Recombination Dramatically Speeds Up Evolution of Finite Populations

We study the role of recombination, in the form of bacterial transformation, in speeding up Darwinian evolution. This is done by adding a new process to a previously studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that, for a wide range of intermediate population sizes, recombination dramatically speeds up the rate of evolutionary advance.

Figure 1

Velocity (averaged over 200 samples) measured between $x=95$ and $x=105$ starting with an average fitness of 50. $L=200$, $\mu =0.1$. (a) $v$ measured as a function of population size, $N$, for various $f_s$. Error bars are shown for one value of $f_s$, and are typical of all the data. (b) $v$ measured as a function of $f_s$ for various $N$. As $N$ increases, the velocity saturates at an $f_s$-independent value.

Figure 2

The probability of making an up-and-down move due to recombination as a function of individual fitness when the average fitness of the population was 75. For this run, $N=1000$, $L=100$, $f_s=1$, $\mu =0.1$. The “naive” probabilities are those derived assuming equal distribution of alleles at every locus.

Figure 3

Velocity vs average fitness for simulations of the noncutoff MFE [Eq. (1)] for various $f_s$. Parameters are $\mu =0.1$, $L=1000$, initial fitness $x_0=500$. The curve for $f_s=\infty$ is taken from Eq. (3).

Figure 4

(a) Fitness as a function of time averaged over 50 runs, $N=1000$, compared to a numerical solution of the cutoff MFE with cutoff $P_c=1/5000$. $\mu =0.1$, $f_s=2$, $L=50$, $x_0=25$. (b) Cutoff for which $v$ is 90% of its maximal ($\mathrm{\text{cutoff}}=0$) value as a function of $f_s$ for $L=200$, 400. $\mu =0.001$. Velocity measured between $x=L/2\pm 5$, with initial $x=5$. Dotted line represent fits to Eq. (5).