Muñoz Enrique, Park Jeong-Man, Deem Michael W
Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061921. doi: 10.1103/PhysRevE.78.061921. Epub 2008 Dec 23.
We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic recombination on the steady-state mean fitness and distribution of individuals in the population, through an analytic field theoretic mapping. We investigate both horizontal gene transfer from a population and recombination between pairs of individuals. Somewhat surprisingly, these nonlinear generalizations of quasispecies theory to modern biology are analytically solvable. For two-parent recombination, we find two selected phases, one of which is spectrally rigid. We present exact analytical formulas for the equilibrium mean fitness of the population, in terms of a maximum principle, which are generally applicable to any permutation invariant replication rate function. For smooth fitness landscapes, we show that when positive epistatic interactions are present, recombination or horizontal gene transfer introduces a mild load against selection. Conversely, if the fitness landscape exhibits negative epistasis, horizontal gene transfer or recombination introduces an advantage by enhancing selection towards the fittest genotypes. These results prove that the mutational deterministic hypothesis holds for quasispecies models. For the discontinuous single sharp peak fitness landscape, we show that horizontal gene transfer has no effect on the fitness, while recombination decreases the fitness, for both the parallel and the Eigen models. We present numerical and analytical results as well as phase diagrams for the different cases.
我们引入了分子进化的并行模型（即克劳 - 木村模型）和艾根模型的一种推广形式，以表示种群中个体间遗传信息的交换。我们通过解析场论映射，研究了不同遗传重组方案对种群稳态平均适应度和个体分布的影响。我们既研究了从一个种群的水平基因转移，也研究了个体对之间的重组。有点令人惊讶的是，这些准物种理论对现代生物学的非线性推广在解析上是可解的。对于双亲重组，我们发现了两个选择阶段，其中一个是谱刚性的。我们根据一个最大值原理，给出了种群平衡平均适应度的精确解析公式，该公式通常适用于任何置换不变的复制率函数。对于平滑的适应度景观，我们表明当存在正上位性相互作用时，重组或水平基因转移会引入轻微的选择负荷。相反，如果适应度景观表现出负上位性，水平基因转移或重组通过增强对最适应基因型的选择而带来优势。这些结果证明了突变确定性假设对准物种模型成立。对于不连续的单尖峰适应度景观，我们表明对于并行模型和艾根模型，水平基因转移对适应度没有影响，而重组会降低适应度。我们给出了不同情况的数值和解析结果以及相图。
