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SummaryAn approximate method for estimating the sample size in simple random sampling and a systematic way of transformation of sample data are derived by using the parameters α and β of the regression of mean crowding on mean density in the spatial distribution per quadrat of animal populations (Iwao, 1968). If the values of α and β have been known for the species concerned, the sample size needed to attain a desired precision can be estimated by simply knowing the approximate level of mean density of the population to be sampled. Also, an appropriate variance stabilizing transformation of sample data can be obtained by the method given here without restrictions on the distribution pattern of the frequency counts.

Summary A method of sequential sampling for grading population level in relation to a critical density is proposed. The method is based on the m*−m relationship and can be used without restrictions on the distribution patterns. The formulae for simple random sampling as well as for two‐stage sampling are given.

WC adds only modestly to the prediction of coronary risk in younger subjects once BMI is known, and adds nothing to the production of risk in older subjects.

Summary and ConclusionThe measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ and Cp, are derived as geometric and weighted arithmetic means of the same component ratios related to inter‐and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita's (1959)Cσ index. Indices to measure the degree of spatial correlation between species, Ω and Rμ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion.Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species.The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra‐and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested.