一般时间变化环境中的适应
Adaptation in general temporally changing environments
摘要：
我们分析了一个非局部偏微分方程模型描述的动态适应的表型结构的人口，突变和选择的影响下，在不断变化的环境。以前的研究已经分析了这种模型的大时间行为，具有特定形式的环境变化，线性变化或周期性波动。我们在这里使用一个完全不同的数学方法，它使我们能够考虑非常普遍的形式的环境变化，并给出一个完整的适应轨迹，包括瞬态阶段，在达到一个稳定的行为分析描述。我们的方法背后的主要思想是研究一个二元分布的两个“健身组件”，其中包含足够的信息来描述在任何时候的健身分布。这种分布解决了退化抛物方程，通过定义与分布相关的多维累积量生成函数，并求解相关的输运方程来处理。我们将我们的结果应用到几个例子中，并检查其准确性，使用随机个人为基础的模拟作为基准。这些例子说明了能够描述适应的瞬态动力学以了解病原体耐药性发展的重要性。
英文摘要：
We analyze a nonlocal PDE model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior of such models, with particular forms of environmental changes, either linearly changing or periodically fluctuating. We use here a completely different mathematical approach, which allows us to consider very general forms of environmental variations and to give an analytic description of the full trajectories of adaptation, including the transient phase, before a stationary behavior is reached. The main idea behind our approach is to study a bivariate distribution of two `fitness components' which contains enough information to describe the distribution of fitness at any time. This distribution solves a degenerate parabolic equation that is dealt with by defining a multidimensional cumulant generating function associated with the distribution, and solving the associated transport equation. We apply our results to several examples, and check their accuracy, using stochastic individual-based simulations as a benchmark. These examples illustrate the importance of being able to describe the transient dynamics of adaptation to understand the development of drug resistance in pathogens.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
