  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.
