Abstract
Genetic mapping functions translate the observed recombination rate between two loci into the corresponding map distance in Morgan units. Different mapping functions give different weights to multiple crossing over and therefore lead to different results. This points out that not every function is best suited to fit a data set. The data used in this study originated from 2214 sperm from 37 Norwegian bulls, which were genotyped for 11 markers. The optimal functions for the chromosomes 6, 23 and the sex chromosome of cattle were derived using the maximum likelihood method, the likelihood ratio test and empirical discriminant analysis. It became apparent that for each chromosome a different function fitted the data best. These were the function of Rao et al. (Human Heredity 1977, 27, 99-104) with p = 0.63 for chromosome 6, the function of Goldgar & Fain (American Journal of Human Genetics 1988, 43, 38-45) with C0 = 0.42, C1 = 0.47, C2 = 0.07 and C3 = 0.04 for chromosome 23 and the function of Felsenstein (Genetics 1979, 91, 769-75) with K = 0.23 for the sex chromosome. The well known functions of Haldane (Journal of Genetics 1919, 8, 299-309) and Kosambi (Annals of Eugenics 1944, 12, 172-5) were shown to be suboptimal in most cases. A function is said to be multilocus feasible if the evaluation of the probability of all possible recombination events does not lead to negative values. The optimal function for chromosome 23 turned out to be multilocus feasible, whereas the functions for chromosome 6 and the sex chromosome were not. The choice of the correct mapping function is shown to have a considerable impact in mapping studies, when double recombinations have to be taken into account. Since there is no unique best mapping function, it is argued that it might be useful to use a simple parametric mapping function (like the one of Felsenstein 1979) and to estimate the respective parameter specifically for a given data set.
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