A distance measure of spatial pattern in a biological population |
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Authors: | Masae Shiyomi and Sachio Kubo |
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Institution: | (1) Present address: National Institute of Agricultural Sciences, Nishigahara, Kitaku, Tokyo, Japan;(2) The National Grassland Research Institute, Nishinasuno, Tochigi, Japan |
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Abstract: | Summary Suppose thatn individuals locate independently and randomly on a segment of line of finite length (habitat). Let the theoretical and observed
ranges of the sites of the individuals on the segment be μ
n-1 andr
n-1, respectively. Then, the degree of dispersion of the individual sites is measured by the ratio, T
n
=n
n-1/μ
n-1, as follows: A random spatial pattern forI
r−1
=1 An aggregated spatial pattern for 0≤I
r
<1 A uniform spatial pattern for (n+1)/(n−1)≥I
r
>1.
Another method was derived. Let the probability that an observed range is less thanr
n−1
beI
p
, under the hypothesis of a Beta distribution. Then
indicates A random spatial pattern forI
p
=1/2 An aggregated spatial pattern forI
p
<1/2 A uniform spatial pattern forI
p
>1/2.
The first index can be used for comparing populations having the same number of individuals, whereas the second one can be
used for comparing populations with different numbers of individuals. |
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Keywords: | |
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