1911.] Stable Simple Mendelian Population. 



41 



Now, in a population stable both as regards type and number, the total 

 quantity of allelomorphs, whether dominant or recessive, must remain 

 unaltered. Hence we have at once, 



2L + M = and 2N + M = 0. 



Putting L = f(p, q), the result above is obtained at once. 



In the case of the children of brother-sister marriages f(p, q) = pq/4: ; for 

 the children of first cousins, for s = oo ,f{p, q) — pql§, and so on. 



Inbreeding thus accentuates both the pure dominant strain and the pure 

 recessive in any stock to the same extent, and at the expense of the hybrid 

 element. 



The already noted agreement between the actually observed somatic 

 correlations and the theoretical Mendelian gametic correlations appears to 

 negative the existence of absolute dominance. Suppose, then, we are 

 dealing with a harmful recessive characteristic, the result of inbreeding is 

 that for every individual with patent evil added to the community, a 

 useful individual of pure dominant type is also added, and two individuals 

 of neutral type are got rid of. It is quite conceivable that this process- 

 might be a gain to the community, owing to a selective action on the patent, 

 evil. 



It would, of course, in the present state of our knowledge, be impossible to 

 insist on this view : but, at the same time, it must be pointed out that 

 much of the argument against inbreeding fails if the phenomenon of domin- 

 ance be not complete. In the particular case in which the heterozygote 

 has a mean " utility " between the utilities of the two homozygotes 

 inbreeding is neither advantageous nor the reverse. 



(iii) Further, as Bateson* has pointed out, it may be that some valuable 

 qualities are recessive in character. 



In that case, and especially for a very rare recessive, as the preceding 

 analysis shows, inbreeding will serve a useful purpose in bringing the- 

 recessive quality to light. 



(iv) The analysis has dealt solely with matings between collaterals of the- 

 same rank. It may, however, be pointed out that where the marriages of 

 first cousins once removed are considered, these should probably be regarded 

 in the same light as second cousin marriages, so far as resemblance can be 

 used as a test. For, just as it has been found that first cousins resemble 

 each other to about the same extent as uncle and nephew or aunt and nieces, 

 so it appears likely that the correlation between first cousins once removed 

 will be equal to the correlation between second cousins. But whether this. 



* ' Mendel's Principles of Heredity,' 1909. 



