Preprint proposes carrier-set topology framework to characterise linkage disequilibrium structure

A preprint deposited on bioRxiv introduces a geometric framework for characterising the topology of carrier sets at pairs of biallelic loci — describing whether carriers of one variant are fully nested within, partially overlapping with, or entirely disjoint from carriers of another variant. The authors argue that widely used scalar summaries of linkage disequilibrium (LD), such as r² and D', conflate structurally distinct patterns that have different implications for association mapping, fine-mapping, and population-genetic inference.

The framework is grounded empirically in data from the 1000 Genomes Project and is also explored through a two-locus Wright–Fisher model. The authors describe how carrier-set topology forms, persists across generations, and breaks down under recombination and drift.

The work is relevant to statistical geneticists developing fine-mapping and colocalisation methods, to population geneticists studying haplotype structure, and to researchers working on rare-variant association analyses where haplotype nesting patterns can strongly influence power and interpretation. The preprint has not yet been peer-reviewed.