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.     

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.     

Sensitized polygenic trait analysis

Genetic variation in many biological processes and evolutionary adaptations is caused by polygenes – genes that act in combination to affect a particular trait. Despite the recent identification of several polygenes, many remain to be found, suggesting that new experimental and analytical methods are needed to facilitate their discovery. Here we discuss sensitized polygenetic trait analysis, a method that has emerged recently for simplifying the genetic analysis of polygenic traits. The method uses a known single gene mutation in linkage testing crosses to ‘sensitize’ the analysis. By increasing the frequency of affected individuals in segregating populations, linkages are more readily detected. This method has considerable potential, especially given the increasing variety of mutations that can be used to sensitize the genetic analysis of polygenic traits.     

Constructing a new integrated genetic linkage map and mapping quantitative trait loci for vegetative mycelium growth rate in Lentinula edodes

The most saturated linkage map for Lentinula edodes to date was constructed based on a monokaryotic population of 146 single spore isolates (SSIs) using sequence-related amplified polymorphism (SRAP), target region amplification polymorphism (TRAP), insertion–deletion (InDel) markers, and the mating-type loci. Five hundred and twenty-four markers were located on 13 linkage groups (LGs). The map spanned a total length of 1006.1 cM, with an average marker spacing of 2.0 cM. Quantitative trait loci (QTLs) mapping was utilized to uncover the loci regulating and controlling the vegetative mycelium growth rate on various synthetic media, and complex medium for commercial cultivation of L. edodes. Two and 13 putative QTLs, identified respectively in the monokaryotic population and two testcross dikaryotic populations, were mapped on seven different LGs. Several vegetative mycelium growth rate-related QTLs uncovered here were clustered on LG4 (Qmgr1, Qdgr1, Qdgr2 and Qdgr9) and LG6 (Qdgr3, Qdgr4 and Qdgr5), implying the presence of main genomic areas responsible for growth rate regulation and control. The QTL hotspot region on LG4 was found to be in close proximity to the region containing the mating-type A (MAT-A) locus. Moreover, Qdgr2 on LG4 was detected on different media, contributing 8.07 %–23.71 % of the phenotypic variation. The present study provides essential information for QTL mapping and marker-assisted selection (MAS) in L. edodes.     

Mapping of a new quantitative trait locus for resistance to malaria in mice by a comparative mapping approach with human Chromosome 5q31-q33

A number of linkage studies in human populations have identified a locus (pfbi) on Chromosome 5q31-q33 controlling Plasmodiun falciparum blood infection levels. This region contains numerous candidate genes encoding immunological molecules such as cytokines, growth factors and growth-factor receptors. We have used an F₁₁ advance intercross line (AIL) population of mice infected with Plasmodium chabaudi to identify additional mouse quantitative trait loci (QTL) for control of parasitaemia on Chrs 11 and 18, which carry regions homologous to human Chr 5q31-q33. Herein, we report a novel QTL for parasitaemia control (char8) on the mouse Chr 11, linked to marker D11Mit242, and involved in the clearance stages of the parasites from the bloodstream. Strikingly, several Th2 cytokines that are located within char8 have been identified to play a predominant role in the late stages of the infection.     

A new approach for mapping quantitative trait loci using complete genetic marker linkage maps

A new approach based on nonlinear regression for the mapping of quantitative trait loci (QTLs) using complete genetic marker linkage maps is advanced in this paper. We call the approach joint mapping as it makes comprehensive use of the information from every marker locus on a chromosome. With this approach, both the detection of the existence of QTLs and the estimation of their positions, with corresponding confidence intervals, and effects can be realized simultaneously. This approach is widely applicable because only moments are used. It is simple and can save considerable computer time. It is especially useful when there are multiple QTLs and/or interactions between them on a chromosome.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Power analysis for quantitative trait locus mapping in populations derived by multiple backcrosses

 Populations derived by multiple backcrosses are potentially useful for quantitative trait locus (QTL) mapping studies. Comparisons of relative power to detect QTL using populations derived by multiple back-crosses are needed to make decisions when mapping projects are initiated. The objective of this study was to theoretically compare the power to detect QTL in populations derived by multiple backcrosses relative to mapping in a recombinant inbred population of equal size. Backcrossing results in a reduction in genetic variance with each generation and also results in an increasing frequency of the recurrent parent marker genotype. The relevant outcome for QTL mapping is a reduction in genetic variance to partition between marker genotype classes and increasing unbalance of the number of individuals contributing to the mean of the marker genotypes. Both of these factors lead to a decrease in the power to detect a QTL as the number of backcross generations increases. Experimental error was held constant with the populations compared. From a theoretical standpoint, backcross-derived populations offer few advantages for QTL detection. If, however, a backcrossing approach is the most efficient method to achieve a desired breeding objective and if QTL detection is an objective of equal or less importance, backcross-derived populations are a reasonable approach to QTL detection. Received: 4 August 1996 / Accepted: 4 April 1997     

Near-periodic substitution and the genetic variance induced by environmental change

We investigate a model that describes the evolution of a diploid sexual population in a changing environment. Individuals have discrete generations and are subject to selection on the phenotypic value of a quantitative trait, which is controlled by a finite number of bialleic loci. Environmental change is taken to lead to a uniformly changing optimal phenotypic value. The population continually adapts to the changing environment, by allelic substitution, at the loci controlling the trait. We investigate the detailed interrelation between the process of allelic substitution and the adaptation and variation of the population, via infinite population calculations and finite population simulations. We find a simple relation between the substitution rate and the rate of change of the optimal phenotypic value.     

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.     

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.     

A general mixture model for mapping quantitative trait loci by using molecular markers

Summary In a segregating population a quantitative trait may be considered to follow a mixture of (normal) distributions, the mixing proportions being based on Mendelian segregation rules. A general and flexible mixture model is proposed for mapping quantitative trait loci (QTLs) by using molecular markers. A method is discribed to fit the model to data. The model makes it possible to (1) analyse non-normally distributed traits such as lifetimes, counts or percentages in addition to normally distributed traits, (2) reduce environmental variation by taking into account the effects of experimental design factors and interaction between genotype and environment, (3) reduce genotypic variation by taking into account the effects of two or more QTLs simultaneously, (4) carry out a (combined) analysis of different population types, (5) estimate recombination frequencies between markers or use known marker distances, (6) cope with missing marker observations, (7) use markers as covariables in detection and mapping of QTLs, and finally to (8) implement the mapping in standard statistical packages.     

QTL analysis of body weight and conformation score in commercial broiler chickens using variance component and half-sib analyses

The aim of the study was to investigate quantitative trait loci (QTL) in previously identified regions of chicken chromosomes 1, 4 and 5 relating to 40-day body weights and conformation scores. Half-sib (HS) and variance component analyses were implemented and compared using QTL Express software. Data were from a two-generation design and consisted of 100 dam families nested in 46 sire families with trait values for 2,708 offspring. Chicken chromosome 4 showed nominal significance for QTL affecting body weight and conformation, and linkage was confirmed for both traits on chromosome 5. Results varied according to method of analysis and with common parent in the HS method.     

Optimum spacing of genetic markers for determining linkage between marker loci and quantitative trait loci

The cost of experiments aimed at determining linkage between marker loci and quantitative trait loci (QTL) was investigated as a function of marker spacing and number of individuals scored. It was found that for a variety of experimental designs, fairly wide marker spacings (ca. 50 cM) are optimum or close to optimum for initial studies of marker-QTL linkage, in the sense of minimizing overall cost of the experiment. Thus, even when large numbers of more or less evenly spaced markers are available, it will not always be cost effective to make full utilization of this capacity. This is particularly true when costs of rearing and trait evaluation per individual scored are low, as when marker data are obtained on individuals raised and evaluated for quantitative traits as part of existing programs. When costs of rearing and trait evaluation per individual scored are high, however, as in human family data collection carried out primarily for subsequent marker — QTL analyses, or when plants or animals are raised specifically for purposes of marker — QTL linkage experiments, optimum spacing may be rather narrow. It is noteworthy that when marginal costs of additional markers or individuals are constant, total resources allocated to a given experiment will determine total number of individuals sampled, but not the optimal marker spacing.     

Genetics and QTL mapping of somatic incompatibility and intraspecific interactions in the basidiomycete Heterobasidion annosum s.l

Somatic incompatibility (SI) is a system by which filamentous fungi can distinguish self from non-self by delimiting the own mycelia from that of other individuals of the same species. In this study, we show that SI in the basidiomycete Heterobasidion annosum sensu lato is controlled by four loci by observing the frequency of somatically compatible pairings in two experiments where isolates were paired in all possible combination. The first experiment utilized 63 heterokaryons each with one unique nucleus chosen from an array of sibling homokaryons paired with one unrelated nucleus of homokaryotic isolate TC-39-7. The second experiment used 39 heterokaryons each with one unique nucleus from the array of sibling homokaryons backcrossed with one of the parental strains (TC-122-12). We observed that SI allelic differences in a pairing alone are not enough to determine the degree of somatic incompatibility. In the first experiment, we also observed other interactions such as hyphal walls in interaction zones, increased exudation of dark-coloured metabolites and increased production of aerial hyphae. QTLs for the respective traits were positioned to a genetic linkage map of the H. annosum genome. Map-based cloning of the corresponding loci will shed much new light on intraspecific interactions in basidiomycetes.     

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.     

Genetic mapping of a quantitative trait locus (QTL) that enhances the shoot differentiation rate in Hordeum vulgare L.

A quantitative trait locus (QTL) controlling shoot differentiation from immature embryo callus was identified by linkage analysis with morphological and isozyme markers in barley, Hordeum vulgare L. Immature embryos were isolated from cvs Azumamugi (difficult to differentiate), Kanto Nakate Gold (easy to differentiate), their hybrids (F₁) and a backcross population derived from a cross Azumamugi x F₁. The embryos were cultured in vitro for callus initiation and subsequent shoot differentiation. The shoot differentiation rate was closely associated with ear type (v locus), isocitrate dehydrogenase isozyme (Idh-2), and esterase isozyme (Est-11). These markers were found to reside in a chromosome segment of approximately 30cM on chromosome 2. Recombination frequency was 9.9% between v and a proposed QTL named Shd1 (shoot differentiation), 11.5% between Idh-2 and Shd1, and 21.3% between Est-11 and Shd1. All data showed the Idh-2, v, Shdl and Est-11 loci to be arranged in this order from proximal to distal on the long arm of chromosome 2.     

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.     

Quantitative trait locus mapping using sets of near-isogenic lines: relative power comparisons and technical considerations

 The power to detect QTL using near-isogenic line (NIL) comparisons versus recombinant inbred (RI) populations was assessed. The power to detect QTL was found to be generally greater when using RI populations than when using NIL contrasts. Power to detect QTL with NIL contrasts never exceeded that of RI populations when the number of RI lines is maximized relative to replication of lines for a given number of experimental units. The relative power of NIL contrasts is highest for traits with high heritability and when a gain in precision is realized due to increased replication of entries. Although NIL populations are generally less powerful than RI populations of similar size, some practical considerations may enhance the value of these materials. Availability of NILs allows the genetic effect of a specific chromosome region to be determined by comparing two lines; all RI lines in a population need to be rescored for each new trait even if the effect of a specific chromosome region is suspected. NIL comparisons may allow genetic differences to be detected by visual inspection; genetic effects can only be expressed as means and variances with recombinant inbred populations. In summary, RI populations generally, and in some cases, substantially, provide better power for QTL detection than NIL comparisons. Practical considerations, however, indicate that many factors need to be considered when choosing a population structure to meet an experimental objective. Received: 12 December 1996 / Accepted: 21 March 1997     

Quantitative trait loci involved in the reproductive success of a parasitoid wasp

Dissecting the genetic basis of intraspecific variations in life history traits is essential to understand their evolution, notably for potential biocontrol agents. Such variations are observed in the endoparasitoid Cotesia typhae (Hymenoptera: Braconidae), specialized on the pest Sesamia nonagrioides (Lepidoptera: Noctuidae). Previously, we identified two strains of C. typhae that differed significantly for life history traits on an allopatric host population. To investigate the genetic basis underlying these phenotypic differences, we used a quantitative trait locus (QTL) approach based on restriction site‐associated DNA markers. The characteristic of C. typhae reproduction allowed us generating sisters sharing almost the same genetic content, named clonal sibship. Crosses between individuals from the two strains were performed to generate F2 and F8 recombinant CSS. The genotypes of 181 clonal sibships were determined as well as the phenotypes of the corresponding 4,000 females. Informative markers were then used to build a high‐quality genetic map. These 465 markers spanned a total length of 1,300 cM and were organized in 10 linkage groups which corresponded to the number of C. typhae chromosomes. Three QTLs were detected for parasitism success and two for offspring number, while none were identified for sex ratio. The QTLs explained, respectively, 27.7% and 24.5% of the phenotypic variation observed. The gene content of the genomic intervals was investigated based on the genome of C. congregata and revealed 67 interesting candidates, as potentially involved in the studied traits, including components of the venom and of the symbiotic virus (bracovirus) shown to be necessary for parasitism success in related wasps.