Generative models versus underlying symmetries to explain biological pattern

Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative models confirm the plausibility of an explanation and make testable hypotheses for further experiments. However, studies rarely consider the broad family of alternative models that match the same observed pattern. The symmetries that define the broad class of matching models are in fact the only aspects of information truly revealed by observed pattern. Commonly observed patterns derive from simple underlying symmetries. This article illustrates the problem by showing the symmetry associated with the observed rate of increase in fitness in a constant environment. That underlying symmetry reveals how each particular generative model defines a single example within the broad class of matching models. Further progress on the relation between pattern and process requires deeper consideration of the underlying symmetries.