Calculation of Linkage Intensities Where Duplicate Factors Are Concerned.

For the calculation of linkage intensities, i t is of distinct advantage to back-cross the heterozygote on the double recessive since the gametic ratio can then be determined directly from the zygotic types. In some plants, as corn, for example, back-crosses are easily and readily made, but in others, as soy-beans, the practical difficulties attending artificial hybridization are too great to admit of back-crosses in sufficiently large numbers. The calculation of linkage intensities in this plant, therefore, is confined to F2 distributions. EMERSON (1 91 6) has developed formulae for calculating the gametic ratio directly from any given zygotic series representing dihybrid distributions. By means of these formulae one can calculate from the F2 zygotic types the degree of linkage between any two factor pairs almost as readily and accurately as from the progeny of back-crosses. HALDANE (1919) has also given us formulae for calculating the percentage of crossing over directly from the observed Fz results. Hence, it cannot be considered a deterrent handicap to be confined, for linkage studies in soy-beans, to F2 distributions, exclusively. However, a problem in soy-bean inheritance presented itself in the solution of which neither EMERSON’S nor HALDANE’S formulae could be used. The problem was to determine, from an F2 trihybrid distribution, the degree of linkage between two factors, one of which was a duplicate, but inherited independently, of the third factor involved in the cross. Perhaps the obvious procedure was to separate the duplicate factors in different lines and obtain lines segregating for the linked factors only. Then EMERSON’S or HALDANE’S formulae could be readily applied. As this procedure would involve a great deal of time, the degree of linkage was determined, instead, from F, trihybrid distributions, by means of