Spatial pattern indices based on distances between individuals on a line-segment with finite length |
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Authors: | Masae Shiyomi and Kohji Yamamura |
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Institution: | (1) National Grassland Research Institute, Ecology Department, Senbonmatsu 768, Nishinasuno, 329-27 Nasu, Tochigi, Japan;(2) Division of Information Analysis, National Institute of Agro-Environmental Sciences, Kannondai 3-1-1, Tsukuba, 305 Ibaraki, Japan |
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Abstract: | Summary Let us consider a strip-wise habitat of line-segment, like a corridor, to simplify the subject mathematically, and assume
that the length of the habitat is γ and there aren individuals. Here, we assume that the spatial pattern of the individuals is random if then distances from the left end of the habitat to each individual follow a uniform distribution on the strip. Under such an assumption,
the variance of the distances between any two neighbors is represented by the formulanθ
2(n+1)−2(n+2)−1 and the variance betweenn+1 distances betweenn individuals from the left end to the right end to the strip, is represented by the formulanθ
2(n+1)−2(n+2)−1. These two kinds of variances can be used for determining (1) the spatial pattern of a population on the strip and (2) the
spatial structure within the population, by comparison with the variances calculated from the data. Two examples cited from
the literature, a cattle population on a pasture and an aphid population on a sycamore leaf, are presented. |
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Keywords: | distance measure spatial pattern index strip-wise habitat of line-segment |
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