Drake's rule as a consequence of approaching channel capacity

Abstract

How mutations accumulate in genomes is the central question of molecular evolution theories. However, our understanding of this process is far from complete. Drake's rule is a notoriously universal property of genomes from microbes to mammals-the number of (functional) mutations per-genome per-generation is approximately constant within a phylum, despite the orders of magnitude differences in genome sizes and diverse populations' properties. So far, there is no concise explanation for this phenomenon. A formal model for the storage of genetic information suggests that a genome of any species operates near its maximum informational storage capacity, and the mutation rate per-genome per-generation is near its upper limit, providing a simple explanation for the rule with minimal assumptions.

Fig. 1

Convergence of GI _ρ for different parameters. Common parameters for all demonstrated cases are: N = 1,000; n _d = 2; P _ti = 2/3; W = (W _j = (0.8, 0.2, 0, 0) if j is even, else W _j = (0.5, 0.3, 0.1, 0.1)). Color determines organism length (L): green corresponds to L = 100, blue to L = 200, and red to L = 400. Line style determines probability of mutation per base (P _m): solid corresponds to P _m = 0.01 and dashed corresponds to P _m = 0.04

Fig. 2

Fluctuation of positional nucleotide frequencies during GI-steady state for different selection weights (W) and population sizes (N). Common fixed parameters are P _m = 2⁻⁶, P _ti = 2/3, L = 128, n _d = 2. In all three subfigures (a, b, c), the line style defines population size: the dash and dot lines correspond to N = 10,000; the solid line to N = 100. a Fluctuations of nucleotide frequencies in a position (P) with selection weights W _P = (0.4, 0.38, 0.12, 0.1). b Fluctuations of nucleotide frequencies in a position (P) with selection weights W _P = (0.5, 0.3, 0.1, 0.1). c Dynamics of GI _steady

Fig. 3

Relationship between the mutation rate per site per-generation (u _b) and the genome size (L) observed in the simulation. Color determines density of genetic information in the steady state (GI _steady): red corresponds to GI _steady = 1.2 bit/site, blue to GI _steady = 1.4 bit/site, and green to GI _steady = 1.6 bit/site. The shape of the marker determines selection weights (W): the pentagon corresponds to W _pentagon = (W _j = (0.8, 0.2, 0, 0) if j is even, else W _j = (0.5, 0.3, 0.1, 0.1)), the triangle corresponds to W _triangle = (W _j = (0.9, 0.1, 0, 0) if j is even, else W _j = (0.4, 0.3, 0.2, 0.1)). Lines represent linear regression on a log-log scale. Dark red/blue/green lines correspond to light red/blue/green markers; dash and dot lines correspond to pentagons, dashed lines correspond to triangles. Regression lines and corresponding correlation coefficients (r2): GI _steady = 1.2, W _pentagon (red dash and dot line): log₂ u _b = − 0.68 − 0.98 log₂ L, (r2 = 0.99). GI _steady = 1.2, W _triangle (red dashed line): log₂ u _b = − 1.02 − 0.97 log₂ L, (r2 = 0.99). GI _steady = 1.4, W _pentagon (blue dash and dot line): log₂ u _b = − 1.29 − 0.98 log₂ L, (r2 = 0.99). GI _steady = 1.4, W _triangle (blue dashed line): log₂ u _b = − 1.52 − 0.97 log₂ L, (r2 = 0.99). GI _steady = 1.6, W _pentagon (green dash and dot line): log₂ u _b = − 2.31 − 0.93 log₂ L, (r2 = 0.99). GI _steady = 1.6, W _triangle (green dashed line): log₂ u _b = − 2.23 − 0.96 log₂ L, (r2 = 0.99)

Fig. 4

Dependence of total genetic information (GI _total) and density of genetic information (GI _ρ) on the length of genome (L) when the rate of mutations (P _m) is fixed. Each point represents a population with organisms having genome of size L∈[100, 120, …, 1080, 1100]. For convenience of orientation, some points are colored in red and genome size of corresponding population is labeled. Mutation rate (P _m) was fixed to 0.007. Also, all other parameters were identical for all populations, namely N = 1,000; n _d = 2; P _ti = 2/3; W = (W _j = (0.8, 0.2, 0, 0) if j is even, else W _j = (0.5, 0.3, 0.1, 0.1))