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-宿​​主相互作用形成病毒传播，在空间扩展中产生不同类别的行波

反应扩散波长期以来一直被用来描述经历空间范围扩展的人口的增长和传播。这种波浪通常被归类为拉动，其中动力学由前沿的最尖端驱动并且随机波动很高，或者被推动，其中增长或分散的合作导致波动被抑制的体驱动波。这些概念已经在群体中进行了很好的实验研究，在这些群体中，合作导致了密度依赖的增长率。相比之下，对表现出密度依赖性扩散的实验种群知之甚少。使用噬菌体 T7 作为测试生物，我们提出了新的实验测量，证明噬菌体 T7 在宿主大肠杆菌的草坪中的扩散, 受到与宿主细菌细胞的空间相互作用的阻碍。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有效的密度依赖性扩散系数，类似于合作行为。使用反应扩散方程系统，我们表明这种效应可以导致从拉力膨胀到推力膨胀的转变。此外，我们发现由于病毒潜伏期，噬菌体扩散的第二个独立的密度依赖性效应自发地出现，在此期间，噬菌体被困在宿主体内，无法扩散。额外的基于随机代理的模拟表明，裂解时间显着影响病毒扩增的多样性损失率。综合起来，