Estimation of heritability using variety trials data from incomplete blocks

An assessment of the heritability of a trait is useful in formulating a breeding strategy for crop improvement. We have considered the estimation of broad-sense heritability from a single-location trial and from multi-locational trials conducted in incomplete blocks. Using residual maximum likelihood estimates of variance components, we estimated the heritability and obtained expressions for the estimate of its bias and its standard error. The estimation procedure is illustrated for 25 barley genotypes evaluated at four locations in West Asia and North Africa during 1992.     

Estimating the heritability of female lifetime fecundity in a locally adapted Drosophila melanogaster population

The heritability of genome‐wide fitness that is expected in finite populations is poorly understood, both theoretically and empirically, despite its relevance to many fundamental concepts in evolutionary biology. In this study, we used two independent methods of estimating the heritability of lifetime female fecundity (the predominant female fitness component in this population) in a large, outbred population of Drosophila melanogaster that had adapted to the laboratory environment for over 400 generations. Despite strong directional selection on adult female fecundity, we uncovered high heritability for this trait that cannot be explained by antagonistic pleiotropy with juvenile fitness. The evolutionary significance of this high heritability of lifetime fecundity is discussed.     

Clonal variation for shoot ontogenetic heteroblasty in maritime pine (Pinus pinaster Ait.)

Pine seedling shoots undergo sharp heteroblastic changes during the early ontogenetic stages. The rate of these changes has been seen to vary between species and provenances within species, but there is a marked lack of information about its genetic control at the lower hierarchical levels. We used clonal replicates of maritime pine to determine broad-sense heritability of shoot ontogenetic heteroblasty and its correlation to rooting ability. We applied a simple ontogenetic index based on the proportion of basal nodes with secondary needles in rooted cuttings of 15 clones from 9 environmentally contrasting origins. We found a high clonal heritability for shoot ontogenetic index and a moderately high heritability for rooting ability, but both genetic and phenotypic correlations between these two traits were weak and non-significant. These results indicate that both developmental phenomena are genetically controlled, but not strictly associated in this species.     

Genetics of Callous-Unemotional Behavior in Children

Callous-unemotional behavior (CU) is currently under consideration as a subtyping index for conduct disorder diagnosis. Twin studies routinely estimate the heritability of CU as greater than 50%. It is now possible to estimate genetic influence using DNA alone from samples of unrelated individuals, not relying on the assumptions of the twin method. Here we use this new DNA method (implemented in a software package called Genome-wide Complex Trait Analysis, GCTA) for the first time to estimate genetic influence on CU. We also report the first genome-wide association (GWA) study of CU as a quantitative trait. We compare these DNA results to those from twin analyses using the same measure and the same community sample of 2,930 children rated by their teachers at ages 7, 9 and 12. GCTA estimates of heritability were near zero, even though twin analysis of CU in this sample confirmed the high heritability of CU reported in the literature, and even though GCTA estimates of heritability were substantial for cognitive and anthropological traits in this sample. No significant associations were found in GWA analysis, which, like GCTA, only detects additive effects of common DNA variants. The phrase ‘missing heritability’ was coined to refer to the gap between variance associated with DNA variants identified in GWA studies versus twin study heritability. However, GCTA heritability, not twin study heritability, is the ceiling for GWA studies because both GCTA and GWA are limited to the overall additive effects of common DNA variants, whereas twin studies are not. This GCTA ceiling is very low for CU in our study, despite its high twin study heritability estimate. The gap between GCTA and twin study heritabilities will make it challenging to identify genes responsible for the heritability of CU.     

Missing heritability of complex diseases: Enlightenment by genetic variants from intermediate phenotypes

Diseases of complex origin have a component of quantitative genetics that contributes to their susceptibility and phenotypic variability. However, after several studies, a major part of the genetic component of complex phenotypes has still not been found, a situation known as “missing heritability.” Although there have been many hypotheses put forward to explain the reasons for the missing heritability, its definitive causes remain unknown. Complex diseases are caused by multiple intermediate phenotypes involved in their pathogenesis and, very often, each one of these intermediate phenotypes also has a component of quantitative inheritance. Here we propose that at least part of the missing heritability can be explained by the genetic component of intermediate phenotypes that is not detectable at the level of the main complex trait. At the same time, the identification of the genetic component of intermediate phenotypes provides an opportunity to identify part of the missing heritability of complex diseases.     

Variance,Inter-Trait Correlation,Heritability, and Marker-Trait Association of Rubber Yield-Related Characteristics in <Emphasis Type="Italic">Taraxacum kok-saghyz</Emphasis>

Rubber dandelion (Taraxacum kok-saghyz or TK) is a potential industrial crop species that can produce high-quality natural rubber in its roots. The present study estimated trait variance, inter-trait correlation, and entry-mean heritability for rubber yield-related traits and analyzed associations between these traits and 42 single-nucleotide polymorphism (SNP) markers. A trial was conducted at three environments to assess a biparental progeny of 66 F₁ full-sibs, in a randomized complete block design (RCBD) with two replicates. Significant correlations, broad ranges of variation, and significant genotypic variance components were identified for five measured phenotypic traits. Moderate broad-sense heritability on an entry-mean heritability estimates (0.51–0.61) were obtained for five rubber yield-related traits based on a 1-year trial. However, the broad-sense heritability in general sense ranged from 0.09 to 0.15 depending on the trait. Two linkage groups were identified. Association analysis identified seven significant marker-trait gene associations, and only one marker was related to two traits. The implications of trait correlations and heritability for selection and improvement are discussed.     

How meaningful are heritability estimates of liability?

It is commonly acknowledged that estimates of heritability from classical twin studies have many potential shortcomings. Despite this, in the post-GWAS era, these heritability estimates have come to be a continual source of interest and controversy. While the heritability estimates of a quantitative trait are subject to a number of biases, in this article we will argue that the standard statistical approach to estimating the heritability of a binary trait relies on some additional untestable assumptions which, if violated, can lead to badly biased estimates. The ACE liability threshold model assumes at its heart that each individual has an underlying liability or propensity to acquire the binary trait (e.g., disease), and that this unobservable liability is multivariate normally distributed. We investigated a number of different scenarios violating this assumption such as the existence of a single causal diallelic gene and the existence of a dichotomous exposure. For each scenario, we found that substantial asymptotic biases can occur, which no increase in sample size can remove. Asymptotic biases as much as four times larger than the true value were observed, and numerous cases also showed large negative biases. Additionally, regions of low bias occurred for specific parameter combinations. Using simulations, we also investigated the situation where all of the assumptions of the ACE liability model are met. We found that commonly used sample sizes can lead to biased heritability estimates. Thus, even if we are willing to accept the meaningfulness of the liability construct, heritability estimates under the ACE liability threshold model may not accurately reflect the heritability of this construct. The points made in this paper should be kept in mind when considering the meaningfulness of a reported heritability estimate for any specific disease.     

Inheritance of resistance to coffee wilt disease (Fusarium xylarioides Steyaert) in Robusta coffee (Coffea canephora Pierre) and breeding perspectives

Knowledge on heritability is essential for selecting varieties resistant against coffee wilt disease caused by Fusarium xylarioides, which is currently devastating coffee in East and Central Africa. Variability of the resistance against coffee wilt disease in Coffea canephora and its inheritance were investigated in three experiments corresponding to a clonal trial involving 20 clones, a 10-parent partial diallel progeny, and a half-sib progeny test. There were significant quantitative genetic variations among the clones and progenies, suggesting polygenic control of the resistance. Around 50–65 % tree mortality was the optimal disease level for calculating heritability and genetic gains. General and specific combining abilities calculated within the optimal disease range for partial diallel analysis were significant. Broad-sense heritability for the same analysis and same disease range was moderate (0.329), and corresponding narrow-sense heritability was low (0.112). Broad-sense heritability from clones in the field at the same disease range was also moderate (0.333). Narrow-sense heritability from regression of half-sib progeny means onto parent means in the field and screen house was 0.183 and 0.369, respectively. Selecting tolerant clones for improvement against the disease is possible, and genetic gains are possible by using tolerant parents in breeding programs.     

Evidence of genetic influence on central body fat in middle-aged twins

The heritability of centrally and peripherally deposited subcutaneous body fat, as measured by thickness of subscapular and triceps skinfolds respectively, was examined in 173 monozygotic and 178 dizygotic pairs of white male twins, ages 54 to 65 years, who participated in the second examination of the National Heart, Lung, and Blood Institute's Twin Study. The heritability of two indices of body fat distribution (subscapular/triceps ratio and subscapular-triceps difference) and two indices of overall obesity (body mass index and sum of skinfolds) were also assessed. Evidence for a genetic influence on central deposition of body fat was suggested in that the classical estimate of heritability for subscapular skinfold thickness was 0.77 (p less than 0.0001). After adjusting subscapular skinfold for the overall level of obesity, heritability was reduced but remained highly significant (0.40, p = 0.003). Heritability estimates for triceps skinfold thickness and for the two fat distribution indices were substantially lower and were not statistically significant after adjustment for overall obesity. High classical estimates of heritability were also observed for both measures of overall obesity: 0.70 for BMI and 0.73 for sum of skinfolds. However, these two estimates were biased upward because of lower total variances among monozygotic compared to dizygotic twins in this sample. The more conservative and unbiased among-component estimates also suggested substantial heritability for each measure (0.35, p = 0.08 and 0.53, p = 0.01, respectively). The heritability of overall obesity emphasizes the importance of adjusting measures of fat distribution for overall obesity before assessing its heritability.     

Range size heritability in Carnivora is driven by geographic constraints

Range size heritability refers to an intriguing pattern where closely related species occupy geographic ranges of similar extent. Its existence may indicate selection on traits emergent only at the species level, with interesting consequences for evolutionary processes. We explore whether range size heritability may be attributable to the fact that range size is largely driven by the size of geographic domains (i.e., continents, biomes, areas given by species' climatic tolerance) that tend to be similar in phylogenetically related species. Using a well-resolved phylogeny of Carnivora, we show that range sizes are indeed constrained by geographic domains and that the phylogenetic signal in range sizes diminishes if the domain sizes are accounted for. Moreover, more detailed delimitation of species' geographic domain leads to a weaker signal in range size heritability, indicating the importance of definition of the null model against which the pattern is tested. Our findings do not reject the hypothesis of range size heritability but rather unravel its underlying mechanisms. Additional analyses imply that evolutionary conservatism in niche breadth delimits the species' geographic domain, which in turn shapes the species' range size. Range size heritability patterns thus emerge as a consequence of this interplay between evolutionary and geographic constraints.     

Multilocus estimation of selfing and its heritability

We describe a new method of estimating the selfing rate (S) in a mixed mating population based on a population structure approach that accounts for possible intergenerational correlation in selfing rate, giving rise to an estimate of the upper limit for heritability of selfing rate (h(2)). A correlation between generations in selfing rate is shown to affect one- and two-locus probabilities of identity by descent. Conventional estimates of selfing rate based on a population structure approach are positively biased by intergenerational correlation in selfing. Multilocus genotypes of individuals are used to give maximum-likelihood estimates of S and h(2) in the presence of scoring artifacts. Our multilocus estimation of selfing rate and its heritability (MESH) method was tested with simulated data for a range of conditions. Selfing rate estimates from MESH have low bias and root mean squared error, whereas estimates of the heritability of selfing rate have more uncertainty. Increasing the number of individuals in a sample helps to reduce bias and root mean squared error more than increasing the number of loci of sampled individuals. Improved estimates of selfing rate, as well as estimates of its heritability, can be obtained with this method, although a large number of loci and individuals are needed to achieve best results.     

‘Heritability’ of dispersal propensity in a patchy population

Although dispersal is often considered to be a plastic, condition-dependent trait with low heritability, growing evidence supports medium to high levels of dispersal heritability. Obtaining unbiased estimates of dispersal heritability in natural populations nevertheless remains crucial to understand the evolution of dispersal strategies and their population consequences. Here we show that dispersal propensity (i.e. the probability of dispersal between habitat patches) displays a significant heritability in the collared flycatcher Ficedula albicollis, as estimated by within-family resemblance when accounting for environmental factors. Offspring of dispersing mothers or fathers had a higher propensity to disperse to a new habitat patch themselves. The effect of parental dispersal status was additional to that of local habitat quality, as measured by local breeding population size and success, confirming previous results about condition-dependent dispersal in this population. The estimated levels of heritability varied between 0.30±0.07 and 0.47±0.10, depending on parent–offspring comparisons made and correcting for a significant assortative mating with respect to dispersal status. Siblings also displayed a significant resemblance in dispersal propensity. These results suggest that variation in between-patch natal dispersal in the collared flycatcher is partly genetically determined, and we discuss ways to quantify this genetic basis and its implications.     

Assumptions and Properties of Limiting Pathway Models for Analysis of Epistasis in Complex Traits

For most complex traits, results from genome-wide association studies show that the proportion of the phenotypic variance attributable to the additive effects of individual SNPs, that is, the heritability explained by the SNPs, is substantially less than the estimate of heritability obtained by standard methods using correlations between relatives. This difference has been called the “missing heritability”. One explanation is that heritability estimates from family (including twin) studies are biased upwards. Zuk et al. revisited overestimation of narrow sense heritability from twin studies as a result of confounding with non-additive genetic variance. They propose a limiting pathway (LP) model that generates significant epistatic variation and its simple parametrization provides a convenient way to explore implications of epistasis. They conclude that over-estimation of narrow sense heritability from family data (‘phantom heritability’) may explain an important proportion of missing heritability. We show that for highly heritable quantitative traits large phantom heritability estimates from twin studies are possible only if a large contribution of common environment is assumed. The LP model is underpinned by strong assumptions that are unlikely to hold, including that all contributing pathways have the same mean and variance and are uncorrelated. Here, we relax the assumptions that underlie the LP model to be more biologically plausible. Together with theoretical, empirical, and pragmatic arguments we conclude that in outbred populations the contribution of additive genetic variance is likely to be much more important than the contribution of non-additive variance.     

Experimental life-history evolution: selection on the allocation to sexual reproduction and its plasticity in a clonal plant

Abstract.— Allocation to sexual reproduction is an important life-history trait in clonal plants. Different selection pressures between competitive and competition-free environments are likely to result in the evolution of specialized genotypes and to maintain genetic variation in reproductive allocation. Moreover, selection may also result in the evolution of plastic allocation strategies. The necessary prerequisite for evolution, heritable genetic variation, can best be studied with selection experiments. Starting from a base population of 102 replicated genotypes of the clonal herb Ranunculus reptans , we imposed selection on the proportion of flowering rosettes in the absence of competition (base population: mean = 0.391, broad-sense heritability = 0.307). We also selected on the plasticity in this trait in response to competition with a naturally coexisting grass in a parallel experiment (base population: 14% lower mean in the presence of competition, broad-sense heritability = 0.072). After two generations of bidirectional selection, the proportion of flowering rosettes was 26% higher in the high line than in the low line (realized heritability ± SE = 0.205 ± 0.017). Moreover, genotypes of the high line had 11% fewer carpels per flower, a 22% lower proportion of rooted rosettes, and a 39% smaller average distance between rosettes within a clone. In the second experiment, we found no significant responses to selection for high and low plasticity in the proportion of flowering rosettes (realized heritability ± SE =–0.002 ± 0.013). Our study indicates a high heritability and potential for further evolution of the proportion of flowering rosettes in R. reptans , but not for its plasticity, which may have been fixed by past evolution at its current level. Moreover, our results demonstrate strong genetic correlations between allocation to sexual reproduction and other clonal life-history characteristics.     

Inheritance of hypodontia in twins

The aim of this study was to establish prevalence of hypodontia in the twin sample and to assess the degree of its heritability. A study was performed in a sample of 96 twin pairs, 38 pairs being monozygotic (MZ) and 58 pairs dizygotic (DZ), from north-west Croatia. The sample included 25.82% of all twins born in the region during a ten-year period. The twin zygosity was determined according to the WHO recommendations (1996). A revised Holzinger's index (Hc') according to Allen was applied to calculate the degree of heritability. Hypodontia was found in 22 out of the total of 192 twins analyzed (11.5%). Among 96 pairs of twins, hypodontia was observed in 17 pairs (7 MZ and 10 DZ pairs). Among the MZ, 4 pairs were found to be concordant for hypodontia, among the DZ one pair only. The heritability index was 0825. A prevalence of hypodontia in twins observed in this study is significantly higher than in the general population. A high index of heritability (Hc' = 0.825) points to a high genetic determination.     

使用多因素易患性阈值模型评估双相情感障碍的遗传度缺失

为了评估双向情感障碍的遗传度缺失,文章通过查询美国国家人类基因组研究所(National Human Genome Research Institute,NHGRI)的gwascatalog目录,检索出所有已发现的双相情感障碍易感变异,使用多因素易患性阈值模型计算每个易感变异对双相情感障碍遗传度的解释度。将所有易感变异遗传度解释度求和得到双相情感障碍已知易感变异对遗传度的总解释度,使用此总解释度评估双相情感障碍的遗传度缺失。结果显示,已知双相情感障碍易感变异对双相情感障碍遗传度的合计解释度为38.34%,尚有61.66%的遗传度无法被已有易感变异解释,属于遗传度缺失。双相情感障碍38.34%的遗传度解释度较早前国外同类研究大幅度提高,表明随着新的双相情感障碍易感变异被不断发现,双相情感障碍遗传度缺失得到大幅度减小。但双相情感障碍遗传度缺失依然存在且数目较大的事实也表明双相情感障碍尚存在许多未知的分子遗传学机制有待进一步阐明。     

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.     

Is cladogenesis heritable?

The heritability of speciation rates and extinction risks is a crucial parameter in models of macroevolution, but little direct evidence has been available to assess the occurrence, strength, or generality of this heritability. We tested for heritability using correlations between ancestral and descendent branch lengths in phylogenetic trees, an approach first applied to a bird phylogeny by Harvey et al. (1991, pages 123-137 in Genes in ecology [R. J. Berry et al., eds.], Blackwell Scientific, Oxford). We applied Harvey et al.'s test to some of the largest DNA sequence-based phylogenetic analyses published to date for plants, insects, fungi, and bacteria. If one of two parent lineages splits first and if this is the case for any heritable reason, then on average we expect its daughter lineages to also split first. We also used a randomization procedure to assess significance of branch length heritability. Using maximum parsimony and maximum likelihood branch lengths and trees made ultrametric after nonparametric rate smoothing or by enforcing a molecular clock, we found a pattern for most clades consistent with heritable net cladogenesis. Heritability of cladogenesis may be a general phenomenon, detectable across a large number of lineages and a broad range of taxa.     

Interpreting estimates of heritability – A note on the twin decomposition

While most outcomes may in part be genetically mediated, quantifying genetic heritability is a different matter. To explore data on twins and decompose the variation is a classical method to determine whether variation in outcomes, e.g. IQ or schooling, originate from genetic endowments or environmental factors. Despite some criticism, the model is still widely used. The critique is generally related to how estimates of heritability may encompass environmental mediation. This aspect is sometimes left implicit by authors even though its relevance for the interpretation is potentially profound. This short note is an appeal for clarity from authors when interpreting the magnitude of heritability estimates. It is demonstrated how disregarding existing theoretical contributions can easily lead to unnecessary misinterpretations and/or controversies. The key arguments are relevant also for estimates based on data of adopted children or from modern molecular genetics research.     

Quantitative genetics of cranial nonmetric traits in randombred mice: heritability and etiology

Cheverud and Buikstra (1981) demonstrated a tendency for nonmetric traits representing the number of foramina to have lower heritabilities than those representing hyperstotic or hypostotic traits in a sample of rhesus macaques. Based on this observation, Cheverud and Buikstra hypothesize that differences in the heritability of the two sets of traits may be due to differences in trait etiology. This study addresses the proposed relationship between trait heritability and etiology. Heritability values are calculated for 35 cranial nonmetric traits in a sample of 320 randombred mice using analysis of variance. The results are minimally consistent with the etiological hypothesis, but only 4 of the 35 traits showed statistically significant heritability values. These results are discussed with reference to the assumption that nonmetric traits have a strong genetic component. It is concluded that the developmental pathways that genetic variation traverses before being expressed in the form of nonmetric traits must be understood before variation in nonmetric traits can be used to its fullest potential.