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<p>Trait-based ecology seeks to explain species’ responses to environmental gradients through their functional traits, aiming for generalizable predictions of community assembly. The fourth-corner problem formalizes this challenge by integrating species traits, environmental variables, and species abundances. Recently, fourth-corner generalized linear latent variable models (GLLVMs) have been proposed as a solution to capture both unobserved ecological gradients and trait–environment interactions. This paper shows—through theoretical analysis, empirical data, and simulations—that current fourth-corner GLLVMs often overstate confidence in inferred relationships, inflating type I error rates. In contrast, double-constrained correspondence analysis (dc-CA) and a generalized linear mixed model with random species-specific environmental and random site-specific trait effects (GLMM3) offer more reliable inference. While GLMM3, potentially extended with latent variables, may provide the most powerful framework, its practical use is limited by computational demands. dc-CA emerges as a robust and accessible alternative, balancing statistical rigor with interpretability by treating both species and sites as units of analysis. I argue that trait–environment models should not only fit observed data but also generalize to new trait values and ecological contexts. Overconfident conclusions from any supervised learning model that ignores species- or site-level variation risk misleading ecological understanding and misinforming conservation and management decisions.</p>

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Fourth-corner latent variable models overstate confidence in trait–environment relationships and what to use instead

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Cajo J. F. ter Braak

摘要

Trait-based ecology seeks to explain species’ responses to environmental gradients through their functional traits, aiming for generalizable predictions of community assembly. The fourth-corner problem formalizes this challenge by integrating species traits, environmental variables, and species abundances. Recently, fourth-corner generalized linear latent variable models (GLLVMs) have been proposed as a solution to capture both unobserved ecological gradients and trait–environment interactions. This paper shows—through theoretical analysis, empirical data, and simulations—that current fourth-corner GLLVMs often overstate confidence in inferred relationships, inflating type I error rates. In contrast, double-constrained correspondence analysis (dc-CA) and a generalized linear mixed model with random species-specific environmental and random site-specific trait effects (GLMM3) offer more reliable inference. While GLMM3, potentially extended with latent variables, may provide the most powerful framework, its practical use is limited by computational demands. dc-CA emerges as a robust and accessible alternative, balancing statistical rigor with interpretability by treating both species and sites as units of analysis. I argue that trait–environment models should not only fit observed data but also generalize to new trait values and ecological contexts. Overconfident conclusions from any supervised learning model that ignores species- or site-level variation risk misleading ecological understanding and misinforming conservation and management decisions.