Regression-based quantitative trait loci mapping: robust, efficient and effective

Abstract

Regression has always been an important tool for quantitative geneticists. The use of maximum likelihood (ML) has been advocated for the detection of quantitative trait loci (QTL) through linkage with molecular markers, and this approach can be very effective. However, linear regression models have also been proposed which perform similarly to ML, while retaining the many beneficial features of regression and, hence, can be more tractable and versatile than ML in some circumstances. Here, the use of linear regression to detect QTL in structured outbred populations is reviewed and its perceived shortfalls are revisited. It is argued that the approach is valuable now and will remain so in the future.Keywords: quantitative trait loci mapping; regression; structured outbred populations HISTORYThe idea of using markers associated with a trait of interest, for example, to predict the performance of individuals in the trait, is not new. Initially, however, the markers used were not identified at the molecular level but rather through the phenotype, for example, coat colour or by the use of simple biochemical procedures such as blood groups. An early implementation in plants is presented by Sax (1923) and by Neimann-Sorensen & Robertson (1961) in livestock. These original studies used a single marker at a time, because there were few markers and information about the location of the markers in the genome was insufficient. The phenotypes could be analysed either by directly fitting the marker genotype in a classic analysis of variance (ANOVA) or linkage could be modelled through a maximum likelihood (ML) approach. Rebaï et al. (1995) showed that these two approaches are asymptotically equivalent in terms of power. The marker effect estimated in the ANOVA approach can be reparametrized as a combination of the effect and recombination distance from the marker, but these two parameters cannot be estimated separately. On the other hand, the ML approach uses information about the distribution of the phenotypes within the marker genotype and, theoretically, can distinguish quantitative trait loci (QTL) with large effect some distance from the marker from one close by with a smaller effect (equivalent models for ANOVA). There is not much information coming from the phenotypic distribution within marker genotype, however, and most evidence for QTL is obtained from differences between the marker means and, hence, the ability of ML to correctly locate the QTL is limited.

Merino sheep: a further look at quantitative trait loci for wool production

“…This demonstrates the benefit of conducting additional tests to the one-QTL analysis (ii) The residual variance is inflated by segregating QTLs even if these are not located on the chromosome scanned. In this situation, it may be useful to include genotype probabilities at selected positions as cofactors, or to test other genetic models fitting interactions between QTLs (Knott, 2005). This was not done in this study as interval mapping coded in the software used did not consider information from other markers.…”

Mapping of quantitative trait loci for cholesterol, LDL, HDL, and triglyceride serum concentrations in pigs

“…The second point that needs to be discussed makes reference to the discrepancies found between whole population and within-family analyses. Knott (37) pointed out that QTL scans in outbred populations suffer from several drawbacks that explain why QTL associations are not always found across different analyses. First, parents are only informative if they harbor heterozygous genotypes for both the analyzed marker and the QTL.…”

Evaluating the performance of a block updating MCMC sampler in a simple genetic application

“…It only applies to simple designs like the half-sib design, does not use all the information in the data, does not deal with random polygenic effects and does not provide estimates of many of the parameters of interest other than the QTL position. Nonetheless, such methods are frequently used in practice as they are computationally straightforward and quite robust to violations of the assumptions (Knott 2005). If all that is required is whether or not the data provide evidence for a QTL affecting a particular trait, an approximate regression analysis may be just as efficient as an McMC approach in certain circumstances.…”