| The first operation will be to input values of two parameters ER and DR.
Counters M and N will be set to 500 and 7, respectively. The first of these
is the number of meiotic events required, so 500 events of meiosis II will
give a total of 1000 meiotic products. The second is the number of the univalent
chromatids. The program will then enter a loop which will be repeated the
required number of times (=500). Increment controls NC1 and NC2
will be both set to zero in order to count the numbers of univalents which
will move to one pole and the other, respectively. Subsequently, the program
will enter the inner loop which will simulate univalent elimination and
distribution. It is now in a position that parameter ER will determine if
a univalent is eliminated. If so, the program will return to the beginning
of the second loop. If not, parameter DR will determine towards which pole
the univalent migrates. The implementation by these two parameters is :
If the elimination rate ER is x, and then random number (RN1)
between 0 and 1 is generated and a univalent is eliminated if this random
number does not exceed x. Also, if the distribution rate DR is y,
and then the other random number (RN2) is generated and one gamete
to be produced receives the un-eliminated univalent if this random number
is greater than y ; otherwise its counterpart receives it. For example,
if y=0.1, the chance of one gamete receiving each un-eliminated univalent
would be 90%, and that of its counterpart would be 10%. The univalents would
distribute at random when y=0.5. After a cycle from 1 to 7 is completed,
the number of univalents (NC1 and NC2) in a pair of
the female gametes will be printed out, and then the program will return
to the beginning of the first loop (meiosis cycle). Simulation data were obtained from computer runs of a FORTRAN program. Comparisons were made between the estimated distributions by simulations at various elimination and distribution rates and the actual distributions. Statistical analyses were done by using 2 x 7 chi-square tests of independence, in which two types with 6 and 7 D- genome chromosomes were pooled because of small expected values in some cases. The estimated dsitributions were tested with the actual distribution obtained by KIHARA & WAKAKUWA (1935), and the change in chi-square value is presented in Fig. 2, from which it can be seen that chi-square values were very small and not statistically significant when ER was 0.15-0.20 and DR was 0.30. Similarly, there were satisfactory fits of the estimated distributions with the actual distribution obtained by MAKINO (1974) when ER was 0.15-0.20 and DR was 0.25-0.30. These simulation results indicated that 15-20% univalent elimination was a naturally occurring event in the pentaploid wheat hybrids investigated by those workers. In fact, NAKAMURA (1945) reported 12-19% elimination by observing micronuclei in quartets from several pentaploid hybrids. Both were comparable to each other. Our results also indicated that in actuality the univalent chromatids did not necessarily distribute at random (the 3:7 or 7:3 univalent segregation was the best estimate in the present work). Evidence has not yet been available for non-randomness in univalent distribution in wheat, and moreover it may not be an easy task to experimentally prove it. In higher plants other than wheat, however, there have been several reports on this subject. SMITH-WHITE (1948) has reported polarized univalent segregation during meiosis I in a Leucopogon juniperinus triploid. Therefore, we could postulate that there may be some mechanism to disturb random orientation of univalent chromatids in meiosis II of the pentaploid gametogenesis. As shown above, our method seems to be useful to simulate univalent elimination and distribution, although it may not be a very good representation of reality. The present work has been preliminary, and further improvement of the algorithm and mathematical treatment, if possible, will be needed to have better understanding of univalent behavior during meiosis. |
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