Empirically calibrated simulations reveal the limits of phenotypic clustering algorithms for biodiversity assessment in data-scarce crops

PLOS One | https://doi.org/10.1371/journal.pone.0329254 December 17, 2025 11 / 14 Empirically identifying these detectability boundaries would help practitioners to: 1. Distinguish biologically diffuse population structure from methodological artefacts; 2. Establish data-driven guidelines for the applicability and interpretation of clustering analyses in NUS research; and 3. Develop generalizable frameworks that explicitly account for differentiation level rather than relying on one-size-fits-all approaches. Such gradient-based analyses represent a natural extension of the current simulation framework, which can be readily parameterized to explore Pst values ranging from near-neutral differentiation (Pst ≈ 0.05) to strong divergence (Pst > 0.25). This line of research will form the basis of future work aimed at quantifying the relationship between clustering detectabil- ity and the intensity of phenotypic differentiation. 9. Broad impact and future extensions: Our study challenges current NUS phenotypic research paradigms—routinely reliant on K-means, GMM, or DBSCAN. Instead, we propose a robust methodological reform grounded in empirically calibrated simulations, combined validation diagnostics, and context-aware algorithm selection. This paradigm is gen- eralizable to NUS with varying sample sizes, trait distributions, complex correlations, and population structures. Future extensions should also incorporate explicit handling of missing data mechanisms (MCAR/MAR), extreme sample

imbalance, continuous differentiation gradients, and integration with genomic validation [34], following the statistical principles outlined by Little & Rubin [35]. 10. Toward biologically meaningful clustering metrics: Our results confirm that standard external indices such as ARI and NMI rapidly lose discriminative power when phenotypic differentiation is weak (Pst < 0.2). This limitation, already noted in population genomics and community ecology [15,12], highlights the need for alternative, biologically informed criteria. The inclusion of internal indices such as Silhouette and Davies–Bouldin partially alleviates this issue by quantifying within-group cohesion and between-group separation without reference to true labels. However, these metrics remain geometry-based and do not account for biological plausibility or trait redundancy. Future developments should therefore explore hybrid approaches — combining statistical validation with biological con- straints (e.g., trait heritability, ecological coherence, or phenotypic dispersion; [28]) — to define more meaningful clustering diagnostics in agrobiodiversity research. 11. Practical implications for NUS research and conservation: Practical recommendations for biodiversity practi- tioners and breeders before clustering: • Calibrate expectations via simulation. Use the R framework provided (Zenodo DOI: [10.5281/zenodo.15877863]) to benchmark expected algorithmic performance under your crop’s specific trait architecture before analyzing real

data. Parameterizing simulations with empirical trait means, variances, correlations, and heteroscedasticity enables realistic assessment of clustering detectability. During analysis: • Combine multiple validation approaches. Supplement ARI and NMI with internal cohesion metrics (Silhouette, Davies–Bouldin), visual diagnostics (PCA, UMAP), and biological expertise. Integrated interpretation mitigates over- reliance on purely statistical indices, especially in weakly differentiated datasets. For decision-making: • Prioritize reproducibility over peak performance. When clusters inform breeding or conservation actions, favor sta- ble and interpretable algorithms (e.g., PAM, Ward) that yield consistent results across resampling rather than complex models that are numerically optimal but unstable (e.g., GMM).