标题： 在时间波动的空间结构集合种群中的固定与灭绝 显示英文标题

标题： Fixation and extinction in time-fluctuating spatially structured metapopulations

摘要： 细菌在易变的环境中和复杂的空间结构中进化。迁移、波动和环境变化因此对微生物种群的进化有着显著影响。我们考虑了一类以规则图（循环图）排列的空间显式元种群模型，在这些模型中，野生型细胞和突变型细胞在一个随时间波动的环境中竞争，其中各个小群体（亚种群）通过缓慢的细胞迁移相互连接。每个小群体的承载能力相同，并在与恶劣和温和环境条件相关的两个值之间无尽切换。当切换速率既不太慢也不太快时，动态特征表现为瓶颈效应，且种群容易出现波动或灭绝。我们分析了缓慢迁移、空间结构和波动如何影响完全图、环图和正方形晶格元种群中的固定和灭绝现象。当承载能力保持较大时，瓶颈效应较弱，可以忽略小群体的灭绝。因此，动态可以用粗粒度描述来捕捉，从而解析地获得固定概率和平均固定时间。这使我们能够表明，与静态环境不同的是，固定概率取决于迁移率。我们还表明，固定概率和平均固定时间可能表现出非单调依赖于切换速率的情况。当在恶劣条件下承载能力较小，瓶颈效应强烈时，元种群的进化由小群体灭绝与菌株竞争之间的耦合作用塑造。这导致了丰富的动态场景，从中我们确定了最佳条件，可以在不使元种群灭绝的情况下根除突变体。我们在理想化治疗背景下对这些发现进行了解释，并讨论了我们模型的可能推广。 显示英文摘要

摘要： Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations, and environmental variability therefore have a significant impact on the evolution of microbial populations. We consider a class of spatially explicit metapopulation models arranged as regular (circulation) graphs where wild-type and mutant cells compete in a time-fluctuating environment where demes (subpopulations) are connected by slow cell migration. The carrying capacity is the same at each deme and endlessly switches between two values associated with harsh and mild environmental conditions. When the rate of switching is neither too slow nor too fast, the dynamics is characterised by bottlenecks and the population is prone to fluctuations or extinction. We analyse how slow migration, spatial structure, and fluctuations affect the phenomena of fixation and extinction on clique, cycle, and square lattice metapopulations. When the carrying capacity remains large, bottlenecks are weak, and deme extinction can be ignored. The dynamics is thus captured by a coarse-grained description within which the probability and mean time of fixation are obtained analytically. This allows us to show that, in contrast to what happens in static environments, the fixation probability depends on the migration rate. We also show that the fixation probability and mean fixation time can exhibit a non-monotonic dependence on the switching rate. When the carrying capacity is small under harsh conditions, bottlenecks are strong, and the metapopulation evolution is shaped by the coupling of deme extinction and strain competition. This yields rich dynamical scenarios, among which we identify the best conditions to eradicate mutants without dooming the metapopulation to extinction. We offer an interpretation of these findings in the context of an idealised treatment and discuss possible generalisations of our models.