douconca (version 1.2.3)

anova_species: Utility function: Species-level Permutation Test in Double Constrained Correspondence Analysis (dc-CA)

Description

anova_species performs the species-level permutation test of dc-CA which is part of anova.dcca. The test uses residual predictor permutation (ter Braak 2022), which is robust against differences in species total abundance in the response in dc_CA (ter Braak & te Beest, 2022). The arguments of the function are similar to those of anova.cca, but more restrictive.

Usage

anova_species(
  object,
  permutations = 999,
  rpp = TRUE,
  n_axes = "all",
  by = NULL
)

Value

A list with two elements with names table and eigenvalues. The table is as from anova.cca and eigenvalues gives the dc-CA eigenvalues. This output can be used for scripting forward selection of traits, similar to the forward selection of environmental variables in the demo dune_select.r.

Arguments

object

an object from dc_CA.

permutations

a list of control values for the permutations as returned by the function how, or the number of permutations required (default 999) or a permutation matrix where each row gives the permuted indices.

rpp

Logical indicating residual predictor permutation (default TRUE). When FALSE, residual response permutation is used.

n_axes

number of axes used in the test statistic (default: "all"). Example, the test statistic is the sum of the first two eigenvalues, if n_axes=2. With a numeric n_axes and model ~X + Condition(Z), the residuals of X with respect to Z are permuted with a test statistic equal to the sum of the first n_axes eigenvalues of the fitted Y in the model Y ~ X + Z, with Y the response in the model. In the default "all", the test statistic is all eigenvalues of the model Y ~ X|Z, i.e. the effects of X after adjustment for the effects on Y of Z. If by = "axis", the setting of n_axes is ignored.

by

character "axis" which sets the test statistic to the first eigenvalue of the dc-CA model. Default: NULL which set the test statistic to the inertia (sum of all double constrained eigenvalues; named constraintsTE in the inertia element of dc_CA). This is the environmentally constrained inertia explained by the traits (without trait covariates), which is equal to the trait-constrained inertia explained by the environmental predictors (without covariates). The default is quicker computationally as it avoids computation of an svd of permuted data sets.

Details

In anova_species, the first step extracts the species-niche centroids (SNC) with respect to all dc-CA ordination axes from an existing dc-CA analysis. The second step, applies a weighted redundancy analysis of these SNCs with the traits as predictors. The second step is thus a species-level analysis, but the final results (eigenvalues/ordination axes) are identical to those of the analyses steps in dc_CA.The second step uses R-code that is analogous to that of anova.wrda.

References

ter Braak, C.J.F. & te Beest, D.E. 2022. Testing environmental effects on taxonomic composition with canonical correspondence analysis: alternative permutation tests are not equal. Environmental and Ecological Statistics. 29 (4), 849-868. tools:::Rd_expr_doi("10.1007/s10651-022-00545-4")

ter Braak, C.J.F. (2022) Predictor versus response permutation for significance testing in weighted regression and redundancy analysis. Journal of statistical computation and simulation, 92, 2041-2059. tools:::Rd_expr_doi("10.1080/00949655.2021.2019256")

Examples

data("dune_trait_env")

# rownames are carried forward in results
rownames(dune_trait_env$comm) <- dune_trait_env$comm$Sites

mod <- dc_CA(formulaEnv = ~ A1 + Moist + Mag + Use + Manure,
             formulaTraits = ~ SLA + Height + LDMC + Seedmass + Lifespan,
             response = dune_trait_env$comm[, -1],  # must delete "Sites"
             dataEnv = dune_trait_env$envir,
             dataTraits = dune_trait_env$traits,
             verbose = FALSE)
anova(mod)

a_species <- anova_species(mod)
a_species
# anova_species can be used for manual forward selection of
# trait variables, as done for environmental variables in the demo 
# dune_FS_dcCA.r, based on the first eigenvalue and its significance
# and adding the first axis of the constrained species scores from mod to 
# the Condition of a new mod.
(eig1_and_pval <- c(eig = a_species$eig[1], pval = a_species$table$`Pr(>F)`[1]))
a_species$eig
anova_sites(mod)