INBRED LINES FOR HETEROSIS TESTS? 345 



From equation (4) we can now express average progress per locus from selec- 

 tion for cross performance with a homozygous tester as: 



M\ = [ qfq.(i-q.) ( 1 - ^)-+ ( 1 - qr^Qj ( 1 - 9.) d + ^) ^1 ^ (7) 



z a j> 



Rate of improvement in cross performance from reciprocal selection (equa- 

 tion 3) approaches zero as gene frequencies approach the equilibrium ex- 

 pected if rates of reproduction of individuals were directly proportional to 

 their phenotypes (i.e., 9 = [1 + k]/2k). Hence, progress from reciprocal selec- 

 tion may be expressed more usefully in terms of the deviation of gene fre- 

 quencies from (1 + k)/2k, as follows: 



^''' = £['■('-'■> Gr - "')' + ^= ( ' - '') (Vr - *'T 



4 k-' 



— 2k 'Aqi' Aqod (8) 



Comparisons of expected progress per generation from homozygous tester 

 and from reciprocal selection may be made from equations (7) and (8), re- 

 spectively. The comparison may be visualized by plotting rate of improve- 

 ment against deviations of gene frequencies from an initial equilibrium value 

 of (1 + k)/2k, using qi and q-i for the two populations under reciprocal selec- 

 tion, and qi and qj for loci that are AA and aa, respectively, in the tester, for 

 homozygous tester selection. 



In Figure 21.5, it is assumed that k = 2, and qi is shown approaching 

 {k -\- \):ik — 1) times as fast as q, approaches 1. Actually, qt would 

 move more slowly than Qj at first because {Aa — A A) = {k — \)d and 

 (.4 a — aa) = (1 + k)d. However, A^,- increases as qi falls from .75 toward 

 .5 because of the increased variance of qi and consequent increase in genetic 

 variance and in covariance with progeny means, and then Aqi declines as 

 qi moves from .5 toward 0. There is a steady decline in Aq, as qj rises from 

 .75 toward 1.0. 



Under reciprocal selection, if q\ and q^ are near an equilibrium of (1 + k)/2k 

 at the outset, initial progress will be slight compared with that from homozy- 

 gous tester selection and will not equal APh until qi and q^ differ, in opposite 

 directions from (1 -\- k)/2k, by an average of about .50. Only during the late 

 generations of selection will reciprocal selection surpass homozygous tester 

 selection in effectiveness. 



Another possible disadvantage of reciprocal selection is that gene fre- 

 quencies at most loci for which k> \ may be somewhat below (1 -\-k)/2k. 

 This will occur if the advantage oi Aa over .4.4 and aa individuals in rate of 

 reproduction is made greater by intensive individual or family selection than 

 it would be if reproductive rates were directly proportional to phenotypic 

 levels of performance. This would amount to increasing the effective degree 



