[Paper Review] A variational synthesis of evolutionary and developmental dynamics

Karl Friston, Daniel Friedman+4 more|arXiv (Cornell University)|Mar 8, 2023

Evolution and Genetic DynamicsBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper presents a variational Bayesian framework that unifies evolutionary and developmental dynamics by formulating adaptive fitness as a path integral of phenotypic fitness. It shows that phenotypic paths of least action correspond to inference under a generative model, while phylogenetic paths correspond to Bayesian model selection, revealing that populations must be understood as nested meta-populations of distinct natural kinds rather than conspecific groups per se.

ABSTRACT

This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain - and are constrained by - fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (bayesian model selection). The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations - and nested meta-populations - of different natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses - and identify points of contact with related mathematical formulations of evolution.

Motivation & Objective

• To develop a unified mathematical framework for evolutionary and developmental processes using variational principles.
• To clarify how phenotypic and phylogenetic dynamics are constrained by and influence each other.
• To reformulate fitness and adaptation in terms of inference and learning via path integrals.
• To demonstrate that populations cannot be modeled as conspecific groups but must be understood as meta-populations of distinct natural kinds.
• To lay the groundwork for future simulations and numerical analyses of evolutionary dynamics using this formalism.

Proposed method

• Formulates adaptive fitness as a path integral over phenotypic trajectories, using variational principles to derive optimal paths.
• Applies Bayesian mechanics to model how phenotypes infer their econiche state under a generative model.
• Uses the principle of minimum free energy to derive phenotypic inference as a path of least action.
• Introduces natural (Bayesian) model selection as the mechanism for phylogenetic learning across generations.
• Models populations not as conspecifics but as nested meta-populations of different natural kinds that influence one another.
• Employs variational inference to unify developmental (phenotypic) and evolutionary (phylogenetic) processes under a single formalism.

Experimental results

Research questions

• RQ1 How can evolutionary and developmental dynamics be formally unified using variational principles?
• RQ2 What is the role of path integrals in characterizing adaptive fitness across phenotypic and phylogenetic scales?
• RQ3 Why is it incoherent to model populations as conspecific groups in this framework?
• RQ4 How do generative models and Bayesian inference underlie phenotypic inference and learning?
• RQ5 What mathematical structure emerges when fitness is treated as a variational free energy functional?

Key findings

• Phenotypic paths of least action correspond to inference under a generative model of the econiche.
• Phylogenetic paths of least action correspond to Bayesian model selection, representing learning across generations.
• Fitness is formally expressed as a path integral over phenotypic trajectories, linking continuous dynamics to adaptive optimization.
• Populations cannot be modeled as conspecifics; instead, nested meta-populations of distinct natural kinds are required for consistency.
• The framework reveals that both development and evolution emerge from variational principles grounded in Bayesian mechanics.
• The synthesis provides a foundation for future simulations and numerical analysis of evolutionary dynamics using this variational formulation.