Optimal Control and the Dynamics of Ancestral Lineages

Abstract

In resource-constrained populations, the growth rate of an allele is coupled to the frequency of its competitors. Since these frequencies are unobserved, exact inference of evolutionary parameters demands integrating over the full ensemble of possible frequency histories. This high-dimensional path integral is computationally prohibitive, and standard phylogenetic approaches avoid its evaluation by treating lineages as unconstrained birth-death processes. However, ignoring the carrying capacity comes at a cost: it necessitates an abundance of free parameters to describe simple allelic replicator dynamics and implicitly assumes an incorrect drift model. We propose a new approach by defining the fitness potential ({Psi})-- a dynamical quantity formally equivalent to the logarithm of reproductive value. By exploiting a duality between evolutionary dynamics and stochastic optimal control, we show that {Psi} allows for the analytic marginalization of the unknown population history. This transformation yields a tractable likelihood function that strictly enforces competitive constraints while accounting for the information loss due to genetic drift in finite populations. We demonstrate that this framework enables parsimonious, site-specific inference of selection coefficients from phylogenetic trees. This dual-control framework shows ancestral lineages behave as optimal agents: they do not simply climb local fitness gradients, but "anticipate" future selection by navigating a global landscape of reproductive value.