A picture guide to cancer progression and monotonic accumulation models: evolutionary assumptions, plausible interpretations, and alternative uses

Cancer progression and monotonic accumulation models were developed to discover dependencies in the irreversible acquisition of binary traits from cross-sectional data. They have been used in computational oncology and virology to understand dependencies in the accumulation of mutations but also in widely different problems such as malaria progression. These tools have been used to make predictions about future and unobserved states of the system, identify different routes of feature acquisition in subsets of the data, and improve patient stratification based on the evolutionary trajectories. But these methods have shortcomings, in particular with respect to key evolutionary assumptions and interpretations. After an overview of the available methods, I focus on how and why the methods can fail and why their inferences might not be about the process we intend. I first examine interpretations and violations of assumptions when methods are used to infer within-cell restrictions in the accumulation of events. The discussion uses fitness landscapes and highlights the difficulties that arise from bulk sequencing and reciprocal sign epistasis, from the conflation of lines of descent, path of the maximum, and mutational profiles, and from the ambiguous use of the concepts of exclusivity and alternative evolutionary paths. Next, I suggest that users recognize the limitations that arise from their sampling designs, and I examine how the previous concerns are modified when bulk sequencing is accounted for. I also highlight how bulk sequencing can create an opportunity for addressing dependencies that arise from frequency-dependent selection. This review should help identify major standing issues and research opportunities, and encourage the use of these methods in other areas with a possibly better fit between entities and model assumptions.