Tspecies , Rapid Optimization for Estimating Species Divergence Time Using K _s Distribution

K _s distribution, the distribution of the synonymous substitutions, has been widely used to estimate the species divergence using orthologous genes. However, conventional approaches often ignore the underlying bias that species divergence is delayed to average gene divergence by 2 N _e generations, where N _e represents the ancestral effective population size, due to the lack of scalable methods for N _e inference. Here, we demonstrate through simulations that K _s distribution variance correlates with N _e , enabling direct estimation of ancestral population parameters from standard K _s data. Leveraging this relationship, we present Tspecies , an R package that corrects divergence time estimates using only substitution rates and K _s distributions, without requiring additional genomic data. Our practical application of Tspecies in Liriodendron has inferred a divergence time between North American and East Asian lineages (3.49 Ma) that align with late Pliocene cooling, and a large ancestral N _e (∼5 × 10 ⁵ ) consistent with fossil evidence. By incorporating a readily estimated N _e , our tool resolves a long-standing bias in K _s -based dating while maintaining computational efficiency and broad applicability.

Tspecies is freely available under an MIT license at https://github.com/limj0987/Tspecies.git .