Fast Estimation of Recombination Rates Using Topological Data Analysis

Accurate estimation of recombination rates is critical for studying the origins and maintenance of genetic diversity. Because the inference of recombination rates under a full evolutionary model is computationally expensive, an alternative approach using topological data analysis (TDA) has been proposed. Previous TDA methods used information contained solely in the first Betti number (β1)of the cloud of genomes, which relates to the number of loops that can be detected within a genealogy. While these methods are considerably less computationally intensive than current biological model-based methods, these explorations have proven difficult to connect to the theory of the underlying biological process of recombination, and consequently have unpredictable behavior under different perturbations of the data. We introduce a new topological feature with a natural connection to coalescent models, which we call ψ. We show that ψ and β1 are differentially affected by changes to the structure of the data and use them in conjunction to provide a robust, efficient, and accurate estimator of recombination rates, TREE. Compared to previous TDA methods, TREE more closely approximates of the results of commonly used model-based methods. These characteristics make TREE well suited as a first-pass estimator of recombination rate heterogeneity or hotspots throughout the genome. In addition, we present novel arguments relating β1 to population genetic models; our work justifies the use of topological statistics as summaries of distributions of genome sequences and describes a new, unintuitive relationship between topological summaries of distance and the footprint of recombination on genome sequences.