HORSE: Harmonize regional and global stratigraphic records through horizon sequencing

A uniform, high-resolution geological timescale is essential for studying Earth's history, including the dynamics of biodiversity and environmental change. Quantitative stratigraphy combines stratigraphic data with statistical and computational approaches into a global timescale that allows them to be correlated simultaneously. For example, Constrained Optimization (CONOP), built upon Graphic Correlation, sequences geological events to generate a composite sequence by resolving inconsistencies among stratigraphic records. However, CONOP determines only the global order of events (e.g., first or last appearances of species) and cannot assign ages to local records, e.g., a locally observed fossil occurrence. Horizon Annealing (HA) addresses this by using a simulated annealing algorithm to sequence sampling “horizons” while preserving local stratigraphic details. Here, we report HORizon SEquencing (HORSE), a generalized and optimized method for HA, with an implementation including parallel computing and genetic algorithms to enable fast, automatic stratigraphic correlation on large datasets. We evaluate HORSE, HA, and CONOP on three datasets—two empirical and one simulated—and assess their performance in terms of accuracy, efficiency, and robustness. HORSE greatly outperforms HA in computational efficiency and performs comparably to CONOP in event sequencing with greater robustness. Beyond constructing high-resolution geological timescales or life histories in deep time, HORSE uniquely preserves local stratigraphic information, enabling applications in palaeogeographical or palaeoecological studies, as well as evaluations of preservation and sampling biases—capabilities not possible with CONOP.