On Information in Evolutionary Processes

Enrico M Bucci 

Since the first attempts to introduce an information-theoretical formalism into the description of evolutionary processes, several authors have argued that such approaches are inappropriate because biological evolution does not unfold in a predefined space of possibilities.
To properly address that objection, we need to separate the semantics of the emergence of biological functions from the statistical structure of the selection processes.
Here, we propose a unified framework that treats Darwinian evolution as a population-level process and selection as a change in the frequency distributions of equivalence classes of the population components, independently of individual organisms, fitness assignments, or mechanistic implementations. The selection process is thus a population distribution restructuring, which can be quantitatively examined using divergence measures between pre- and post-selection distributions, independent of the selection process's adaptive nature.
In this framework, if the selection process is adaptive, then the statistical coupling between a set of relevant environmental variables/states and the population distribution is directly quantified by the mutual information connecting these two distributions, providing a non-semantic, operational measure of adaptation at the species level, conditional on a pre-specified infotype support and selective-domain definition. After selection, variety may be reintroduced into the population under scrutiny by several means: this is the process that opens and reshapes the space of selectable configurations, enabling the population to evolve iteratively through new selection and variation stages.
At the level of single organisms, fitness is formalized, within selective regimes in which persistence weights can be assigned to infotypes without explicit dependence on current population composition or density, as the function that projects the frequency of the corresponding selection equivalence class from the initial distribution to the final one during the selection process. Within this scope, fitness can be decomposed into components linked to individual information extraction from the environment, and non-informational contributions that modulate the persistence of the particular equivalence class considered. Regimes in which persistence depends explicitly on population composition or density require a state-dependent extension of the present framework and fall outside the scope of the present treatment.
We thus show how, using the Shannonian formalism, a unified, structurally constrained description of selection and evolution remains applicable across biological and non-biological domains, while explicitly delineating its scope and limits.