Double and single backcross linkage estimates in autotetraploid maize.

INKAGE estimates in autotetraploids are more complicated than in diploids for three reasons outlined by FISHER (1949) : 1) The multiplicity of segregating genotypes-for IWO loci with two alleles at each there are 19 doubly heterogenic genotypes in an autotetraploid, compared with only two in a diploid. 2) The eleven possible modes of gamete formation, compared with only two in diploidstetraploid gametes may contain all combinations of recombinant and non-recombinant chromatids, whereas diploids may be only recombinant or non-recombinant. 3) The frequencies of different gametic genotypes cannot be identified by a single backcross to a tester. In this study, for example, where the linked genes were shrunken and waxy on chromosome 9, doubly dominant progeny of the first backcross could have been produced by five gametic genotypes,ShWx/ShWx, ShW.x/Shwx, ShWx/shWx, ShWx/shwx, and Shwx/ shWx. Three of the gametes had recombinant chromatids, but all gametes were indistinguishable in the first backcross. The gametic series may be determined, however, if these progeny of the first backcross are subjected to a second backcross. Each gamete is then recognized, not by the appearance of one individual, but by the frequency distribution observed in a second-backcross family from that individual. FISHER’S monumental paper (1947) set forth the general theory of polysomic linkage and accounted for all the complexities. He then applied this theory to tetrasomic linkage anabysis in Lythrum salicaria (1 949), using double-backcross data. The second backcross, although laborious, is an extremely powerful tool in unravelling the complex gametic segregation and providing unbiased recombination estimates. The time and space required to raise and identify the progeny of a second backcross are almost inmx”ntab1e problems in higher plants. Hence, most linkage estimates in autotetraploids have been computed from single-backcross data. These include DEWINTON and HALDANE (1931) with Primula, SANSOME, (1933) with Solanum, and WELCH (1962) with maize. Single-backcross linkage can be estimated comparatively easily using maximum likelihood ( MATHER 1938). However, a single backcross cannot directly identify the recombinant