On the bias of recombination fractions, Kosambi's and Haldane's distances based on frequencies of gametes

Abstract

The estimation of recombination frequencies is a crucial step in genetic mapping. For the construction of linkage maps, nonadditive recombination fractions must be transformed into additive map distances. Two of the most commonly used transformations are Kosambi’s and Haldane’s mapping functions. This paper reports on the calculation of the bias associated with estimation of recombination fractions, Kosambi’s distances, and Haldane’s distances. I calculated absolute and relative biases numerically for a wide range of recombination fractions and sample sizes. I assumed that the ratio of recombinant gametes to the total number of gametes can be adequately represented by a binomial function. I found that the bias in recombination fraction estimates is negative, i.e., the estimator is an underestimate. However, significant values were only obtained when recombination fractions were large and sample sizes were small. The relevant estimates of recombination fractions were, therefore, nearly unbiased. Haldane’s and Kosambi’s distances were found to be strongly biased, with positive bias for the most interesting values of recombination fractions and sample sizes. The bias of Kosambi’s distance was considerably smaller than the bias of Haldane’s distance.