Data from: A mathematical model of marine bacteriophage evolution

To explore how particularities of a cell-virus system affects viral evolution, we formulate a mathematical model of marine bacteriophage evolution. The intrinsic simplicity of real-life phage-bacteria systems allows to have a reasonably simple model. The model constructed in this paper is based upon Beretta-Kuang model of bacteria-phage interaction. Compared to the Beretta-Kuang model, the model assumes the existence of a multitude of viral variants which correspond to continuously distributed phenotypes. It is noteworthy that this model does not include any explicit law or mechanism of evolution; instead it is assumed, in agreement to the principles of Darwinian evolution, that evolution in this system can occur as a result of random mutations and natural selection. Simulations with a leaner fitness landscape (which is chosen for the convenience of demonstration only) show that a pulse-type traveling wave moving towards increasing Darwinian fitness appears in the phenotype space. This implies that the overall fitness of a viral quasispecies steadily increasing in time. That is, the simulations demonstrate that for an uneven fitness landscape random mutations combined with a mechanism of natural selection lead to the Darwinian evolution. It is noteworthy that in this system the speed of propagation of this wave (and hence the rate of evolution) is not constant but varies, depending on the current viral fitness and the abundance of susceptible bacteria.

为探究细胞-病毒系统（cell-virus system）的特有属性如何影响病毒演化进程，我们构建了一套海洋噬菌体（bacteriophage）演化的数学模型。真实噬菌体-细菌系统固有的简洁性，使得我们能够构建一个复杂度适中的简化模型。本文所构建的模型基于细菌-噬菌体互作的Beretta-Kuang模型（Beretta-Kuang Model）。相较于原始Beretta-Kuang模型，本模型假设存在大量病毒变体，这些变体对应着连续分布的表型。值得注意的是，本模型并未纳入任何明确的演化规律或演化机制；相反，其遵循达尔文进化论的核心原则，假设该系统内的演化可通过随机突变与自然选择得以实现。针对简化型适应度景观（fitness landscape，仅为演示方便而选取）开展的模拟实验显示，表型空间中会出现一类朝着达尔文适应度不断提升方向传播的脉冲型行波。这意味着病毒准种（viral quasispecies）的整体适应度会随时间稳步提升。换言之，模拟实验证明，在非均匀适应度景观下，随机突变与自然选择机制共同作用可驱动达尔文式演化。值得注意的是，该系统中此类行波的传播速度（即演化速率）并非恒定，而是会随当前病毒适应度与易感细菌的丰度发生动态变化。