Abstract
1) The progress in the chiasma-type theory and the studies of tetrad analyses in lower plants have made clear that each locus in a given chromosome has its specific frequency of the equational separation at the first division of meiosis.
But some additional statistical theories whould be necessary to make the state of the chromosome reduction clearer.
In this paper following two problems were dealt with:
(a) To obtain the frequency distribution of the length of pre- and post- reductional segments in the chromosome tetrads.
(b) To calculate the mean length of such segments for some genetically well studied chromosomes.
2) For telomitic chromosomes with genetical length of 100l units and without chromatid interference, the frequency distribution of the length (ξ) of post-reductional segments is given by the following formula, if multiple cross-overs are negligible in frequency.
Φ(ξ)=φ'(ξ)+2φ'(l-ξ)-(l-ξ)φ”.ξ)-1,
where φ(ξ) is the recombination probability between two genes which are 100ξ units apart.
For X-chromosome of Drosophila melanogaster (70 units in length), the above formula becomes
Φ(ξ)= cos2ξ+2cos(1.4-2ξ)+(1.4-2ξ)sin2ξ-1,
the graph of which is shown in Fig. 2.
3) Taking the chromosome as the abscissa and assuming that f(x) represents the probability of the post-reduction of a point x, then the mean length of post-reductional parts of the chromosome or chromosomal segment ab is
L=∫baf(x)dx,
which equals the area bounded by the curve Y=f(x), the axis of x and the ordina_??_es x=a, and x=b (cf. Fig. 6).
4) The proportions (in percent) of the length of pre- and post-reductional segments calculated by the above method are listed for some genetically well studied chromosomes as follows:
l-L/l L/l
Neurospora crassa, sex-chromosome 66.5% 33.5%
Sphaerocarpus Donnellii,
squamifera-chromosome 52.2% 47.8%
Drosophila melanogaster,
X-chromosome {46% 54% 48%_??_ 52%_??_
II-chromosome 48% 52%
Drosophila virilis,
X-chromosome {40.7% 59.3% 40.0%_??_ 60.0%_??_
In this table l-L/l and L/l represent respectively the proportion of pre- and post-reductional segments and the values with the asterisks were calculated on the cytological maps, while other values were all calculated on the genetical maps.
