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:

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

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):

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

Note, not to be confused with Morisita’s index of dispersion.