Observation delays can bias inference of selective advantage in evolutionary competition

Abstract

Relative-frequency trajectories are often used to infer selective advantage in competing biological populations. A common empirical approach is to fit a linear function to the logit-transformed frequency of an invading type and interpret the slope as the relative advantage. Here we test how this estimator is affected when the competing types are observed after type-specific delays. We use SARS-CoV-2 variant replacement in the United Kingdom as empirical motivation and study the mechanism with simple two-type models. In an ideal exponential replacement model, fixed or randomly distributed observation delays change the intercept of the observed log-odds trajectory but not its slope, provided that delayed counts are aggregated before frequencies are formed and boundary effects are absent. In nonlinear SIR-type models, where the relative growth is time-dependent, delays can compare the competing variants at different dynamical phases and substantially bias the fitted logit slope. This bias can occur even when the delayed replacement trajectory remains nearly linear on the logit scale. Thus, a good logistic fit to the observed data is not sufficient to guarantee that the inferred logit slope approximates well the relative growth advantage. Observation delays should therefore be accounted for when logit slopes are used as proxies for relative fitness in nonlinear evolutionary competition.