Implements the phylogenetic beta-diversity framework of Peres-Neto & Kembel
(2015), a distance-based redundancy analysis (Legendre & Anderson 1999;
McArdle & Anderson 2001) of phylo_beta() on the predictors. The test
statistic is the pseudo-F. It is tested by permuting sites, which breaks the
link between composition and environment, and by permuting species across the
tips, which breaks the link between composition and phylogeny. The association
requires both, so the p-value to report is the larger of the two.
Arguments
- comm
Matrix with one row per site and one column per species, named as the tips of
tree. Every site needs at least one individual.- tree
A
phyloobject with the same species ascomm.- env
Predictor, or matrix or data frame of predictors, with one row per site.
- n_perm
Number of permutations of sites and of species.
- site_permutations
Optional matrix of site indices with one permutation per row, for example from
torus_permutations(), to use instead of free permutations of sites.
Value
List of class mc_phylo_beta with r2, the adjusted R2; statistic,
the pseudo-F; p_site, p_taxa and p_max; scores, the sites on the
principal coordinates of the predicted matrix, which the authors suggest
using to order sites in a heatmap of the community matrix; and permutations.
Details
The equations printed in the article omit the 1 in the adjusted R2, the
transpose in the hat matrix and the centring of the matrix that is regressed.
Here the predictors and the matrix are centred, and the residual degrees of
freedom are n - p - 1, with n - 1 for the total, instead of the printed
n - p and n. The pseudo-F and R2 therefore equal those of a distance-based
redundancy analysis in vegan. The printed degrees of freedom would multiply
the pseudo-F by a constant, which does not change the permutation tests.
The authors used presences and absences. Abundances are accepted, as weights
in phylo_beta().
References
Legendre, P., & Anderson, M. J. (1999). Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69, 1–24. doi:10.1890/0012-9615(1999)069[0001:DBRATM]2.0.CO;2
McArdle, B. H., & Anderson, M. J. (2001). Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology, 82, 290–297. doi:10.1890/0012-9658(2001)082[0290:FMMTCD]2.0.CO;2
Peres-Neto, P. R., & Kembel, S. W. (2015). Phylogenetic gradient analysis: environmental drivers of phylogenetic variation across ecological communities. Plant Ecology, 216, 709–724. doi:10.1007/s11258-014-0405-0
See also
pcc_test(), the other framework of the same article.
Examples
set.seed(1)
tree <- treeshapesim::sim_tree_shape(20)
traits <- species_traits(tree, lambda = 1, optima_range = c(-1, 101),
rmax_range = c(0, 30))
env <- runif(50, 0, 100)
comm <- simulate_static(traits, env, incidence = TRUE)$abundance
keep <- rowSums(comm) > 0
phylo_beta_test(comm[keep, ], tree, env[keep], n_perm = 99)
#> <mc_phylo_beta> phylogenetic beta diversity
#> adjusted R2: 0.221 pseudo-F: 14.9
#> permutations: 99 free of sites, 99 of species; smallest possible p: 0.01
#> p (sites): 0.01 p (species): 0.01 p (max): 0.01