The effect of bacterial recombination on adaptation on fitness landscapes with limited peak accessibility

Abstract

There is ample empirical evidence revealing that fitness landscapes are often complex: the fitness effect of a newly arisen mutation can depend strongly on the allelic state at other loci. However, little is known about the effects of recombination on adaptation on such fitness landscapes. Here, we investigate how recombination influences the rate of adaptation on a special type of complex fitness landscapes. On these landscapes, the mutational trajectories from the least to the most fit genotype are interrupted by genotypes with low relative fitness. We study the dynamics of adapting populations on landscapes with different compositions and numbers of low fitness genotypes, with and without recombination. Our results of the deterministic model (assuming an infinite population size) show that recombination generally decelerates adaptation on these landscapes. However, in finite populations, this deceleration is outweighed by the accelerating Fisher-Muller effect under certain conditions. We conclude that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.

Figure 1. (A) A landscape with no LFG and (B) an example of a fitness landscape with 7 LFGs in the four-locus case.

Darker colors correspond to lower relative finesses. Arrows show point mutation steps directed toward fitter genotypes.

Figure 2. Dynamics in the two-locus model.

Panel A shows four two-locus fitness landscapes with no LFG, one LFG (strong sign epistasis) and two LFGs (strong reciprocal sign epistasis). In B, the frequency of the fittest genotype is shown for the three types of fitness landscapes (green: no LFG, blue: one LFG, red: two LFGs), without recombination (solid lines) and with recombination (dashed lines). Plot C shows the corresponding LD dynamics of the three fitness landscapes without recombination. Parameters take the values .

Figure 3. Effect of the number of LFGs in fitness landscapes on the relative rate of adaptation with recombination, T_fix.

A) no baseline epistasis (), B) positive baseline epistasis (), C) negative baseline epistasis (). Each box shows the distribution of T_fix across all fitness landscapes with the respective number of LFGs. The boxes give the interquartile range. Outliers are represented with the points in more than 1.5 times the interquartile range from the end of the boxes. The whiskers are extended to the farthest points from the end of the boxes that are not outliers. The black line connects the median of the boxes. The red dashed lines show T_fix on the landscape with no LFG with the corresponding baseline epistasis. In the absence of baseline epistasis and LFGs in the fitness landscape, recombination has no effect on the rate of adaptation (T_fix , orange dashed lines). Parameters take the values .

Figure 4. Effect of different parameters on T _fix on all possible four-locus fitness topographies with up to 10 LFGs.

In all plots, the standard parameter set was used and one parameter was varied. Solid lines shows independently ranked T _fix values for all fitness topographies. For comparison, the dashed lines show T _fix in the corresponding fitness landscape with no LFG. A) Effect of recombination rate. Red, green, orange and brown curves correspond to r values of 0.1, 0.075, 0.05 and 0.01, respectively. B) Effect of baseline epistasis. Green, orange and red curves correspond to values of 0.95, 1.0 and 1.05, respectively. C) Effect of mutation rate. Red, orange and green curves correspond to values of 10⁻⁶, 10⁻⁵ and 10⁻⁴, respectively. D) Effect of selection coefficient. Orange, red and green curves correspond to values of 0.050, 0.075 and 0.1, respectively. Note the different scales of the y-axes in plots A to D.

Figure 5. Robustness of the relative rate of adaptation T_fix with regard to the parameters of the model: A) recombination rate, B) baseline epistasis, C) mutation rate and D) selection coefficient.

Each point in the above plots represents one fitness topography and its position is given by T_fix with two different parameter values. Other parameters take the same values as in Figure 4.

Figure 6. Scatter plot of estimated physiological epistasis against T_fix for all fitness landscapes with 6 LFGs.

Each point corresponds to one landscape. Parameters take values . See main text for a description of how we measured physiological epistasis on these fitness landscapes.

Figure 7. Effect of recombination on the rate of adaptation in finite populations.

We screened a total of 150 randomly sampled fitness topographies with 3, 5 and 7 LFGs. T_fix was determined for three different population sizes: (red), (blue) and (green). All T_fix values are sorted according to their recombination effect in the deterministic model (brown). Parameters take standard values (see also Figures 4 and 5), and in plots B to D we varies one of the parameters: A) Standard parameter set, B) , C) and D) .