Morisita's overlap index

Morisita's overlap index, named after Masaaki Morisita, is a statistical measure of dispersion of individuals in a population. It is used to compare overlap among samples (Morisita 1959). This formula is based on the assumption that increasing the size of the samples will increase the diversity because it will include different habitats (i.e. different faunas).

Formula:

C_{D}={\frac {2\sum _{i=1}^{S}x_{i}y_{i}}{(D_{x}+D_{y})XY}}

x_i is the number of times species i is represented in the total X from one sample.

y_i is the number of times species i is represented in the total Y from another sample.

D_x and D_y are the Simpson's index values for the x and y samples respectively.

S is the number of unique species

C_D = 0 if the two samples do not overlap in terms of species, and C_D = 1 if the species occur in the same proportions in both samples.

Horn's modification of the index is (Horn 1966):

C_{H}={\frac {2\sum _{i=1}^{S}x_{i}y_{i}}{\left({\sum _{i=1}^{S}x_{i}^{2} \over X^{2}}+{\sum _{i=1}^{S}y_{i}^{2} \over Y^{2}}\right)XY}}\,.

References

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). "I_δ-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. JSTOR 2459242
Linton, L. R.; Davies, Ronald W.; Wrona, F. J. (1981) "Resource Utilization Indices: An Assessment", Journal of Animal Ecology, 50 (1), 283-292 JSTOR 4045
Ricklefs, Robert E.; Lau, Michael (1980) "Bias and Dispersion of Overlap Indices: Results of Some Monte Carlo Simulations", Ecology, 61 (5), 1019-1024 JSTOR 1936817
Garratt, Michael W.; Steinhorst, R. Kirk (1976). "Testing for significance of Morisita’s, Horn’s and related measures of overlap". American Midland Naturalist 96 (1), 245-251 JSTOR 2424587

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