Clustering Genetically Closely Related SARS-CoV-2 Lineages that Share the Same Relative Effective Reproduction Number Using BIC–Based Model Selection

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has evolved continuously, producing a large number of viral lineages. Natural selection favors lineages with advantageous mutations, and these lineages increase in frequency, replacing previously circulating lineages. Several lineage replacement models have been developed to estimate the relative effective reproduction number of circulating lineages. When a large number of lineages are circulating in a population simultaneously, the number of model parameters representing viral transmissibility increases, making it difficult to explore mutations affecting viral transmissibility. Therefore, clustering viral lineages with similar genetic backgrounds and the same relative effective reproduction numbers may help us explore the genetic and phenotypic relationships among circulating lineages. In this paper, we present a new algorithm called FindPart-w-ϵ, which identifies groups of genetically closely related viral lineages that share the same relative effective reproduction numbers from temporal count datasets of observed viral lineages. We formalize groups of genetically closely related viral lineages using ϵ-connected partitions, and FindPart-w-ϵ searches for an ϵ-connected partition that minimizes the Bayesian information criterion. By applying the algorithm to datasets of SARS-CoV-2 lineage counts from the United States of America and the United Kingdom, we showed that FindPart-w-ϵ improves the interpretability of the resulting lineage partitions while retaining major lineage-specific transmissibility patterns.