resassoc.cca: Residual Species Associations in Constrained Ordination

In jarioksa/natto: An Extreme 'vegan' Package of Experimental Code

Residual Species Associations in Constrained Ordination

Description

Function finds residual species association after fitting the constraints (and conditions) in constrained ordination (cca, rda).

Usage

resassoc.cca(x, rank)

Arguments

x	Constrained ordination result from cca or rda.
rank	Number of unconstrained ordination axes that are used to compute the species associations. If missing, the rank is chosen by brokenstick distribution (bstick).

Details

The residual unconstrained axes can be used to assess if there is any important unexplained variation in constrained ordination. This approach was proposed already in the first papers on constrained ordination (ter Braak 1986). However, this has been rarely done, mainly because there are no easily available tools to assess the unconstrained axes. Bayesian analysis of species communities (Tikhonov et al. 2020) is conceptually similar to constrained ordination. There the random effects are analysed via correlated species responses that are interpreted to be caused by unknown environmental variables or residual inter-species association. The random effects are found as Bayesian latent factors which are conceptually similar to residual axes in constrained ordination (although these are maximum likelihood principal components). It is customary represent these residual correlations as ordered correlation matrix (Tikhonov et al 2017). This function provides similar tools for constrained correpsondence analysis (CCA) and redundancy analysis (RDA) as perfomed in vegan functions cca and rda.

In Bayesian framework, we only try to extract a low number of latent factors needed to describe correlated random variation. In constrained ordination, all residual variation is accounted for by residual axes. For meaningful analysis, we should only look at some first axes which may reflect systematic unexplained variation. With all axes, the residual correlations are usually nearly zero and systematic variation is masked by non-systematic noise. Therefore we should only have a look at some first axes. Users can either specify the number of axes used, and the default is to use brokenstick distribution (vegan function (bstick) to assess the number of axes that have surprisingly high eigenvalues and may reflect unaccounted systematic variation. The function returns inter-species associations as correlation-like numbers, where values nearly zero mean non-associated species. These values can be plotted in correlation plot or analysed directly. The correlations are directly found from the residual ordination axes.

It is an attractive idea to interpret inter-species association to describe ecological interactions among species (Tikhonov et el. 2017). This indeed is possible, but there are other alternative explanations, such as missing environmental variables or modelling errors (model formula, scaling of species, scaling of environmental variables, assumptions on the shape of species response etc.). You should be cautious in interpreting the results (and the same applies also to the analogous Bayesian model).

Value

Correlation-like association matrix between species with added argument "rank" of the unconstrained data used to compute associations.

References

ter Braak, C.J.F. (1986) Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67, 1167–1179.

Tikhonov, G., Abrego, N., Dunson, D. and Ovaskainen, O. (2017) Using joint species distribution models for evaluating how species-to-species associations depend on the environmental context. Methods in Ecology and Evolution 8, 443- 452.

Tikhonov et al. (2020) Joint species distribution modelling with the R-package Hmsc. Methods in Ecology and Evolution 11, 442–447.

See Also

Hmsc has analogous function computeAssociations. However, in Hmsc the associations are based on Bayesian latent factors which are an essential natural component of the analysis whereas here we apply post-analysis tricks to extract something similar.

Examples

library(vegan)
data(dune, dune.env)
mod <- cca(dune ~ A1 + Moisture, dune.env)
resassoc.cca(mod)

jarioksa/natto documentation built on Feb. 20, 2025, 3:29 p.m.