In the present paper a theoretical consideration was made on the problems of differentiation and homology-relationship of the genom. Though tentatively the followings were concluded.
(1) In two genoms which are in 'intimate homology', the chromosome pairing is nearly complete, the modal class of number of pairing per nucleus corresponding to the basic chromosome number, n (Fig. 1, a), while in the ease of 'remote homology' the number of pairing is considerably variable, the modal class being 0 (Fig. 1, b). A good example of these extreme pairing ways is found in Trillium Hague (3n=15, K1K2T). The mode of pairing between K1 and K2 represents intimate homology and that between (K1+K2) and T remote one (Fig. 1, the ordinate indicates frequency of PMCs in percentage and the coordinate number or pairing per nucleus. cf. Haga 1937 and Tables 1-2).
(2) As a general rule it will be stated that the increase in the degree of genetic differentiation decreases the quantity of pairing proportionally to the grade or quantity of the differentiation. The relative value of the quantity of genetic differentiation will be then expressed by the quantity of pairing which will be adequately given by the following percentage index : 100× (Total number of pairing observed) /n× (Total number of PMCs observed).
Theoretically, we can expect all values of the index ranging from 0 to 100. Values of the two modes of pairing. in Trillium Hague were 95.7 for K1-K2 and and 5.6 for (K1+K2) -T, respectively, the former showing the intimate relation and the latter the remote one (Fig. 1, these values are indicated in italics beside the polygons). A more or less continuous variation in this value is evident in a series of diploid hybrids (2n=14) of Aegilops and Triticum (Fig. 2, the ordination and indication of the value are the same as in Figure 1. cf. Table 3). An interesting fact in the present case is that the decrease in quantity of pairing is accompanied by the transposition of the mode of frequency distribution in the direction from the intimate to the remote relation. The most continuous range of variation is obvious in a series of various diploid hybrids (2n=26) in Gossypium. The mean number of bivalents per nucleus shows a complete series from 13 to 2 (v. Skovsted 1937), The pairing relation in the inter- and intra-generic hybrids (2n=14) of Aegilops, Triticum. and Haynaldia is like-wise very suggestive for the present considerations (Fig. 3, only the maximum numbers of bivalents per nucleus are shown after the data compiled by Kihara 1937).
(3) The above considerations, will support the inference that : genetic differentiations will express, though superficially, a property of a continuous system. Thus homology is naturally the relation between any two of the genoms differentiated variously in a continuous system. In other words all the relations are included in the term 'homology', which ranges however in quantity of pairing from 0 to 100. Thus it is probable that 'homologous' or 'non-homologous' relation in the cytological sense implys nothing else intonate or remote relation respectively. Theoretically, only the 'identical' relationship-equality in quality, quantity and arrangement of all genes-may be absolute. This consideration naturally leads to the nullification of the critical boundary between auto- and allo-polyploidy.
(4) Certain differentiation as a whole of two or more sub-genoms in an allopolyploid would eventually lead to the formation of a new genom, which is no longer indivisible into the ancestral genoms. The new genom is polyploid in chromosome number but functionally diploid.. In the light of the recent knowledge it seems quite probable that the secondary polyploidy is an evolutional product. Then a genom has a potentiality to give rise to a non-pol
