Modelling bacterial speciation

Abstract

A central problem in understanding bacterial speciation is how clusters of closely related strains emerge and persist in the face of recombination. We use a neutral Fisher-Wright model in which genotypes, defined by the alleles at 140 house-keeping loci, change in each generation by mutation or recombination, and examine conditions in which an initially uniform population gives rise to resolved clusters. Where recombination occurs at equal frequency between all members of the population, we observe a transition between clonal structure and sexual structure as the rate of recombination increases. In the clonal situation, clearly resolved clusters are regularly formed, break up or go extinct. In the sexual situation, the formation of distinct clusters is prevented by the cohesive force of recombination. Where the rate of recombination is a declining log-linear function of the genetic distance between the donor and recipient strain, distinct clusters emerge even with high rates of recombination. These clusters arise in the absence of selection, and have many of the properties of species, with high recombination rates and thus sexual cohesion within clusters and low rates between clusters. Distance-scaled recombination can thus lead to a population splitting into distinct genotypic clusters, a process that mimics sympatric speciation. However, empirical estimates of the relationship between sequence divergence and recombination rate indicate that the decline in recombination is an insufficiently steep function of genetic distance to generate species in nature under neutral drift, and thus that other mechanisms should be invoked to explain speciation in the presence of recombination.

Figure 1

Genetic cartography of samples taken during the evolution of a population in the absence of recombination. Samples of 1000 were drawn at intervals from an evolving population of 10⁶ bacteria with θ=2. The relationships between these strains were measured by the pairwise allelic mismatches at 140 loci and were displayed by MDS. The number of generations of the simulation is shown in the top left of each panel. All strains are initially identical.

Figure 2

Genetic cartography of samples taken during the evolution of a population with a low rate of recombination. Details are as in figure 1, except that recombination occurs with the same frequency as mutation (θ=2, ρ=2).

Figure 3

Genetic cartography of samples taken during the evolution of a population with high rates of recombination. Details are as in previous figures, except θ=2 and ρ=20.

Figure 4

Evolution of a population with distance-scaled recombination. (a) The declining rate of recombination with increasing genetic (allelic) distance between strains is shown by the solid line. The dashed line shows the situation in figures 2 and 3, in which recombination is equally probable between all strains. Allelic distance is the number of the 140 loci that differ between the donor and recipient strain. (b) Genetic cartography of samples taken during the evolution of a population with distance-scaled recombination. θ=2 and ρ=50 for recombination between identical strains and ρ declines as a log-linear function of the genetic distance between strains, as described in the text.

Figure 5

Dynamics of major cluster formation, divergence and extinction. Pairwise allelic distance is shown on the x-axis and time (in model generations) on the y-axis. The proportion of the population within each area of the figure is shown by shading according to the scale shown. Clusters of similar strains are visible as shaded areas close to the y-axis and their diversification is represented by an increase in genetic (allelic) distance with time. The composition of the population at any generation of the model can be seen by drawing a horizontal line at that position. (a) Representation of the population sampled in figure 1. Numerous small clusters emerge and become extinct. (b) The population sampled in figure 3. A single large cluster persists and becomes more divergent over the timespan studied. (c) The population sampled in figure 4b, in which there is distance-scaled recombination and multiple clusters arise.