Dou, W.; Lv, Z.; Ji, D.; Zhao, C.; Wang, N.; Yang, F.; Jiang, L.

Polyploid genomes exhibit complex allelic interactions driven by polysomic inheritance that cannot be adequately captured by conventional pairwise linkage disequilibrium (LD) models, leaving higher-order dependency structures largely unresolved. Here, we develop a unified population-genetic framework that jointly infers double reduction and higher-order allelic associations in autopolyploids. By modeling dosage-dependent gametic structure, our approach reformulates LD as a hierarchical system, enabling decomposition of allelic dependencies beyond pairwise interactions. Through simulations, we show that conventional estimators systematically confound higher-order allelic structure with pairwise LD, leading to biased inference and loss of identifiability under dosage uncertainty. In contrast, our joint likelihood framework achieves asymptotically unbiased estimation and reveals that effective double reduction emerges as a composite parameter linking meiotic configuration to population-level allelic reshaping. Applying this model to Arabidopsis arenosa and cultivated potato, we uncover fundamental contrasts in genomic architecture. In natural populations, higher-order LD self-organizes into structured, long-range dependency networks, whereas predominantly clonal populations exhibit collapse of higher-order dependency structure. We further identify a spatial antagonism between double reduction and higher-order LD, demonstrating that elevated double reduction compresses the physical scale of allelic interactions. Our results demonstrate that autopolyploid genomes are organized as higher-order dependency systems rather than collections of pairwise associations, establishing higher-order allelic structure as a fundamental extension of classical LD theory.