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.

Linkage analysis with molecular genetic markers is a very powerful tool in the biological research of quantitative traits. The lack of an easy way to know what areas of the genome can be designated as statistically signi®cant for containing a gene a ecting the quantitative trait of interest hampers the important prediction of the rate of false positives. In this paper four tables, obtained by large-scale simulations, are presented that can be used with a simple formula to get the false-positives rate for analyses of the standard types of experimental populations with diploid species with any size of genome. A new de®nition of the term`suggestive linkage' is proposed that allows a more objective comparison of results across species.Keywords: linkage, molecular marker, QTL, signi®cance, statistics. IntroductionSince the introduction of molecular genetic markers, linkage analysis has become one of the most important tools in biological research. A special type of linkage analysis can be carried out for quantitative traits. Quantitative traits, often called complex traits in contrast to simple Mendelian traits, are traits where the relation between genotype and phenotype cannot be observed directly. A gene a ecting a quantitative trait is called a quantitative trait locus (QTL). The genetic dissection of a quantitative trait Ð so-called QTL analysis Ð is usually carried out using interval mapping (Lander & Botstein, 1989) or a related method (Haley & Knott, 1992;Jansen, 1992Jansen, , 1993 Martinez & Curnow, 1992; Zeng, 1993 Zeng, , 1994. For this purpose an experimental population segregating for the quantitative trait is created and its linkage map of molecular markers is calculated. The basic procedure of the QTL analysis is such that on many positions on the linkage map a test statistic is calculated. In analogy with the genetic mapping of simple Mendelian traits, this statistic is the LOD score. This is essentially a likelihood ratio statistic. Subsequently, regions on the genome are identi®ed that show signi®cant values of the test statistic; such regions are supposed to contain a QTL. This procedure, however simple, has a major problem: what value of the test statistic constitutes a signi®cant value? A single LOD score is approximately related to a chi-squared distribution; the distribution of the maximum of a series of LOD scores, however, cannot be determined in a straightforward manner. Because of linkage, tests on neighbouring positions on the genome are not independent Ð closely linked markers will have equivalent test statistics. Also, the larger the genome, the more tests will be performed, thus increasing the probability that a ®xed LOD threshold will be exceeded. Hence, if for the QTL analyses in various species an equal experimentwise signi®cance level is desired Ð usually 5% Ð the appropriate LOD thresholds will depend on the genome size of the species (in terms of recombination). Genome size varies greatly over species. Although most chromosome map lengths lie within the range of 50±250 cM, the...

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.

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The genetic differences for seed germination between two commonly used Arabidopsis thaliana ecotypes Ler and Col, both showing a low level of seed dormancy, were investigated. The analysis was performed with 98 recombinant inbred lines (RILs) derived from the cross between the two ecotypes, and these lines had previously been analysed for molecular marker composition by Lister and Dean (Norwich, UK). The analysis of germination was performed on seeds grown in three different maternal environments and each seed batch was tested in three different germination environments: in light, in darkness and in the presence of the gibberellin inhibitor paclobutrazol. Fourteen loci were identified using the multiple-QTL-model (MQM) procedure for mapping quantitative trait loci. At nine loci no significant interaction between the detection of the locus and environmental factors could be detected.However, three other distinct loci controlling the germination behaviour in the presence of the gibberellin inhibitor paclobutrazol had a much lower or no effect when germination was tested in water either in light or darkness. Two other loci affecting germination in darkness and/or light had practically no effect on germination in the presence of paclobutrazol.