Key points are not available for this paper at this time.
Abstract This paper develops further the mathematical aspects of a theory of interference put forward recently in ‘The sex chromosome in the house mouse’ by Fisher, Lyon & Owen (1947). A mathematical model of a long chromosome is set up under simplifying assumptions, the principal one being that there exists a special interference metric specifying the positions of loci. It is assumed that the metrical lengths of the intercepts formed on a strand by the points of exchange of material have independent probability distributions. Restricting attention to chromosome arms of great length, general analytical expressions are obtained for the quantities which are genetically observable. Under some additional assumptions special formulae are derived for map distance and recombination, in finite terms suitable for computation, and involving a disposable constant related to the intensity of the interference. It is shown that with sufficiently intense interference the recombination fraction over a segment is an oscillatory function of the map length of the segment, and that recombinations in excess of 50% are therefore in some cases to be expected.
Andrew Owen (Mon,) studied this question.