EVOLUTION 471 



2.731 inches and of mothers of daughters 2.274 inches; 

 hence we find for the mid-parent : — 



(2.731 \ 

 TO + 66 = 74.63 inches, 

 2.274 ) '^ ^ 



or the mid-parent is taller than the father, because the 

 woman's mother is considerably above the average height. 

 Accordingly we simplify our consideration of bi-parental 

 inheritance by replacing our mixed population of male 

 and female by a population of single parents, the mid- 

 parents. Upon these mid-parents all bi-parental inherit- 

 ance depends. These mid -parents have a variability 

 represented by S = sj\^ ^ + '''■?)^v ^"*^ ^ correlation with 

 their offspring R = rj/\/|-(i -\-r.^. 



Now see what results flow from this : — 



(i.) Suppose absolutely perfect assortative mating, 

 possibly the case of self- fertilisation, then ^3=1, and 

 S = o"!, R = /'i, or in this case the mid-parent is as vari- 

 able as the individual parent, and is only as closely 

 correlated with the offspring as the single parent. 



(ii.) Suppose pangamic mating, r.^ = o, then S = 

 ^ Jo- = .7 070-, and R=: ^^2^^ = 1.414/'! = .4242, if r^ take 

 its theoretical value for pangamic blended inheritance .3. 



Thus with bi-sexual reproduction and no sexual 

 selection the population of mid-parents, on which the 

 inheritance depends, is less variable than the individual 

 parents. The offspring are, however, more like their 

 mid-parents than their individual parents, the coefficients 

 of heredity being as .424 to .3. Further, the regression 

 is given by R^'=2ri^ or if we put i\=^ .1, and suppose 

 the race stable as regards variability, i.e. 0-3 = o-j, then 



/«3 = .6H. 



Thus the type of the array due to a given mid-parent 

 possesses .6 of the deviation possessed by the given mid- 

 parent, while it would only possess .3 of the deviation 

 due to a single parent. Further, let us examine the 

 variability of the array in the two cases. Select 



