92 GENETICS [Bot. Absts., Vol. IV, 



590. Haldane, J. B. S. The probable errors of calculated linkage values, and the most 

 accurate method of determining gametic from certain zygotic series. Jour. Genetics 8 : 291-297. 

 Sept., 1919. — Assuming Bayes's theorem to be accurate, this paper derives probable error for- 

 mulae for linkage and reduplication values calculated from the offspring of crosses of types 

 AB. abXab ab, Ab. aBXab ab, AB. afcXAB. ab and Ab. aBXAb. aBXAbXaB. 



If the cross is Aa Bb X aa bb where n equals total number of zygotes obtained, P 

 the observed value of p in a heterozygote Aa Bb producing gametes in the proportion 



— AB: Ab: aB: —ab, the probable error of P is 



2 2 2 2' 



V :i 



iP(l-P) 



0.6745 ' 



n 

 of the observed X (coefficient in gametic series in case of coupling) 



0.6745 (X + 1) -J*- 



of the observed Y (coefficient in gametic series in case of repulsion) 



0.6745 (Y + 1) W| 



Considering the F 2 zygotic series obtained by inter se mating of Fi zygotes the expected 

 proportions of which are 



2 _±P! A B:^l>l , A6 : LlP' oB: P! a() . 



4 4 4 4 



Put t = p 2 , let t a be an approximate value of t, while T = t + 5 the most probable value 

 from observation. Ti, T 2 , T 3 , T 4 be the four values of t calculated from the four observed 

 classes observed. 



Hence 



T _ 3t a ti + (2 + t a ) U 

 2+4t a 



while P = VT 



for t a take t t in repulsion or J (ti + t 4 ) in coupling. 



« 



Hence 



V4T (2 

 

 n 



2 + T) (1 - T) 



(1 + 2T) 



V(2 + p») (1 — p 2 ) 

 — ; » 

 (1 + 2P»)n 



