Morisita Index

What is the Morisita Index?

The Morisita Index of Dispersion (or Morisita overlap index) is a measure of how similar or different two sets of data are. The index ranges from 0 (no similarity) to 1 (complete similarity). It can, however, give values larger or smaller than 1, which may lead to misleading interpretations. This is especially true for small samples (Chao et. al, 2006).

How to find the Morisita Index

It’s not common to find the Morisita index built into statistical software packages.

By hand, the formula is:

Where:

x_i = number of times an item appears in sample 1.
y_i = number of times an item appears in sample 2.
Dx and Dy = Simpson’s diversity index for samples 1 and 2.
S = number of unique items.

Criticism

The index has been criticized for being complicated to use and interpret. For example, researchers Gaden and Tuck (1996) attempted to use the index on their data and concluded that “…computation of the Morisita index is difficult and we find it impossible to conceptualize what we are actually measuring.” The index has been known to give two completely different sets of data an index of more than one, and two completely identical sets of data scores of less than one (Chao, 2006). Several authors have offered modifications in order to make the index more usable, including Krebs (1999) who converts it to a scale of -1 to +1. However, this easier scale comes with the drawback of many more steps to calculate the index (see: Bakus p.126).

References:
Bakus, G. (2007). Quantitative Analysis of Marine Biological Communities: Field Biology and Environment. John Wiley & Sons.
Chao, A. et. al. (2006). Abundance-Based Similarity Indices and Their Estimation When There Are Unseen Species in Samples. Biometrics. 62, 361–371.
Gaden, R & Tuck, K. (1995). Diversity of Small Moths in Borneo. In Tropical Rainforest Research — Current Issues. Springer Science & Business Media.
Krebs, C. J. 1999. Ecological Methodology. 2nd ed. Benjamin Cummings Publishers.
Morisita, M. (1959). “Measuring of the dispersion and analysis of distribution patterns”. Memoires of the Faculty of Science, Kyushu University, Series E. Biology. 2: 215–235.
Morisita, M. (1962). “Iδ-Index, A Measure of Dispersion of Individuals”. Researches on Population Ecology, 4 (1), 1–7.
Horn, H. S. (1966). Measurement of “Overlap” in comparative ecological studies. The American Naturalist” 100:419-424.