2018/07/12 by Leonardo Aguirre, Aguirre, Leonardo
Biochemistry, Genetics and Molecular Biology · Mathematics · Social Sciences · #60F10 #60G10 #92D25 #Configuration space #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Finitary #Fitness landscape #Gene Regulatory Network Analysis #Geodesic #Geometry #Information geometry #Markov chain #Markov process #Mathematics #Neutral theory of molecular evolution #Population #Primary 60D05 #Probability (math.PR) #Pure mathematics #Replicator equation #Secondary 60F05 #Statistical physics #math.PR #msc:60D05 #msc:60F05 #msc:60F10 #msc:60G10 #msc:92D25
paper · pdf · doi:10.48550/arxiv.1807.04704
52 pages, 5 figures
openalex publication_date 2018/07/12 · arxiv created 2018/07/25 · arxiv updated 2018/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under consideration is that of finite causal-state processes, known from the computational mechanics programme, along with their minimal unifilar hidden Markov generators. The respective configuration space is exhibited as a collection of combinatorially related Riemannian manifolds wherein the metric tensor field is an infinitesimal version of the relative entropy rate. Furthermore, a certain evolutionary inference iteration is defined which can be executed by generator-carrying agents and generalizes the Wright-Fisher model from population genetics. The induced dynamics on configuration space is studied from the large deviation point of view and it is shown that the associated asymptotic expectation dynamics follows the Riemannian gradient flow of a given fitness potential. In fact, this flow can formally be viewed as an information-geometric generalization of the replicator dynamics from population biology.