Darwin as Minimum Description Length: Selection, Variation, and Modularity as Code–Length Optimization

Abstract

We develop a methods‑first theory that identifies fitness with negative description length. For an environment \(\mathcal{E}\) and an organism \(g\), we define the evolutionary code length \(L_g = L(\text{model}_g) + L(\text{errors}\mid \mathcal{E})\). If replication rates obey \(r(g) \propto e^{-\beta L_g}\) for resource factor \(\beta>0\), then replicator dynamics descend the mean code length and the stationary distribution is \(\pi^*(g) \propto e^{-\beta L_g}\). Variation follows an anisotropic proposal law \(q(\Delta)\propto e^{-\Delta J}\) where \(J\) is a symmetric, convex ledger cost, and modularity is favored when environmental tasks share information \(M\), yielding reuse savings at least \(M-b\) bits for a module of size \(b\). The empirical program is operational and auditable under a preregistered MDL protocol with explicit falsifiers.