324 A. J. MANGELSDORF 



heterozygous condition of which is superior to either homozygote. It is to be 

 expected that such a linkage will eventually be broken. However, there may 

 be regions in the chromosomes, such as the centromere region, for example, 

 where crossing over is reduced, and where a group of genes may act indefi- 

 nitely as a single gene. We may for convenience designate the effect of such 

 reciprocal apposition of favorable dominants to their less favorable reces- 

 sives as a pseudo-overdominance effect. It will be noted that such a balanced 

 defective situation conforms with the dominance and linkage hypothesis ad- 

 vanced by Jones as an explanation of the heterosis phenomenon. 



5. Even in the absence of linkage, an overdominance type of reaction (but 

 resulting from pseudo-overdominance) must assert itself whenever each of 

 the two members of a pair of gametes is able to supply the favorable domi- 

 nant alleles required to counteract the less favorable recessives carried by 

 the other member of the pair. The likelihood of success in retaining, in suc- 

 cessive generations of selfing, all of the favorable dominants heterozygous 

 in Fi, and eliminating all of the less favorable recessives, diminishes ex- 

 ponentially with increasing numbers of loci heterozygous in Fi. It would 

 seem that naturally cross-fertilized organisms which carry, at many loci, 

 deleterious recessives of low per locus frequency in the population could 

 hardly fail to manifest a pseudo-overdominance type of response to inbreed- 

 ing and outcrossing. 



6. From an evolutionary standpoint, it may be important to distinguish 

 between the consequences of (a) true overdominance (heterozygosis at the 

 locus level) and {b) pseudo-overdominance (heterozygosis at the zygote level 

 resulting from the reciprocal masking of deleterious recessives by their 

 dominant alleles). From the standpoint of the breeder who is of necessity 

 working against time, this distinction may have little practical importance 

 if many loci are involved in the pseudo-overdominance effect. A breeding 

 plan designed to deal efficiently with one of these alternatives should be 

 effective also in dealing with the other. 



7. Whether due to true overdominance or to pseudo-overdominance, the 

 widespread if not universal occurrence among naturally cross-fertilized or- 

 ganisms of an overdominance type of response to inbreeding and outcrossing 

 poses a problem which the breeder cannot afford to disregard. 



8. Neither overdominance nor pseudo-overdominance can be called upon 

 to explain the differences in vigor between different varieties of wheat, beans, 

 sorghums, and other self-fertilized forms. Such differences are determined by 

 genes in the homozygous state, as are also the differences between homozy- 

 gous inbred lines of corn. 



ROLE OF LIMITING FACTORS 



A consideration of the role of limiting factors in quantitative inheritance 

 leads us to a third group of postulates: 



