vegan (version 2.0-10)

dispindmorisita: Morisita index of intraspecific aggregation

Description

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

Usage

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

Arguments

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.

na.rm

logical. Should missing values (including NaN) be omitted from the calculations?

Value

• Returns a data frame with as many rows as the number of columns in the input data, and with four columns. Columns are: imor the unstandardized Morisita index, mclu the clumpedness index, muni the uniform index, imst the standardized Morisita index, pchisq the Chi-squared based probability for the null hypothesis of random expectation.

encoding

UTF-8

Details

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 ($i = 1, 2, \ldots, n$). $Imor$ 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 (null hypothesis) can be tested using criticalvalues of the Chi-squared distribution with $n-1$ degrees of freedom. Confidence intervals 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 crit = 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.

References

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.

Examples

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