start-ver=1.4 cd-journal=joma no-vol=97 cd-vols= no-issue=1 article-no= start-page=17 end-page=24 dt-received= dt-revised= dt-accepted= dt-pub-year=2008 dt-pub=200802 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=人為同質４倍体集団における全兄弟及び半兄弟共分散の数学モデル kn-title=Mathematical Model for the Calculation of Full and Half Sib Covariance in an Artificial Autotetraploid Population Including Aneuploids en-subtitle= kn-subtitle= en-abstract=人為同質４倍体集団の遺伝分散を求めるため，両親が近交系数Ｆ＝０の同質４倍体家族の全兄弟と半兄弟の共分散を検討した．Kempthorne のモデルにおいて定義された分散の係数を①Ａ，Ｄ，Ｔ，Ｑと②φ，ψの２つに分割し た．①は互いに独立な相加，２遺伝子，３遺伝子，４遺伝子効果の組み合わせの確率である．②は兄弟が片親から受け取る同一対立遺伝子の数と対立遺伝子ペアの数である．これは兄弟が片親から対立遺伝子と対立遺伝子の組を受け取る確率の関数であり，この確率は減数分裂での染色体行動と配偶子の染色体数によって決まる.この確率を推定するため，Ⅳ価染色体は確率κ，λ（κ＋λ＝１）で２-２と１-３で分配され，Ⅲ価染色体とⅤ価染色体は１-２と２-３に分配されると仮定した．本報告では，四染色体が完全にⅣ価染色体を形成するとして，全ての雌雄の配偶子がその染色体数に関係なく受精できる単純な場合について検討した．共分散の分散成分の構造は兄弟の組み合わせと家族によって異なる．したがって，家族の共分散は各兄弟の共分散 とその組み合わせ頻度を用い平均すれば求めることができ，集団の平均の共分散は家族の共分散と集団での家族の頻度を用い平均すれば求めることができる． kn-abstract=For the estimation of genetic variance of an artificial autotetraploid population, a mathematical model of full and half sib covariances between sibs with various chromosome numbers, which were derived from euploid or aneuploid parents, was devised for a case where the inbreeding coefficient of the parents was F＝0. The coefficients defined in Kempthorne's model were separated into two parts: (i) A, D, T and Q, and (ii) φ and ψ. The former four parameters were defined as probabilities of factor combinations, which could be compared between various sibs, for additive, digenic, trigenic, and quadrigenic effects, and were mutually independent. The latter two parameters, which were the numbers of the identical allele and the identical allele pair combinations that two sibs inherited from a parent, were defined as linear functions of the probabilities that two sibs inherited allele or allele pair from a parent, respectively. These probabilities depend on chromosome behavior during meiosis and the chromosome number of the gametes. For the estimation, it was assumed that quadrivalent chromosomes were distributed by 2-2 and 1-3 with probabilities κ and λ (κ＋λ＝ 1), respectively. The distribution of trisomic and pentasomic chromosomes to the poles was assumed to be 1-2 and 2-3. Then, the probabilities were estimated for the simple case where all male and female gametes could equally fertilize irrespective of their chromosome number, provided that tetrasomic chromosomes completely formed a quadrivalent chromosome. 　The constitution of variance components were different according to the sib combinations and family. Therefore, for the calculation of the covariance of a family, the covariances between various sibs were averaged by the combination frequency in a family, and for the calculation of the covariance of population, the family's covariances were averaged by the family's frequency in the population. en-copyright= kn-copyright= en-aut-name=MorisawaTetsuo en-aut-sei=Morisawa en-aut-mei=Tetsuo kn-aut-name=森澤徹男 kn-aut-sei=森澤 kn-aut-mei=徹男 aut-affil-num=1 ORCID= en-aut-name=KatoKenji en-aut-sei=Kato en-aut-mei=Kenji kn-aut-name=加藤鎌司 kn-aut-sei=加藤 kn-aut-mei=鎌司 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=高知県立安芸高等学校 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=artificial autotetraploid kn-keyword=artificial autotetraploid en-keyword=covariance kn-keyword=covariance en-keyword=variance component kn-keyword=variance component en-keyword=euploid kn-keyword=euploid en-keyword=aneuploid kn-keyword=aneuploid END start-ver=1.4 cd-journal=joma no-vol=97 cd-vols= no-issue=1 article-no= start-page=25 end-page=31 dt-received= dt-revised= dt-accepted= dt-pub-year=2008 dt-pub=200802 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=異数体を含むレンゲ人為同質４倍体集団での全兄弟と半兄弟の共分散の計算 kn-title=Calculation of Full and Half Sib Covariances in an Artificial Autotetraploid Population Including Aneuploids, in Astragalus Sinica L. en-subtitle= kn-subtitle= en-abstract=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． kn-abstract=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. en-copyright= kn-copyright= en-aut-name=MorisawaTetsuo en-aut-sei=Morisawa en-aut-mei=Tetsuo kn-aut-name=森澤徹男 kn-aut-sei=森澤 kn-aut-mei=徹男 aut-affil-num=1 ORCID= en-aut-name=KatoKenji en-aut-sei=Kato en-aut-mei=Kenji kn-aut-name=加藤鎌司 kn-aut-sei=加藤 kn-aut-mei=鎌司 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=高知県立安芸高等学校 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=full and half sib covariances kn-keyword=full and half sib covariances en-keyword=quadrivalent chromosomes kn-keyword=quadrivalent chromosomes en-keyword=additive genetic variance kn-keyword=additive genetic variance en-keyword=variance of a family kn-keyword=variance of a family en-keyword=covariance of a population kn-keyword=covariance of a population END