Accumulation and maintenance of information in evolution

Selection accumulates information in the genome — it guides stochastically evolving populations towards states (geno-type 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.