Maximum-likelihood variance components analysis of heritabilities of cranial nonmetric traits

Nonmetric traits of the cranium are often used to support hypotheses of the history and divergence of human populations. These studies rely on the assumption that nonmetric traits are heritable, yet few skeletal series exist with associated pedigree information that allow for the calculation of additive genetic variance, or heritability. In addition, traits for which heritabilities have been published represent dichotomous present/absent forms instead of the range of expression that can be observed for many nonmetric characters. In the present study I use a maximum-likelihood variance components analysis to calculate univariate narrow-sense heritability estimates on the skeletal series from Hallstatt, Austria, for 9 sutural bones, 27 multilevel traits, and dichotomized present/absent forms for 19 of these multilevel characters. Most of the trait heritabilities do not differ significantly from a model of h2 = 0, and they have large standard errors. In a heuristic comparison of multilevel versus dichotomous trait forms, most of the nonmetric characters showed no differences in heritability between the two methods used for parsing the phenotypic variation, although where differences were noted, the presence-absence version had higher heritabilities. These results have implications not only for the use of particular nonmetric traits in population studies but also for the practice of character dichotomization in data collection.     

Realized Sampling Variances of Estimates of Genetic Parameters and the Difference between Genetic and Phenotypic Correlations

A data set of 1572 heritability estimates and 1015 pairs of genetic and phenotypic correlation estimates, constructed from a survey of published beef cattle genetic parameter estimates, provided a rare opportunity to study realized sampling variances of genetic parameter estimates. The distribution of both heritability estimates and genetic correlation estimates, when plotted against estimated accuracy, was consistent with random error variance being some three times the sampling variance predicted from standard formulae. This result was consistent with the observation that the variance of estimates of heritabilities and genetic correlations between populations were about four times the predicted sampling variance, suggesting few real differences in genetic parameters between populations. Except where there was a strong biological or statistical expectation of a difference, there was little evidence for differences between genetic and phenotypic correlations for most trait combinations or for differences in genetic correlations between populations. These results suggest that, even for controlled populations, estimating genetic parameters specific to a given population is less useful than commonly believed. A serendipitous discovery was that, in the standard formula for theoretical standard error of a genetic correlation estimate, the heritabilities refer to the estimated values and not, as seems generally assumed, the true population values.     

Quantitative genetics of skeletal nonmetric traits in the rhesus macaques on Cayo Santiago. I. Single trait heritabilities

The use of skeletal nonmetric traits in studies of biological relationships often involves the assumption that variation in these traits is genetic. Studies of nonmetric traits in human groups and in inbred strains of mice and rabbits have indicated a genetic component to nonmetric trait variation. Skeletons of animals with known matrilineage membership were obtained from the Cayo Santiago skeletal collection in order to obtain a direct estimate of the heritabilities of several nonmetric traits in the free-ranging population of rhesus macaques on Cayo Santiago. Falconer's (1965) method was used to calculate heritability. Heritability estimates range from zero to one, and half of them are greater than 0.5. This indicates that there is a considerable amount of genetic variation for these traits among the Cayo macaques. There is a significant tendency for traits scoring the number of foramina to have lower heritabilities than those scoring hyperstotic or hypostotic traits.     

Accounting for female space sharing in St. Kilda Soay sheep (Ovis aries) results in little change in heritability estimates

When estimating heritability in free‐living populations, it is common practice to account for common environment effects, because of their potential to generate phenotypic covariance among relatives thereby biasing heritability estimates. In quantitative genetic studies of natural populations, however, philopatry, which results in relatives being clustered in space, is rarely accounted for. The two studies that have been carried out so far suggest absolute declines in heritability estimates of up to 43% when accounting for space sharing by relatives. However, due to methodological limitations these estimates may not be representative. We used data from the St. Kilda Soay sheep population to estimate heritabilities with and without accounting for space sharing for five traits for which there is evidence for additive genetic variance (birthweight, birth date, lamb August weight, and female post‐mortem jaw and metacarpal length). We accounted for space sharing by related females by separately incorporating spatial autocorrelation, and a home range similarity matrix. Although these terms accounted for up to 18% of the variance in these traits, heritability estimates were only reduced by up to 7%. Our results suggest that the bias caused by not accounting for space sharing may be lower than previously thought. This suggests that philopatry does not inevitably lead to a large bias if space sharing by relatives is not accounted for. We hope our work stimulates researchers to model shared space when relatives in their study population share space, as doing so will enable us to better understand when bias may be of particular concern.     

Unconstrained cranial evolution in Neandertals and modern humans compared to common chimpanzees

A variety of lines of evidence support the idea that neutral evolutionary processes (genetic drift, mutation) have been important in generating cranial differences between Neandertals and modern humans. But how do Neandertals and modern humans compare with other species? And how do these comparisons illuminate the evolutionary processes underlying cranial diversification? To address these questions, we used 27 standard cranial measurements collected on 2524 recent modern humans, 20 Neandertals and 237 common chimpanzees to estimate split times between Neandertals and modern humans, and between Pan troglodytes verus and two other subspecies of common chimpanzee. Consistent with a neutral divergence, the Neandertal versus modern human split-time estimates based on cranial measurements are similar to those based on DNA sequences. By contrast, the common chimpanzee cranial estimates are much lower than DNA-sequence estimates. Apparently, cranial evolution has been unconstrained in Neandertals and modern humans compared with common chimpanzees. Based on these and additional analyses, it appears that cranial differentiation in common chimpanzees has been restricted by stabilizing natural selection. Alternatively, this restriction could be due to genetic and/or developmental constraints on the amount of within-group variance (relative to effective population size) available for genetic drift to act on.     

Quantitative genetics of skeletal nonmetric traits in the rhesus macaques of Cayo Santiago. III. Relative heritability of skeletal nonmetric and metric traits

This study addresses the long-standing controversy in skeletal biology concerning the relative utility of skeletal metric and nonmetric traits for studies of biological relationship. This controversy centers on the relative heritability of these two trait sets. This paper presents heritabilities for a series of skeletal metric and nonmetric traits measured with the same sample of mother-offspring pairs from the Cayo Santiago skeletal collection of rhesus macaques. Skeletal nonmetric traits display significantly greater heritability estimates than metric traits. This difference is due primarily to the high heritability estimates of hyperostotic nonmetric traits. Foraminal traits are not significantly more heritable than skeletal metric traits. The generality of this pattern of heritability values, in which hyperostotic nonmetric traits are more highly heritable than foraminal nonmetric and metric traits, depends on future empirical study of the correlation of heritability values in populations and theoretical work.     

Estimating heritabilities and genetic correlations: comparing the 'animal model' with parent-offspring regression using data from a natural population

Quantitative genetic parameters are nowadays more frequently estimated with restricted maximum likelihood using the 'animal model' than with traditional methods such as parent-offspring regressions. These methods have however rarely been evaluated using equivalent data sets. We compare heritabilities and genetic correlations from animal model and parent-offspring analyses, respectively, using data on eight morphological traits in the great reed warbler (Acrocephalus arundinaceus). Animal models were run using either mean trait values or individual repeated measurements to be able to separate between effects of including more extended pedigree information and effects of replicated sampling from the same individuals. We show that the inclusion of more pedigree information by the use of mean traits animal models had limited effect on the standard error and magnitude of heritabilities. In contrast, the use of repeated measures animal model generally had a positive effect on the sampling accuracy and resulted in lower heritabilities; the latter due to lower additive variance and higher phenotypic variance. For most trait combinations, both animal model methods gave genetic correlations that were lower than the parent-offspring estimates, whereas the standard errors were lower only for the mean traits animal model. We conclude that differences in heritabilities between the animal model and parent-offspring regressions were mostly due to the inclusion of individual replicates to the animal model rather than the inclusion of more extended pedigree information. Genetic correlations were, on the other hand, primarily affected by the inclusion of more pedigree information. This study is to our knowledge the most comprehensive empirical evaluation of the performance of the animal model in relation to parent-offspring regressions in a wild population. Our conclusions should be valuable for reconciliation of data obtained in earlier studies as well as for future meta-analyses utilizing estimates from both traditional methods and the animal model.     

On the sampling variance of intraclass correlations and genetic correlations.

Widely used standard expressions for the sampling variance of intraclass correlations and genetic correlation coefficients were reviewed for small and large sample sizes. For the sampling variance of the intraclass correlation, it was shown by simulation that the commonly used expression, derived using a first-order Taylor series performs better than alternative expressions found in the literature, when the between-sire degrees of freedom were small. The expressions for the sampling variance of the genetic correlation are significantly biased for small sample sizes, in particular when the population values, or their estimates, are close to zero. It was shown, both analytically and by simulation, that this is because the estimate of the sampling variance becomes very large in these cases due to very small values of the denominator of the expressions. It was concluded, therefore, that for small samples, estimates of the heritabilities and genetic correlations should not be used in the expressions for the sampling variance of the genetic correlation. It was shown analytically that in cases where the population values of the heritabilities are known, using the estimated heritabilities rather than their true values to estimate the genetic correlation results in a lower sampling variance for the genetic correlation. Therefore, for large samples, estimates of heritabilities, and not their true values, should be used.     

The quantitative genetics of fluctuating asymmetry: a comparison of two models

The genetic basis of fluctuating asymmetry (FA), a measure of random deviations from perfect bilateral symmetry, has been the subject of much recent work. In this paper we compare two perspectives on the quantitative genetic analysis of FA and directional asymmetry (DA). We call these two approaches the character-state model and the environmental responsiveness model. In the former approach, the right and left sides are viewed as separate traits whose genetic coupling is manifested by the genetic correlation. This model leads to the relationship, h2(DA) = h2[(1-rA)/(1-rp)), where h2 is the heritability of each component trait (assumed to be the same), rA and rp are the genetic and phenotypic correlations between traits, respectively. Simulation shows that, under this model, the heritability of FA is considerably less than that of DA, except when heritabilities are very close to zero. The environmental responsiveness model permits genetic variance in FA even when the genetic correlation between traits is + 1. Simulation shows that under this model the heritability of FA can be uncoupled from that of DA. The additive and nonadditive components of the component (right and left) traits, their DA and FA values are estimated using a diallel cross of seven inbred lines of the sand cricket, Gryllus firmus. Four leg measurements were made and both the individual DA and FA values and the compound measures DASUM and CFA estimated. The heritabilities of the compound measures are slightly larger than the individual estimates. Dominance variance is observed in the individual traits but predicted to be an even smaller component of the phenotypic variance than the additive genetic variance. The estimated values confirm this, although a previous study has demonstrated that dominance variance is present. Because the heritabilities of FA are generally larger than those of DA, which never exceed 0.02, the environmental responsiveness model is more consistent with the data than the character-state model. A review of other data suggests that both sources of variation might be found in some species.     

Estimation of components of genetic variance and heritability for flowering time and yield in gerbera using Derivative-Free Restricted Maximum Likelihood (DFRML)

Summary Additive genetic components of variance and narrow-sense heritabilities were estimated for flowering time (FT) and cut-flower yield (Y) for six generations of the Davis Population of gerbera using Derivative-Free Restricted Maximum Likelihood (DFRML). Additive genetic variance accounted for 54% of the total variability for FT and 30% of the total variability for Y. The heritability of FT (0.54) agreed with previous ANOVA-based estimates. However, the heritability of Y (0.30) was substantially lower than estimates using ANOVA. The advantages of DFRML and its applications in the estimation of components of genetic variance and heritabilities of plant populations are discussed.     

Estimates of genetic parameters of certain characters in Hevea brasiliensis

Summary Heritability estimates of five quantitative characters, namely, yield, girth, girth increment, virgin bark and renewed bark thickness, of the breeding Phase III Hevea families have been obtained by variance component analyses. In general, the combined heritability estimates for various characters were low to moderate. The heritabilities of these characters based on female variance components, however, were high, suggesting that considerable improvement of each of the characters could be achieved in properly designed experiments.Estimates of heritability for average yields (Range: 0.11–0.34) over different years showed that the first three years' yield was adequate for predicting estimates of genetic variance for the average of five years' yield.Correlation studies on yield with other characters indicated considerable influence of environment, with genetic correlations accounting for about 0.07 to 0.36 in the characters studied.Expected direct response to selection in yield and correlated response in yield to selection for girth at opening and virgin bark thickness have been calculated using three arbitrary values of selection intensity. The efficiency of the correlated response was found to be approximately half that of the direct response. However, the indirect selection for yield using virgin bark thickness appeared to be more favourable than that using the girth at opening favoured by earlier workers.     

Heritability and evolvability of fitness and nonfitness traits: Lessons from livestock

Data from natural populations have suggested a disconnection between trait heritability (variance standardized additive genetic variance, V_A) and evolvability (mean standardized V_A) and emphasized the importance of environmental variation as a determinant of trait heritability but not evolvability. However, these inferences are based on heterogeneous and often small datasets across species from different environments. We surveyed the relationship between evolvability and heritability in >100 traits in farmed cattle, taking advantage of large sample sizes and consistent genetic approaches. Heritability and evolvability estimates were positively correlated (r = 0.37/0.54 on untransformed/log scales) reflecting a substantial impact of V_A on both measures. Furthermore, heritabilities and residual variances were uncorrelated. The differences between this and previously described patterns may reflect lower environmental variation experienced in farmed systems, but also low and heterogeneous quality of data from natural populations. Similar to studies on wild populations, heritabilities for life‐history and behavioral traits were lower than for other traits. Traits having extremely low heritabilities and evolvabilities (17% of the studied traits) were almost exclusively life‐history or behavioral traits, suggesting that evolutionary constraints stemming from lack of genetic variability are likely to be most common for classical “fitness” (cf. life‐history) rather than for “nonfitness” (cf. morphological) traits.     

A meta-analysis of the heritability of developmental stability

The existence of additive genetic variance in developmental stability has important implications for our understanding of morphological variation. The heritability of individual fluctuating asymmetry and other measures of developmental stability have frequently been estimated from parent-offspring regressions, sib analyses, or from selection experiments. Here we review by meta-analysis published estimates of the heritability of developmental stability, mainly the degree of individual fluctuating asymmetry in morphological characters. The overall mean effect size of heritabilities of individual fluctuating asymmetry was 0.19 from 34 studies of 17 species differing highly significantly from zero (P < 0.0001). The mean heritability for 14 species was 0.27. This indicates that there is a significant additive genetic component to developmental stability. Effect size was larger for selection experiments than for studies based on parent-offspring regression or sib analyses, implying that genetic estimates were unbiased by maternal or common environment effects. Additive genetic coefficients of variation for individual fluctuating asymmetry were considerably higher than those for character size per se. Developmental stability may be significantly heritable either because of strong directional selection, or fluctuating selection regimes which prevent populations from achieving a high degree of developmental stability to current environmental and genetic conditions.     

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.     

Genetic parameters for body weight,longissimus muscle depth and fat depth for Suffolk sheep in the Czech Republic

In this study, heritabilities and (co)variance components for body weight at 100 days (BW), muscle depth (MD) and fat depth (FD) were estimated for Suffolk, the most common sheep breed in the Czech Republic. Data from 1996 to 2004 were extracted from the sheep recording database of the Czech Sheep and Goat Breeding Association. Genetic parameters were estimated using multivariate animal models, including both direct and maternal genetic effects and permanent environmental effects. Average values for BW, MD and FD were 27.91 kg, 25.5 mm and 3.3 mm, respectively. Direct and maternal heritability for BW were 0.17 and 0.08, respectively, and direct heritabilities were 0.16 for MD and 0.08 for FD. Maternal heritability estimates for ultrasonic measurements were generally low. Direct genetic correlations between BW and MD and maternal genetic correlations between BW and MD were positive and favourable. Both direct genetic correlations between BW and FD and maternal genetic correlations between BW and FD were negative, but not significantly different from zero. The favourable genetic correlations between BW and MD make ultrasound measurements a valuable tool in breeding programs focusing on growth and carcass characteristics.     

Quantitative genetic analysis of skin reflectance: a multivariate approach.

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

Comparing Evolvability and Variability of Quantitative Traits

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

Genetic Control of Glycolysis in Human Erythrocytes

We have studied heritability of the concentration of each glycolytic intermediate and adenine nucleotide in the cytosol of human erythrocytes obtained from a random sample of apparently healthy young individuals. Preliminary to analysis of heritability, each trait was statistically described and the effects attributable to variation in measured concomitants were removed by regression. Heritability was estimated using the family-set method. This method removes covariances between the index case, sibling and first cousin, due to those environmental determinants of the phenotypic values that are shared with a matched, unrelated control member of the family set. It also removes covariances due to environments that are shared by siblings and first cousins. Heritability was estimated by employing the fact that the variance of differences between first cousins minus the variance of differences between full siblings estimates three-fourths of the additive genetic variance. The heritability estimates for G6P†, F6P, ATP and some other metabolite concentrations are high and significantly greater than zero. The heritabilities of G6P and F6P are likely attributable to genetic variation in the in vivo activity of HK and/or PFK, because the concentrations of these metabolites are tightly controlled by the two regulatory enzymes. Statistically significant heritability estimates for HK and PFK mass action ratios strongly suggest genes are responsible for a portion of the quantitative variation in these enzyme activities. Since HK and PFK regulate glycolysis and the production of ATP, genetic variation in their activities might be causally related to the heritability of ATP concentration.     

Comparison of REML and Gibbs sampling estimates of multi-trait genetic parameters in Scots pine

Multi-trait (co)variance estimation is an important topic in plant and animal breeding. In this study we compare estimates obtained with restricted maximum likelihood (REML) and Bayesian Gibbs sampling of simulated data and of three traits (diameter, height and branch angle) from a 26-year-old partial diallel progeny test of Scots pine (Pinus sylvestris L.). Based on the results from the simulated data we can conclude that the REML estimates are accurate but the mode of posterior distributions from the Gibbs sampling can be overestimated depending on the level of the heritability. The mean and median of the posteriors were considerably higher than the expected values of the heritabilities. The confidence intervals calculated with the delta method were biased downwardly. The highest probablity density (HPD) interval provides a better interval estimate, but could be slightly biased at the lower level. Similar differences between REML and Gibbs sampling estimates were found for the Scots pine data. We conclude that further simulation studies are needed in order to evaluate the effect of different priors on (co)variance components in the genetic individual model.     

Broad and narrow heritabilities of quantitative traits in a founder population

Estimation of the components of variance for a quantitative trait allows one to evaluate both the degree to which genetics influences the trait and the trait's underlying genetic architecture. For particular traits, the estimates also may have implications for discriminating between potential models of selection and for choosing an appropriate model for linkage analysis. Using a recently developed method, we estimate the additive and dominance components of variance--or, equivalently, the narrow and broad sense heritabilities--of several traits in the Hutterites, a founder population with extensive genealogical records. As a result of inbreeding and because Hutterite individuals are typically related through multiple lines of descent, we expect that power to detect dominance variance will be increased relative to that in outbred studies. Furthermore, the communal lifestyle of the Hutterites allows us to evaluate the genetic influences in a relatively homogeneous environment. Four phenotypes had a significant dominance variance, resulting in a relatively high broad heritability. We estimated the narrow and broad heritabilities as being, respectively,.36 and.96 for LDL,.51 and 1.0 for serotonin levels, and.45 and.76 for fat free mass (FFM). There was no significant additive component for systolic blood pressure (SBP), resulting in a narrow heritability of 0 and a broad heritability of.45. There were several traits for which we found no significant dominance component, resulting in equal broad and narrow heritability estimates. These traits and their heritabilities are as follows: HDL,.63; triglycerides,.37; diastolic blood pressure,.21; immunoglobulin E,.63; lipoprotein(a),.77; and body-mass index,.54. The large difference between broad and narrow heritabilities for LDL, serotonin, FFM, and SBP are indicative of strong dominance effects in these phenotypes. To our knowledge, this is the first study to report an estimate of heritability for serotonin and to detect a dominance variance for LDL, FFM, and SBP.