Analysis of quantitative trait loci using hybrid pedigrees: quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral chi(2) distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are original data for the analysis of a quantitative trait.     

Analysis of quantitative trait loci using hybrid pedigrees: Quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral x ² distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are initial data for the analysis of a quantitative trait.     

Selective sweeps in multilocus models of quantitative traits

We study the trajectory of an allele that affects a polygenic trait selected toward a phenotypic optimum. Furthermore, conditioning on this trajectory we analyze the effect of the selected mutation on linked neutral variation. We examine the well-characterized two-locus two-allele model but we also provide results for diallelic models with up to eight loci. First, when the optimum phenotype is that of the double heterozygote in a two-locus model, and there is no dominance or epistasis of effects on the trait, the trajectories of selected mutations rarely reach fixation; instead, a polymorphic equilibrium at both loci is approached. Whether a polymorphic equilibrium is reached (rather than fixation at both loci) depends on the intensity of selection and the relative distances to the optimum of the homozygotes at each locus. Furthermore, if both loci have similar effects on the trait, fixation of an allele at a given locus is less likely when it starts at low frequency and the other locus is polymorphic (with alleles at intermediate frequencies). Weaker selection increases the probability of fixation of the studied allele, as the polymorphic equilibrium is less stable in this case. When we do not require the double heterozygote to be at the optimum we find that the polymorphic equilibrium is more difficult to reach, and fixation becomes more likely. Second, increasing the number of loci decreases the probability of fixation, because adaptation to the optimum is possible by various combinations of alleles. Summaries of the genealogy (height, total length, and imbalance) and of sequence polymorphism (number of polymorphisms, frequency spectrum, and haplotype structure) next to a selected locus depend on the frequency that the selected mutation approaches at equilibrium. We conclude that multilocus response to selection may in some cases prevent selective sweeps from being completed, as described in previous studies, but that conditions causing this to happen strongly depend on the genetic architecture of the trait, and that fixation of selected mutations is likely in many instances.     

Range limits in spatially explicit models of quantitative traits

In an influential paper, Kirkpatrick and Barton (Am Nat 150:1–23 1997) presented a system of diffusive partial differential equations modeling the joint evolution of population density and the mean of a quantitative trait when the trait optimum varies over a continuous spatial domain. We present a stability theorem for steady states of a simplified version of the system, originally studied in Kirkpatrick and Barton (Am Nat 150:1–23 1997). We also present a derivation of the system.     

Multifactorial genetic models for quantitative traits in humans.

Quantitative traits measured in human families can be analyzed to partition the total population variance into genetic and environmental components, or to elucidate the genetic mechanism involved. We review the estimation of variance components directly from human pedigree data, or in the form of path coefficients from correlations between pairs of relatives. To elucidate genetic mechanisms, a mixed model that allows for segregation at a major locus, a polygenic effect and a sibling environmental correlation is described for nuclear families. In each case appropriate likelihoods are derived as a basis, using numerical maximum likelihood methods, for parameter estimation and hypothesis testing. A general model is then described that allows for several familial sources of environmental variation, assortative mating, and both major gene and polygenic effects; and an algorithm for calculating the likelihood of a pedigree under this model is indicated. Finally, some of the remaining problems in this area of biometric analysis are pointed out.     

Power of the joint segregation analysis method for testing mixed major-gene and polygene inheritance models of quantitative traits

Understanding the genetic architecture of quantitative traits can greatly assist the design of strategies for their manipulation in plant-breeding programs. For a number of traits, genetic variation can be the result of segregation of a few major genes and many polygenes (minor genes). The joint segregation analysis (JSA) is a maximum-likelihood approach for fitting segregation models through the simultaneous use of phenotypic information from multiple generations. Our objective in this paper was to use computer simulation to quantify the power of the JSA method for testing the mixed-inheritance model for quantitative traits when it was applied to the six basic generations: both parents (P₁ and P₂), F₁, F₂, and both backcross generations (B₁ and B₂) derived from crossing the F₁ to each parent. A total of 1968 genetic model-experiment scenarios were considered in the simulation study to quantify the power of the method. Factors that interacted to influence the power of the JSA method to correctly detect genetic models were: (1) whether there were one or two major genes in combination with polygenes, (2) the heritability of the major genes and polygenes, (3) the level of dispersion of the major genes and polygenes between the two parents, and (4) the number of individuals examined in each generation (population size). The greatest levels of power were observed for the genetic models defined with simple inheritance; e.g., the power was greater than 90% for the one major gene model, regardless of the population size and major-gene heritability. Lower levels of power were observed for the genetic models with complex inheritance (major genes and polygenes), low heritability, small population sizes and a large dispersion of favourable genes among the two parents; e.g., the power was less than 5% for the two major-gene model with a heritability value of 0.3 and population sizes of 100 individuals. The JSA methodology was then applied to a previously studied sorghum data-set to investigate the genetic control of the putative drought resistance-trait osmotic adjustment in three crosses. The previous study concluded that there were two major genes segregating for osmotic adjustment in the three crosses. Application of the JSA method resulted in a change in the proposed genetic model. The presence of the two major genes was confirmed with the addition of an unspecified number of polygenes. Received: 18 August 2000 / Accepted: 9 March 2001     

Theoretical models of selection and mutation on quantitative traits

Empirical studies of quantitative genetic variation have revealed robust patterns that are observed both across traits and across species. However, these patterns have no compelling explanation, and some of the observations even appear to be mutually incompatible. We review and extend a major class of theoretical models, 'mutation-selection models', that have been proposed to explain quantitative genetic variation. We also briefly review an alternative class of 'balancing selection models'. We consider to what extent the models are compatible with the general observations, and argue that a key issue is understanding and modelling pleiotropy. We discuss some of the thorny issues that arise when formulating models that describe many traits simultaneously.     

Inheritance of dermatoglyphic asymmetry in 500 Indian pedigrees: complex segregation analysis

The major aim of this study is to determine the mode of inheritance of asymmetry of quantitative dermatoglyphic traits based on principal factors through the application of complex segregation (genetic model fitting) analyses on a large ethnically homogeneous sample of 500 Indian pedigrees (2435 individuals) of two generations. By segregation analysis of the traits- PC1_FA both Mendelian and Environmental models were rejected (< 0.001) with the General model, i.e. that despite presence of significant inheritance (rejection of Environmental model), the nature of inheritance is more complex, than Mendelian one. Although a little genetic effect was observed due to familial correlations on asymmetry traits, no evidence was found of major gene contribution to be involved, but this does not contradict the notion postulated by several earlier authors that asymmetry (fluctuating) provides a measure of developmental instability in human.     

Inheritance of 18 quantitative dermatoglyphic traits based on factors in MZ and DZ twins

18 quantitative finger and palmar dermatoglyphic traits were analyzed with the aim of determining genetic effects and common familial environmental influences on a large (358 nuclear pedigrees) number of twins (MZ and DZ). Genetic analysis based on principal factors includes variance and bivariate variance decomposition analysis. Especially, Factor 1 (digital pattern size) is remarkable, due to its degree of universality. The results of genetic analysis revealed all three extracted factors have significant proportion of additive genetic variance (93.5% to 72.9%). The main results of bivariate variance decomposition analysis appears significant correlation in residual variance between digital pattern size factor (Factor 1) versus finger pattern intensity factor (Factor 4), and palmar main lines factor (Factor 2) verses a-b ridge count (Factor 3), but there was no significant correlation in the genetic variance of factors.     

Admixture mapping of quantitative traits in Populus hybrid zones: power and limitations

Uncovering the genetic architecture of species differences is of central importance forunderstanding the origin and maintenance of biological diversity. Admixture mapping can beused to identify the number and effect sizes of genes that contribute to the divergence ofecologically important traits, even in taxa that are not amenable to laboratory crossesbecause of their long generation time or other limitations. Here, we apply admixturemapping to naturally occurring hybrids between two ecologically divergent Populusspecies. We map quantitative trait loci for eight leaf morphological traits using 77mapped microsatellite markers from all 19 chromosomes of Populus. We applymultivariate linear regression analysis allowing the modeling of additive and non-additivegene action and identify several candidate genomic regions associated with leaf morphologyusing an information-theoretic approach. We perform simulation studies to assess the powerand limitations of admixture mapping of quantitative traits in natural hybrid populationsfor a variety of genetic architectures and modes of gene action. Our results indicate that(1) admixture mapping has considerable power to identify the genetic architecture ofspecies differences if sample sizes and marker densities are sufficiently high, (2)modeling of non-additive gene action can help to elucidate the discrepancy betweengenotype and phenotype sometimes seen in interspecific hybrids, and (3) the geneticarchitecture of leaf morphological traits in the studied Populus species involvescomplementary and overdominant gene action, providing the basis for rapid adaptation ofthese ecologically important forest trees.     

Maximum likelihood estimation by counting methods under polygenic and mixed models in human pedigrees.

For pedigree data, the maximum likelihood estimates of the parameters in polygenic and mixed models are derived analytically although not in closed form but in terms of "counting equations" allowing an iterative solution. Likelihood computations, tests of significance, and tests of goodness of fit are presented. Accelerating the (linear) rate of convergence by a very simple method is demonstrated.     

Bayesian inference of mixed models in quantitative genetics of crop species

The objectives of this study were to implement a Bayesian framework for mixed models analysis in crop species breeding and to exploit alternatives for informative prior elicitation. Bayesian inference for genetic evaluation in annual crop breeding was illustrated with the first two half-sib selection cycles in a popcorn population. The Bayesian framework was based on the Just Another Gibbs Sampler software and the R2jags package. For the first cycle, a non-informative prior for the inverse of the variance components and an informative prior based on meta-analysis were used. For the second cycle, a non-informative prior and an informative prior defined as the posterior from the non-informative and informative analyses of the first cycle were used. Regarding the first cycle, the use of an informative prior from the meta-analysis provided clearly distinct results relative to the analysis with a non-informative prior only for the grain yield. Regarding the second cycle, the results for the expansion volume and grain yield showed differences among the three analyses. The differences between the non-informative and informative prior analyses were restricted to variance components and heritability. The correlations between the predicted breeding values from these analyses were almost perfect.     

Modeling relationships between calving traits: a comparison between standard and recursive mixed models

Background

The use of structural equation models for the analysis of recursive and simultaneous relationships between phenotypes has become more popular recently. The aim of this paper is to illustrate how these models can be applied in animal breeding to achieve parameterizations of different levels of complexity and, more specifically, to model phenotypic recursion between three calving traits: gestation length (GL), calving difficulty (CD) and stillbirth (SB). All recursive models considered here postulate heterogeneous recursive relationships between GL and liabilities to CD and SB, and between liability to CD and liability to SB, depending on categories of GL phenotype.

Methods

Four models were compared in terms of goodness of fit and predictive ability: 1) standard mixed model (SMM), a model with unstructured (co)variance matrices; 2) recursive mixed model 1 (RMM1), assuming that residual correlations are due to the recursive relationships between phenotypes; 3) RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4) RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes.

Results

For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB.Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible.

Conclusions

The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the phenotypic recursion may be an important cause of the observed patterns of genetic and environmental correlations.     

Inheritance of acquired traits in plants: Reinstatement of Lamarck

Since Lamarck proposed the idea of inheritance of acquired traits 200 years ago, much has been said for and against it, but the theory was finally declined after the 1930s. Despite of the negative opinions of the majority of geneticists, botanists and plant breeders have long recognized that altered properties during the growth were occasionally transmitted to the offspring. This was also the case with artificially altered properties such as dwarfism, flowering timing and plant stature, which were induced by a non-mutagenic chemical, 5-azacytidine and its derivatives. As these drugs are powerful inhibitors of DNA methylation in vivo, a close correlation between methylation and phenotypic expression was suggested. Subsequent studies showed that rice plants acquired disease resistance upon demethylation of the corresponding resistant gene, and that both resistant trait and hypomethylated status were inherited by the progeny up to nine generations. Whether or not the methylation pattern changes under natural condition was then questioned, and recent studies have indicated that it indeed naturally changes in response to environmental stresses. Whether or not the altered methylation pattern during the vegetative growth is heritable was also questioned, and studies on toadflax and rice affirmed the question, showing stable maintenance of hypermethylation in the former and hypomethylation in the latter for 250 and 10 years, respectively. The observation strongly suggested that acquired traits can be heritable as far as the acquired methylation pattern is stably transmitted. This concept is consistent with the Lamarck''s theory of the inheritance of acquired traits, which therefore should be carefully reevaluated to reestablish his impaired reputation.Key words: acquired traits, cytosine methylation, disease resistance, environmental stress, epigenetics, Lamarckian inheritanceIn 1809, the French naturalist, Jean Baptiste de Lamarck (1744–1829) proposed two laws of evolution—the law of use/disuse and the law of inheritance of acquired traits. The theory was declined almost completely after the 1930s. In plants, however, phenomena showing apparent inheritance of acquired traits have long been observed. This article briefly summarizes the current view of the “Lamarckian inheritance” in higher plants. Many excellent review articles related to this topic have been published, and readers are strongly suggested to refer to them for further information on molecular aspects.^1–3     

Generalized linear mixed models for mapping multiple quantitative trait loci

Many biological traits are discretely distributed in phenotype but continuously distributed in genetics because they are controlled by multiple genes and environmental variants. Due to the quantitative nature of the genetic background, these multiple genes are called quantitative trait loci (QTL). When the QTL effects are treated as random, they can be estimated in a single generalized linear mixed model (GLMM), even if the number of QTL may be larger than the sample size. The GLMM in its original form cannot be applied to QTL mapping for discrete traits if there are missing genotypes. We examined two alternative missing genotype-handling methods: the expectation method and the overdispersion method. Simulation studies show that the two methods are efficient for multiple QTL mapping (MQM) under the GLMM framework. The overdispersion method showed slight advantages over the expectation method in terms of smaller mean-squared errors of the estimated QTL effects. The two methods of GLMM were applied to MQM for the female fertility trait of wheat. Multiple QTL were detected to control the variation of the number of seeded spikelets.     

QTL Express: mapping quantitative trait loci in simple and complex pedigrees

QTL Express is the first application for Quantitative Trait Locus (QTL) mapping in outbred populations with a web-based user interface. User input of three files containing a marker map, trait data and marker genotypes allows mapping of single or multiple QTL by the regression approach, with the option to perform permutation or bootstrap tests.