Beyond fitness: selection and information flow through the constructive steps in lifecycles

The replicator is the fundamental abstraction of evolutionary genetics. Only for replicators do Darwin’s concept of fitness as differential reproductive success, and the formalization by Fisher and Price in terms of apportionment of descendant populations to ancestors, coincide without ambiguity or potential conflict. The organization of the Price equation, causal interpretations of Fisher’s Fundamental Theorem and its relatives, and the abstraction of fitness as the sole channel through which information flows in from environments to form the adapted states of evolving populations, all follow from properties of replicators imposed artificially on the genetics of more complex lifecycles. Here it is shown how to generalize this role of the replicator to the autocatalytic flows in the generators of Stoichiometric Populations Processes, and to generalize from the unique summary statistic of fitness to a class of summary statistics that appear as regression coefficients against the autocatalytic flows associated with reproduction, including replication but also including constructive operations beyond simple copying. Both the statistical construction and the causal interpretation of Fisher’s Theorem and the Price Equation generalize from replicators and fitness to the wider class of regressions. Ad hoc corrections for mis-specified fitness models, which the conventional Price equation groups with “environment” effects, become part of a Fisher covariance on the basis of flows, which takes on a consistent causal interpretation in terms of an expanded concept of selection recognizing distributed information. A measure is derived for the information in the trajectory of a population evolving under a stoichiometric stochastic process, as the large-deviation function for that trajectory from a null model. The interpretation of fitness and other regression coefficients as channels for causation and information flow is derived from their inner product with the gradient of the trajectory entropy.