Accurate estimation of speciation ( \(\lambda \) ) and extinction ( \(\mu \) ) rates from phylogenetic trees is central to studies of diversification, yet it remains unclear whether commonly used estimators are unbiased. Here we examine two sources of error: (1) statistical bias in the estimators themselves, and the (2) structural bias introduced by how small trees are handled in likelihood calculations. For the Yule process, we re-derive the expected bias of the standard estimator, showing that \(\hat{\lambda }\) underestimates \(\lambda \) by a factor of \((n-2)/(n-1)\) . Extending to the general birth–death model, we use symbolic regression to find functional forms that minimize the bias in both \(\lambda \) and \(\mu \) . The best-performing correction for \(\lambda \) is identical to the Yule result, while the bias in \(\mu \) depends on both sample size and the estimated extinction fraction ( \(\mu /\lambda \) ). Applying these corrections substantially improves the fit between the estimated and generating values. When these corrected estimators are used to derive other diversification-related parameters, turnover is nearly unbiased, but net diversification ( \(\lambda - \mu \) ) remains systematically underestimated due to the slight overestimation of \(\mu \) . On the whole, these results begin to clarify the statistical and structural sources of bias in diversification rate estimation and provide a general framework for improving inference under birth-death models.
