In order to analyse the genic system for purple coloration of the pericarp and its linkage relations, the F₂ ratios for the purple coloration of pericarp were investigated with particular attention to its linkage relations to the anthocyanic pigmentation of various other organs. When strains with colored and colorless pericarps are crossed, 9 purple : 3 brown : 4 colorless ratios were found in the F₂. It was assumed that two genes Pp and Pb are concerned with the purple coloration of the pericarp; Pp is epistatic to Pb, and Pp was found to be closely linked with A, one of apiculus-coloration genes, with a recombination fraction of 5.1-9.4 %. They belong to the linkage group III of NAGAO and TAKAHASHI.

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We previously reported on the extraordinary modes of F₂ segregation of anthocyanin coloration in some hybrids between distantly related rice varieties (Kondo and Mizushima, 1964). Other anomalous ways of segregation observed in crosses in which an Indian variety 'Surjamkhi' always took part as a parent are described here. The varieties used in the crosses consisted of nine Japanese and three Indian ones as shown in Table 1.

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In order to explore the possibility of hybrid seed production in Chinese cabbage, a series of experi mnents were carried out to first ascertain the exis. tence or otherwise of selective fertilization in in this crop. Combination of any two from among the five varieties, viz., Matsushimashin No. 2, Kashin, Hotoren, Nozaki No.2 and Aichi were mix-planted in isolated fields (Tables 1 and 2) .

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In February of 1964, two grains of “sectorial chimera kernel” of rice were found out unexpectedly among a great many hybrid seeds in F₃∼F₅ generations bred by crossing between the glutinous and non-glutinous paddy rice varieties. The “chimera kernel” possesses an endosperm being divided sharply into the glutinous and non-glutinous parts by the shallow notch surrounding the middle of the kernel, and both the “chimera kernel” are glutinous in the lower parts of the endosperms bounding on the embryos. Now, the reason for the occurrence of “chirnera kernels” is courpletely unaccountable. However, based upon past studies conducted from the genetic or physiological point of view, the following two hypotheses may be suggested.

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Cold resistance in rice plants shows high correlation with cold water tolerance, so the cold water irrigation method has been used for the testing method of cold resistance. This cold water irrigation method takes a long irrigating period from transplanting to maturing, and requires too large a plot size for accurate evaluation for testing a number of lines at the same, time. So this investigation was conducted to establish some efficient method for accurate testing on the cold resistance of a number of bred lines. The newly devised methods are as follows. For keeping the effect of cold water in the paddy field as homogeneous as possible, the cold water irrigation was practised only at night time, from the premordia stage of the early varieties to the starting time of the heading of the late varieties, and the inlets and outlets of the water were interchanged in every seven or eight days. Owing to this testing method, the distribution of water temperature was highly hornogenized in the field (Fig. 2), and so the uniformity of the sterility occurrence could be kept at a high level.

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Rice seeds were treated with X-rays, thermal neutron or diepoxybutane at BNL in 1957. The progeny populations were cultured in every year without artiflcial selection until the M₆ genetation. Variations of several quantitative characteristics related to grain yield were compared with those of controls (original variety) in M₆ under randomized block design. The significant differences were found in mean values of the panicle weight per stock, weight of a panicle and panicle length among the treated and between treated and controls. These may be caused by natural selections during M₂ - M₆. Also were found some differences among treated and between treated and controls in variance of inter individuals of each population in the wgt, of paniclesper stock, number of panicles and stem length. The wgt of panicles per stock in X-rayed and diepoxybutane treated plots were enlarged in meanvalues and increased in inter-individual variances in M₆, indicating that there are some possibilities. of obtaining high yield strains from these treated populations by selection. However, there was no difierence in mean values or variances between progeny derived from M₂ which segregated chlorophyll mutations in M₂ and that from M₂ in which no chlorophyll mutations segregated. The prediction of frequencies of polygene mutations in progenies by that of chlorophyll mutations in M₂ seems improbable, aithough it was reported that the frequencies of morphological mutations in M₂ adults could be predicted by that of chlorophyll mutations in M₂ nurseries.

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In the course of intervarietal crossing in freesias since 1956, a hypotriploid plant (2n=33-1) was obtained unexpectedly from crossing between tetraploid Golden Buttercup (2n=44) and diploid Super Giant Yellow (2n=22). It grows slowly and has a few slender, short, somewhat twisted and palegreen leaves. Each flowerlet born on a curved flower stalk is very small and light-brownish colored, consisting of 5 perigons (3 inner and 2 outer). The maturation division in pollen mother cells is so irregular that almost all pollen grains are degenerate, and thus the plant is completely sterile. Regarding the occurrence of such an abnormal hypotriploid plant, some inferences are described as follows. It is well known, hitherto, that many normally growing aneuploid plants or cultivars have been found in some popular bulbous flowering plants euch as crocus, hyacinth, daffodils etc. These peculiar plants grow vigorously in most cases at present, probably due to their genomic heterognity, namely, partial allopolyploid constitution, transmitted from different kinds of ancestors, and also due to successive natural and artificial selections against long term inferior or lethal characteristics. On the contrary, in some bulbous plants such as canna or freesia, which were derived from ancestors af closely-related or of almost similar genomic constitutions and also were introduced into the horticultural circles in recent centuries, vigorous-growing aneuploid plants would not occur yet, although the normal polyploid levels are present and many tri- or tetraploid strains are used as cultivars already. Furthermore, it is considered that any aneuploid plants will ntver appear in species such as babiana or tritonia which only has single Stable diploid genomes and was newly introduced into Europe in this century from Southern Africa.

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In order to apply statistical genetics to actual breeding, we should describe strictly genetic structures of quantitative characteristics based on the probability theory, which is the purpose of this report. But the starting point must be from a single stochastic model. Then, in Part 1 of the series of reports, the linkage and the epistasis are excluded from consideration. Consequently, some results which have been well known are proved perfectly. In addition some new results are given, for instance the genetic covariance is partitioned into the genic (additive) and the dominant one, just as the case of the variance.

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By the morphological studies on flowers and heads of 385 varieties of. “Wangul” cultivated in Korea (382 of Cyperus lwasakii M. and 3 of C. gloleceratus L. ) the following results were obtained. ( 1 ) C. Iwasakii and C. glomeratus can be distinguished by the form of flowers. In the head-length there is not much difference between them, but C. lwasakii has much more peduncles and is wider in angle between stern and peduncle than those of C. glomeratus. ( 2 ) The length and number of peduncles and so-called head-type (angle between stem and peduncle) of all the varieties belonging to C. lwasakii were statistically studied, and the results, indicated that all the characteristics showed the normal curves and there was not observed any variation suggesting the necessity of establishing the sub-species.

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