Spatial pattern indices based on distances between individuals on a line‐segment with finite length

Abstract

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 6 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 nO2(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 O2(n + 1)-X(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.KEYWOl~S: distance measure, spatial pattern index, strip-wise habitat of line-segment.

Gaps and patches in the ocean:a one-dimensional analysis of planktonic distributions

“…Due to the three-dimensional nature of the sampling device and the one-dimensional nature of the output, the true nearest neighbor measures cannot be calculated; however the next value is known within the one-dimensional series. In recent years, this application of neighbor analysis from one-dimensional series has become well established (Selkirk & Neave 1984, Shiyomi & Yamamura 1993, Weingart & Selvin 1995. In this paper we present a method of analyzing patch dynamics in planktonic systems using a one-dimensional Distance to Next Encounter (DNE) technique, from a spatial data series collected by the OPC.…”