The gift of novelty: repeat-robust k-mer-based estimators of mutation rates

Estimating mutation rates between evolutionarily related sequences is a central problem in molecular evolution. Due to the rapid expansion of datasets, modern methods avoid costly alignment and instead focus on comparing sketches of sets of constituent k-mers. While these methods perform well on many sequences, they are not robust to highly repetitive sequences such as centromeres. In this paper, we present three new estimators that are robust to the presence of repeats. The estimators are applicable in different settings, based on whether they need count information from zero, one, or both of the sequences. We evaluate our estimators empirically using highly repetitive alpha satellite sequences. Our estimators each perform best in their class and our strongest estimator outperforms all other tested estimators. Our software is open-source and freely available on https://github.com/medvedevgroup/Accurate_repeat-aware_kmer_based_estimator.