In the present paper, the distribution pattern of the deposited eggs of the red-rust flour beetle, Tribolium castaneum. (HEREST) was described statistically by the coefficient of dispersion (V/X^^-, …X^^- : mean number of insects in a quadrate, V : variance of it). The results are as follows. : (1) The accumulated curve of the deposited eggs in each successive day shows a sigmoid-shape. The maximum number of the total eggs was 1442 after six days from the start of the experiment and the maximum number of the deposited eggs per day was 528 after three days from the start of the experiment. (2) The distribution of the deposited eggs shows more or less uneven distribution. The pattern of distribution changes with the days elasped. For example, V/X^^- was 1.182 at the 1st day 4.847 at the 4th day and 2.035 at the 6th day. (3) It seems that the coefficient of dispersion (V/X^^-) changes with the number of the deposited eggs per day reaches the maximum (Fig.2). It is very interesting that the spatial pattern of distribution of the deposited eggs depends partly upon the total number of the deposited eggs which accumulated with the population history. (4) The distribution pattern of the adult beetles in the same quadrate size (approximately 12cm^3 in flour) was also uneven (V/X^^- : 1.888±0.564). It seems that the uneven distribution of the deposited eggs depends on the distribution pattern of the adult.

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The investigation was conducted on Mt. Daisen, an extinct volcano in Tottori Prefecture, Lat. 35゜ 20'N., 133゜30'E. (Fig.1), where there occurs a characteristic plant community decidedly dominated by the dwarf coniferous tree, Taxus cuspidata var. nana REHD., which in rare cases is accompanied by Alnus hirsuta TURCZ., Sorbus Commixta HBDL. and Salix vulpina ANDERS. The epiphytic bryophyte community in this dwarf coniferous forest is composed mainly of Orthodicranum hakkodense Lesquereuxia robusta and Ptilidium pulcherrimum. Orthodicranum hakkodense and Lesquereuxia robusta are the dominant species in the crown layer of this community. Rhacomitrium canescens, which grows usually on rocks and soils, characteristically develops only on trees exposed to strong winds and laden with the granules of sandy soil picked up from eroded and barren places. It is significant that these species are absent in all other layers of the community, being restricted to the crown layer. Ptilidium pulcherrimum, new to the bryophyte flora of Mt. Daisen, is dominant to a considerable degree on the tree trunks, while lsothecium subdiversiforme and Dolichomitriopsis diversiformis grow only at the base of the trunk.

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The pronounced effect of population density. on the reproductive rate has been observed in the experimental population of single species, but the problem has not been solved whether it is operative under the attack of its parasite or predator. To solve this problem, the density effect was estimated by measuring the body weight of the azuki bean weevil, Callosobruchus chinensis, in the mixed population interacting the weevil and its parasite, Neocatolaccus mamezophagus or Heterospilus prosopidis. The average body weight of the weevil in a single population was heavier than that in the interacting population of host and parasite and also that reared under low percentage of parasitism was heavier than that under high percentage. It is presumed from these results that the density effect is not so highly operative in the interacting population of host and parasite, to control the growth of the host population, as observed in the single population of the host species.

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From May to September in 1953,cultural experiments with 27 Species of terrestrial mosses submerged in water were carried out. The adopted materials were collected from the vicinities of Saijo City, Ehime Pref., Shikoku. The obtained results are shown in Table 1. In 11 of the 27 species remarkable growth and modification of the leaves is recognized. The 11 species are generally of the ectohydric or endohydric species from which grow runners or creeping stems. The types in the modifications of the leaves are shown in Table 2 and Figs.1 and 2. The growth exhibited at least in the 11 species seems to be caused by the nutrients absorbed through the surface of the materials, especially through the leaves.

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The canes cut from the bamboos three months affer budding, are arranged in the campus of the Tohoku University, filled with tap-water, and in a few days, the protister community begins to appear at the bottoms of them. This community changes successively into the others with the lapse of time. The benthonic protister was sampled from the containers every three days from July to September of 1953. At first, to clarify the changes of the numerical compositions of the so-called sere in the successive course, the correlation coefficient between the individual number of each species in one catch and that of corresponding species in the following next catch was calcurated (Fig.1). From such a statistical treatment, it was known that this course is characterized by the changeable composition in late July, and also by the unchangeable one in early July and August. In September, however, these two compositions are found. The structures of the communities in the five periods as given above were examined quantitatively from the following view points.1) Both the kind and individual number of the constituent species, and the community-size which may be indicated by the logarithmic number of the dominant species. 2) The distribution in the relative number of the constituent species. As to the quantitative estimation of the latter. "Index of numerical distribution" induced from the LORENZ-curve, which is frequently applied in the economic statistics, is first used. When cummulative percentage of the estimated number of species is represented in abscissa, and also that of individual numbers is in ordinate according to the rank in number, various lines are obtainable. In this case, when the species number is equal to the estimated one, and also the individual number is equal in every species, the straight line, ORQ in figure 2,is obtained. When the numerical distribution is not equal or the species number is less than the estimated one, the curve, OMQ in the same figure, is given. Thus, it is known that the area enclosed with such straight line and curve as mentioned above is determined in accordance with the state of the numerical distribution, and also the number of constituent species. In a community comprised of only one species, the area reaches the maximum and remains constant. Thus, the distribution of the relative number can be estimated quantitatively from the ratio of the area in a given community to that in the community just mentioned. The writer designates this ratio as "Index of numerical distribution". When the communities found in the five periods are examined by the form of histogram of these attributes, it is noticed that they are characterized by the following definite structures : 1) The communities found in early July, viz., group A, which may correspond to the pioneer community, mainly comprise Heteromita. They incline to maintain the constancy in "Index of distribution", but the community-size changes gradually with the lapse of time, 2) In late July, the communities, viz., group B. show a changeable value not only in "Index of distribution" but also in the size of the community. Glaucoma and Chlamydomonas are important species in these communities. 3) The communities in August are composed of the two groups, viz., group C_1 and group C_2,which are characterized by different structures. The former shows a large value to some extent in "Index of distridution" and in the community-size comparing with the group C_2. The group C_1 precedes the other. These groups are composed of Chlamydomonas and Cercomonas, of which the former is considered as the dominant species and the latter the subordinant. 4) In Septemder, the communities with a stable composition, viz., group D, present the same structure as group C_2. However, in the communities characterized by a changeable composition, viz., group E, the value of "Index of

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More commonly the radiation and branching of rhizomes in all directions from the original centre result when isolated in symmetrical colonies of the ever increasing circumference. In this case, the death of the older portion in the interior of such a colony results in the formation of a circle, which is well known as "dead centre" in certain plants. The present paper deals with the results of studies on the "dead centre" recognized by the mathematical treatment. From the results, the "dead centre" is defined as the centre of gravity in a colony, it is expressed by the following formula : [numerical formula] in which a=the length of underground stem ; n=the branched number of underground stem ; a= the angle of underground stem. By using this formula, the author discussed the growth of the colony of Juncus tennis.

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It is a pressing problem in the production of the wild silkworm eggs to determine whether the low fertility of these eggs is attributable to the meagre copulation ratio of their parent moths or instinctively originates in the laid eggs themselves that contain numerous unfertilized eggs. To clarify this point, experiments were made on the 15th, the 18th and the 20th of August, 1952,by the use of the moths emerged on the same day from the cocoons reared at the Ariake Wild Silkworm Experiment Station, Nagano Prefecture. For the purpose of the sample test, a pair of the moths were put in a moth cage which was hung under a cedar tree to protect it from the direct ray of the sun and which was covered with 0.3cm mesh to avoid other male moths to stray into. After these moths had died the laid eggs were tested. Those eggs of A. pernyi ♀×A. pernyi δ, A. pernyi ♀×A. yamamai δ and A. yamamaia ♀×A. pernyi δ, hatch 10-11 days after laying and since microscopic observation reveals that not any developemeot of embryo is seen in the unhatched eggs, the hatched eggs were, in this test, classified as fertilized eggs and the unhatched ones as unfertilized ones. Though A.yamamai eggs are hybernating, the embryos develop nearly to the full size within ten days after they had been laid, so that microscopic observation is competent in detecting the fertility of them. The results shown in Tables 1-3. are summarized as follows : - (1) The A. pernyi eggs (A.pernyi ♀×A. pernyi δ) are nearly satisfactory in fertility. (2) Concerning the A. yamamai eggs (A. yamamai ♀×A. yamamai δ), the ratio of the unfertilized eggs is so great as about 70 per cent. The scrutinization into the individual layiigs, however, shows that there are two kinds of layings regarding fertility ratio, that is, the one is those layings, the fertility ratio of which is nearly perfect, and the other is the ones, whose fertility ratio is null. There exists good coincidence between the copulation ratio of the moths of this species and the unfertilized ratio of the laid eggs. Moreover, those moths, whose copulations the writers had ascertained, laid without fail, perfect fertilized eggs. Hence the existence of numerous impotent male moths is responsible to the low fertility of the laid eggs, that is, those moths as were successful in copulating lay fertilized eggs and those which were unsuccessful, on the contrary, laid unfertilized ones. (3) The eggs of A.yamamai ♀×A.pernyi δ are low in fertility because presumably of the unsmoothness of the mating between the different species. (4) The eggs of A.pernyi ♀×A.yamamai δ are extraordinarily low in fertility ratio. This obstacle in this industry will be, perhaps, attributable to the additive effect of the cause mentioned in (3) and the existence of numerous impotent male A.yamamai moths as is the case of (2) though the writers hope to study this problem further.

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I. Two groups of leaves under the ordinary salt spray are recognized : A) Deposit Type : Cl' deposits on their surface and scarcely enters into the tissue of the leaves. Therefore the leaves are not injured. The leaves of the ever-green trees generally belong to this group. B) Entrance Type : Cl' soon enters into the leaves and damages are found. The leaves of deciduous trees generally belong to this group. II. Daphniphyllum glaucescens, Cinnamomum japonicum, Camellia japonica, Ilex integ a, Textoria trijida and Machilus Thubnergii belong to the deposit type above-mentioned. The coastal forest in Central Japan mainly consists of these species. III. Ficus erecta, Celtis sinensis, Mallotus japonicus and Clerodendron trichotomum have leaves of the entrance type. These species can be found in the area protected with the plants of the deposit type. IV. Even when a large amount of Cl' (1〜2 % Cl' of oven dry weight) enters into the leaves of Euonymus japonica, Pittosporum Tobira and Elaeagnus macrophylla, they are scarcely injured. These species are usually found in the front part of the coastal forest. V.Under special strong salt spray, for example, as caused by a typhoon, even the leaves of the deposit type are effected by the so-called V shaped damage. In such cases a large amount of Cl' (2〜3 % of oven dry weight) is found in the damaged part of the leaves. VI. It is concluded that the damage caused by the wind-transported salt spray is due to the Cl' entering into the tissue of leaves.

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These studies were undertaken to find the fundamental principle of animal communities in a bamboo forest of simple and natural conditions. Among the environmental conditions, the relative humidity, illumination, temperatures or the air, ground surface and at a depth of 5 cm below the surface were measured. The animals were collected by means of a sweep-net at intervals of three hours during a dav of each month from Feb. 1949 to Jan. 1950. The space of the bamboo forest was divided into three strata, viz. the upper, intermediate, and lower, and animals were collected from each of these strata. The results were that the diurnal activities, seasonal fluctuations and both temporal and spacial structures and functions of the animal communities could be summarized as follows. I.The air temperature usually reached its maximum at about 2 p.m., and its minimum at about 5 a.m. During the daytime the temperature of the ground surface was lower than that of the air owing to the particular characters of the evergreen forest. At night, the temperature at the depth of 5 cm below the surface was also higher than the air and the ground surface. Generally, the relative humidities in the forest were higher, reaching nearly 100 per cent especially at night. The illumination in the forest was much lower than that in the open field. II. In the diurnal migrations of the forest animals, no vertical movement was perceived, but in the case of some species, both horizontal migrations and nocturnal activities were observed. Different species of spiders, insects, springtails and Armadillidium appeared according to the seasonal changes, and these could be classified into some types, namely, vernal, and autumnal, estival and hiemal, etc. The vertical migrations throughout the four seasons could not be so distinctly detected as those of the deciduous forest, but some species were ascertained to migrate from one stratum to another according as the change of conditions. Some of these animal communities seemed to remain in their habitats fixed in each stratum, viz. upper, intermediate and lower, of the forest space. III. Thus the structure of the animal communities in the bamboo forest throughout the year can clearly be illustrated on the basis of the combinaton of seasonal and spacial segregations, and the dynamic functions of the communities can be solved by observations on the relations between the animal activities, environmental conditions, food chains, symbiosis, and parasitism, etc.

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The pattern of spatial distribution of the adult of the large twenty-eight-spotted lady beetle, Epilachna 28-maculata MOTSCHULSKY, was analysed statistically by using the data on the population censuses at several egg-plant fields near Kyoto city. The frequency distribution of the beetles on a plant is random at low density. As the density increases over about 0.5 per plant, the distribution becomes concentrated and is represented by the POLYA-EGGNBERGER'S distribution. Some analyses were made to understand this phenomenon. When the number of beetles is small the insect is dtstributed randomly to the plant. At higher densities, ranging from about 0.5 to 2.0 per plant, the beetle is aggregated chiefly to such plant as is found with insects at lower densities. Namely, each plant in a field shows differential attractiveness to the beetle. It is considered that the cause of such difference among the plants is due to the complex, both the tendency of the insect itself and the heterogeneity of the environmental conditions. When the density approaches to 3.10 per plant it seems that the distribution decreases its degree of concentration and exhibits randomness again. But the data are too scarce to clear up this point.

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