Quadrat counts

This module provides statistics on the distribution of points in quadrats. The input data consist of a single column of counts of points in equal-sized quadrats (the order is arbitrary). For a random point pattern, the data are expected to follow a Poisson distribution.

The Morisita index (Morisita 1959) is expected to have value Id=1 for a random pattern, Id<1 for an overdispersed (spaced) pattern, and Id>1 (up to Id=n) for a clustered pattern.

The significance test follows Morisita (1959), with an F ratio statistic. The degrees of freedom are n-1 and infinity. In addition, a Monte Carlo test is carried out with 9999 replicates, each with random distribution of points on quadrats.

The 95% confidence limits (lower and upper) around Id=1 (random pattern) are called the uniform and the clumped indices, respectively (Krebs 1999).

The Standardized Morisita Index, MIS, was suggested by Smith-Gill (1975). It ranges from -1 to 1, with MIS=0 for a random pattern and with 95% confidence limits [-0.5, 0.5].

For computational details see the Past manual.


Krebs, C.J. 1999. Ecological Methodology, 2nd ed. Benjamin Cummings Publishers.

Morisita, M. 1959. Measuring of the dispersion of individuals and analysis of the distributional patterns. Memoirs of the Faculty of Science, Kyushu University, Series E (biology) 2:215-235.

Smith-Gill, S. J. 1975. Cytophysiological basis of disruptive pigmentary patterns in the leopard frog, Rana pipiens. II. Wild type and mutant cell specific patterns. Journal of Morphology 146:35–54.

Published Aug. 31, 2020 9:26 PM - Last modified Aug. 31, 2020 9:26 PM