Morisita's (1959) index of the counts in n equal quadrats, I = n (sum x^2 - S) / (S^2 - S) with S the total: 1 for a random pattern,
above for clumping (n when all fall in one quadrat), below for an even
spread. The uniform and clumped indices are the values of I at the
crit / 2 tails of chi-square on n - 1 degrees of freedom, and the
standardised index of Smith-Gill (1975) maps I onto [-1, 1] with
them at -0.5 and 0.5; chi = I (S - 1) + n - S has the chi-square
distribution under randomness. These are the values of
vegan::dispindmorisita().
Arguments
- counts
The counts: numbers from 0, at least two, adding up to more than 1 (a
qdrtst()count matrix will do).- crit
The level of the critical indices, above 0 and below 1.
References
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(1), 35-54. doi:10.1002/jmor.1051460103
Examples
morsta(c(3, 0, 7, 12, 1, 4, 0, 9))
#> imor mclu muni imst chi p
#> 1.676190e+00 1.257508e+00 8.482820e-01 5.310481e-01 3.066667e+01 7.161935e-05