Estimating extinction time using radiocarbon dates

The extinction of a species is a key demographic event often signalling major climatic, ecological and/or evolutionary shifts that can be investigated using the fossil record. In that context, radiocarbon (14C) dating has become a popular tool to time and test for scenarios of extinction that can inform on how species respond to past and future ecosystem changes. We develop CRIWM, a method for estimating extinction (and arrival) time from time series of 14C dates while accounting for probability density functions (PDF) deriving from 14C calibration. The sister method GRIWM assumes normal chronometric errors and is inappropriate for 14C chronologies as PDFs are often non-Gaussian and multi-modal. Compared to GRIWM, CRIWM reduces by 4-fold the gap between true and estimated extinction times and the width of the confidence intervals, and is less sensitive to sample size, dating errors and the temporal distribution of specimens in a species' fossil record. We build the R package Rextinct with three user-friendly functions for computing CRIWM and GRIWM, and the PDF moments, modes and intercepts of 14C calibrations. CRIWM and GRIWM accept time series comprising only 14C dates or observations (fossils, sightings) dated by multiple chronometric methods, and calibration curves for fossils sampled in the Northern and Southern Hemispheres and marine environments. For both methods, we implement two different estimators of extinction time whether they are reliant on a p-value (original conceptualization) or not (novel). CRIWM and Rextinct are robust tools to time extinction and arrival events using 14C chronologies spanning the entire Holocene to 50,000 calendar years Before Present, and can be used to investigate demographic phenomena queried through the fossil record such as migrations, domestications and extirpations.