The Informational Model of the Holobiont: Statistical Tests for Selection and Extension to a Theory of Variable Interactions

Abstract

We review, clarify, and generalize a recently proposed evolutionary information-theoretic model of the holobiont, in which evolutionary change is quantified using Jeffreys divergence and partitioned into contributions from the host, microbial components, and host-microbiome associations. Building on these partitions, we develop statistical tests to identify whether observed informational change is attributable to selection acting on host types, microbial-component states, or particular host-microbiome combinations. We then extend the framework to multicomponent groups subject to within- and between-group selection and, ultimately, to a general hierarchical formulation that we call the Theory of Variable Interactions (TVI). In this formulation, biological units may contain interacting components and may themselves form higher-level sets, allowing informational change to be partitioned recursively into marginal and association components across an arbitrary number of organizational levels. The framework encompasses previously studied models of the tragedy of the commons and of aggregate and multicomponent holobiont selection, and, as a further specialization, informational models of non-random mating and sexual selection. TVI therefore provides a unified information-theoretic framework for quantifying evolutionary change in both biological entities and their interactions, with local statistical dimensionality preserved across hierarchical levels while higher levels introduce additional relational dimensions.