PERMANOVA and dispersion tests on community composition — beta

beta_permanova() tests whether composition differs with site variables using permutational multivariate analysis of variance (vegan::adonis2(), Anderson 2001). beta_dispersion() tests whether groups differ in their spread (multivariate dispersion, vegan::betadisper(), Anderson 2006). PERMANOVA is sensitive to differences in dispersion, so report both.

Usage

beta_permanova(
  data,
  site = site,
  species = species,
  abundance = NULL,
  formula,
  env = NULL,
  distance = "bray",
  transform = "none",
  by = c("margin", "terms", "model"),
  strata = NULL,
  permutations = 999
)

beta_dispersion(
  data,
  site = site,
  species = species,
  abundance = NULL,
  group,
  env = NULL,
  distance = "bray",
  transform = "none",
  type = c("median", "centroid"),
  permutations = 999
)

Arguments

data: A data frame in long format, with one row per record.
site, species: <tidy-select> The column holding site identifiers and the column holding species names.
abundance: <tidy-select> The column holding counts. If NULL (the default), a column called abundance is used when present, otherwise every row counts as one individual.
formula: One-sided formula of site variables, such as ~ elevation + season.
env: A data frame of site variables with a column named like the site column. By default, site variables are taken from data: every column that is constant within each site.
distance: Dissimilarity for "pcoa", "nmds" and "dbrda", passed to vegan::vegdist(), such as "bray" (the default) or "jaccard".
transform: Transformation of the community matrix before the analysis: "hellinger" (the default for PCA and RDA, which otherwise overweight abundant species; Legendre and Gallagher 2001), "chord", "log" (log(x) + 1 for x > 0), "sqrt", "pa" (presence-absence) or "none" (the default for the other methods).
by: "margin" (the default: each term tested after all the others, so the result does not depend on the order of terms), "terms" (sequential: each term after those listed before it, so order matters when terms are correlated) or "model" (all terms together). Note that vegan::adonis2() defaults to "terms"; set by = "terms" to reproduce its default output.
strata: Optional site variable (unquoted) within which to restrict permutations, for example a block or transect.
permutations: Number of permutations for the tests of passive variables.
group: Site variable (unquoted) defining the groups.
type: Distance to the group spatial "median" (the default, as in vegan) or "centroid".

Value

A tibble: one row per term, with df, sum_sq, r2, statistic (pseudo-F) and p.value.

For beta_dispersion(), a tibble with one row per site (group, distance to its group centre) and the permutation test as attribute "test" (also printed). Use autoplot() to draw it.

Details

Site variables are taken from the data when they are constant within sites, as in ord_fit(), or from env.

References

Anderson, M. J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26, 32-46. doi:10.1111/j.1442-9993.2001.01070.pp.x

Anderson, M. J. (2006). Distance-based tests for homogeneity of multivariate dispersions. Biometrics, 62, 245-253. doi:10.1111/j.1541-0420.2005.00440.x

Examples

ants <- dplyr::mutate(png_ants, unit = paste(site, season, transect))
set.seed(1)
beta_permanova(ants, site = unit, formula = ~ elevation + season,
               permutations = 199)
#> # A tibble: 4 x 6
#>   term         df sum_sq     r2 statistic p.value
#>   <chr>     <dbl>  <dbl>  <dbl>     <dbl>   <dbl>
#> 1 elevation     1  1.33  0.169       3.75   0.005
#> 2 season        1  0.526 0.0669      1.49   0.105
#> 3 Residual     17  6.01  0.765      NA     NA    
#> 4 Total        19  7.87  1          NA     NA    
beta_dispersion(ants, site = unit, group = season, permutations = 199)
#> Multivariate dispersion by season 
#> # A tibble: 20 x 3
#>    unit         season distance
#>    <chr>        <fct>     <dbl>
#>  1 MW0200 dry 1 dry       0.564
#>  2 MW0200 dry 2 dry       0.607
#>  3 MW0200 wet 1 wet       0.590
#>  4 MW0200 wet 2 wet       0.537
#>  5 MW0700 dry 1 dry       0.574
#>  6 MW0700 dry 2 dry       0.573
#>  7 MW0700 wet 1 wet       0.576
#>  8 MW0700 wet 2 wet       0.533
#>  9 MW1200 dry 1 dry       0.607
#> 10 MW1200 dry 2 dry       0.563
#> 11 MW1200 wet 1 wet       0.508
#> 12 MW1200 wet 2 wet       0.504
#> 13 MW1700 dry 1 dry       0.676
#> 14 MW1700 dry 2 dry       0.668
#> 15 MW1700 wet 1 wet       0.636
#> 16 MW1700 wet 2 wet       0.655
#> 17 MW2200 dry 1 dry       0.647
#> 18 MW2200 dry 2 dry       0.651
#> 19 MW2200 wet 1 wet       0.729
#> 20 MW2200 wet 2 wet       0.671
#> 
#> Permutation test:
#> # A tibble: 2 x 5
#>   term         df  sum_sq statistic p.value
#>   <chr>     <int>   <dbl>     <dbl>   <dbl>
#> 1 Groups        1 0.00182     0.466   0.485
#> 2 Residuals    18 0.0702     NA      NA