420 



THE AMEBIC AN NATURALIST [Vol. L 



the approximate method, might be due to errors of ran- 

 dom sampling. 



As an illustration of the fact that the approximate 

 method can not be used in some cases of repulsion, even 

 when the observed frequencies fit fairly well the series 

 calculated by the association-coefficient method, an ex- 

 ample of linkage between dark axils and fertile anthers 

 in sweet peas quoted from Punnett by Bridges (1914) 

 may be taken. The observed frequencies are 1335 -f- 643 

 + 714 + 2 = 2694. The value of r can not be determined 

 by formula II nor by III and IV, because 1335 + 2 - (643 

 + 714) is a negative quantity (—20) and has no real 

 root. The coefficient of association is —.988, which is 

 equivalent to a gametic ratio of 1:17, though Bridges 

 assumed a ratio of 1 : 20. On the basis of this 1 : 20 ratio, 

 x> = 5.68 and P= .1309. On the basis of the 1 : 17 ratio, 

 a;2_4 t 04 and P = .2615, or odds of about 3 to 1 against 

 the occurrence of deviations as great as those observed. 



It may be said, then, that the formulae suggested here 

 afford a convenient method of approximating gametic 

 ratios from zygotic series, when the observed frequencies 

 are in fair accord with a series based on formula I— or 

 the formulae of Bateson and Punnett. When the ob- 

 served frequencies are far from this type no method 

 gives a close fit between observed and calculated results. 



LITEKATURE CITED 



of Certain Terms. Jour. Genetics, 1: 293-302. 1911. & 

 Bridges, Calvin B. The Chromosome Hypothesis of Linkage Applied to 



Cases in Sweet Peas and Primula. Amer. Nat., 48: 524-534. 1914. 

 Collins, G. N. Gametic Coupling as a Cause of Correlations. Amee. Nat., 



46: 569-590. 1912. 

 Elderton, W. Palin. Tables for Testing the Goodness of Fit of Theory to 



Harris, J. Arthur. A Simple Test of the Goodness of Fit of Mendelian 



Ratios. Amer. Nat., 46: 741-745. 1912. 

 Pearson, Karl. Tables for Statisticians and Biometricians. Cambridge 



University Press, Table XII, pages 26-28. 1914. 

 Punnett, R. C. Reduplication Series in Sweet Peas. Jour. Genetics, 3: 77- 



103. 1913. 



