本征模型和Crow-Kimura模型的精确可解动力学
Exactly solvable dynamics of the Eigen and the Crow-Kimura models
摘要：
我们介绍了一种新的方法来研究分子进化内完善的汉密尔顿-雅可比形式主义，表明，对于广泛的一类适应度景观，它是可能的动力学解析内的$1/N$ -准确性，其中$N$是基因组长度。对于光滑单调的适应度函数，该方法给出了两个动力学阶段：光滑动力学和不连续动力学。后一阶段自然出现，没有显式的奇异适应度函数，这与直觉相反。Hamilton-Jacobi方法对于利用适应度作为来自参考基因组序列的汉明距离的函数的模型产生直接的分析结果。我们还展示了这种方法给多峰健身动态相结构的方式。
英文摘要：
We introduce a new way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the $1/N$-accuracy, where $N$ is genome length. For smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics, and discontinuous dynamics. The latter phase arises naturally with no explicit singular fitness function, counter-intuitively. The Hamilton-Jacobi method yields straightforward analytical results for the models that utilize fitness as a function of Hamming distance from a reference genome sequence. We also show the way in which this method gives dynamical phase structure for multi-peak fitness.
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