Quantitative Trait Loci

Although the interval mapping method is widely used for mapping quantitative trait loci (QTLs), it is not very well suited for mapping multiple QTLs. Here, we present the results of a computer simulation to study the application of exact and approximate models for multiple QTLs. In particular, we focus on an automatic two-stage procedure in which in the first stage “important” markers are selected in multiple regression on markers. In the second stage a QTL is moved along the chromosomes by using the preselected markers as cofactors, except for the markers flanking the interval under study. A refined procedure for cases with large numbers of marker cofactors is described. Our approach will be called MQM mapping, where MQM is an acronym for “multiple-QTL models” as well as for “marker-QTLmarker.” Our simulation work demonstrates the great advantage of MQM mapping compared to interval mapping in reducing the chance of a type I error ( L e . , a QTL is indicated at a location where actually no QTL is present) and in reducing the chance of a type I1 error ( i . e . , a QTL is not detected). T HE advent of maps of molecular markers enables geneticists to detect and map individual loci affecting quantitative traits ( c f . PATERSON et al. 1988). In the ideal case all genetic variance of the trait is explained by detected quantitative trait loci (QTLs). In practice a number of QTLs may be missed (a type I1 error) and at the same time a number of false positives may occur, indicating QTLs at map positions (or regions) where actually no QTLs are present (a type I error). The actual balance between the cost of false positives and the benefit of detected QTLs depends on the aim of the experiment (e.g., map-based cloning or introgression breeding). Nevertheless, one often strives for keeping at least the chance of a type I error below 5%. Therefore, the QTL mapping method used should keep the chance of a type I error below 5%, but at the same time it should minimize the chance of a type I1 error. The interval mapping method (LANDER and BOTSTEIN 1989) is widely used, but it is now generally recognized that the chance of a type I or a type I1 error is higher in interval mapping than it is in simultaneous mapping of multiple QTLs ( cf. HALEY and KNOTT 1992; MARTINEZ and CURNOW 1992; JANSEN 1993b). This has motivated theoretical research for multiple QTL mapping methods. Recently, JANSEN (1992,1993b) and JANSEN and STAM (1994) developed a unifjmg framework of exact and approximate models for multiple QTLs, from now on called MQM mapping. MQM is an acronym for “multiple-QTL models” but also for “marker-QTLmarker” (which reflects the insertion of QTLs between markers on the genetic linkage map). The framework includes interval mapping and regression on markers (COWEN 1989; STAM 1991; RODOLPHE and LEFORT 1993; ZENG 1993) and also includes their “hybrid” in which the phenotype is regressed on a single Genetics 138 871-881 (November, 1994) putative QTL in a given marker interval, and at the same time on a number of markers located elsewhere on the genome. The rationale behind using markers as cofactors is that these markers will eliminate the major part of the variation induced by nearby QTLs. Some simulation work (JANSEN 1993b) and a practical application (JANSEN and STAM 1994) indicated that the MQM m a p ping method is computationally feasible and substantially more powerful than interval mapping. For the present paper a computer simulation study was set up to study more thoroughly the chances of a type I or I1 type error in MQM mapping, and to compare MQM m a p ping with interval mapping. A number of QTL configurations were studied by simulation, covering the most relevant multiple-QTL configurations; the results are presented and discussed. STATISTICAL MODELS FOR MQM MAPPING In this section statistical aspects of MQM mapping are summarized. For more details see JANSEN (1992,199313) and JANSEN and STAM (1994). Further refinements to MQM mapping are proposed, concerning the testing for the presence of a putative QTL, and concerning the parameter estimation for the case that many marker cofactors are used. The framework: We restrict ourselves to backcross progenies, but the same method applies to other inbred or outbred progenies. Furthermore, we assume a normally distributed environmental error. The general model in MQM mapping is Y = m + xiat + E, where Y is the phenotypic trait, m is the mean, a, are the allele substitution effects of individual loci and E is the (environmental) error; the summation is over all loci affecting the trait. The x, are indicator variables specifylng