Timing and clustering co-occurring genome amplifications in cancers

Clonal evolution in cancer is driven by genomic alterations that accumulate over time, shaping tumour progression, therapy resistance, and metastasis. Among these somatic events, genomic amplifications are a broad class of copy number alterations (CNAs) that can be mathematically timed (i.e., mapped to an abstract timeline). Existing methods successfully order amplifications in time but fail to understand their co-occurrence patterns. This limitation makes it harder to understand abrupt shifts of clonal and selection dynamics possibly linked to clones that acquire profound mutant genotypes and hold the potential to establish a novel evolutionary lineage. Here, we introduce TickTack , a hierarchical Bayesian mixture model for reconstructing the temporal order of copy number amplifications across the genome while simultaneously detecting co-occurrent events, offering a more comprehensive view of tumour evolutionary dynamics. This new model allows us to determine whether copy number amplifications accumulate gradually over multiple generations or occur in rapid succession within short time frames, providing deeper insights into genomic instability and tumor progression beyond traditional linear models. We validated our approach with synthetic data under various uncertainty settings and against competing approaches. Applying TickTack to 2,777 samples from the Pan-Cancer Analysis of Whole Genomes (PCAWG) project, a comprehensive resource spanning 38 tumor types, we inferred the temporal order of copy number amplifications, identifying cancer-specific co-occurring events. Our analysis revealed associations between early chromosomal instability and key driver mutations (TP53, BRCA1/2) in Esophageal Adenocarcinoma and uncovered recurrent evolutionary trajectories shaped by focal and arm-level copy gains. These findings highlight the role of saltational evolution in tumorigenesis and provide insights into genomic instability with possible implications for prognosis and targeted therapies.