Should ecologists prefer model- over distance-based multivariate methods?

Area of Science:

• Ecology
• Statistical Ecology
• Environmental Science

Background:

• Ecological data commonly record species abundance and explanatory variables.
• Multivariate statistical methods are crucial for analyzing ecological data, but model-based approaches are less common than distance-based ones.
• Systematic performance evaluations of these methods are needed to guide ecologists.

Purpose of the Study:

• To compare the performance of model-based (MvGLMs, CQO) and distance-based (dbRDA, CCA) methods in ecological data analysis.
• To evaluate the ability of these methods to distinguish between causal and noise variables.
• To assess method performance across various sample sizes and data distributions.

Main Methods:

• Simulation-based performance evaluation of four multivariate statistical methods.
• Comparison of multivariate generalized linear models (MvGLMs), constrained quadratic ordination (CQO), distance-based redundancy analysis (dbRDA), and canonical correspondence analysis (CCA).
• Analysis of 190 simulated data sets with varying sample sizes and data distributions.

Main Results:

• MvGLM and dbRDA demonstrated high accuracy in differentiating causal from noise variables.
• MvGLM exhibited the lowest false-positive rate (0.008); dbRDA had the lowest false-negative rate (0.027).
• CQO and CCA showed higher error rates, especially for data with linear responses, with CQO having a high false-negative rate (0.291) and CCA a high false-positive rate (0.256).

Conclusions:

• Both model-based (MvGLM) and distance-based (dbRDA) methods are reliable tools for ecologists analyzing species-environment relationships.
• CQO and CCA methods have considerable limitations, particularly when dealing with linear environmental gradients.
• The choice of method depends on the specific ecological data and research question, with MvGLM and dbRDA recommended for robust causal inference.