Quantum entropy reveals chromosomal disorder of ancestry tracts in genetic admixture

Ancestry tracts are contiguous haplotype blocks inherited from distinct groups of common ancestors. The genomic distribution of ancestry tracts (or local ancestry) provides rich information about evolutionary mechanisms shaping the genetic composition of hybrids. The correlation structure of ancestry tracts has been particularly useful in both empirical and theoretical studies, but there is a lack of descriptive measures operating on arbitrarily large genomic blocks to summarize this correlation structure without imposing too many assumptions about admixture. We here develop an approach inspired by quantum information theory to quantify this correlation structure. The key innovation is to represent local ancestry as quantum states, where less correlation in local ancestry leads to elevated quantum entropy. By leveraging a variety of entropy measures on local ancestry signals, we show that entropy is deeply connected to co-ancestry probabilities between and within haplotypes, so that ancestral recombination graphs become pivotal to the study of entropy dynamics in admixture. We use this approach to characterize a standard neutral admixture model with an arbitrary number of sources, and recover entropic laws governing the dynamics of ancestry tracts under recombination and genetic drift, which resembles the second law of thermodynamics. In application, entropy is well-defined on arbitrarily large genomic blocks with either phased or unphased local ancestry, and is insensitive to a small amount of noise. These properties are superior to simple statistics on ancestry tracts such as tract length and junction density. Finally, we construct an entropic index reflecting the degree of intermixing among ancestry tracts over a chromosomal block. This index confirms that the Z chromosome in a previously studied butterfly hybrid zone has the least potential of ancestry mixing, thus conforming to the “large-X/Z” effect in speciation. Together, we show that quantum entropy provides a useful framework for studying ancestry tract dynamics in both theories and real systems.