BALANCED INVIABILITY.
The determination of the cross-over values of the factors was at first hindered because of the poor viability of some of the mutants. If the viability of each mutant type could be determined in relation to the viability of the normal, "coefficients of viability" could serve as corrections in working with the various mutant characters. But it was found (Bridges and Sturtevant, 1914) that viability was so erratic that coefficients might mislead. At the same time it was becoming more apparent that poor viability is no necessary attribute of a character, but depends very largely on the condition of culture. Competition among larvæ was found to be the chief factor in viability. Mass cultures almost invariably have extremely poor viability, even though an attempt is made to supply an abundance of food. Special tests (Morgan and Tice, 1914) showed that even those mutants which were considered the very poorest in viability were produced in proportions fairly close to the theoretical when only one female was used for each large culture bottle and the amount and quality of food was carefully adjusted.
For the majority of mutants which did well even under heavy competition in mass cultures the pair-breeding method reduced the disturbances due to viability to a point where they were negligible.
Later a method was devised (Bridges, 1915) whereby mutations of poor viability could be worked with in linkage experiments fairly accurately and whereby the residual inviability of the ordinary characters could be largely canceled. This method consists in balancing the data of a certain class with poor viability by means of an equivalent amount of data in which the same class occurs as the other member of the ratio. Thus in obtaining data upon any linkage case it is best to have the total number of individuals made up of approximately equal numbers derived from each of the possible ways in which the experiment may be conducted. In the simplest case, in which the results are of the form AB:Ab:aB:ab, let us suppose that the class ab has a disproportionately low viability. If, then, ab occurs in an experiment as a cross-over class, that class will be too small and a false linkage value will be calculated. The remedy is to balance the preceding data by an equal amount of data in which ab occurs as a non-cross-over. In these latter the error will be the opposite of the previous one, and by combining the two experiments the errors should be balanced to give a better approximation to the true value. When equal amounts of data, secured in these two ways, are combined, all four classes will be balanced in the required manner by occurring both as non-cross-overs and as cross-overs. The error, therefore, should be very small. For three pairs of gens there are eight classes, and in order that each of them may appear as a non-cross-over, as each single cross-over, and as the double cross-over, four experiments must be made.
HOW THE FACTORS ARE LOCATED IN THE CHROMOSOMES.
A character is in the first chromosome if it is transmitted by the grandfather to half of his grandsons, while, in the reciprocal cross, the mother transmits her character to all her sons (criss-cross inheritance) and to half of her granddaughters and to half of her grandsons; in other words, if the factor that differentiates the character has the same distribution as the X chromosome. If, however, a new mutant type does not show this sex-linked inheritance, its chromosome is determined by taking advantage of the fact that in Drosophila there is no crossing-over in the male between factors in the same chromosome. For instance, if a new mutant type is found not to be sex-linked, its group is determined by the following tests: It is crossed to black, whose factor is known to be in the second chromosome, and to pink, whose factor lies in the third chromosome. If the factor of the new form should happen to be in the second chromosome, then, in the cross with black, no double recessive can appear, so that the F2 proportion is 2:1:1:0; but with pink, the mutant type should give the proportion 9:3:3:1, typical of free assortment.
If, however, the factor of the new form is in the third chromosome, then, when crossed to black, the double recessive and the 9:3:3:1 proportion appear in F2. But when crossed to pink no double recessive appears in F2, and the proportion 2:1:1:0 occurs.
If these tests show that the new mutant does not belong to either the second or third chromosome, that is, if both with black and with pink the 9:3:3:1 ratio is obtained, then by exclusion the factor lies in the fourth chromosome, in which as yet only two factors have been found.