1992 年 13 巻 2 号 p. 77-85
Let us consider a strip-wise grazing pasture, likc a corridor, to simplify the subject mathematically, and suppose that the length of pasture is θ meters and there are n individuals of cattle. Here, we define that the spatial pattern of individuals is random if the n distances from the left end of pasture to each individual follow a uniform distribution on the strip. Under such an assumption, the variance of distances between any two neighbors is given by n θ2(n+1)-2(n+2)-1; and the variance between n+1 distances formed by n individuals from the left end to the right end of pasture, is given by θ2(n+1)-1(n+2)-1. These two kinds of variance can be used for determining (1) spatial pattern of a cattle population on the strip and (2) spatial pattern of individuals within the cattle population, by comparing with the variances calculated from data.
From analysis of data observed at an 88m×6m experimental pasture, where 6 individuals of cattle were released, the following results were obtained: (1) the individuals were not randomly dispersed on the whole area of strip, but crowded at some part on the strip, and (2) the individuals distributed randomly or exclusively within the population.