Xo.505] 



LINKAGE INTENSITIES 



U5 



5, and the first term the sum of the second and third plus 

 three times the fourth. 



An approximation of gametic ratios can he obtained 

 from observed zygotic ratios by simple formulae derived 

 from formula I. If the actual values of s 2 + 2rs could 

 be assumed to be identical in all cases, it would follow 

 from formula I_that 4:V 2 = AB -f ab — (Ab .+ aB) and r 

 = ^(AB + ab-Ab-aB)/4. ^Similarly, 4(s 2 + 2rs) 

 =AB+Ab+aB-3r 2 and s=V (AB+Ab+aB+r 2 )/±-r 

 = V (AB + Ab + aB + ab)/i - r. If E is the sum of the 

 extreme terms and M the sum of the middle terms of the 

 observed zygotic series, the formulae for approximating 

 gametic ratios are, then, 3 



8 = ME + M-r 

 If it is desired to compare the observed F 2 frequencies 

 with a calculated series of frequencies, the procedure, 

 obviously, is to calculate the gametic ratio by formulae II 

 —or by means of the coefficient of association— and then 

 to calculate the zygotic series by formula I— or by one of 

 the two formula of Bateson and Punnett. This procedure 

 is not always necessary, however, for a theoretical zygotic 

 series can usually be readily computed directly from the 

 observed frequencies. If AB, Ab, aB, ab is the series to 

 be calculated from the observed frequencies, it follows 

 from formulae I and II that 



Ab = aB=M/2 



ab=(E~M)/4: (HI) 

 AB = M + 3ab 

 Since a zygotic series calculated in this way necessarily 

 meets the conditions imposed by formula I, the gametic 

 ratio can be approximated from it more readily than from 

 the observed frequencies. Since by formulae I and II 

 ab = r 2 and s = .oVE~+M — r, 



