41,s 



THE AMEBIC AN NATURALIST [Vol. L 



data and afford a means of comparing it with the associ- 

 ation-coefficient method. 



Harris (1912) has quoted an example of coupling in 

 sweet peas from the studies of Bateson, Saunders, and 

 Punnett 4 and calculated P where the gametic ratios are 

 taken as 7:1 and 15:1, the only xatios considered in the 

 original paper. The phenotypic classes are based on shape 

 of pollen and color of flowers and the observed frequen- 

 cies are purple long 493, purple round 25, red long 25, 

 red round 138, total 681. As determined by Harris, on the 

 basis of a 7:1 gametic ratio, P = .0053 or x 2 = 12.7699. 

 On the 15 : 1 basis, P = .3086 or x 2 = 3.6375. The chances 

 against the 7 : 1 ratio are, therefore, 199 to 1 and against 

 the 15 : 1 ratio about 2 to 1. For this same material, Col- 

 lins (1912), using the association-coefficient method— 

 Coef. Assoc. = . 982 ± .004— naturally suggested a 12:1 

 gametic ratio — Coef. Assoc. also — .982— and pointed out 

 the fact that the deviation from the 7 : 1 ratio is 9 times 

 and from the 15:1 ratio about twice the probable error. 

 By formula? Ill, the calculated series becomes 485.75 

 +25.0+25.0+145.25=681. Byformuhe IV, r = 12.052 and 

 s = .996 or a gametic ratio of 12.1 : 1. The 12 : 1 ratio ob- 

 tained by the association-coefficient method gives a zygotic 

 series of 485.5 + 25.2 + 25.2 + 145.1 = 681. Both meth- 

 ods, then, give gametic ratios approximately the same and 

 practically identical zygotic series, namely, 485 + 25 

 + 25 + 145. On the basis of this series, x 2 = .4387 and 

 P is so large that it is useless to determine it. In short, 

 both methods give gametic ratios that fit the observed 

 data extremely well. 



The next example of coupling presents a very different 

 condition. It has been quoted by Bridges (1914) from 

 Punnett 's (1913) summary of reduplication series in 

 sweet peas. The phenotypic classes are based upon ster- 

 ility of anthers and form of flowers and the observed 

 frequencies are fertile normal 165, fertile cretin 58, 

 sterile normal 58, sterile cretin 78, total 359. It can be 

 seen at a glance that these frequencies are far from 



♦Rept. Evol. Com., 4: 11. 



