Optimizing phylogenetic eigenvector regression: Union eigenvectors, robust estimation, and flexible application to comparative analyses

Phylogenetic eigenvector regression (PVR) is widely used in ecology and evolution by representing phylogenetic structure through separable eigenvectors. Despite this flexibility, its implementation faces three key challenges: (1) the selection of eigenvectors, (2) the reduced robustness of ordinary least-squares (OLS) regression under shift-like evolutionary heterogeneity, and (3) the applicability of conventional model complexity rules such as the \"samples-per-variable (SPV) ≥ 10\" guideline. Here, we propose an optimized PVR framework that addresses these limitations. First, we show that trait-specific selections of eigenvectors often diverge, sometimes producing inconsistent results, and that using their union offers stronger control of phylogenetic non-independence. Second, we evaluate robust regression estimators within PVR, demonstrating that PVR-MM – and in most cases PVR-L2, the standard OLS estimator – maintains high accuracy under non-stationary evolutionary shifts where other ..., , # Data from: Optimizing phylogenetic eigenvector regression: Union eigenvectors, robust estimation, and flexible application to comparative analyses

Dataset DOI: [10.5061/dryad.4tmpg4frg](https://doi.org/10.5061/dryad.4tmpg4frg)

## Description of the data and file structure

The data used to plot the main text figures and supplementary figures

### Files and variables

#### File: Supplementary_Tables.xlsx

**Description:** The data used to plot Figures 2 - 5 (corresponding to Table S1, S4, S5, and S6), and Table 1,2 (corresponding to Table S2 and S3), and performance of spatial methods (Table S7)

##### Variables

* Table S1: `group` - the eigenvector adding case; `scenario` - the traits simulation scenario; digital ` 10^{-4}`  ` 0.01`  ` 1`  ` 4`  ` 16`  ` 64`  ` 256`  ` 1024` - the magnitude of noise term variance and shift 
* Table S2: same as Table S1
* Table S3: same as Table S1
* Table S4: `diff_r` - absolute differences i..., ,