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THE AMERICAN NATURALIST [Vol. L 



The method of determining the closeness of fit between 

 calculated and observed numbers used by Bateson, Pun- 

 nett and their co-workers was mere inspection. (See 

 Bateson and Punnett, 1911.) The unreliability of this 

 method was pointed out by Collins (1912) who made 

 use of Yule's coefficient of association for the same 

 purpose. The well-known formula for this coefficient is 

 (ad — be) /(ad + be), where a, b, c, d are the frequencies 

 of the phenotypic forms AB, Ab, aB, ab, respectively. 

 From a table giving the coefficients of association for a 

 series of gametic ratios, the best fitting gametic ratio 

 is chosen by inspection or interpolation. This method is 

 satisfactory except for the higher gametic ratios where 

 slight differences in the coefficients of association corre- 

 spond to wide differences in the gametic ratios. Since 

 the same intensity of linkage gives somewhat higher 

 coefficients of association for coupling than for repulsion, 

 particularly for the lower linkage values where the asso- 

 ciation coefficient method is most reliable, two tables must 

 be used. 



Formulae, by which gametic ratios can be approximated 

 directly from F 2 data without the use of coefficients of 

 association and without respect to whether coupling or 

 repulsion is involved, would seem to merit trial. Such 

 formulae are presented later in this paper. Moreover, it 

 is often desirable to reverse the calculation, that is, to 

 determine zygotic frequencies from assumed gametic 

 ratios. A single formula suggested for this purpose 

 gives accurate results for both coupling and repulsion. 

 This formula will be presented first because the others 

 are developed from it. 



Bateson and Punnett (1911) suggested two empirical 

 formulae for calculating zygotic frequencies from assumed 

 gametic ratios, one for coupling and the other for repul- 

 sion. Neither one, of course, is applicable to both types 

 of linkage, though both formulae are true for independent 

 inheritance. If A and a are allelomorphic genes and B 

 and b are a similar allelomorphic pair— the capital letters 



