Complete author-written abstract
This paper introduces a variational formulation of natural selection, paying special atten-
tion 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 ensu-
ing 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 of distinct 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.
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Findings and contributions
- The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness, with least-action paths read as inference (phenotypic) and learning (phylogenetic).
- The synthesis implies that a population of conspecifics cannot be modelled per se; one must consider populations of distinct natural kinds that influence each other.
- Genotype and phenotype fitness are both selected through minimisation of the same free energy functional (Bayesian model evidence).
- In the synaptic-selection simulation, free energy progressively decreased at the slow timescale as synapses enabling the cell to predict its inputs were selected.
- The authors caution that the account is limited to mathematical apparatus, is not a process theory, and did not examine when the variational fitness lemma holds.
Methods
- Bayesian mechanics of particular partitions (free energy principle) — Particular partitions are used to analyze how slow phylogenetic processes constrain and are constrained by fast phenotypic processes.
- Two coupled random dynamical systems linked by a renormalisation group — Phylogenetic and phenotypic processes are modelled as two random dynamical systems coupled via renormalisation-group reduction and grouping operators.
- Variational recipe: Bayesian filtering plus stochastic gradient descent on action — A four-step protocol samples particles, finds least-action paths by generalised Bayesian filtering, scores the free-energy path integral, and updates parameters.
- Numerical simulation of synaptic selection in a single neuron — A single dendrite with 20 synapses over five segments was simulated over 64 cycles, with synapses eliminated via Bayesian model reduction on synaptic precision.
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