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I HE AMEBIC AX NATURALIST [VoL.LV 



may be expected is presented in Table II, which gives the 

 number of individuals necessary to provide an even 

 chance of obtaining at least one individual homozygous 

 for different numbers of characters in crosses when from 

 two to 15 character pairs are involved. It should be 

 kept in mind that even though one should obtain an indi- 

 vidual homozygous for a sufficiently large percentage of 

 the characters involved to approximate closely the Fj in 

 vigor, it would be necessary to grow a progeny from this 

 individual before its inherent vigor could be demon- 

 strated. The numbers given in the tables might thus be 

 taken to represent Fg progeny rows instead of Fg in- 

 dividuals. 



The conclusion is that perjugate progenies equalling 

 or even closely approximating Fj in vigor are hardly to 

 be expected in breeding experiments and consequently 

 no assumptions are necessary to account for their non- 

 appearance. 



Skew Distribution Due to Dominance 

 The second objection, that of the failure of Fo pro- 

 genies to show a skew distribution, may now be consid- 

 ered. There can be no question that a series of inde- 

 pendent, dominant characters influencing size would 

 bring about a skew distribution. Assuming the charac- 

 ters to have equal effect, two characters would give a dis- 

 tribution of 1, 6, 9, three, a distribution of 1, 9, 27, 27, 

 and with four characters the distribution would be 1, 12, 

 54, 108, 81. It is apparent that with an increase in the 

 number of characters the skewness becomes less pro- 

 nounced. It may be of interest to determine whether, 

 with a reasonably large number of characters, the skew- 

 ness would be detected in populations of the size usually 

 grown in experiments. 



With 20 pairs of characters giving 21 classes 1,099,- 

 514,627,776 individuals would have to be grown to obtain 

 a representative population. Of this population 99.91 

 per cent, would fall in the 12 classes with the largest 



