Genomic Dimensionality Bounds Mixed-Model Association Power and Fine-Mapping Resolution

Mixed-model genome-wide association studies (GWAS) behave differently in livestock than in humans, yet a unified explanation is lacking. Analyses using the full genomic relationship matrix (full-GRM; from genome-wide SNPs) yield only a few significant peaks even with hundreds of thousands of animals, whereas leave-one-chromosome-out (LOCO), numerator-relationship-matrix, and sparse-GRM approaches report many broad associations over similar data. Here we develop a framework that traces these behaviors to the low effective genomic dimensionality, Me, of small-Ne populations. Starting from the mixed-model association statistic, we derive the per-SNP non-centrality parameter under full-GRM testing and show that its sample-size dependence is fully captured by a sigmoid sum S(N) over LD-matrix eigenmodes. S(N) grows concavely with N toward a practical ceiling Me, from which the framework predicts a full-GRM detection floor qmin {approx} 30 h2/Me on per-SNP proportion of phenotypic variance explained at 50% power (e.g., ~0.09% for cattle at h2 = 0.3), and a fine-mapping resolution limit through both Me and 4Ned-scaled LD decay. LOCO bypasses the full-GRM ceiling but detects LD-aggregated block-level signals rather than SNP-level excess effects, explaining its inflation in livestock and agreement with full-GRM in humans. The framework is supported by analyses of real livestock chip panels, coalescent eigenvalue spectra, and phenotype simulations. The same sigmoid sum, normalized as {phi}(N) {approx} S(N)/Me, recovers the in-sample average GBLUP reliability, unifying why genomic prediction is comparatively easy in livestock while SNP-level mapping and fine-mapping remain difficult. For livestock GWAS aimed at SNP-level interpretation (e.g., candidate-gene prioritization, fine-mapping, or molecular-QTL colocalization), the framework supports full-GRM approaches as the appropriate default.