Full and half sib covariances were investigated in an artificial autotetraploid population with
random mating in Astragalus sinicus L.. Since a set of homologous chromosomes is not necessarily
involved in aneuploidy, the covariances must be averaged for two cases, that is, with and
without involvement. To average the covariances, the probability that a set of homologous chromosomes
was involved in aneuploidy was assumed as 3/8, where “8” and “3” represent the
chromosome number of a genome and the mean number of quadrivalent chromosomes formed
in a euploid, respectively. The covariances were calculated under the assumption that quadrivalent
chromosomes were distributed to the poles by 2-2 and 1-3 with probabilities κ＝ 0.8 and λ
＝0.2 (κ＋λ＝1) respectively, and that trisomic and pentasomic chromosomes were distributed
by 1-2 and 2-3 both with a probability of 1. It was also assumed that the inbreeding coefficient
of the parents was F＝ 0, and that 2x and 2x＋ 1 pollens and all female gametes could fertilize
equally. The covariance of a family was taken as an average of the covariance of each sib combination
in a family. As a result, the covariance of a population could be obtained as an average of
the covariance of each family in a population. The coefficients of variance components calculated
under these assumptions were different from those calculated under the same condition except
that 2x＋ 1 pollen could not fertilize. Differences in the coefficient of additive genetic variance
components were about 3.3% and 7.2% for full and half sib covariances, respectively.
Coefficients of the other variance components were also different between the two cases.
However, 2x＋1 pollen could rarely fertilize, since their ability to fertilize in a practical population
were lower than 2x pollen. Therefore, it would be valid to calculate full and half sib covariances
in an artificial autotetraploid population of Astragalus sinicus L. under the condition
thatonly 2x pollen could fertilize.任意交配するレンゲ人為同質４倍体集団における全兄弟と半兄弟の共分散を計算した．特定の相同染色体が必ずしも異数体に関わるとは限らないので，特定の相同染色体が関わる場合と関わらない場合について共分散を計算し，平均しなければならない．共分散を平均するため，特定の相同染色体が異数性に関わる確率を３/８とした“８”と“３”はゲノム染色体数と正４倍体で形成される４価染色体数の平均値である．４価染色体は MI で確率κ＝ 0.8とλ＝ 0.2（κ＋λ＝１）で２-２と１-３に分配され，Ⅲ価染色体とⅤ価染色体は確率１で１-２と２-３に分配されるとし，２xと２x＋１花粉と雌性配偶子は等しく受精するとして共分散を計算した．両親の近交系数はＦ＝０であると仮定した．次いで家族の共分散を家族内の兄弟間の共分散の平均として計算し，集団の共分散を家族の共分散の平均として計算した．仮定に基づき求めた共分散の分散成分の係数は２x花粉のみが受精するとして計算した値と違っていた．相加遺伝分散成分の係数は全兄弟と半兄弟でそれぞれ3.3％と7.2％ずつ違っていた．他の分散成分も同様であった．実際のレンゲ人為同質４倍体集団では２x＋１花粉は受精能力が２x花粉より低く稀にしか受精しないので，２x花粉のみが受精するとして全兄弟と半兄弟の共分散を計算しても問題はないであろう
