| An analysis of meiotic chromosome pairing by a mathematical
model in Aegilops speltoides and its hybrids carrying B-chromosomes
Jun'ichi SANO and Masatake TANAKA Plant Germ-plasm Institute, Faculty of Agriculture, Kyoto University An analysis was made on Ae. speltoides (2n=14; SS) and its hybrids involving the diploid wheat (2n=14; AA) or the tetraploid wheat of the emmer group (2n=28; AABB), some of which included various numbers of B-chromosomes. The mathematical model used in the present study assumes that the process of chromosome pairing consists of two successive, independent events. The first event is the association of chromosomes as entire units, and the second event is the chiasma formation between arms of the associated chromosomes, occurring with probability a and c, respectively (DRISCOLL et al., 1979). The probability with which one radomly sampled chromosome is involved in various configurations was calculated and is indicated in Table 1. In the calculation about the Ae. speltoides x diploid wheat hybrids, it was assumed that there was an interchange per cell which might show a chain configuration. Varying numbers of cells were observed for each material, and one chromosome was randomly sampled from each pair of homologues in the case of Ae. sepltoides and from each cell in the cases of its hybrids involving either the diploid or the tetraploid wheat. Estimation of the two parameters, a and c, was performed by the method of maximum likelihood, based on the polynomial distribution (Table 1). The observed and expected frequencies of various configurations are shown in Tables 2 and 3. These results indicate that the present model of chromosome pairing explains the observations reasonably well. Therefore it is worthwhile to compare the values of the estimates of the two parameters (a and c) among these materials. The values of a and c of the 0B-class of Ae. sepltoides were 1.0 and 0.93, respectively. The presence of various numbers of B's (1 to 5) had almost no effects on these values (Table 2). When 0B-classes were considered, there were no significant differences concerning the value of a between homologous chromosome pairing in Ae. speltoides and homoeologous chromosome pairing in the hybrids (Tables 2 and 3), but the values of c of the latter (0.49 and 0.70) were smaller than the former (0.93). Therefore reduced amount of pairing generally seen between homoeologues may result from the failure of chiasma formation. When B's were present in the hybrids, further reduction in the amount of homoeologous chromosome pairing was observed. In these cases, the values of a also decreased in addition to further decrease of the c values (Tables 2 and 3). Therefore it is concluded that presumably both association and chiasma formation of homoeologous chromosomes are suppressed by the presence of B's and that those of homologous chromosomes are not affected by their presence. |