Weakly deleterious mutations and low rates of recombination limit the impact of natural selection on bacterial genomes

Abstract

Free-living bacteria are usually thought to have high effective population sizes, so that tiny selective differences can drive their evolution. However, because recombination is infrequent, "background selection" against slightly-deleterious alleles should reduce the effective population size (N_e) by orders of magnitude. For example, for a well-mixed population with 10¹² individuals and a typical level of homologous recombination (r/m=3, or nucleotides change due to recombination at three times the mutation rate), we predict that N_e < 10⁷. An argument for high N_e in bacteria has been the high genetic diversity within many bacterial "species," but this diversity may be due to population structure: diversity across subpopulations can be far higher than diversity within a subpopulation, which makes it difficult to estimate N_e correctly. Given an estimate of N_e, standard population genetics models imply that selection should be sufficient to drive evolution if N_e * s > 1, where s is the selection coefficient. We show that this remains approximately correct if background selection is occuring or when population structure is present. Overall, we predict that even for free-living bacteria with enormous populations, natural selection is only a significant force if s is above 10^-7 or so.

Downloads

• R code -- both simulations and theoretical calculations
• Steps for reproducing simulations
  • Also see helper scripts RunR.R, BackselR.R, std_small.R, and sweeps.R
• R images from simulations of background selection with clonal evolution:
  • N = 10⁶ to 10⁹, 10⁶ sites with weakly-deleterious alleles (s_back = 0.001), reversible mutation rate of 2*10^-7, and a neutral focal site
    • bigbackD: N = 10⁶ to 10⁹
  • Similarly with N = 10⁷ and a range of selection coefficients at the focal site
    • big3A: s_focal = 0
    • big3B: s_focal = 0.0003
    • big3C: s_focal = 0.001
    • big3D: s_focal = 0.003
• R images from detailed small simulations of background selection with local recombination (5,000 individuals, 1,000 sites, s_back = 0.02, U = 0.4)
  • noR: R=0
  • hi1: R=0.4,rSites=1
  • hi10: R=0.4,rSites=10
  • hi50: R=0.4,rSites=50
  • lo1: R=0.1,rSites=1
  • lo10: R=0.1,rSites=10
  • lo50: R=0.1,rSites=50
  • lo500: R=0.1,rSites=500
• R images from fast approximate simulations of background selection with local recombination:
  • Matching the small simulations above (R=0.1 or 0.4, 1 to 500 sites):
  • fast.noR R=0
  • fast.lo1 R=0.1,rSize=1,rVar=0.0485
  • fast.lo10 R=0.1,rSize=10,rVar=0.487
  • fast.lo50 R=0.1,rSize=50,rVar=2.280
  • fast.lo500 R=0.1,rSize=500,rVar=19.8
  • fast.hi1 R=0.4,rSize=1,rVar=0.0492
  • fast.hi10 R=0.4,rSize=10,rVar=0.469
  • fast.hi50 R=0.4,rSize=50,rVar=1.955
  • Large simulations (10⁷ individuals, 10⁶ sites, s_back = 0.001, μ=2*10^-7, 300 sites exchanged, V_r ≤ 9). (For N=1e8 and N=1e9 with R < 0.9, these are tab-delimited files, not images.)
    • c6A: N = 1e6, R = 0
    • c6B: N = 1e6, R = 0.001
    • c6C_c: N = 1e6, R = 0.003
    • c6D_b: N = 1e6, R = 0.01
    • c6E: N = 1e6, R = 0.03
    • c6F: N = 1e6, R = 0.1
    • c6G: N = 1e6, R = 0.3
    • w6H: N = 1e6, R = 0.9
    • c7A_a: N = 1e7, R = 0
    • c7B_c: N = 1e7, R = 0.001
    • c7C: N = 1e7, R = 0.003
    • c7D_f: N = 1e7, R = 0.01
    • c7E: N = 1e7, R = 0.03
    • c7F: N = 1e7, R = 0.1
    • c7G: N = 1e7, R = 0.3
    • w7H: N = 1e7, R = 0.9
    • b8A: N = 1e8, R = 0
    • b8B: N = 1e8, R = 0.001
    • b8C: N = 1e8, R = 0.003
    • b8D: N = 1e8, R = 0.01
    • b8E: N = 1e8, R = 0.03
    • b8F: N = 1e8, R = 0.1
    • b8G: N = 1e8, R = 0.3
    • w8H: N = 1e8, R = 0.9
    • b9A: N = 1e9, R = 0
    • b9B: N = 1e9, R = 0.001
    • b9C: N = 1e9, R = 0.003
    • b9D: N = 1e9, R = 0.01
    • b9E: N = 1e9, R = 0.03
    • b9F: N = 1e9, R = 0.1
    • b9G: N = 1e9, R = 0.3
    • w9H: N = 1e9, R = 0.9
• R images from simulations of population structure:
  • 100 subpopulations of 100 individuals each, a reversible mutation rate of 10^-6, and varying migration rates
  • sims5: s = 0 or s = -5/nTot
  • sims6: s = -50/nTot
  • sims7: biased mutation (3x faster towards unfavorable allele), s = 0 or s = -5/nTot
  • sims8: intermediate selection (s = -20/nTot or -10/nTot) with 0.01 or 0.1 migrants per generation
• R images from "rescaled" simulations with no subpopulation structure and reduced N_e:
  • sims5_scaled: s = -5/nTot, rescaled
  • sims6_scaled: s = -50/nTot, rescaled