The multipoint Morisita index for the analysis of spatial patterns

Abstract

In many fields, the spatial clustering of sampled data points has significant consequences. Therefore, several indices have been proposed to assess the degree of clustering affecting datasets (e.g. the Morisita index, Ripley's K-function and Rényi's generalized entropy). The classical Morisita index measures how many times it is more likely to select two sampled points from the same quadrats (the data set is covered by a regular grid of changing size) than it would be in the case of a random distribution generated from a Poisson process. The multipoint version takes into account m points with m ≥ 2. The present research deals with a new development of the multipoint Morisita index (m-Morisita) for (1) the characterization of environmental monitoring network clustering and for (2) the detection of structures in monitored phenomena. From a theoretical perspective, a connection between the m-Morisita index and multifractality has also been found and highlighted on a mathematical multifractal set.

A New Approach for Interpreting the Morisita Index of Aggregation through Quadrat Size

“…We recognize that the Morisita Index of aggregation has experienced a lack of attention, perhaps because of its difficulties in interpretation and similar techniques such as Ripley's K function appear to be easier to interpret. Golay et al [16] stated a robust and interesting methodology to deal with the notion of scale and the Morisita Index, nevertheless we propose a simpler method based on the same index to classify any population in random or non-random spatial distribution. If local clusters are found, we can use the derivative plot (Figure 8) to quantify the degree of clustering compared to either the population itself as a whole or clusters in different populations.…”

“…The theory stated by Morisita [19] and further studies [18,54,55] do not specify how to define the range of the quadrat size or how to choose a quadrat size for I Mr . Golay et al [16] tackled the scale problem by linking I Mr index and the multifractality concept through quadrat-based methods, i.e., Rényi's generalized dimensions and the lacunarity index [16,17,56]. It appears that we are approaching the problem of scale by measuring the degree of crowding for different quadrat sizes.…”

“…If the individuals were randomly distributed (from a Poisson distribution), I M values were close to 1, greater than 1 if clustered, and less than 1 if dispersed [49]. Golay et al [16] pointed out that the index can approach 0 for dispersed patterns at small scales.…”

Morisita-based space-clustering analysis of Swiss seismicity

“…The multipoint Morisita index [42,45] is based on a grid of Q cells of changing size δ. The grid is superimposed on the points of the studied data set and the index measures how many times more likely it is to randomly select m (m ≥ 2) points belonging to the same cell than in the case of a random distribution generated from a Poisson process.…”

“…[42]. This index has revealed its potential to detect structures in spatial patterns, and it was shown to be related to Rényi's generalized dimensions.…”