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.     

The heritability of fitness: some single gene models

Summary Because directional selection exhausts additive-genetic variance, it is frequently claimed that the heritability of fitness should be very close to zero. However, mutation-selection balance generates a certain amount of additive-genetic variance, so that even parent-offspring measures of heritability may be greater than zero at equilibrium. Intra-generation heritability may also be non-zero, providing the potentials for genetic change following environmental change.     

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 influence of aberrant values on the statistics related to a selection program

Summary Examples are presented to illustrate some of the effects aberrant values, in particular, measurement errors, may have on estimates of the genetic parameters related to selection studies. It is shown that aberrant values may cause observed response to selection pressure to differ considerably from predicted response. Possible dangers of indiscriminate screening are also discussed.     

Responses of alloplasmic (cytoplasm=Triticum timopheevii) and euplasmic wheats (Triticum aestivum) to photoperiod and vernalization

Summary Heritability estimated from sire family variance components, ignoring dams, pools conventional paternal and maternal half sib estimates, in a way which is biased upward, and sub-optimal for minimizing the sampling variance. Standard error of a sire family estimate will be smaller than that of the equivalent paternal half sib estimate, but not as small as that of an estimate obtained by optimal pooling of paternal and maternal half sib estimates. If only additive genetic variance components are significant, the bias may be removed by use of a computed average genetic relationship for sire families, in place of a nominal R = 0.25. Average genetic relationship may be computed from mean and variance of dam family size within sire families. If dominance, epistatic, or maternal components are significant, this simple correction is not appropriate. In situations likely to be encountered in large domestic species such as sheep and cattle (dam family size small and uniform) bias will be negligible. The method could be useful where cost of dam identification is a limiting factor.     

利用单元内方差分析法估计遗传参数的探讨

在遗传力的估计过程中,需将多种非遗传因素的影响从公畜间方差或者母畜间方差中剔除。在我国常使用的是盛志廉教授提出的单元内同胞相关法。本文对该法从理论上进行了更详细的证明,并将其推广到两层分类方差分析时的情况。同时还给出了当公母畜彼此间有亲缘关系时,利用单元内方差分析估计遗传力的方法。这些方法既可使遗传力的估计简便,又具有多因方差分析的功用。     

The concept of group heritability

This paper investigates the role of the concept of group heritability in group selection theory, in relation to the well-known distinction between type 1 and type 2 group selection (GS1 and GS2). I argue that group heritability is required for the operation of GS1 but not GS2, despite what a number of authors have claimed. I offer a numerical example of the evolution of altruism in a multi-group population which demonstrates that a group heritability coefficient of zero is perfectly compatible with the successful operation of group selection in the GS2 sense. A diagnosis of why group heritability has wrongly been regarded as necessary for GS2 is suggested.     

Prediction of the power of detection of marker-quantitative trait locus linkages using analysis of variance

Analysis of variance can be used to detect the linkage of segregating quantitative trait loci (QTLs) to molecular markers in outbred populations. Using independent full-sib families and assuming linkage equilibrium, equations to predict the power of detection of a QTL are described. These equations are based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed. A simple prediction of power from the mean squares is used that assumes a random model so that in the mixed-model situation this is an approximation. Simulation is used to illustrate the failure of the random model to predict mean squares and, hence, the power. The mixed model is shown to provide accurate prediction of the mean squares and, using the approximation, of power.     

Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

Sampling bias in estimating Design II variance components with S1 families

Summary The use of several S₁ individuals to represent an S₀ individual permits the use of a Design II mating scheme for plants with only one pistillate flower per plant. Estimates of additive (V _A ) and dominance (V _D ) variance from this mating scheme will be biased upwards, when a small number (10) of individuals of each S₁ line are used. This bias can be computed, and the additive and dominance estimates can be corrected. Of particular interest is the observation that the additive genetic variance contributes to bias in estimates of V _D . When S₀ plants are non inbred and their selfedprogeny (S₁ lines) are used to represent them in developing families for use in the Design II, where m₁ is the number of individuals used to represent an S₁ line in developing half sib-families and m₂ is the number of individuals used to represent the S₁ line in making up full sib-families. For example, in a 3×3 Design II, with about 10 individuals used to represent each S₁ line in each cross, m₂ = 10 and m₁ = 30. When m₁ = m₂ = 1, and Joint contribution from Department of Agronomy, University of Nebraska 68583, and the S. S. Cameron Laboratory, Werribee, Victoria 3030, Australia. Published as paper No. 7395, Journal Series     

Estimation of the contribution of quantitative trait loci (QTL) to the variance of a quantitative trait by means of genetic markers

The estimation of the contribution of an individual quantitative trait locus (QTL) to the variance of a quantitative trait is considered in the framework of an analysis of variance (ANOVA). ANOVA mean squares expectations which are appropriate to the specific case of QTL mapping experiments are derived. These expectations allow the specificities associated with the limited number of genotypes at a given locus to be taken into account. Discrepancies with classical expectations are particularly important for two-class experiments (backcross, recombinant inbred lines, doubled haploid populations) and F₂ populations. The result allows us firstly to reconsider the power of experiments (i.e. the probability of detecting a QTL with a given contribution to the variance of the trait). It illustrates that the use of classical formulae for mean squares expectations leads to a strong underestimation of the power of the experiments. Secondly, from the observed mean squares it is possible to estimate directly the variance associated with a locus and the fraction of the total variance associated to this locus (r _l ² ). When compared to other methods, the values estimated using this method are unbiased. Considering unbiased estimators increases in importance when (1) the experimental size is limited; (2) the number of genotypes at the locus of interest is large; and (3) the fraction of the variation associated with this locus is small. Finally, specific mean squares expectations allows us to propose a simple analytical method by which to estimate the confidence interval of r _l ² . This point is particularly important since results indicate that 95% confidence intervals for r _l ² can be rather wide:2–23% for a 10% estimate and 8–34% for a 20% estimate if 100 individuals are considered.     

Prediction of effects of genetic drift on variance components under a general model of epistasis

For a model of diallelic loci with arbitrary epistasis, Barton and Turelli [2004. Effects of genetic drift on variance components under a general model of epistasis. Evolution 58, 2111-2132] gave results for variances among and within replicate lines obtained by inbreeding without selection. Here, we discuss the relation between their population genetic methods and classical quantitative genetic arguments. In particular, we consider the case of no dominance using classical identity by descent arguments, which generalizes their results from two alleles to multiple alleles. To clarify the connections between the alternative methods, we obtain the same results using an intermediate method, which explicitly identifies the statistical effects of sets of loci. We also discuss the effects of population bottlenecks on covariances among relatives.     

Genetic Variance–covariance Matrices: A Critique of the Evolutionary Quantitative Genetics Research Program

This paper outlines a critique of the use of the genetic variance–covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations – contrary to what assumed by most practicing biologists. I suggest that the search for a general solution to the difficult problem of identifying causal structures given observed correlation’s has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners.     

Whole genome approaches to quantitative genetics

Apart from parent-offspring pairs and clones, relative pairs vary in the proportion of the genome that they share identical by descent. In the past, quantitative geneticists have used the expected value of sharing genes by descent to estimate genetic parameters and predict breeding values. With the possibility to genotype individuals for many markers across the genome it is now possible to empirically estimate the actual relationship between relatives. We review some of the theory underlying the variation in genetic identity, show applications to estimating genetic variance for height in humans and discuss other applications.     

Selection,structure and the heritability of behaviour

Characters which are closely linked to fitness often have low heritabilities (V_A/V_P). Low heritabilities could be because of low additive genetic variation (V_A), that had been depleted by directional selection. Alternatively, low heritabilities may be caused by large residual variation (V_R=V_P – V_A) compounded at a disproportionately higher rate than V_A across integrated characters. Both hypotheses assume that each component of quantitative variation has an independent effect on heritability. However, V_A and V_R may also covary, in which case differences in heritability cannot be fully explained by the independent effects of elimination‐selection or compounded residual variation. We compared the central tendency of published behavioural heritabilities (mean=0.31, median=0.23) with morphological and life history data collected by 26 ). Average behavioural heritability was not significantly different from average life history heritability, but both were smaller than average morphological heritability. We cross‐classified behavioural traits to test whether variation in heritability was related to selection (dominance, domestic/wild) or variance compounding (integration level). There was a significant three‐way interaction between indices of selection and variance compounding, related to the absence of either effect at the highest integration level. At lower integration levels, high dominance variance indicated effects of selection. It was also indicated by the low CV_A of domestic species. At the same time CV_R increased disproportionately faster than CV_A across integration levels, demonstrating variance compounding. However, neither CV_R nor CV_A had a predominant effect on heritability. The partial regression coefficients of CV_R and CV_A on heritability were similar and a path analysis indicated that their (positive) correlation was also necessary to explain variation in heritability. These results suggest that relationships between additive genetic and residual components of quantitative genetic variation can constrain their independent direct effects on behavioural heritability.