Inferring relatedness and heritability using molecular markers in radiata pine

A set of eight unlinked microsatellite markers was used to estimate relatedness among 355 individuals of a Pinus radiata breeding population. The average performance of open-pollinated progeny of each individual, for wood density, was considered to represent the phenotype of all 355 individuals. Marker-based estimates of relationship were compared with the pedigree-based coefficients of relationships. The phenotypic similarity among all pairs of individuals was regressed on marker-estimated relatedness to estimate the inheritance of wood density. The marker-based estimate of heritability was compared with that obtained using classical quantitative genetic methods. Overall, a low correlation (0.13) was observed between marker-based and pedigree-based estimates of relatedness. After discarding negative estimates of relatedness, the average coefficient of relationship among known groups of maternal half-sibs, full-sibs and unrelated individuals, increased from 0.24 to 0.29 (0.25 expected), from 0.43 to 0.48 (0.50 expected) and from –0.04 to 0.15 (0 expected), respectively. Marker-based and conventional estimates of heritability of wood density were 0.79 and 0.38, respectively. However, by using only marker loci with expected Hardy–Weinberg frequencies, marker-based estimate of heritability was 0.33, which is very similar to that obtained from conventional approaches. The use of molecular markers to understand quantitative genetic variation is discussed.     

The quantitative genetics of incipient speciation: heritability and genetic correlations of skeletal traits in populations of diverging Favia fragum ecomorphs

Recent speciation events provide potential opportunities to understand the microevolution of reproductive isolation. We used a marker-based approach and a common garden to estimate the additive genetic variation in skeletal traits in a system of two ecomorphs within the coral species Favia fragum: a Tall ecomorph that is a seagrass specialist, and a Short ecomorph that is most abundant on coral reefs. Considering both ecomorphs, we found significant narrow-sense heritability (h(2) ) in a suite of measurements that define corallite architecture, and could partition additive and nonadditive variation for some traits. We found positive genetic correlations for homologous height and length measurements among different types of vertical plates (costosepta) within corallites, but negative correlations between height and length within, as well as between costosepta. Within ecomorphs, h(2) estimates were generally lower, compared to the combined ecomorph analysis. Marker-based estimates of h(2) were comparable to broad-sense heritability (H) obtained from parent-offspring regressions in a common garden for most traits, and similar genetic co-variance matrices for common garden and wild populations may indicate relatively small G × E interactions. The patterns of additive genetic variation in this system invite hypotheses of divergent selection or genetic drift as potential evolutionary drivers of reproductive isolation.     

Marker-based quantitative genetics in the wild?: the heritability and genetic correlation of chemical defenses in eucalyptus

Marker-based methods for estimating heritability and genetic correlation in the wild have attracted interest because traditional methods may be impractical or introduce bias via G x E effects, mating system variation, and sampling effects. However, they have not been widely used, especially in plants. A regression-based approach, which uses a continuous measure of genetic relatedness, promises to be particularly appropriate for use in plants with mixed-mating systems and overlapping generations. Using this method, we found significant narrow-sense heritability of foliar defense chemicals in a natural population of Eucalyptus melliodora. We also demonstrated a genetic basis for the phenotypic correlation underlying an ecological example of conditioned flavor aversion involving different biosynthetic pathways. Our results revealed that heritability estimates depend on the spatial scale of the analysis in a way that offers insight into the distribution of genetic and environmental variance. This study is the first to successfully use a marker-based method to measure quantitative genetic parameters in a tree. We suggest that this method will prove to be a useful tool in other studies and offer some recommendations for future applications of the method.     

Pedigree-free animal models: the relatedness matrix reloaded

Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.     

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.     

A MARKER-BASED METHOD FOR INFERENCES ABOUT QUANTITATIVE INHERITANCE IN NATURAL POPULATIONS

A marker-based method for studying quantitative genetic characters in natural populations is presented and evaluated. The method involves regressing quantitative trait similarity on marker-estimated relatedness between individuals. A procedure is first given for estimating the narrow sense heritability and additive genetic correlations among traits, incorporating shared environments. Estimation of the actual variance of relatedness is required for heritability, but not for genetic correlations. The approach is then extended to include isolation by distance of environments, dominance, and shared levels of inbreeding. Investigations of statistical properties show that good estimates do not require great marker polymorphism, but rather require significant variation of actual relatedness; optimal allocation generally favors sampling many individuals at the expense of assaying fewer marker loci; when relatedness declines with physical distance, it is optimal to restrict comparisons to within a certain distance; the power to estimate shared environments and inbreeding effects is reasonable, but estimates of dominance variance may be difficult under certain patterns of relationship; and any linkage of markers to quantitative trait loci does not cause significant problems. This marker-based method makes possible studies with long-lived organisms or with organisms difficult to culture, and opens the possibility that quantitative trait expression in natural environments can be analyzed in an unmanipulative way.     

Intra-population comparison of vegetative and floral trait heritabilities estimated from molecular markers in wild Aquilegia populations

Measuring heritable genetic variation is important for understanding patterns of trait evolution in wild populations, and yet studies of quantitative genetic parameters estimated directly in the field are limited by logistic constraints, such as the difficulties of inferring relatedness among individuals in the wild. Marker-based approaches have received attention because they can potentially be applied directly to wild populations. For long-lived, self-compatible plant species where pedigrees are inadequate, the regression-based method proposed by Ritland has the appeal of estimating heritabilities from marker-based estimates of relatedness. The method has been difficult to implement in some plant populations, however, because it requires significant variance in relatedness across the population. Here, we show that the method can be readily applied to compare the ability of different traits to respond to selection, within populations. For several taxa of the perennial herb genus Aquilegia, we estimated heritabilities of floral and vegetative traits and, combined with estimates of natural selection, compared the ability to respond to selection of both types of traits under current conditions. The intra-population comparisons showed that vegetative traits have a higher potential for evolution, because although they are as heritable as floral traits, selection on them is stronger. These patterns of potential evolution are consistent with macroevolutionary trends in the European lineage of the genus.     

Estimates of genetic parameters and breeding values from western larch open-pollinated families using marker-based relationship

The availability and affordability of genetic markers made it possible to estimate quantitative genetic parameters without mating designs' structured pedigree. Here, we compared 4-year height's heritability and individuals' breeding values for a western larch common-garden population of 1,418 offspring representing 15 open-pollinated families from a 41-clone seed orchard using (a) classical pedigree models such as half- and full-sib families and (b) a molecular marker-based pedigree-free model using four pair-wise relationship estimation methods using eight informative SSR markers. The results highlighted the commonly observed inflated estimates of genetic parameters often obtained from half-sib analyses, as well as demonstrating some of the full-sib analyses' caveats. The pedigree reconstruction permitted the identification of selfed individuals, thus allowing evaluating the impact of selfing on marker-based genetic parameter estimation. The results demonstrated the utility of marker-based methods as an alternative to the classical pedigree-based approaches. Unlike the pedigree-based methods, the marker-based approach allowed better partitioning the variance components as well as separating the non-additive and additive genetic variance. The theoretical underpinning of the marker-based approach was discussed.     

EVOLUTIONARY POTENTIAL OF A LARGE MARINE VERTEBRATE: QUANTITATIVE GENETIC PARAMETERS IN A WILD POPULATION

Estimating quantitative genetic parameters ideally takes place in natural populations, but relatively few studies have overcome the inherent logistical difficulties. For this reason, no estimates currently exist for the genetic basis of life-history traits in natural populations of large marine vertebrates. And yet such estimates are likely to be important given the exposure of this taxon to changing selection pressures, and the relevance of life-history traits to population productivity. We report such estimates from a long-term (1995–2007) study of lemon sharks ( Negaprion brevirostris ) conducted at Bimini, Bahamas. We obtained these estimates by genetically reconstructing a population pedigree (117 dams, 487 sires, and 1351 offspring) and then using an "animal model" approach to estimate quantitative genetic parameters. We find significant additive genetic (co)variance, and hence moderate heritability, for juvenile length and mass. We also find substantial maternal effects for these traits at age-0, but not age-1, confirming that genotype–phenotype interactions between mother and offspring are strongest at birth; although these effects could not be parsed into their genetic and nongenetic components. Our results suggest that human-imposed selection pressures (e.g., size-selective harvesting) might impose noteworthy evolutionary change even in large marine vertebrates. We therefore use our findings to explain how maternal effects may sometimes promote maladaptive juvenile traits, and how lemon sharks at different nursery sites may show "constrained local adaptation." We also show how single-generation pedigrees, and even simple marker-based regression methods, can provide accurate estimates of quantitative genetic parameters in at least some natural systems.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

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.     

(Co)Variance components and genetic parameter estimates for growth traits in Moghani sheep

Genetic parameters were estimated for birth weight (BW), weaning weight (WW), yearling weight (YW), average daily gain from birth to weaning (ADG1) and average daily gain from weaning to yearling (ADG2) in Moghani sheep. Maximum number of data was 4237 at birth, but only 1389 records at yearling were investigated. The data was collected from 1995 to 2007 at the Breeding Station of Moghani sheep in Jafarabad, Moghan, Iran. (Co)Variance components and genetic parameters were estimated with different models which including direct effects, with and without maternal additive genetic effects as well as maternal permanent environmental effects using restricted maximum likelihood (REML) method. The most appropriate model for each trait was determined based on likelihood ratio tests and Akaike's Information Criterion (AIC). Maternal effects were important only for pre-weaning traits. Direct heritability estimates for BW, ADG1, WW, ADG2 and YW were 0.07, 0.08, 0.09, 0.09 and 0.17, respectively. Fractions of variance due to maternal permanent environmental effects on phenotypic variance were 0.08 for ADG1. Maternal heritability estimates for BW and WW were 0.18 and 0.06, respectively. Multivariate analysis was performed using the most appropriate models obtained in univariate analysis. Direct genetic correlations among studied traits were positive and ranged from 0.37 for BW–ADG2 to 0.85 for ADG1–YW. Maternal genetic correlation estimate between BW and WW was 0.33. Phenotypic and environmental correlation estimates were generally lower than those of genetic correlation. Low direct heritability estimates imply that mass selection for these traits results in slow genetic gain.     

Egg shell quality in Japanese quail: characteristics,heritabilities and genetic and phenotypic relationships

The objective of the present study was to estimate heritabilities as well as genetic and phenotypic correlations for egg weight, specific gravity, shape index, shell ratio, egg shell strength, egg length, egg width and shell weight in Japanese quail eggs. External egg quality traits were measured on 5864 eggs of 934 female quails from a dam line selected for two generations. Within the Bayesian framework, using Gibbs Sampling algorithm, a multivariate animal model was applied to estimate heritabilities and genetic correlations for external egg quality traits. The heritability estimates for external egg quality traits were moderate to high and ranged from 0.29 to 0.81. The heritability estimates for egg and shell weight of 0.81 and 0.76 were fairly high. The genetic and phenotypic correlations between egg shell strength with specific gravity, shell ratio and shell weight ranging from 0.55 to 0.79 were relatively high. It can be concluded that it is possible to determine egg shell quality using the egg specific gravity values utilizing its high heritability and fairly high positive correlation with most of the egg shell quality traits. As a result, egg specific gravity may be the choice of selection criterion rather than other external egg traits for genetic improvement of egg shell quality in Japanese quails.     

Genomic Heritability: What Is It?

Whole-genome regression methods are being increasingly used for the analysis and prediction of complex traits and diseases. In human genetics, these methods are commonly used for inferences about genetic parameters, such as the amount of genetic variance among individuals or the proportion of phenotypic variance that can be explained by regression on molecular markers. This is so even though some of the assumptions commonly adopted for data analysis are at odds with important quantitative genetic concepts. In this article we develop theory that leads to a precise definition of parameters arising in high dimensional genomic regressions; we focus on the so-called genomic heritability: the proportion of variance of a trait that can be explained (in the population) by a linear regression on a set of markers. We propose a definition of this parameter that is framed within the classical quantitative genetics theory and show that the genomic heritability and the trait heritability parameters are equal only when all causal variants are typed. Further, we discuss how the genomic variance and genomic heritability, defined as quantitative genetic parameters, relate to parameters of statistical models commonly used for inferences, and indicate potential inferential problems that are assessed further using simulations. When a large proportion of the markers used in the analysis are in LE with QTL the likelihood function can be misspecified. This can induce a sizable finite-sample bias and, possibly, lack of consistency of likelihood (or Bayesian) estimates. This situation can be encountered if the individuals in the sample are distantly related and linkage disequilibrium spans over short regions. This bias does not negate the use of whole-genome regression models as predictive machines; however, our results indicate that caution is needed when using marker-based regressions for inferences about population parameters such as the genomic heritability.     

Heritability of phenolics in Quercus laevis inferred using molecular markers.

Studies of quantitative inheritance of phenotypes do not generally encompass the range of environmental conditions to which a population may be exposed in a natural setting and are rarely conducted on long-lived species due to the time required for traditional crossing experiments. We used a marker-based method to estimate relatedness with microsatellite markers in a natural population of a long-lived oak, then used this inferred relatedness to examine quantitative genetic variation in the concentration of foliar phenolics. Estimating heritability using this method requires both significant relatedness and variance in relatedness over distance. However, this population did not show significant variance of relatedness, so only the presence of heritability, and its ranking among traits and environments, could be estimated. Seven foliar phenolics showed a significant relationship between phenotypic similarity and relatedness. The significance of this relationship varied among individual phenolic compounds, as well as by season. Genetic factors appeared to have a more measurable influence on the production of secondary compounds early in the season. After leaf expansion, covariance of relatedness and phenotypic variance appear to become less significant. Therefore heritability may vary seasonally for these traits.     

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.     

Genetic parameters of coat colour in golden fox (Vulpes vulpes L.)

Genetic parameters (heritability, genetic and phenotypic correlations) of chosen coat colour traits of golden fox were estimated. 1013 animals, born on the Sniaty fox farm (Poland) in 1985-1999 were evaluated. In 1993-1999 colour type was additionally assessed for 833 animals, by detailed evaluation of coat colour on the back and sides of the body, throat colour, belly colour and the amount of silver hair. The REML method was used to estimate genetic (co)variance components. Data were transformed using the probit transformation. Heritability estimates for coat traits were low (0.04 to 0.22). Values of most of the estimated genetic parameters (h2, rG, rP) were comparable to those frequently reported for other colour types of silver fox.     

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).     

Genetic parameters for litter size in sheep: natural versus hormone-induced oestrus

The litter size in Suffolk and Texel-sheep was analysed using REML and Bayesian methods. Litters born after hormonal induced oestrus and after natural oestrus were treated as different traits in order to estimate the genetic correlation between the traits. Explanatory variables were the age of the ewe at lambing, period of lambing, a year*flock-effect, a permanent environmental effect associated with the ewe, and the additive genetic effect. The heritability estimates for litter size ranged from 0.06 to 0.13 using REML in bi-variate linear models. Transformation of the estimates to the underlying scale resulted in heritability estimates from 0.12 to 0.17. Posterior means of the heritability of litter size in the Bayesian approach with bi-variate threshold models varied from 0.05 to 0.18. REML estimates of the genetic correlations between the two types of litter size ranged from 0.57 to 0.64 in the Suffolk and from 0.75 to 0.81 in the Texel. The posterior means of the genetic correlation (Bayesian analysis) were 0.40 and 0.44 for the Suffolk and 0.56 and 0.75 for the Texel in the sire and animal model respectively. A bivariate threshold model seems appropriate for the genetic evaluation of prolificacy in the breeds concerned.     

The common quantitative genetic basis of wing morphology and diapause occurrence in the cricket Gryllus veletis

A covariation between wing morphology and diapause occurrence has been observed in many insect species, but the genetic basis of this covariation has never been established. This study measures the heritability of, and genetic correlation between, these two ecologically important threshold traits in the cricket Gryllus veletis. A total of 81 full-sib families were reared in the laboratory to estimate these parameters. A comparison of laboratory and field samples showed that these two traits are highly plastic. The heritability of wing morphology was 0.25 (0.09), the heritability of diapause occurrence was 0.77 (0.11) and the genetic correlation between them was 0.61 (0.19). These estimates did not differ between males and females. The significance of these quantitative genetic parameters is discussed with reference to the monomorphism of natural populations of G. veletis for diapause occurrence and with reference to the trade-off between the ability to disperse by flight and the ability to diapause found in at least one closely related species. A survey of the literature reveals that genetic correlations between diapause occurrence or wing morphology and various other traits are common in insects, suggesting that these two traits are often genetically integrated in insect life-histories.