with significant effects on both classes of traits, ten provided evidence of an antagonistic relationship between productivity and fertility. However, we found four SNPs with favourable effects on fertility and on yield traits, one SNP with favourable effects on fertility and percentage traits, and one SNP with antagonistic effects on two fertility traits. While most quantitative genetic studies have proven genetic antagonisms between yield and functional traits, improvements in both production and functionality may be possible when focusing on a few relevant SNPs. Investigations combining input from quantitative genetics and functional genomics with association analysis may be applied for the identification of such SNPs.     

Heritability and social brood effects on personality in juvenile and adult life‐history stages in a wild passerine

How has evolution led to the variation in behavioural phenotypes (personalities) in a population? Knowledge of whether personality is heritable, and to what degree it is influenced by the social environment, is crucial to understanding its evolutionary significance, yet few estimates are available from natural populations. We tracked three behavioural traits during different life‐history stages in a pedigreed population of wild house sparrows. Using a quantitative genetic approach, we demonstrated heritability in adult exploration, and in nestling activity after accounting for fixed effects, but not in adult boldness. We did not detect maternal effects on any traits, but we did detect a social brood effect on nestling activity. Boldness, exploration and nestling activity in this population did not form a behavioural syndrome, suggesting that selection could act independently on these behavioural traits in this species, although we found no consistent support for phenotypic selection on these traits. Our work shows that repeatable behaviours can vary in their heritability and that social context influences personality traits. Future efforts could separate whether personality traits differ in heritability because they have served specific functional roles in the evolution of the phenotype or because our concept of personality and the stability of behaviour needs to be revised.     

GENETIC AND SOCIAL INHERITANCE OF BODY AND EGG SIZE IN THE BARNACLE GOOSE (BRANTA LEUCOPSIS)

We present heritability estimates for final size of body traits and egg size as well as phenotypic and genetic correlations between body and egg traits in a recently established population of the barnacle goose (Branta leucopsis) in the Baltic area. Body traits as well as egg size were heritable and, hence, could respond evolutionarily to phenotypic selection. Genetic correlations between body size traits were significantly positive and of similar magnitude or higher than the corresponding phenotypic correlations. Heritability estimates for tarsus length obtained from full-sib analyses were higher than those obtained from midoffspring-midparent regressions, and this indicates common environment effects on siblings. Heritabilities for tarsus length obtained from midoffspring-mother regressions were significantly higher than estimates from midoffspring-father regressions. The results suggest that this discrepancy is not caused by maternal effects through egg size, nor by extra-pair fertilizations, but by a socially inherited foraging site fidelity in females.     

Genetic factors controlling wool shedding in a composite Easycare sheep flock

Historically, sheep have been selectively bred for desirable traits including wool characteristics. However, recent moves towards extensive farming and reduced farm labour have seen a renewed interest in Easycare breeds. The aim of this study was to quantify the underlying genetic architecture of wool shedding in an Easycare flock. Wool shedding scores were collected from 565 pedigreed commercial Easycare sheep from 2002 to 2010. The wool scoring system was based on a 10‐point (0–9) scale, with score 0 for animals retaining full fleece and 9 for those completely shedding. DNA was sampled from 200 animals of which 48 with extreme phenotypes were genotyped using a 50‐k SNP chip. Three genetic analyses were performed: heritability analysis, complex segregation analysis to test for a major gene hypothesis and a genome‐wide association study to map regions in the genome affecting the trait. Phenotypes were treated as a continuous or binary variable and categories. High estimates of heritability (0.80 when treated as a continuous, 0.65–0.75 as binary and 0.75 as categories) for shedding were obtained from linear mixed model analyses. Complex segregation analysis gave similar estimates (0.80 ± 0.06) to those above with additional evidence for a major gene with dominance effects. Mixed model association analyses identified four significant (P < 0.05) SNPs. Further analyses of these four SNPs in all 200 animals revealed that one of the SNPs displayed dominance effects similar to those obtained from the complex segregation analyses. In summary, we found strong genetic control for wool shedding, demonstrated the possibility of a single putative dominant gene controlling this trait and identified four SNPs that may be in partial linkage disequilibrium with gene(s) controlling shedding.     

SNP‐based heritability and genetic architecture of tarsal osteochondrosis in North American Standardbred horses

Osteochondrosis is a common developmental orthopedic disease characterized by a failure of endochondral ossification. Standardbred horses are recognized as being predisposed to tarsal osteochondrosis. Prior heritability estimates for tarsal osteochondrosis in European Standardbreds and related trotting breeds have been based on pedigree data and range from 17–29%. Here, we report on genetic architecture and heritability based on high‐density genotyping data in a cohort of North American Standardbreds (n = 479) stringently phenotyped for tarsal osteochondrosis. Whole‐genome array genotyping data were imputed to ~2 million single nucleotide polymorphisms (SNPs). SNP‐based heritability of osteochondrosis in this population was explained by 2326 SNPs. The majority of these SNPs (86.6%) had small effects, whereas fewer SNPs had moderate or large effects (10% and 2.9% respectively), which is consistent with a polygenic/complex disease. Heritability was estimated at 0.24 ± 0.16 using two methods of restricted maximum likelihood analysis, as implemented in gcta (with and without a weighted relatedness matrix) and ldak software. Estimates were validated using bootstrapping. Heritability estimates were within the range previously reported and suggest that osteochondrosis is moderately heritable but that a significant portion of disease risk is due to environmental factors and/or genotype × environment interactions. Future identification of the genes/variants that have the most impact on disease risk may allow early recognition of high‐risk individuals.