The general theory of mapping functions for random genetic recombination.

The general theory of mapping functions for random genetic recombination is derived without reference to physical models. The results are of particular relevance to asymmetric recombination (preferential recombination of the alleles of either parent) and include the effects of lethal lesions. It is noted that the assumption of randomness determines the mapping functions uniquely so that they are independent of the specifications of any stochastic physical model of recombination. In particular, the functions derived from physical models by Haldane, Wu, Wood and Verhoef and de Haan are special cases of those derived here. A general principle for the testing of genetic linkage is formulated which is valid for both symmetric and asymmetric recombination.