Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit density-dependent dispersal. Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion coefficient akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which phage is trapped inside the host unable to disperse. Additional stochastic agent-based simulations reveal that lysis time dramatically affects the rate of diversity loss in viral expansions. Taken together, our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.

中文翻译：

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病毒与宿主的相互作用会影响病毒的扩散，从而在空间扩展中产生不同类别的行波

长期以来，反应扩散波一直用于描述经历空间范围扩展的种群的增长和扩散。此类波通常被分类为拉动波或推动波，其中波动由前部的最前端驱动，随机波动较大，而推动波在增长或分散方面的协同作用会导致整体波动，从而抑制了波动。这些概念已经在人群合作导致密度依赖的增长率的实验中得到了很好的研究。相比之下，关于表现出密度依赖性分散的实验种群的知之甚少。使用噬菌体T7作为测试生物，我们提出了新颖的实验测量方法，这些实验表明噬菌体T7在宿主大肠杆菌的草坪中扩散，与宿主细菌细胞的空间相互作用会阻碍这种作用。病毒感染引起的宿主密度，噬菌体扩散和细胞裂解之间的耦合导致类似于协同行为的有效的依赖于密度的扩散系数。使用反应扩散方程组，我们证明了这种效应会导致从拉动到推挤的过渡。此外，我们发现，由于病毒潜伏期，噬菌体被困在无法分散的宿主体内，第二个独立的，依赖于密度的效应自发地出现在噬菌体的扩散上。其他基于随机代理的模拟表明，裂解时间会极大地影响病毒扩增中多样性丧失的速度。在一起