论文标题
生态学中的非本地机械模型：数值方法和参数推断
Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferencing
论文作者
论文摘要
动物使用各种过程来告知自己的环境，并就如何移动和构成自己的领土做出决定。在某些情况下，人群通过在距离，气味标记或个人遇到竞争人群的位置的记忆或记忆中的观察来告知自己。由于收集此信息的过程本质上是非本质的，因此已经提出了包括非本地术语的机械模型来研究物种的运动。自然，这些模型会带来分析和计算挑战。在这项工作中，我们研究了具有非本地对流的多物种模型。我们使用光谱方法介绍了一种有效的数值方案，以计算大量相互作用物种的非局部反应 - 辅助扩散系统的解决方案。此外，我们研究了参数和相互作用潜力对人口密度的影响。最后，我们提出了一种使用最大似然估计的方法，以确定驱动物种运动的最重要因素，并使用合成数据测试此方法。
Animals use various processes to inform themselves about their environment and make decisions about how to move and form their territory. In some cases, populations inform themselves of competing groups through observations at distances, scent markings, or memories of locations where an individual has encountered competing populations. As the process of gathering this information is inherently nonlocal, mechanistic models that include nonlocal terms have been proposed to investigate the movement of species. Naturally, these models present analytical and computational challenges. In this work we study a multi-species model with nonlocal advection. We introduce an efficient numerical scheme using spectral methods to compute solutions of a nonlocal reaction-advection-diffusion system for a large number of interacting species. Moreover, we investigate the effects that the parameters and interaction potentials have on the population densities. Finally, we propose a method using maximum likelihood estimation to determine the most important factors driving species' movements and test this method using synthetic data.
