注記 |
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.
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