Sequential sampling in determining linkage between marker loci and quantitative trait loci

Summary As compared to classical, fixed sample size techniques, simulation studies showed that a proposed sequential sampling procedure can provide a substantial decrease (up to 50%, in some cases) in the mean sample size required for the detection of linkage between marker loci and quantitative trait loci. Sequential sampling with truncation set at the required sample size for the non-sequential test, produced a modest further decrease in mean sample size, accompanied by a modest increase in error probabilities. Sequential sampling with observations taken in groups produced a noticeable increase in mean sample size, with a considerable decrease in error probabilities, as compared to straightforward sequential sampling. It is concluded that sequential sampling has a particularly useful application to experiments aimed at investigating the genetics of differences between lines or strains that differ in some single outstanding trait.     

Cloning quantitative trait loci by insertional mutagenesis

Summary This study explores the theoretical potential of insertional mutagenesis (i.e., mutagenesis as a result of integration of novel DNA sequences into the germ line), as a means of cloning quantitative trait loci (QTL). The approach presented is based on a direct search for mutagenic effects of a quantitative nature, and makes no assumptions as to the nature of the loci affecting quantitative trait value. Since there are a very large number of potential insertion sites in the genome but only a limited number of target sites that can affect any particular trait, large numbers of inserts will have to be generated and screened. The effects of allelic variants at any single QTL on phenotype value are expected to be small relative to sampling variation. Thus two of three stages of replicate testing will be required for each insert in order to bring overall Type I error down to negligible proportions and yet maintain good statistical power for inserts with true effects on the quantitative traits under consideration. The overall effort involved will depend on the spectrum of mutagenic effects produced by insertional mutagenesis. This spectrum is presently unknown, but using reasonable estimates, about 10,000 inserts would have to be tested, at reasonable replicate numbers (n 30) and Type I error (=0.01) in the first testing stage, to provide a high likelihood of detecting at least one insert with a true effect on a given quantitative trait of interest. Total offspring numbers required per true quantitative mutagenic effect detected decrease strongly with increased number of traits scored and increased number of inserts per initial transformed parent. In fact, it would appear that successful implementation of experiments of this sort will require the introduction of multiple independent inserts in the original parent individuals, by means of repeated transformation, or use of transposable elements as inserts. When biologically feasible, selfing would appear to be the method of choice for insert replication, and in all cases the experiments must be carried out in inbred lines to reduce error variation due to genetic segregation, and avoid confounding mutational effects of the insert with effects due to linkage with nearby segregating QTL. The special qualifications of Arabidopsis thaliana for studies of this sort are emphasized, and problems raised by somaclonal variation are discussed.Contribution from the Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel. No. 1834-E, 1986 series     

Accuracy of mapping quantitative trait loci in autogamous species

Summary The development of linkage maps with large numbers of molecular markers has stimulated the search for methods to map genes involved in quantitative traits (QTLs). A promising method, proposed by Lander and Botstein (1989), employs pairs of neighbouring markers to obtain maximum linkage information about the presence of a QTL within the enclosed chromosomal segment. In this paper the accuracy of this method was investigated by computer simulation. The results show that there is a reasonable probability of detecting QTLs that explain at least 5% of the total variance. For this purpose a minimum population of 200 backcross or F₂ individuals is necessary. Both the number of individuals and the relative size of the genotypic effect of the QTL are important factors determining the mapping precision. On the average, a QTL with 5% or 10% explained variance is mapped on an interval of 40 or 20 centiMorgans, respectively. Of course, QTLs with a larger genotypic effect will be located more precisely. It must be noted, however, that the interval length is rather variable.     

Mapping quantitative trait loci in oligogenic models

We discuss strategies for mapping quantitative trait loci with emphasis on certain issues of study design that have recently received attention: e.g. genotyping only selected pedigrees and the comparative value of large pedigrees versus sib pairs. We use a standard variance components model and a parametrization of the genetic effects in which the 'segregation' parameters are locally orthogonal to the 'linkage' parameters. This permits simple explicit expressions for the expectation of the score statistic, which we use to compare the power of different strategies. We also discuss robustness of the score statistic.     

The effects of selective genotyping on estimates of proportion of recombination between linked quantitative trait loci

Selective genotyping is the marker assay of only the more extreme phenotypes for a quantitative trait and is intended to increase the efficiency of quantitative trait loci (QTL) mapping. We show that selective genotyping can bias estimates of the recombination frequency between linked QTLs — upwardly when QTLs are in repulsion phase, and downwardly when QTLs are in coupling phase. We examined these biases under simple models involving two QTLs segregating in a backcross or F₂ population, using both analytical models and computer simulations. We found that bias is a function of the proportion selected, the magnitude of QTL effects, distance between QTLs and the dominance of QTLs. Selective genotyping thus may decrease the power of mapping multiple linked QTLs and bias the construction of a marker map. We suggest a large proportion than previously suggested (50%) or the entire population be genotyped if linked QTLs of large effects (explain > 10% phenotypic variance) are evident. New models need to be developed to explicitly incorporate selection into QTL map construction.     

Efficiency of direct selection on quantitative trait loci for a two-trait breeding objective

Selection on known loci affecting quantitative traits (DSQ) was compared to phenotypic selection index for a single and a two-trait selection objective. Two situations were simulated; a single known quantitative locus, and ten identified loci accounting for all the additive genetic variance. Selection efficiency of DSQ relative to traitbased selection was higher for two-trait selection, than was selection on a single trait with the same heritability. The advantage of DSQ was greater when the traits were negatively correlated. Relative selection efficiency (RSE) for a single locus responsible for 0.1 of the genetic variance was 1.11 with heritabilities of 0.45 and 0.2 and zero genetic and phenotypic correlations between the traits. RSE of DSQ for ten known loci was 1.5 to 1.8 in the first 3 generations of selection, but declined in each subsequent generation. With DSQ most loci reached fixation after 7 generations. Response to trait-based selection continued through generation 15 and approached the response obtained with DSQ after 10 generations. The cumulative genetic response after 10 generations of DSQ was only 93% to 97% of the economically optimum genotype because the less favorable allele reached fixation for some loci, generally those with effects in opposite directions on the two traits.     

Bayesian point estimation of quantitative trait loci

In this article, we consider the problem of the estimation of quantitative trait loci (QTL), those chromosomal regions at which genetic information affecting some quantitative trait is encoded. Generally the number of such encoding sites is unknown, and associations between neutral molecular marker genotypes and observed trait phenotypes are sought to locate them. We consider a Bayesian model for simple experimental designs, and discuss the existing approaches to inference for this problem. In particular, we focus on locating positions of the best candidate markers segregating for the trait, a situation which is of primary interest in comparative mapping. We introduce a loss function for estimating both the number of QTL and their location, and we illustrate its application via simulated and real data.     

Application of a canonical transformation to detection of quantitative trait loci with the aid of genetic markers in a multi-trait experiment

Effects of individual quantitative trait loci (QTLs) can be isolated with the aid of linked genetic markers. Most studies have analyzed each marker or pair of linked markers separately for each trait included in the analysis. Thus, the number of contrasts tested can be quite large. The experimentwise type-I error can be readily derived from the nominal type-I error if all contrasts are statistically independent, but different traits are generally correlated. A new set of uncorrelated traits can be derived by application of a canonical transformation. The total number of effective traits will generally be less than the original set. An example is presented for DNA microsatellite D21S4, which is used as a marker for milk production traits of Israeli dairy cattle. This locus had significant effects on milk and protein production but not on fat. It had a significant effect on only one of the canonical variables that was highly correlated with both milk and protein, and this variable explained 82% of the total variance. Thus, it can be concluded that a single QTL is affecting both traits. The effects on the original traits could be derived by a reverse transformation of the effects on the canonical variable.     

Determining the minimum sample size required to obtain sufficient progeny with a desired genotype at two quantitative trait loci

In this paper we determine the minimum progeny sample size n needed to obtain, with probability , at least m individuals of a desired two-locus genotype affecting quantitative traits. The two quantitative trait loci (QTLs) of interest may be linked or independent, with or without epistatic interaction between them. Parental genotypes may be known or unknown, and gene action at either locus may range from additive to overdominance. To reduce the required sample size, mating patterns that will produce a high proportion of desired progeny are suggested for different progeny genotypes and dominance levels. Based on the assumption of normally distributed quantitative trait expression, individuals can be classified into a genotype or genotypic group according to their phenotypic expressions. This technique is used to select both parents and progeny with unknown genotypes. Choice of parental classification criteria for a given quantitative trait affects classification accuracy, and hence the probability of obtaining progeny of the desired genotype. The complexity of this probability depends on the dominance level at each locus, the recombination fraction, and the awareness of parental genotypes. The procedure can be expanded to deal with more than two loci.BU-1168-MB in the Biometrics Unit Technical Report Series, 337 Warren Hall, Cornell University, Ithaca, NY 14853, USAFormerly known as S.-F. Shyu     

Expression quantitative trait loci: present and future

The last few years have seen the development of large efforts for the analysis of genome function, especially in the context of genome variation. One of the most prominent directions has been the extensive set of studies on expression quantitative trait loci (eQTLs), namely, the discovery of genetic variants that explain variation in gene expression levels. Such studies have offered promise not just for the characterization of functional sequence variation but also for the understanding of basic processes of gene regulation and interpretation of genome-wide association studies. In this review, we discuss some of the key directions of eQTL research and its implications.     

Correcting for bias in estimation of quantitative trait loci effects

Estimates of quantitative trait loci (QTL) effects derived from complete genome scans are biased, if no assumptions are made about the distribution of QTL effects. Bias should be reduced if estimates are derived by maximum likelihood, with the QTL effects sampled from a known distribution. The parameters of the distributions of QTL effects for nine economic traits in dairy cattle were estimated from a daughter design analysis of the Israeli Holstein population including 490 marker-by-sire contrasts. A separate gamma distribution was derived for each trait. Estimates for both the α and β parameters and their SE decreased as a function of heritability. The maximum likelihood estimates derived for the individual QTL effects using the gamma distributions for each trait were regressed relative to the least squares estimates, but the regression factor decreased as a function of the least squares estimate. On simulated data, the mean of least squares estimates for effects with nominal 1% significance was more than twice the simulated values, while the mean of the maximum likelihood estimates was slightly lower than the mean of the simulated values. The coefficient of determination for the maximum likelihood estimates was five-fold the corresponding value for the least squares estimates.     

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.     

Identification of quantitative trait loci controlling rice mature seed culturability using chromosomal segment substitution lines

The genetic transformation efficiency of a rice variety is largely determined by its tissue culturability. Establishment of a highly efficient tissue-culture system has greatly accelerated the wide spread application of transgenic japonica varieties. However, such process for indica rice was hampered because this type of variety is recalcitrant to in vitro culture. This study aimed to map the quantitative trait loci (QTLs) for mature seed culturability using a chromosomal segment substitution lines (CSSL) population derived from a cross between an indica variety “Zhenshan 97B” and a japonica variety “Nipponbare”. The CSSLs consist of 139 lines each containing a single or a few introgression segments, and together covering the whole “Nipponbare” genome. Every CSSL was tested by culturing on the two medium systems developed for the respective indica and japonica parental varieties. The performance of culturability was evaluated by four indices: frequency of callus induction (CIF), callus subculture capability (CSC), frequency of plant regeneration (PRF) and the mean plantlet number per regenerated callus (MNR). All four traits displayed continuous variation among the CSSLs. With the culture system for japonica rice, three CIF QTLs, three CSC QTLs, three PRF QTLs and three MNR QTLs were detected. With the culture system for indica variety, six CIF QTLs, two CSC QTLs, three PRF QTLs and six MNR QTLs were identified, and these QTLs distributed on nine rice chromosomes. Two QTLs of CIF and two QTLs of MNR were detected in both the japonica and indica rice culture system. The correlation coefficients of all the four traits varied depending on the culture systems. These results provide the possibilities of enhancing the culturability of indica rice by marker-assisted breeding with those desirable alleles from the japonica. Lina Zhao and Hongju Zhou have contributed equally to this work.     

A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.     

The location of major genes and associated quantitative trait loci on chromosome arm 5BL of wheat

Summary Chromosome 5B of bread wheat is known to carry two major genes giving rise to genetic disorders, Ne1 for hybrid necrosis and Vg for winter variegation. Additionally, in many european winter wheat varieties this chromosome is represented in a translocated form, with 5BL-7BL, 5BL-7BS chromosomes rather than the normal 5B and 7B forms of the standard variety Chinese Spring. Genetic analysis has been carried out to map these genes and the translocation break point, and to investigate their pleiotropic effects or those of linked quantitative trait loci (qtl) for economically important characters. This was facilitated by the development of single chromosome recombinant lines between a normal and translocated karyotype, and growing these in field experiments over two seasons. There was differential segregation in favour of the translocated karyotype in the population of recombinant lines. Linkage analysis revealed that the two morphological markers and the isozyme locus Ibf-B1 were located on the long arm of 5B with a gene order of: breakpoint — Ne1 — Vg — Ibf-B1. Analysis of quantitative characters using these genes as landmarks showed pleiotropic effects of Ne1 or effects of tightly linked qtl on most of the quantitative characters related to grain yield. An additional qtl determining spikelet and grain number/ear appeared to be linked to the centromere. Effects on ear emergence time were associated with both Ne1 and Vg, and these interacted with environments. Similarly, effects on plant height were associated with Ne1 and Vg. In addition, there was a further unlocated locus (loci) for height acting independently of the markers.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Mapping of quantitative trait loci on porcine chromosome 4

A F₂ population derived from a cross between European Large White and Chinese Meishan pigs was established in order to study the genetic basis of breed differences for growth and fat traits. Chromosome 4 was chosen for initial study as previous work had revealed quantitative trait loci (QTLs) on this chromosome affected growth and fat traits in a Wild Boar × Large White cross. Individuals in the F₂ population were typed for nine markers spanning a region of approximately 124 c m . We found evidence for QTLs affecting growth between weaning and the end of test (additive effect: 43·4 g/day) and fat depth measured in the mid-back position (additive effect: 1·82 mm). There was no evidence of interactions between the QTLs and sex, grandparents or F₁ sires, suggesting that the detected QTLs were fixed for alternative alleles in the Meishan and Large White breeds. Comparison of locations suggests that these QTLs could be the same as those found in the Wild Boar × Large White cross.     

Genotype-by-environment interaction in genetic mapping of multiple quantitative trait loci

The interval mapping method is widely used for the genetic mapping of quantitative trait loci (QTLs), though true resolution of quantitative variation into QTLs is hampered with this method. Separation of QTLs is troublesome, because single-QTL is models are fitted. Further, genotype-by-environment interaction, which is of great importance in many quantitative traits, can only be approached by separately analyzing the data collected in multiple environments. Here, we demonstrate for the first time a novel analytic approach (MQM mapping) that accommodates both the mapping of multiple QTLs and genotype-by-environment interaction. MQM mapping is compared to interval mapping in the mapping of QTLs for flowering time in Arabidopsis thaliana under various photoperiod and vernalization conditions.