Phylogenetic Derivative: A Tool for Assessing Local Tree Reconstruction in the Presence of Recombination

Recently, much attention has been given to understanding recombination events along a chromosome in a variety of field. For instance, many population genetics problems are limited by the inaccuracy of inferred evolutionary histories of chromosomes sampled randomly from a population. This evolutionary history differs among genomic locations as an artifact of recombination events along a chromosome. Thus, much recent attention has been focused on identifying these recombination points. However, many proposed methods either make simplifying, but unrealistic, assumptions about recombination along a chromosome, or are unable to scale to large genome-wide data like what has become commonplace in statistical genetics. Here, we introduce a \emph{phylogenetic derivative} to describe the relatedness of neighboring trees along a chromosome. This phylogenetic derivative is a computationally efficient, flexible metric that can be also be used assess the prevalence of recombination across a chromosome. These proposed methods are tested and perform well in analyzing both simulated data and a real mouse data set.