114 Probability 



cessives out of 42 plants is 0.0579. Geneticists are usually not so 

 much concerned with the chance that all the members of a certain 

 family will be of a certain phenotype or that a family will segre- 

 gate into a given ratio as with the problem of how truly a certain 

 observed ratio fits a theoretical (expected) one and whether the 

 deviations found in the observed ratio are due to chance alone 

 or whether they are so large in relation to the number of indi- 

 viduals in the population that the ratio cannot be considered a 

 true example of the theoretical one. 



Standard and Probable Error 



Several methods are in use for determining whether a certain 

 observed ratio is a true example of a certain theoretical one. 

 Two methods are the standard error and the probable error. 

 These methods are based on the deviation of the observed ratio 

 from a theoretical ratio comprised of the same number of indi- 

 viduals. The standard error of the ratio is expressed by o- = 



fP ' ^ where p is the probability of the first term of the ratio, 

 \ n 



q the probability of the second term, and n the number of 

 individuals. 



To show how this method is applied in practice, let us take 

 a ratio published by Professor Sewall Wright for guinea pigs. 

 Gene A produces what is called the agouti coat color and its 

 allele produces a nonagouti coat. A heterozygote was crossed 

 with a nonagouti and the offspring segregated into 48 agouti 

 and 63 nonagouti. This is not an exact 1 : 1 ratio, and the prob- 

 lem is to find out why. There are a number of possible reasons. 

 Other genes may be exerting an effect to suppress the action of 

 the agouti gene, the environment may be affecting the expression 

 of the agouti gene so that some agouties actually look like non- 

 agouties, agouti animals may less frequently survive in birth, 

 other genetic explanations may have to be sought, or the devi- 

 ation from the exact ratio may be due to chance alone, in which 

 case this ratio may be considered to be a 1 : 1 ratio even though 

 it deviates to some extent. There are two ways of applying the 

 formula. All the figures must be expressed as actual numbers 

 or they must be converted into percentages, but the two methods 



