Evolution of molecular error rates and the consequences for evolvability

Abstract

Making genes into gene products is subject to predictable errors, each with a phenotypic effect that depends on a normally cryptic sequence. Many cryptic sequences have strongly deleterious effects, for example when they cause protein misfolding. Strongly deleterious effects can be avoided globally by avoiding making errors (e.g., via proofreading machinery) or locally by ensuring that each error has a relatively benign effect. The local solution requires powerful selection acting on every cryptic site and so evolves only in large populations. Small populations with less effective selection evolve global solutions. Here we show that for a large range of realistic intermediate population sizes, the evolutionary dynamics are bistable and either solution may result. The local solution facilitates the genetic assimilation of cryptic genetic variation and therefore substantially increases evolvability.

Fig. 1.

Evolutionary dynamics of the read-through error rate ρ. (A) Coevolution of ρ and of the number of cryptic sequences that are deleterious, L_del. The optimal value of ρ as a function of L_del, calculated as the value maximizing Eq. 2 (Methods), is represented by a thick gray line, and ρ evolves toward this line when L_del is fixed. The equilibrium values of L_del as functions of log₁₀(ρ) are represented by thin lines, for population sizes N = 10³ and N = 10⁵. L_del evolves toward these lines when ρ is fixed. The values of ρ and L_del obtained by simulation are represented by solid crosses (centered on the mean, ±2 SD across replicate populations), each matching the intersection of the thick and one thin line. Movie S1 shows the simulated coevolutionary dynamics. (B) The evolved error rate ρ is low in small populations, high in large populations, and bistable for intermediate populations. Solid and open symbols (error bars ±2 SD; x values were slightly changed to avoid superposition) represent the results of simulations starting with (log₁₀(ρ), L_del) = (−5, 400) and (−2, 0), respectively. (C) The ranges of N at which ρ is low or bistable increase with the total number of loci, L_tot. Bistable outcomes were identified by comparing the results of simulations obtained with the same initial conditions as in B, using a t test with critical value 0.005. Parameter values: γ = 0.01, p_del = 0.4, p_−del = 0.1, δ = 10^−2.5, μ = 10⁻⁸, and L_tot = 500 (A and B).

Fig. 2.

The mean population trait value, x, changes faster after an environmental change with the high -ρ (log₁₀(ρ) = −1.71) than with the low-ρ attractor (log₁₀(ρ) = −2.96). (A) One simulation in which the population with the high-ρ attractor (dashed line) reaches the new optimum before the low-ρ attractor (solid line). A change in the optimal trait value, from −1.5 to 1.5, is simulated at t = 20,000. (B) The time before the population reaches a mean trait value near the optimum (1.4) after an environmental change (time to adaptation) increases with the number of loci coding for the trait, K. The time to adaptation is consistently lower for the high-ρ attractor when K > 5. The size of mutations decreases with K (see text), which explains that the time to fixation of advantageous mutants increases. Keeping the size of mutations independent of K leads to a decreasing time to adaptation with K (Fig. S7), but leads to the same K > 5 condition for high-ρ attractor advantage. The error bars represent the first and third quartiles in the distribution of the time to adaptation, calculated from 20 simulations for each set of parameter values. The two attractors are those shown in Fig. 1 A and B for N = 10⁵. Parameter values: N = 10⁵, σ_m = 0.5, a = 750; other values are the same as in Fig. 1 A and B.