When models choose metrics: Hidden geometry in computational biology

Computational biology often turns biological measurements into fitted models, embeddings, or summaries and then compares them with a distance chosen largely by convention. That choice can shape the scientific question being answered, because different distances emphasize different assumptions about noise, variation, and biological similarity. This Perspective describes the hidden geometry that can arise when a probabilistic model is specified carefully enough to support local metric structure. For regular parametric models, the Fisher information defines a natural local metric, making distance choice part of model specification rather than a separate plotting or clustering preference. Rather than replacing familiar heuristics, information geometry helps explain when common transformations, such as variance stabilization for RNA-seq, approximate a model-implied distance; when dependence or latent nuisance structure limits that approximation; and when misspecification makes empirical, nonparametric, or sensitivity-based comparisons more appropriate. The goal is a clearer, more explicit practice of metric choice.