Two Segregation Ratios Possible

How large a population size do we need to distringuish between two genetic segregation ratios? If n is the total number of F₂ progeny, we would like to determine the minimum number of recessive genotypes required to distinguish between two possible segregation ratios. We approach this problem by determining the number of homozygous recessive progeny which result in the two possible segregation ratios being equally likely.

Example

We would like to determine whether two loci are segregating with complementary epistasis to produce a 9:7 ratio, or whether only one locus is segregating at a 3:1 ratio.

Ho₁:9:7 ratio
Ho₂:3:1 ratio

If more than r recessives are observed, then the 9:7 ratio is more likely. If fewer than r recessives are observed, then the 3:1 ratio is more likely. So we need to determine the total F₂ population size that we be necessary to distinguish the two hypothesized ratios.

See - Mather, K. 1938. The Measure of Linkage in Heredity. John Wiley and Sons, New York. pgs 27-31.

We have two expected segregation ratios which are l₁:1 and l₂:1. If the observed segregation ratio is the (square root of l₁l₂):1 we will have the same X² value for both hypothesis. The(square root of l₁l₂):1 is an ambiguous ratio that does not permit us to distinguish which hypothesis is correct. For our example, the 3:1 ratio is l₁:1, then l₁=3. The 9:7 ratio is l₁:1, then l₂=9/7.

 3  =  l₁   3 = l₁ and  9  =   l ₂  7l₂ = 9
 1      1                     7       1
                                           l₂ = 9/7.

The(square root of l₁l₂):1 is the ambiguous segregation ratio

At the 1.9640:1 ratio we cannot distinguish a 3:1 ratio from a 9:7 ratio. If the ratio is 1.9640:1 then the proportion would be

  1.9640   ₌  1.9640 
 1+1.9640 =  2.9640

for the dominant class.

The proportion for the recessive class is

 2.9640  _-  1.9640  ₌    1    
 2.9640      2.9640     2.9640

If we add 3/4 + 1 = 1 or 1-3/4 = 1/4 then we get the proportion of recessive expected for a 3:1 ratio.