著者

野村 健一 Nomura Kenichi

出版者

九州帝國大學農學部

雑誌

九州帝國大學農學部學藝雜誌

巻号頁・発行日

vol.9, no.2, pp.235-262, 1940-12

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1. In order to indicate, mathematically, the degree of the relationship of faunae or florae between two districts, several methods have been devised by such authorities as MASAMUNE (1931), JACCARD (1932), MOTOMURA (1935), OTSUKA (1936) and others. These methods can be expressed by the following formulae――a, b: the number of species found in the districts A and B respectively; c: the common species between them. (snip). 2. In these methods, however, there is a common failure that the formulae can be applicable within a certain limit, in which the faunae or florae of the districts in question are equal or nearly equal in richness. Thea bovme entionfeodrm ulcaaen b em odifiaesd follow: (snip). From these modified formulae it is clearly recognized that according to the increase of the value k the degree of the relationship given by these methods becomes smaller even if the common species between them are numerous in number. For example, in such case that the affinity of faunae or florae between two districts A and B is the highest as possible (namely c = b), the degree of the affinity between them given by these formulae is not always high as shown in the next table. (snip). Thus in these methods it is apparent: the more the difference of the scale of faunae or florae, (i.e. the value of k), the less applicable are the formulae. 3. Therefore, in order to express the degree of affinity between faunae or florae according to the number of the common species, the "Standard common-ratio", c/b (a> b), should be used instead of such formulae as above, as is emphasized by the author in the previous paper (1939 b). According to this method in such case as mentioned above (c = b), the degree of the affinity is always expressed by the figure 100 %, and in case that c = 0 the figure becomes 0 % , the most rational results expected. In case that k = 1, the value showing the affinity derived from any other formula given above is equal to that given by c/b or the "Standard common-ratio." Therefore, it may be concluded that the "Standard. common-ratio" method is the most suitable in order to express the degree of the relationship between faunae or florae, so far as the quantity of the common species are concerned. 4. In the previous chapter the author noted that the "Standard common-ratio" method was the best of various methods proposed. But in those methods based on the quantity of the common species the following weakness may be recognized that they show only the quantitative relationship but not the qualitative relationship of the faunistic or floristic composition. From this reason in comparison of faunae or florae of complicate composition such methods as the "Standard common-ratio," and others mentioned above, do not always give an accurate index of the relationship of faunae or florae. For example in the comparison of the butterfly-fauna of Kyusyu-Honto and of the Nansei Island,* where the faunistic composition are complicated, sufficient results can not be given by these methods (see tab. 3 and figs. 2-3). The author believes that the faunistic or floristic composition must be also considered for a real comparison. Thus he tried a correlation method based on the ratio of the different elements of the faunae or florae. In this method the Correlation index, (Correlation coefficient+ 1)/2, indicating the variation of the number of species belonging to each element, such as Palaearctic, Oriental, the transitional and others t, between the two districts was taken as the indicator revealing the degree of the relationship of the faunae or florae. The results of the comparison of the butterfly-fauna between two islands of any combination in Kyushu-Hont? and the Nansei Islands, it became appArent that the correlation method was more suitable than any other one (compare with tabs. 3, 5 and figs. 2, 3, 5 respectively). It is also a strong point of this method that the degree of relationship given by this formula becomes smaller according to the increase of the distance between the two islands. 5. While investigating the butterfly-fauna of Kyushu-Honto and the Nansei Islands by the correlation method, the author discovered the fact that the degree of affinity of faunae between two neighbouring districts belonging to different Regions is often larger than that between two more remote districts belonging to the same ones as shown in fig. 6. 6. In conclusion the author recommends the correlation method for expression the degree of the relationship of faunae or florae between different districts, but the "Standard common-ratio" method may also be applied as an abridged one for the same purpose only in such cases that the faunistic or floristic composition of the districts in question is of same or nearly same quality. However it must be mentioned that in such cases as the fauna or flora is very small quantitatively, the accuracy of those methods is reduced owing to the law of the coefficient of occurrence. For example in districts of smaller fauna the ratio of cosmopolitan or Oriental forms becomes larger as compared with its geographical position, as shown in tab. 9, thus the availability of these methods is much reduced. Therefore the comparison of faunae or florae between two districts may be recommeded only in such cases as that both the districts have quantitatively sufficient faunae or florae to show their geographical charasteristics.1. 昆蟲相(生物相)を比較し, 其の關係度を求める方法としては從來次の諸法が行はれて居た。但し, a, b (a>bとす) は夫々兩地方 A, B に於ける所産種類數, c は其の共通種類數とする。(省略)。2. 然し之等の方法では, a, b の差が大となればなる程, それから得られる結果は不正確となる懸念がある。何となれば, 上記諸式を書改めれば次の如くなり。3. 故に共通種類數の多寡を基として關係度を求める場合は, c/b (a>b), 即ち共通種類數を所産種類數の少い方の種類數で除した値を以つてする方がよい。此の値を私は標準共通率と命名したが, 之は實は上記各法の基礎をなすもので, a=b 即ち k=1 の場合は, 上記諸法は全く之と一致する結果となる。上記諸法は k が大なる時は不適であり, k が小なる時にのみ用ふべきであるが, 此の場合では各法とも實は c/b に歸着するのであつて, 結局共通性の多寡を論ずる場合は, 標準共通率に據るべき事が結論される。4. 上記諸法の中では, 標準共通率法が最も適當であるが, 然し之とても單に共通種類數の多寡を示したものであつて, 昆蟲相 (生物相) 構成因子の系統には觸れて居ないから, 之によつては必ずしも眞の關係度は求め得られず, 殊に構成因子の錯雜せる場合は一層此の缺點が張調される。依つて構成因子の系統に重點を置いた方法として, 私は相關法なるものを提唱したが之による時はよく共の目的を達し得る。即ち, 各地間の昆蟲相 (生物相) の關係度を求める目的の爲には本方法が最上である。5. 相關法は生物地理學上の諸問題の檢討に應用され得るが, 私は南西諸島の蝶相を研究中次の事項を認めた。それは所屬區は同一でも遠距離の地方とは關係度が比較的薄く, 逆に所屬區は別であつても近距離にある所とは關係度は却つて高くなる例のある事を知つた。之より推して生物地理學上の區或は亞區を分けても, 實際の各地間の關係度は連續的で, 其の關係は第6圖に示す如きものと考へた。6. 要するに, 昆蟲相 (生物相) の關係度を求める方法としては, 其の構成因子の系統を考慮した相關法に據るべきである。共通種類數の多寡は必ずしも眞の關係度を示さないが, 大體系統の等しいもの相互の比較には便法として適用され得るもので, 而して此の場合は既往の諸方法に據るよりは私の提案した標準共通率法に據る方が至當である。尚此の相關法, 標準共通率法共に, 所産種類數の非常に少い地方を取扱ふ時は, 出現率の法則により餘り正確な結果は得られない事は注意すべきである。即ち, 取扱はれる地方は昆蟲相 (生物相) の地理的特徴を十分に表はすに足る大いさを持つ事が望ましいわけで, 此の範圍外のものに對しては更に別な方法が講ぜられなければならない。