HYBRID VIGOR IN DROSOPHILA 



483 



enters in equal frequency, this means that one-third of the genes are on the 

 average heterozygous. Types 2 to 7 have 2 chromosomes heterozygous, or the 

 average of these types is two-thirds heterozygous. Type 1 is completely 

 heterozygous or 100 per cent. Plotting the average egg production for the 

 four groups shows the effects of different degrees of heterozygosity on the 

 hybrid vigor. 



The property of additivity of the heterotic gene effects would seem to be 

 the logical explanation for this linear relation and also for the absence of in- 

 teractions between the genes of the different chromosomes. It must be real- 

 ized, however, that the chromosomes themselves represent interacting gene 

 effects which give the block reactions. The trend so far considered is an aver- 

 age trend, each point, except that for the completely heterozygous, being 

 based on several types. Interaction — combination effects which are larger or 

 smaller than the sum of the chromosomal effects separately — may exist. Such 

 effects, it is true, must be in opposite directions and equal. The factorial de- 

 sign of the experiment facilitates evaluation of these interactions. The data 

 following gives the three levels of effect each of the chromosomes can assume, 

 together with the two and three chromosome interactions. 



VARIANCE ANALYSIS OF CHROMOSOMAL EFFECTS 



Source of Variation 



I chromosome 



II chromosome 



III chromosome 



I and II chromosomes 



I and III chromosomes . . . . 



II and III chromosomes. . . 

 I, II, and III chromosomes 



d/f 



2 

 2 

 2 

 4 

 4 

 4 

 8 



Mean 

 Square 



574 



1916 



1010 



81 



62 



116 



103 



Apportion- 

 ment of 

 Variation 

 Per Cent 



11 



44 



22 











1 



22 



The effects of the direct order actions of the first, second, and third 

 chromosomes are highly significant. None of the interactions show large vari- 

 ations. Nor are any of these interactions in excess of what would be expected 

 from random differences. Apportioning the variance to its various chromo- 

 somes, 11 per cent is attributable to the first chromosome, 44 per cent to the 

 second, and 22 per cent to the third. 



Analysis of this material shows that the hybrid vigor of the egg yields re- 

 ceives a significant contribution from the heterozygosity of each chromosome 

 pair, and that none of the chromosome interactions are significant. The ho- 

 mozygous chromosomes of the two parental inbreds do not differ in either 

 their direct or interaction effects from zero. 



The linearity of the effect on egg yield and the absence of interactions show 

 that the chromosomes with their contained genes behave as integrated units 



