A critical issue in model-based inference for studying trait-based community assembly and a solution

Abstract

Statistical testing of trait-environment association from data is a challenge as there is no common unit of observation: the trait is observed on species, the environment on sites and the mediating abundance on species-site combinations. A number of correlation-based methods, such as the community weighted trait means method (CWM), the fourth-corner correlation method and the multivariate method RLQ, have been proposed to estimate such trait-environment associations. In these methods, valid statistical testing proceeds by performing two separate resampling tests, one site-based and the other species-based and by assessing significance by the largest of the two p-values (the pmax test). Recently, regression-based methods using generalized linear models (GLM) have been proposed as a promising alternative with statistical inference via site-based resampling. We investigated the performance of this new approach along with approaches that mimicked the pmax test using GLM instead of fourth-corner. By simulation using models with additional random variation in the species response to the environment, the site-based resampling tests using GLM are shown to have severely inflated type I error, of up to 90%, when the nominal level is set as 5%. In addition, predictive modelling of such data using site-based cross-validation very often identified trait-environment interactions that had no predictive value. The problem that we identify is not an “omitted variable bias” problem as it occurs even when the additional random variation is independent of the observed trait and environment data. Instead, it is a problem of ignoring a random effect. In the same simulations, the GLM-based pmax test controlled the type I error in all models proposed so far in this context, but still gave slightly inflated error in more complex models that included both missing (but important) traits and missing (but important) environmental variables. For screening the importance of single trait-environment combinations, the fourth-corner test is shown to give almost the same results as the GLM-based tests in far less computing time.

Simple parametric tests for trait–environment association

“…ter Braak et al. () detected moderate type I error rate inflation in the max test using GLM for testing the trait–environment association. In this study, we showed similar problems using the fourth‐corner and CWM‐ and SNC‐based methods in both the log‐linear model and the two‐dimensional Gaussian model.…”

“…ter Braak et al. () argued that trait–environment interaction is scale‐ and thus model‐dependent. Arguably, there is a trait–environment interaction in this scenario when viewed on any other scale than the log‐linear scale.…”

“…The two‐dimensional Gaussian response model (with ellipsoidal contours with axes parallel to the gradients) is detailed in Supporting information Appendix ; the other two models in Supporting information Appendix of ter Braak et al. () with one difference, namely that the observed trait and environmental values were drawn from a 50–50% mixture of two normal distributions with means at −1 and 1 and common variance 1 and then rescaled to mean 0 and variance 1. The purpose of this was to evaluate whether the parametric approach also works in the case of non‐normal variables.…”

“…In this case, correct type I error rates are assured by taking the maximum of the resulting two p ‐values as the final p ‐value. We call this the “max test” (ter Braak, ; earlier names used were sequential test (ter Braak et al., ) and row–column permutation test (Peres‐Neto et al., ) or max r / c test (ter Braak, Peres‐Neto, & Dray, )). The max test controls for the type I error rate, which means that the rejection rate is at most the nominal level of the test (e.g.…”

Trait‐dependent distributional shifts in fruiting of common British fungi

“…Our approach is an extension of the community assembly via trait selection (CATS) (Warton et al 2015) following a multivariate regression specification (Jamil et al 2013, ter Braak et al 2017) and a joint species distribution model specification (Pollock et al 2014, Ovaskainen et al 2016. Our approach is an extension of the community assembly via trait selection (CATS) (Warton et al 2015) following a multivariate regression specification (Jamil et al 2013, ter Braak et al 2017) and a joint species distribution model specification (Pollock et al 2014, Ovaskainen et al 2016.…”