Evolutionary accumulation models (EvAMs) are an emerging class of machine learning methods designed to infer the evolutionary pathways by which features are acquired. Applications include cancer evolution (accumulation of mutations), anti-microbial resistance (accumulation of drug resistances), genome evolution (organelle gene transfers), and more diverse themes in biology and beyond. Following these themes, many EvAMs assume that features are gained irreversibly -- no loss of features can occur. Reversible approaches do exist but are often computationally (much) more demanding and statistically less stable. Our goal here is to explore whether useful information about evolutionary dynamics which are in reality reversible can be obtained from modelling approaches with an assumption of irreversibility. We identify, and use simulation studies to quantify, errors involved in neglecting reversible dynamics, and show the situations in which approximate results from tractable models can be informative and reliable. In particular, EvAM inferences about the relative orderings of acquisitions and the core dynamic structure of evolutionary pathways -- which features are likely present when another is acquired -- are robust to reversibility in many cases, while estimations of uncertainty and feature interactions are more error-prone.

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