vegan (version 2.0-10)

anosim: Analysis of Similarities

Description

Analysis of similarities (ANOSIM) provides a way to test statistically whether there is a significant difference between two or more groups of sampling units.

Usage

anosim(dat, grouping, permutations = 999, distance = "bray", strata)

Arguments

dat

Data matrix or data frame in which rows are samples and columns are response variable(s), or a dissimilarity object or a symmetric square matrix of dissimilarities.

grouping

Factor for grouping observations.

permutations

Number of permutation to assess the significance of the ANOSIM statistic.

distance

Choice of distance metric that measures the dissimilarity between two observations. See vegdist for options. This will be used if dat was not a dissimilarity structure or a symmetr

strata

An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata.

Value

• The function returns a list of class "anosim" with following items:
• call
  Function call.
• statistic
  The value of ANOSIM statistic $R$
• signif
  Significance from permutation.
• perm
  Permutation values of $R$. The distribution of permutation values can be inspected with function density.anosim.
• class.vec
  Factor with value Between for dissimilarities between classes and class name for corresponding dissimilarity within class.
• dis.rank
  Rank of dissimilarity entry.
• dissimilarity
  The name of the dissimilarity index: the "method" entry of the dist object.

Details

Analysis of similarities (ANOSIM) provides a way to test statistically whether there is a significant difference between two or more groups of sampling units. Function anosim operates directly on a dissimilarity matrix. A suitable dissimilarity matrix is produced by functions dist or vegdist. The method is philosophically allied with NMDS ordination (monoMDS), in that it uses only the rank order of dissimilarity values.

If two groups of sampling units are really different in their species composition, then compositional dissimilarities between the groups ought to be greater than those within the groups. The anosim statistic $R$ is based on the difference of mean ranks between groups ($r_B$) and within groups ($r_W$):

$$R = (r_B - r_W)/(N (N-1) / 4)$$

The divisor is chosen so that $R$ will be in the interval $-1 \dots +1$, value $0$ indicating completely random grouping.

The statistical significance of observed $R$ is assessed by permuting the grouping vector to obtain the empirical distribution of $R$ under null-model. See permutations for additional details on permutation tests in Vegan. The distribution of simulated values can be inspected with the density function.

The function has summary and plot methods. These both show valuable information to assess the validity of the method: The function assumes that all ranked dissimilarities within groups have about equal median and range. The plot method uses boxplot with options notch=TRUE and varwidth=TRUE.

References

Clarke, K. R. (1993). Non-parametric multivariate analysis of changes in community structure. Australian Journal of Ecology 18, 117--143. Warton, D.I., Wright, T.W., Wang, Y. 2012. Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89--101

See Also

mrpp for a similar function using original dissimilarities instead of their ranks. dist and vegdist for obtaining dissimilarities, and rank for ranking real values. For comparing dissimilarities against continuous variables, see mantel. Function adonis is a more robust alternative that should preferred.

Examples

data(dune)
data(dune.env)
dune.dist <- vegdist(dune)
attach(dune.env)
dune.ano <- anosim(dune.dist, Management)
summary(dune.ano)
plot(dune.ano)