The Combination of Linkage Values, and the Calculation of Distances between the Loci of Linked Factors.

On the theory that the degree of linkage between two factors depends on the distance apart of their loci in a chromosome, Morgan and his fellow-workers have taken the distance between two loci as proportional to the cross-over value 1 of the factors located in them. This theory gives consistent results when the cross-over values are small, but, as recognised by Sturtevant, and by Morgan and Bridges(1), is not accurate for larger values. On the reduplication theory Trow(2) has given a formula for the combination of linkage values which is shown below to be inaccurate when the linkage is not close. In the present paper a more accurate theory of the relations inter se of the cross-over values, and of their connexion with the distances apart of the loci of factors in a chromosome, is developed. Some such theory is especially necessary when dealing with a group of factors containing few members not very closely linked.