Extension of the Castle-Wright effective factor estimator to sex linkage and haplodiploidy.

The Castle-Wright effective factor estimator gives a minimum estimate of the number of genes underlying complex traits. Because the Castle-Wright estimator does not rely on genetic markers, it is especially useful in genetically undeveloped species. In this article I describe two extensions of this estimator. The first corrects the estimator in heterogametic (XY) species with a partially sex-linked trait. In this case the traditional estimator underestimates gene number in F2 males and overestimates it in F2 females and backcross females and males. The second extension adapts the Castle-Wright equation to haplodiploid species.     

Shared quantitative trait loci underlying the genetic correlation between continuous traits

We review genetic correlations among quantitative traits in light of their underlying quantitative trait loci (QTL). We derive an expectation of genetic correlation from the effects of underlying loci and test whether published genetic correlations can be explained by the QTL underlying the traits. While genetically correlated traits shared more QTL (33%) on average than uncorrelated traits (11%), the actual number of shared QTL shared was small. QTL usually predicted the sign of the correlation with good accuracy, but the quantitative prediction was poor. Approximately 25% of trait pairs in the data set had at least one QTL with antagonistic effects. Yet a significant minority (20%) of such trait pairs have net positive genetic correlations due to such antagonistic QTL 'hidden' within positive genetic correlations. We review the evidence on whether shared QTL represent single pleiotropic loci or closely linked monotropic genes, and argue that strict pleiotropy can be viewed as one end of a continuum of recombination rates where r=0. QTL studies of genetic correlation will likely be insufficient to predict evolutionary trajectories over long time spans in large panmictic populations, but will provide important insights into the trade-offs involved in population and species divergence.     

A quantitative genetic model for analyzing species differences in outcrossing species

A genetic model based on a two-level intra- and interspecific mating design is proposed to estimate the genetic architecture of species differences and heterosis for outcrossing species. The underlying genetic analyses make use of classical quantitative genetic theories and recent results from molecular genetic studies. Gene effects across different quantitative trait loci (QTL) can be approximated by a geometric series. Under natural selection, gene effects are often associated with allele frequencies in a particular way, which can be approximated by the gamma distribution. By incorporating these approximations into family structural analyses in the mating design, we are able to estimate a number of genetic parameters that contribute to quantitative genetic variation based on a nonlinear optimization approach. These parameters include the number of QTL, their gene effects, and their allele frequencies in the parental populations. We perform simulation studies and illustrate an example to demonstrate the statistical property and procedure of the method.     

Allelic diversity for neutral markers retains a higher adaptive potential for quantitative traits than expected heterozygosity

The adaptive potential of a population depends on the amount of additive genetic variance for quantitative traits of evolutionary importance. This variance is a direct function of the expected frequency of heterozygotes for the loci which affect the trait (QTL). It has been argued, but not demonstrated experimentally, that long‐term response to selection is more dependent on QTL allelic diversity than on QTL heterozygosity. Conservation programmes, aimed at preserving this variation, usually rely on neutral markers rather than on quantitative traits for making decisions on management. Here, we address, both through simulation analyses and experimental studies with Drosophila melanogaster, the question of whether allelic diversity for neutral markers is a better indicator of a high adaptive potential than expected heterozygosity. In both experimental and simulation studies, we established synthetic populations for which either heterozygosity or allelic diversity was maximized using information from QTL (simulations) or unlinked neutral markers (simulations and experiment). The synthetic populations were selected for the quantitative trait to evaluate the evolutionary potential provided by the two optimization methods. Our results show that maximizing the number of alleles of a low number of markers implies higher responses to selection than maximizing their heterozygosity.     

Multivariate analysis of quantitative trait loci influencing variation in anxiety-related behavior in laboratory mice

The number and mode of action of quantitative trait loci (QTL) that contribute to behavioral variation in rodents is still largely unknown. On theoretical grounds, multivariate techniques are expected to yield new insights into this problem, but there are only a few examples of its application in practice. Here we explore the power of multivariate approaches to uncover the genetic architecture of 23 anxiety-related phenotypes in 1636 F₂ laboratory mice. We detected QTL with a genome-wide significance threshold of P < 0.05 on 14 chromosomes, of which 10 correspond to those identified by univariate analysis. Novel QTL were found on Chromosomes 3, 9, 13, and 17. Thus, multivariate analyses increased the yield of QTL exceeding a genome-wide significance threshold by 40%. On the basis of these results and by the application of a QTL estimator, we show that the mean number of QTL influencing anxiety-related behavior in mice is 6, with a 95% upper limit of 14.     

Using mating designs to uncover QTL and the genetic architecture of complex traits

Analysis of quantitative trait loci (QTL) affecting complex traits is often pursued in single-cross experiments. For most purposes, including breeding, some assessment is desired of the generalizability of the QTL findings and of the overall genetic architecture of the trait. Single-cross experiments provide a poor basis for these purposes, as comparison across experiments is hampered by segregation of different allelic combinations among different parents and by context-dependent effects of QTL. To overcome this problem, we combined the benefits of QTL analysis (to identify genomic regions affecting trait variation) and classic diallel analysis (to obtain insight into the general inheritance of the trait) by analyzing multiple mapping families that are connected via shared parents. We first provide a theoretical derivation of main (general combining ability (GCA)) and interaction (specific combining ability (SCA)) effects on F(2) family means relative to variance components in a randomly mating reference population. Then, using computer simulations to generate F(2) families derived from 10 inbred parents in different partial-diallel designs, we show that QTL can be detected and that the residual among-family variance can be analyzed. Standard diallel analysis methods are applied in order to reveal the presence and mode of action (in terms of GCA and SCA) of undetected polygenes. Given a fixed experiment size (total number of individuals), we demonstrate that QTL detection and estimation of the genetic architecture of polygenic effects are competing goals, which should be explicitly accounted for in the experimental design. Our approach provides a general strategy for exploring the genetic architecture, as well as the QTL underlying variation in quantitative traits.     

Bayesian QTL analyses using pedigreed families of an outcrossing species,with application to fruit firmness in apple

Key message

Proof of concept of Bayesian integrated QTL analyses across pedigree-related families from breeding programs of an outbreeding species. Results include QTL confidence intervals, individuals’ genotype probabilities and genomic breeding values.

Abstract

Bayesian QTL linkage mapping approaches offer the flexibility to study multiple full sib families with known pedigrees simultaneously. Such a joint analysis increases the probability of detecting these quantitative trait loci (QTL) and provide insight of the magnitude of QTL across different genetic backgrounds. Here, we present an improved Bayesian multi-QTL pedigree-based approach on an outcrossing species using progenies with different (complex) genetic relationships. Different modeling assumptions were studied in the QTL analyses, i.e., the a priori expected number of QTL varied and polygenic effects were considered. The inferences include number of QTL, additive QTL effect sizes and supporting credible intervals, posterior probabilities of QTL genotypes for all individuals in the dataset, and QTL-based as well as genome-wide breeding values. All these features have been implemented in the FlexQTL^? software. We analyzed fruit firmness in a large apple dataset that comprised 1,347 individuals forming 27 full sib families and their known ancestral pedigrees, with genotypes for 87 SSR markers on 17 chromosomes. We report strong or positive evidence for 14 QTL for fruit firmness on eight chromosomes, validating our approach as several of these QTL were reported previously, though dispersed over a series of studies based on single mapping populations. Interpretation of linked QTL was possible via individuals’ QTL genotypes. The correlation between the genomic breeding values and phenotypes was on average 90 %, but varied with the number of detected QTL in a family. The detailed posterior knowledge on QTL of potential parents is critical for the efficiency of marker-assisted breeding.     

From plant genomics to breeding practice

New alleles are constantly accumulated during intentional crop selection. The molecular understanding of these alleles has stimulated new genomic approaches to mapping quantitative trait loci (QTL) and haplotype multiplicity of the genes concerned. A limited number of quantitative trait nucleotides responsible for QTL variation have been described, but an acceleration in their rate of discovery is expected with the adoption of linkage disequilibrium and candidate gene strategies for QTL fine mapping and cloning. Additional layers of regulatory variation have been studied that could also contribute to the molecular basis of quantitative genetics of crop traits. Despite this progress, the role of marker-assisted selection in plant breeding will ultimately depend on the genetic model underlying quantitative variation.     

An algorithm for molecular dissection of tumor progression

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.     

The genetic basis of interspecific differences in genital morphology of closely related carabid beetles

Marked diversification of genital morphology is common in internally fertilizing animals. Although sexual selection may be the primary process controlling genital evolution, factors promoting genital evolution are controversial, and the genetic background of genital morphology is poorly understood. We analyzed the genetic basis of species-specific genital morphologies in carabid beetles of the subgenus Ohomopterus (genus Carabus, Carabidae) using two parapatric species with hybrid zones. Biometric analyses on experimental F(1) and backcross populations revealed that inheritance of genital morphology is polygenic. Applying Lande's modification of the Castle-Wright estimator to population means and variances to estimate the minimum number of genes involved, we found that a relatively small number of loci is responsible for species differences in genital morphology. In addition, joint-scaling tests indicated that the additive genetic effect accounts for most interspecific differences in genital traits, but dominance and epistatic genetic effects also play roles. Overall, the genetic basis of male and female genitalia is fairly simple, enabling these traits to respond quickly to selection pressures and to diverge rapidly. Our results provide insight into the diversification of genital morphology in carabid beetles, and will hopefully stimulate further studies on the genetic basis of genitalia, such as mapping of quantitative trait loci affecting species-specific genital morphology.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Quantitative traits in plants: beyond the QTL

Phenotypic variation for quantitative traits results from segregation at multiple quantitative trait loci (QTL), the effects of which are modified by the internal and external environments. Because of their favorable genetic attributes (e.g. short generation time, large families and tolerance to inbreeding), plants are often used to test new concepts in quantitative trait analysis. Thus far, the molecular basis underlying allelic variation at QTL is similar to the identified variation for simple mendelian loci; namely, alterations in gene expression or protein function. Further comprehensive dissection of complex phenotypes will depend on our ability to link genetic components of the QTL variation to genomic databases.     

Biased estimators of quantitative trait locus heritability and location in interval mapping

In many empirical studies, it has been observed that genome scans yield biased estimates of heritability, as well as genetic effects. It is widely accepted that quantitative trait locus (QTL) mapping is a model selection procedure, and that the overestimation of genetic effects is the result of using the same data for model selection as estimation of parameters. There are two key steps in QTL modeling, each of which biases the estimation of genetic effects. First, test procedures are employed to select the regions of the genome for which there is significant evidence for the presence of QTL. Second, and most important for this demonstration, estimates of the genetic effects are reported only at the locations for which the evidence is maximal. We demonstrate that even when we know there is just one QTL present (ignoring the testing bias), and we use interval mapping to estimate its location and effect, the estimator of the effect will be biased. As evidence, we present results of simulations investigating the relative importance of the two sources of bias and the dependence of bias of heritability estimators on the true QTL heritability, sample size, and the length of the investigated part of the genome. Moreover, we present results of simulations demonstrating the skewness of the distribution of estimators of QTL locations and the resulting bias in estimation of location. We use computer simulations to investigate the dependence of this bias on the true QTL location, heritability, and the sample size.     

QTL mapping and the genetic basis of adaptation: recent developments

Quantitative trait loci (QTL) mapping has been used in a number of evolutionary studies to study the genetic basis of adaptation by mapping individual QTL that explain the differences between differentiated populations and also estimating their effects and interaction in the mapping population. This analysis can provide clues about the evolutionary history of populations and causes of the population differentiation. QTL mapping analysis methods and associated computer programs provide us tools for such an inference on the genetic basis and architecture of quantitative trait variation in a mapping population. Current methods have the capability to separate and localize multiple QTL and estimate their effects and interaction on a quantitative trait. More recent methods have been targeted to provide a comprehensive inference on the overall genetic architecture of multiple traits in a number of environments. This development is important for evolutionary studies on the genetic basis of multiple trait variation, genotype by environment interaction, host–parasite interaction, and also microarray gene expression QTL analysis.     

Power of different sampling strategies to detect quantitative trait loci variance effects

Summary Many studies have shown that segregating quantitative trait loci (QTL) can be detected via linkage to genetic markers. Power to detect a QTL effect on the trait mean as a function of the number of individuals genotyped for the marker is increased by selectively genotyping individuals with extreme values for the quantitative trait. Computer simulations were employed to study the effect of various sampling strategies on the statistical power to detect QTL variance effects. If only individuals with extreme phenotypes for the quantitative trait are selected for genotyping, then power to detect a variance effect is less than by random sampling. If 0.2 of the total number of individuals genotyped are selected from the center of the distribution, then power to detect a variance effect is equal to that obtained with random selection. Power to detect a variance effect was maximum when 0.2 to 0.5 of the individuals selected for genotyping were selected from the tails of the distribution and the remainder from the center.     

High-resolution mapping of quantitative trait loci for sternopleural bristle number in Drosophila melanogaster.

We have mapped quantitative trait loci (QTL) harboring naturally occurring allelic variation for Drosophila bristle number. Lines with high (H) and low (L) sternopleural bristle number were derived by artificial selection from a large base population. Isogenic H and L sublines were extracted from the selection lines, and populations of X and third chromosome H/L recombinant isogenic lines were constructed in the homozygous low line background. The polymorphic cytological locations of roo transposable elements provided a dense molecular marker map with an average intermarker distance of 4.5 cM. Two X chromosome and six chromosome 3 QTL affecting response to selection for sternopleural bristle number and three X chromosome and three chromosome 3 QTL affecting correlated response in abdominal bristle number were detected using a composite interval mapping method. The average effects of bristle number QTL were moderately large, and some had sex-specific effects. Epistasis between QTL affecting sternopleural bristle number was common, and interaction effects were large. Many of the intervals containing bristle number QTL coincided with those mapped in previous studies. However, resolution of bristle number QTL to the level of genetic loci is not trivial, because the genomic regions containing bristle number QTL often did not contain obvious candidate loci, and results of quantitative complementation tests to mutations at candidate loci affecting adult bristle number were ambiguous.     

Genome-Wide Prediction of Traits with Different Genetic Architecture Through Efficient Variable Selection

In genome-based prediction there is considerable uncertainty about the statistical model and method required to maximize prediction accuracy. For traits influenced by a small number of quantitative trait loci (QTL), predictions are expected to benefit from methods performing variable selection [e.g., BayesB or the least absolute shrinkage and selection operator (LASSO)] compared to methods distributing effects across the genome [ridge regression best linear unbiased prediction (RR-BLUP)]. We investigate the assumptions underlying successful variable selection by combining computer simulations with large-scale experimental data sets from rice (Oryza sativa L.), wheat (Triticum aestivum L.), and Arabidopsis thaliana (L.). We demonstrate that variable selection can be successful when the number of phenotyped individuals is much larger than the number of causal mutations contributing to the trait. We show that the sample size required for efficient variable selection increases dramatically with decreasing trait heritabilities and increasing extent of linkage disequilibrium (LD). We contrast and discuss contradictory results from simulation and experimental studies with respect to superiority of variable selection methods over RR-BLUP. Our results demonstrate that due to long-range LD, medium heritabilities, and small sample sizes, superiority of variable selection methods cannot be expected in plant breeding populations even for traits like FRIGIDA gene expression in Arabidopsis and flowering time in rice, assumed to be influenced by a few major QTL. We extend our conclusions to the analysis of whole-genome sequence data and infer upper bounds for the number of causal mutations which can be identified by LASSO. Our results have major impact on the choice of statistical method needed to make credible inferences about genetic architecture and prediction accuracy of complex traits.     

Poor performance of bootstrap confidence intervals for the location of a quantitative trait locus

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTL) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTL are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the nonparametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals behave poorly and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum-likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately.     

Small- and Large-Effect Quantitative Trait Locus Interactions Underlie Variation in Yeast Sporulation Efficiency

Quantitative trait loci (QTL) with small effects on phenotypic variation can be difficult to detect and analyze. Because of this a large fraction of the genetic architecture of many complex traits is not well understood. Here we use sporulation efficiency in Saccharomyces cerevisiae as a model complex trait to identify and study small-effect QTL. In crosses where the large-effect quantitative trait nucleotides (QTN) have been genetically fixed we identify small-effect QTL that explain approximately half of the remaining variation not explained by the major effects. We find that small-effect QTL are often physically linked to large-effect QTL and that there are extensive genetic interactions between small- and large-effect QTL. A more complete understanding of quantitative traits will require a better understanding of the numbers, effect sizes, and genetic interactions of small-effect QTL.     

Environmental influence on the genetic correlations between life-history traits in Caenorhabditis elegans

Empirical evidence is mounting to suggesting that genetic correlations between life-history traits are environment specific. However, detailed knowledge about the loci underlying genetic correlations in different environments is scant. Here, we studied the influence of temperature (12 degrees C and 24 degrees C) on the genetic correlations between egg size, egg number and body mass in the nematode Caenorhabditis elegans. We used a quantitative trait loci (QTL) approach based on a genetic map with evenly spaced single nucleotide polymorphism markers in an N2 x CB4856 recombinant inbred panel. Significant genetic correlations between various traits were found at both temperatures. We detected pleiotropic or closely linked QTL, which supported the negative correlation between egg size and egg number at 12 degrees C, the positive correlation across temperatures for body mass, and the positive correlation between body mass and egg size at 12 degrees C. The results indicate that specific loci control the covariation in these life-history traits and the locus control is prone to environmental conditions.