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Spatial pattern indices based on distances between individuals on a line‐segment with finite length
Author(s) -
Shiyomi Masae,
Yamamura Kohji
Publication year - 1992
Publication title -
population ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.819
H-Index - 59
eISSN - 1438-390X
pISSN - 1438-3896
DOI - 10.1007/bf02514801
Subject(s) - population , variance (accounting) , habitat , statistics , common spatial pattern , spatial distribution , line (geometry) , mathematics , spatial ecology , biology , ecology , geometry , demography , accounting , sociology , business
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 are n individuals. Here, we assume that the spatial pattern of the individuals is random if the n 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 formula nθ 2 ( n +1) −2 ( n +2) −1 and the variance between n +1 distances between n individuals from the left end to the right end to the strip, is represented by the formula nθ 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.