IV PRESENCE & ABSENCE THEORY 33 



not contain it (r). Half of its gametes, therefore, 

 will contain R and the other half will be without 

 it (r). Similarly half of its gametes will contain P 

 and the other half will be without it (/). It is 

 obvious that the chances of R being distributed to 

 a gamete with or without P are equal. Hence the 

 gametes containing R will be of two sorts, PR and 

 Rp, and these will be produced in equal numbers. 

 Similarly the gametes without R will also be of two 

 sorts, rP and rp, and these, again, will be produced 

 in equal numbers. Each of the hybrid walnut- 

 combed birds, therefore, gives rise to a series con- 

 sisting of equal numbers of gametes of the four 

 different types RP, Rp, rP, and rp ; and the breeding 

 together of such F^ birds means the bringing together 

 of two such series of gametes. When this happens 

 an ovum of any one of the four types has an equal 

 chance of being fertilised by a spermatozoon of any 

 one of the four types. A convenient and simple 

 method of demonstrating what happens under such 

 circumstances is the method sometimes termed the 

 " chessboard " method. For two series each con- 

 sisting of four different types of gamete we require 

 a square divided up into 16 parts. The four terms 

 of the gametic series are first written horizontally 

 across the four sets of four squares, so that the 

 series is repeated four times. It is then written 

 vertically four times, care being taken to keep to 

 the same order. In this simple mechanical way all 

 the possible combinations are represented and in 

 their proper proportions. Fig. 5 shows the result 

 of applying this method to our series RP, Rp, rP, rp, 

 and the 16 squares represent the different kinds of 



D 



