Recombination-Driven Genome Evolution and Stability of Bacterial Species

Abstract

While bacteria divide clonally, horizontal gene transfer followed by homologous recombination is now recognized as an important contributor to their evolution. However, the details of how the competition between clonality and recombination shapes genome diversity remains poorly understood. Using a computational model, we find two principal regimes in bacterial evolution and identify two composite parameters that dictate the evolutionary fate of bacterial species. In the divergent regime, characterized by either a low recombination frequency or strict barriers to recombination, cohesion due to recombination is not sufficient to overcome the mutational drift. As a consequence, the divergence between pairs of genomes in the population steadily increases in the course of their evolution. The species lacks genetic coherence with sexually isolated clonal subpopulations continuously formed and dissolved. In contrast, in the metastable regime, characterized by a high recombination frequency combined with low barriers to recombination, genomes continuously recombine with the rest of the population. The population remains genetically cohesive and temporally stable. Notably, the transition between these two regimes can be affected by relatively small changes in evolutionary parameters. Using the Multi Locus Sequence Typing (MLST) data, we classify a number of bacterial species to be either the divergent or the metastable type. Generalizations of our framework to include selection, ecologically structured populations, and horizontal gene transfer of nonhomologous regions are discussed as well.

Keywords: bacterial evolution; population genetics; recombination.

Figure 1

Schematic of the computation models. (a) Illustration of the numerical model. $N_e$ bacterial organisms evolve together, we show only one pair of strains. Point mutations (red circles) occur at a fixed rate μ per base pair generation and genetic fragments of length $l_{\text{tr}}$ are transferred between organisms at a rate ρ per base pair per generation. (b) The schematics of the three models of recombination. In model (1), recombining stretches have fixed end points. As a result, different recombination tracks do not overlap. In models (2) and (3), the recombining stretches have variable end points and as a result different recombination tracks can potentially overlap with each other.

Figure 2

Three possible outcomes of gene transfer that change the divergence δ. $XD,$ $YD,$ $XY,$ and $XYD$ are the most recent common ancestors of the strains. The divergence ${\delta }_b$ before transfer and ${\delta }_a$ after transfer are shown in red and blue, respectively.

Figure 3

Stochastic evolution of local divergence. A typical evolutionary trajectory of the local divergence $\delta \left(t\right)$ within a single gene between a pair of strains. We have used $\mu ={10}^{-5},$ $\rho =5\times {10}^{-6}$ per base pair per generation, $\theta =1.5\%$, and ${\delta }_{\text{TE}}=1\%\text{.}$ Red tracks indicate the divergence increasing linearly, at a rate $2\mu$ per base pair generation, with time due to mutational drift. Green tracks indicate recombination events that suddenly increase the divergence and blue tracks indicate recombination events that suddenly decrease the divergence. Eventually, the divergence increases sufficiently and the local genomic region escapes the pull of recombination (red stretch at the right).

Figure 4

Stochastic evolution of genome-wide divergence. Genome-wide divergence $\text{Δ}\left(t\right)$ as a function of time at $\theta /{\delta }_{\text{TE}}=\mathrm{0.25.}$ We have used ${\delta }_{\text{TE}}=1\%\text{,}$ $\theta =0.25\%,$ $\mu =2\times {10}^{-6}$ per base pair per generation and $\rho =2\times {10}^{-8},2\times {10}^{-7},{10}^{-5},$ and $2\times {10}^{-5}$ per base pair per generation corresponding to ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}=2,0.2,0.04$, and $2\times {10}^{-3}$, respectively. The dashed black lines represent the ensemble average $\langle \text{Δ}\left(t\right)\rangle .$ See Figure A1 in the Appendix for the evolution of $\text{Δ}\left(t\right)$ over a longer timescale.

Figure 5

Quantifying metastability in genome evolution. The number of generations $t_{\text{div}}$ (in units of the population size $N_e$) required for a pair of genomes to diverge well beyond the average intrapopulation diversity (see main text). We calculate the time it takes for the ensemble average $\langle \Delta \left(t\right)\rangle$ of the genome-wide average divergence to reach $2\theta$ as a function of $\theta /{\delta }_{\text{TE}}$ and ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}.$ We used ${\delta }_{\text{TE}}=1\%\text{,}$ $\mu =2\times {10}^{-6}$ per base pair generation. In our simulations, we varied ρ and θ to scan the $\left(\theta /{\delta }_{\text{TE}},{\delta }_{\text{mut}}/{\delta }_{\text{TE}}\right)$ space. The green diamonds represent four populations shown in Figure 4 and Figure 6 (see below).

Figure 6

Distribution of genome-wide divergences in a population. Distribution of all pairwise genome-wide divergences ${\delta }_{ij}$ in a coevolving population for decreasing values of ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}:$ 2 in (a), 0.2 in (b), 0.04 in (c), and 0.002 in (d) In all four panels, dashed black lines represent time-averaged distributions $\overline{\pi \left(\Delta \right)},$ while solid lines represent typical snapshot distributions $\pi \left(\Delta \right)$ in a single population. Colors of solid lines match those in Figure 4 for the same values of parameters. Time-averaged and snapshot distributions were estimated by sampling $5\times {10}^5$ pairwise coalescent times from the time-averaged coalescent distribution $p\sim e^{-t/N_e}$ and the instantaneous coalescent distribution $p_{\text{c}}\left(t\right)$ correspondingly (see text for details).

Figure 7

Comparison of different models of recombination. (a) The ensemble average $\langle \Delta \left(t\right)\rangle$ of pairwise genome-wide divergence $\Delta \left(t\right)$ as a function of the pairwise coalescent time t in explicit simulations. Model (1) simulations have nonoverlapping transfers of segments of length is 5000 bp. Model (2) simulations have transfers of overlapping 5000-bp segments. Model (3) simulations have overlapping transfer of segments of average length 5000 bp. The value of ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}$ are on the right side. (b) The ensemble average distribution of genome-wide divergence between pairs of strains $\overline{\pi }\left(\Delta \right)$ for the three models of recombination shown in Figure 1a when ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}=\mathrm{0.002.}$

Figure 8

Classifying real bacteria as metastable or divergent. Approximate position of several real-life bacterial spaces on the metastable-divergent phase diagram (see text for details). Abbreviations of species names are as follows: BC, Bacillus cereus; EC, Escherichia coli; EF, Enterococcus faecium; FP, Flavobacterium psychrophilum; HI, Haemophilus influenzae; HP1, Helicobacter pylori; HP2, Haemophilus parasuis; SE, Salmonella enterica; SP1, Streptococcus pneumoniae; SP2, Streptococcus pyogenes; VP, Vibrio parahaemolyticus; VV, Vibrio vulnificus.

Figure A1

Genome-wide divergence $\Delta \left(t\right)$ as a function of time at $\theta /{\delta }_{\text{TE}}=\mathrm{0.25.}$ We have used ${\delta }_{\text{TE}}=1\%\text{,}$ $\theta =0.25\%,$ $\mu =2\times {10}^{-6}$ per base pair per generation and $\rho =2\times {10}^{-8},2\times {10}^{-7},{10}^{-5},$ and $2\times {10}^{-5}$ per base pair per generation corresponding to ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}=2,0.2,0.04$, and $2\times {10}^{-3}$ respectively. The dashed black lines represent the ensemble average $\langle \Delta \left(t\right)\rangle .$ The cyan lines show the time it takes for the ensemble-averaged genomic divergence $\langle \Delta \left(t\right)\rangle$ to reach $2\theta$ when ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}=0.04$ (pink line).

Figure A2

The number of generations $t_{\text{div}}$ (in units of the population size $N_e$) required for a pair of genomes to diverge well beyond the average intrapopulation diversity. We calculate the time it takes for the ensemble average of the genome-wide average divergence to reach $2\theta$ as a function of $\theta /{\delta }_{\text{TE}}$ and ${\delta }_{\text{mut}}/{\delta }_{\text{TE}}.$ We randomly sample θ (between 0.5 and 3%), ${\delta }_{\text{TE}}$ (between 0.5 and 5%), and ρ (between $2\times {10}^{-7}$ and $2\times {10}^{-5}$ per base pair per generation) while keeping the mutation rate constant at $\mu =2\times {10}^{-5}$ per base pair generation.