岡山大学農学部Acta Medica Okayama0474-0254 9712008Mathematical Model for the Calculation of Full and
Half Sib Covariance in an Artificial Autotetraploid
Population Including Aneuploids1724ENTetsuoMorisawaKenjiKatoFor 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.No potential conflict of interest relevant to this article was reported.岡山大学農学部Acta Medica Okayama0474-0254 9712008Calculation of Full and Half Sib Covariances in an Artificial Autotetraploid Population Including Aneuploids, in Astragalus Sinica L.2531ENTetsuoMorisawaKenjiKatoFull 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.No potential conflict of interest relevant to this article was reported.