A Picture Guide to Cancer Progression and Evolutionary Accumulation Models: Systematic Critique, Plausible Interpretations, and Alternative Uses

Cancer progression and evolutionary accumulation models were developed to discover dependencies in the irreversible acquisition of binary traits from cross-sectional data. They have been used in oncology and virology but also in widely different problems such as malaria progression. These methods have been applied to predict future states of the system, identify routes of feature acquisition, and improve patient stratification, and they hold promise for evolutionary-based treatments. New methods continue to be developed. But these methods have shortcomings, which are yet to be systematically critiqued, regarding key evolutionary assumptions and interpretations. After an overview of available methods, we focus on why inferences might not be about the processes we intend. Using fitness landscapes, we highlight difficulties arising from bulk sequencing, from conflating lines of descent, path of the maximum, and mutational profiles, and from the idea of exclusivity. We show that bulk sequencing can severely limit interpretation as inferring within-cell restrictions is only warranted under very strong assumptions. We suggest that limitations and opportunities from bulk sequencing be recognised and exploited explicitly; the methods remain valuable for patient stratification, and we underline opportunities for addressing dependencies due to frequencydependent selection. This review identifies major standing issues, recommends turning inferences into actionable insights for translational impact —which requires careful consideration of empirical entities for causally-justified interpretations—, assessing method performance with entity-appropriate simulations, and should encourage the use of these methods in other areas with a better alignment between entities and model assumptions.