# Supplementary Table S4 | Robustness Check of CT–Metabolite Association Asymmetry

**Three correlation methods applied to the same 18 CT × 624 metabolite pairs (11,232 pairs per variety).**

| Method | Metric | W5 (count) | CK (count) | Asymmetry |
|:---|---|:---:|:---:|:---:|
| Pearson correlation | \|r\| > 0.99 | **55** | 0 | ✅ |
| Pearson correlation | \|r\| > 0.95 | **147** | 0 | ✅ |
| Spearman rank correlation | \|ρ\| > 0.95 | **48** | 0 | ✅ |
| First-differencing Pearson | \|r\| > 0.95 | **41** | 2 | ✅ |
| Permutation test (10,000×) | Median \|r\| > 0.99 | **0** (observed: 55, p < 0.0001) | — | ✅ |

**Interpretation:** All three correlation methods (parametric Pearson, non-parametric Spearman, and detrended first-differencing Pearson) preserve the inter-variety asymmetry pattern, confirming that the finding is not an artefact of the linearity assumption or shared developmental trends.

**Method:**
- **Pearson correlation**: Computed on n = 5 time-point means (df = 3) per variety, FDR-corrected across 11,232 pairs.
- **Spearman rank correlation**: Rank-based non-parametric correlation on the same data.
- **First-differencing (FD) Pearson**: Each time series was first-differenced (x_{t+1} − x_t) before Pearson correlation, removing shared temporal trends.
- **Permutation test**: Time-point labels shuffled 10,000 times; under permutations, median |r| > 0.99 pairs = 0 (95% CI 0–1).