  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.
