Unified theory resolves phenological paradoxes in biocollection data by modeling phenophase duration during Bayesian inference

Phenology is increasingly studied using digitized biocollection data, yet no general theory links observed specimen collection dates to the unobserved processes governing phenological events. We derive a unified mathematical theory that connects biocollection data to phenophase onset, duration, cessation, peak timing, phenological extremes, and phenological sensitivities to environmental change. The theory reveals that both phenophase duration and onset timing impact dates of collection. Failure to model these latent events leads to unsound estimates of phenological timing. Embedding the theory within a Bayesian Gaussian process framework resolves these issues by disentangling their effects. Consequently, the methodology results in explicit models of phenophase duration and onset timing as functions of environmental factors. We demonstrate robustness to model misspecification, illustrate how priors enhance model identifiability, and show improved performance relative to three existing methods. Analyses of 5363 herbarium records spanning 13 spring ephemeral species highlight that variation in duration confounds estimates of phenological sensitivity in every species examined. These empirical results and theory accentuate the need to consider phenophase duration, in general, and population size for phenological extremes. Our R package, phenoCollectR, enables theory-driven phenological inferences from biocollection data, facilitating investigation of links among life-history events, ecosystem services, and anthropogenic change.