dispindmorisita {vegan} | R Documentation |

Calculates the Morisita index of dispersion, standardized index values, and the so called clumpedness and uniform indices.

dispindmorisita(x, unique.rm = FALSE, crit = 0.05)

`x` |
community data matrix, with sites (samples) as rows and species as columns. |

`unique.rm` |
logical, if `TRUE` , unique species (occurring in only one sample) are removed from the result. |

`crit` |
two-sided p-value used to calculate critical Chi-squared values. |

The Morisita index of dispersion is defined as (Morisita 1959, 1962):

`Imor = n * (sum(xi^2) - sum(xi)) / (sum(xi)^2 - sum(xi))`

where *xi* is the count of individuals in sample *i*, and *n* is the
number of samples (*i = 1, 2, ..., n*). *Imor* has values from 0 to
*n*. In uniform (hyperdispersed) patterns its value falls between 0 and
1, in clumped patterns it falls between 1 and *n*. For increasing sample
sizes (i.e. joining neighbouring quadrats), *Imor* goes to *n* as the
quadrat size approaches clump size. For random patterns, *Imor = 1* and
counts in the samples follow Poisson frequency distribution.

The deviation from random expectation can be tested using critical
values of the Chi-squared distribution with *n-1* degrees of
freedom. Confidence interval around 1 can be calculated by the clumped
*Mclu* and uniform *Muni* indices (Hairston et al. 1971, Krebs
1999) (Chi2Lower and Chi2Upper refers to e.g. 0.025 and 0.975 quantile
values of the Chi-squared distribution with *n-1* degrees of
freedom, respectively, for `alpha = 0.05`

):

`Mclu = (Chi2Lower - n + sum(xi)) / (sum(xi) - 1)`

`Muni = (Chi2Upper - n + sum(xi)) / (sum(xi) - 1)`

Smith-Gill (1975) proposed scaling of Morisita index from [0, n]
interval into [-1, 1], and setting up -0.5 and 0.5 values as
confidence limits around random distribution with rescaled value 0. To
rescale the Morisita index, one of the following four equations apply
to calculate the standardized index *Imst*:

(a) `Imor >= Mclu > 1`

: `Imst = 0.5 + 0.5 (Imor - Mclu) / (n - Mclu)`

,

(b) `Mclu > Imor >= 1`

: `Imst = 0.5 (Imor - 1) / (Mclu - 1)`

,

(c) `1 > Imor > Muni`

: `Imst = -0.5 (Imor - 1) / (Muni - 1)`

,

(d) `1 > Muni > Imor`

: `Imst = -0.5 + 0.5 (Imor - Muni) / Muni`

.

Returns a data frame with as many rows as the number of columns
in the input data, and with four columns. Columns are: `imor`

unstandardized Morisita index, `mclu`

the clumpedness index,
`muni`

the uniform index, `imst`

standardized Morisita index.

A common error found in several papers is that when standardizing
as in the case (b), the denominator is given as `Muni - 1`

. This
results in a hiatus in the [0, 0.5] interval of the standardized
index. The root of this typo is the book of Krebs (1999), see the Errata
for the book (Page 217,
http://www.zoology.ubc.ca/~krebs/downloads/errors_2nd_printing.pdf).

P'eter S'olymos, solymos@ualberta.ca

Morisita, M. 1959. Measuring of the dispersion of individuals and
analysis of the distributional patterns. *Mem. Fac. Sci. Kyushu
Univ. Ser. E* 2, 215–235.

Morisita, M. 1962. Id-index, a measure of dispersion of individuals.
*Res. Popul. Ecol.* 4, 1–7.

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. *J. Morphol.* 146, 35–54.

Hairston, N. G., Hill, R. and Ritte, U. 1971. The interpretation of
aggregation patterns. In: Patil, G. P., Pileou, E. C. and Waters,
W. E. eds. *Statistical Ecology 1: Spatial Patterns and Statistical
Distributions*. Penn. State Univ. Press, University Park.

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

data(dune) x <- dispindmorisita(dune) x y <- dispindmorisita(dune, unique.rm = TRUE) y dim(x) ## with unique species dim(y) ## unique species removed

[Package *vegan* version 1.16-32 Index]