基于格点的随机模型促使对基于记忆的扩散给出非线性扩散描述
Lattice-based stochastic models motivate non-linear diffusion descriptions of memory-based dispersal
AI总结：
针对PDE模型中记忆效应输运项不清晰的问题，提出基于格点的个体随机模型，推导出包含基于记忆扩散项的新型非线性扩散方程，并通过模拟验证其准确性。
摘要：
记忆和认知在种群内个体（如动物）运动中的作用，被认为在种群扩散中扮演重要角色。为此，人们越来越感兴趣将空间记忆效应纳入经典动物扩散偏微分方程（PDE）模型中。然而，为准确反映记忆效应，应纳入PDE模型的输运项（如扩散项和平流项）的具体细节仍不清晰。为弥补这一空白，我们提出了一种直观的基于格点的模型，其中个体的运动取决于拥挤效应和模拟内的历史分布。使用基于个体的模型的优势在于，在模拟中提出和实现记忆效应的方式比简单提出经典PDE模型的启发式扩展更具生物学直观性。通过推导随机模型的连续极限描述，我们获得了一个包含基于记忆的扩散项的新型非线性扩散方程。我们首次揭示了基于记忆的扩散与依赖记忆效应的基于个体的运动机制之间的关系。通过重复的随机模拟和平均场PDE模型的数值探索，我们表明新PDE模型准确描述了随机模型的预期行为，并探讨了记忆效应如何影响种群扩散。
英文摘要：
The role of memory and cognition in the movement of individuals (e.g. animals) within a population, is thought to play an important role in population dispersal. In response, there has been increasing interest in incorporating spatial memory effects into classical partial differential equation (PDE) models of animal dispersal. However, the specific detail of the transport terms, such as diffusion and advection terms, that ought to be incorporated into PDE models to accurately reflect the memory effect remains unclear. To bridge this gap, we propose a straightforward lattice-based model where the movement of individuals depends on both crowding effects and the historic distribution within the simulation. The advantage of working with the individual-based model is that it is straightforward to propose and implement memory effects within the simulation in a way that is more biologically intuitive than simply proposing heuristic extensions of classical PDE models. Through deriving the continuum limit description of our stochastic model, we obtain a novel nonlinear diffusion equation which encompasses memory-based diffusion terms. For the first time we reveal the relationship between memory-based diffusion and the individual-based movement mechanisms that depend upon memory effects. Through repeated stochastic simulation and numerical explorations of the mean-field PDE model, we show that the new PDE model accurately describes the expected behaviour of the stochastic model, and we also explore how memory effects impact population dispersal.
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