使用包括误差估计的多尺度框架模拟物种形成过程
Modeling the process of speciation using a multi-scale framework including error estimates
摘要：
本文主要研究了生物物种形成过程的模型化和数值模拟。特别是，给定的条件下，一个或多个物种形成的生态系统内发生的事件，我们的目标是开发必要的建模和仿真工具。我们还注意建立一个坚实的数学基础，我们的建模框架是建立在。这是本文前半部分的主题。第二部分致力于发展一个多尺度的生态进化模型框架，其中相关的尺度分别是物种和个体/种群。因此，相互作用物种的系统可以在物种水平上描述，而对于分支物种，则需要种群水平的描述。因此，我们的多尺度框架包括耦合物种和种群水平模型，其中预先检测物种形成事件，然后在种群规模上求解，直到分支完成。此外，由于人口水平模型制定为PDE，我们首先建立在时间离散设置的适定性，然后推导出后验误差估计，提供了一个完全可计算的能量型误差的上限，包括一般的光滑分布的情况下（这将是有用的物种形成事件的检测）。几个数值测试验证我们的框架在实践中。
英文摘要：
This paper concerns the modeling and numerical simulation of the process of speciation. In particular, given conditions for which one or more speciation events within an ecosystem occur, our aim is to develop the necessary modeling and simulation tools. Care is also taken to establish a solid mathematical foundation on which our modeling framework is built. This is the subject of the first half of the paper. The second half is devoted to developing a multi-scale framework for eco-evolutionary modeling, where the relevant scales are that of species and individual/population, respectively. Hence, a system of interacting species can be described at the species level, while for branching species a population level description is necessary. Our multi-scale framework thus consists of coupling the species and population level models where speciation events are detected in advance and then resolved at the population scale until the branching is complete. Moreover, since the population level model is formulated as a PDE, we first establish the well-posedness in the time-discrete setting, and then derive the a posteriori error estimates which provides a fully computable upper bound on an energy-type error, including also for the case of general smooth distributions (which will be useful for the detection of speciation events). Several numerical tests validate our framework in practice.
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