Accumulation and maintenance of information in evolution

Abstract

Selection accumulates information in the genome—it guides stochastically evolving populations toward states (genotype frequencies) that would be unlikely under neutrality. This can be quantified as the Kullback–Leibler (KL) divergence between the actual distribution of genotype frequencies and the corresponding neutral distribution. First, we show that this population-level information sets an upper bound on the information at the level of genotype and phenotype, limiting how precisely they can be specified by selection. Next, we study how the accumulation and maintenance of information is limited by the cost of selection, measured as the genetic load or the relative fitness variance, both of which we connect to the control-theoretic KL cost of control. The information accumulation rate is upper bounded by the population size times the cost of selection. This bound is very general, and applies across models (Wright–Fisher, Moran, diffusion) and to arbitrary forms of selection, mutation, and recombination. Finally, the cost of maintaining information depends on how it is encoded: Specifying a single allele out of two is expensive, but one bit encoded among many weakly specified loci (as in a polygenic trait) is cheap.

Substitution load revisited: a high proportion of deaths can be selective

“…Kimura calculates the amount of information acquired per sweep in terms of 𝑝 O and then relates this to the cost of selection using Haldane’s equation that 𝐷 = - ln ( 𝑝 O ) (Kimura 1961). More recent approaches treat the bounds placed on the accumulation of information in much more detail, while treating either the Malthusian parameter (McGee et al 2022) or classic discrete time relative fitness (Hledík, Barton, and Tkačik 2022). Both these approaches define an information “cost”, but this is not equal to our cost in terms of selective deaths.…”

Rules, hypergraphs, and probabilities: the three-level analysis of chemical reaction systems and other stochastic stoichiometric population processes

“…Our proposal to use the LDF for currents as a cost measure to tie physiological events to selective events is driven by two considerations: First, relative entropies [122–124] and a variety of functions either derived from [125, 126] or related to [127] them are understood as measures of the both information and cost [31, 118, 120, 121, 124] through selection in population processes. Second, the events within physiology form a nested partition function with the population-level events of reproduction or death through which selection acts in the form of differential rates.…”

The Intransitive Logic of Directed Cycles and Flipons Enhances the Evolution of Molecular Computers by Augmenting the Kolmogorov Complexity of Genomes

“…The term j(i) is the probability that a sub-word is in an alternative DNA conformation, where 0 ≤ j(i) ≤ 1, and varies by context. Another possible approach to capturing the coding capacity of a genome is based on calculating the Kullback-Leibler divergence from a reference genome [36][37][38][39][40]. There is, however, no adjustment for the flipon-mediated effects on coding due to changes in isoform usage, transcript editing, and RNA modification.…”