Recombination Dramatically Speeds Up Evolution of Finite Populations

Abstract

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.

Adaptation in Simple and Complex Fitness Landscapes

“…In addition, the continuum limit of (75) should be carried out on the level of ln Y rather than for Y itself, which leads to a nonlinear drift-diffusion equation replacing (76) [27]. Recent applications of fitness space models that go beyond the present discussion include studies of the in vitro evolution of DNA sequences selected for protein binding [46], viral populations undergoing serial population transfers [91], and the effects of recombination in asexual populations [92].…”

Finite Genome Length Corrections for the Mean Fitness and Gene Probabilities in Evolution Models

“…In [25] we calculated the finite size correction for the recombination model with single-peak fitness. In the present paper we calculate the finite genome length corrections for a diploid model with symmetric * Electronic address: saakian@phys.sinica.edu.tw † Electronic address: hu@phys.sinica.edu.tw landscape [23] as well as for a haploid model with a simple horizontal gene transfer (HGT) [16,20] for a general symmetric fitness landscape. The method may be applied to rather general cases of nonlinear probabilistic models [29].…”

“…The infinite genome length limit has been solved fora more complicated (more nonlinear) evolution model: the horizontal gene transfer model [16,20,23,25]. This model has been solved both for the haploid [16,20], and the hyper-geometric diploid case [7][8][9]23].…”

“…Analytic solutions for models with the infinite genome length may be obtained via several methods, including the maximum principle [12,13], Trotter-Suzuki method in quantum statistical physics [14,15,17,18], quantum field theory [15,18,19] and the Hamiltonian-Jacobi equation method [21][22][23]25]. The infinite genome length limit has been solved fora more complicated (more nonlinear) evolution model: the horizontal gene transfer model [16,20,23,25]. This model has been solved both for the haploid [16,20], and the hyper-geometric diploid case [7][8][9]23].…”

“…After the development of molecular biology, the concepts and methods in statistical physics have been widely used to study molecular models of biological evolution [1][2][3][4][5][6][7][8][9][10][11][12][13], especially in recent years [14][15][16][17][18][19][20][22][23][24][25]. Analytic solutions for models with the infinite genome length may be obtained via several methods, including the maximum principle [12,13], Trotter-Suzuki method in quantum statistical physics [14,15,17,18], quantum field theory [15,18,19] and the Hamiltonian-Jacobi equation method [21][22][23]25].…”