Analysis of Similarities

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

anosim(x, grouping, permutations = 999, distance = "bray", strata = NULL,
    parallel = getOption("mc.cores"))

Arguments

x	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	a list of control values for the permutations as returned by the function how, or the number of permutations required, or a permutation matrix where each row gives the permuted indices.
distance	Choice of distance metric that measures the dissimilarity between two observations. See vegdist for options. This will be used if x was not a dissimilarity structure or a symmetric square matrix.
strata	An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata.
parallel	Number of parallel processes or a predefined socket cluster. With parallel = 1 uses ordinary, non-parallel processing. The parallel processing is done with parallel package.

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 permustats 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.

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 permustats.

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.

control

A list of control values for the permutations as returned by the function how.

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

Note

The anosim function can confound the differences between groups and dispersion within groups and the results can be difficult to interpret (cf. Warton et al. 2012). The function returns a lot of information to ease studying its performance. Most anosim models could be analysed with adonis which seems to be a more robust alternative.

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)
dune.ano <- with(dune.env, anosim(dune.dist, Management))
summary(dune.ano)
#> 
#> Call:
#> anosim(x = dune.dist, grouping = Management) 
#> Dissimilarity: bray 
#> 
#> ANOSIM statistic R: 0.2579 
#>       Significance: 0.011 
#> 
#> Permutation: free
#> Number of permutations: 999
#> 
#> Upper quantiles of permutations (null model):
#>   90%   95% 97.5%   99% 
#> 0.121 0.166 0.208 0.255 
#> 
#> Dissimilarity ranks between and within classes:
#>         0%   25%    50%     75%  100%   N
#> Between  4 58.50 104.00 145.500 188.0 147
#> BF       5 15.25  25.50  41.250  57.0   3
#> HF       1  7.25  46.25  68.125  89.5  10
#> NM       6 64.75 124.50 156.250 181.0  15
#> SF       3 32.75  53.50  99.250 184.0  15
#> 
plot(dune.ano)
#> Warning: some notches went outside hinges ('box'): maybe set notch=FALSE