EVOLUTION 



433 



pangamic mating the numbers of {b) with {a) and {b) 

 with {b) marriages will be «^ X ^ and % X -^ respectively. 



We may thus arrange the following scheme as represent- 

 ing the numbers of each kind of mating : — 



Husbands. 



> 



Now if mating, however, be not random, if like mates 

 with like, then more {a) husbands will seek {a) wives, 

 and more {U) husbands {b) wives than are indicated in 

 this table ; that is, the left-hand top and right-hand 

 bottom compartments will contain more cases than are 

 indicated by the numbers written in them, and they will 

 gain at the expense of the groups ;/^ x ?/^^/N and ii^ x mi,jN. 

 Each of these groups will lose to the other two, so that 

 with correlation we shall have a table of the form : — 



Husbands. 



> 



Ug X mg 



N 



+ «l + ^2 



n-a X nij 



N 



Ub X l/lg 



N 



• €-1 ~~ Cf* 



nj, X mi, 



N 



+ eo + e. 



where e^, e.^, e^, e^ are the respective losses of the {ab) and 

 {ba) groups to the {ad) and {bb) groups. But the total 

 number of husbands in the {a) groups is n^, and this must 



+ ^1 + ^2 + 'N ^2 ~^i = ^^a + ^1 - 'V Hence 



N 



28 



