Swailem Mohamed, Täuber Uwe C
Department of Physics & Center for Soft Matter and Biological Physics, MC 0435, Robeson Hall, 850 West Campus Drive, <a href="https://ror.org/02smfhw86">Virginia Tech</a>, Blacksburg, Virginia 24061, USA.
Faculty of Health Sciences, <a href="https://ror.org/02smfhw86">Virginia Tech</a>, Blacksburg, Virginia 24061, USA.
Phys Rev E. 2024 Jul;110(1-1):014124. doi: 10.1103/PhysRevE.110.014124.
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale, long-time kinetics in such systems are effective, scale-dependent renormalized parameters that need to be either measured experimentally or computed by means of a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. To match the results of any computer simulation to observations or experiments carried out on the macroscale, a mapping is required between the microscopic probabilities that define the Monte Carlo algorithm and the macroscopic reaction rates that are experimentally measured. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities (subject to specific rules of interaction) is a very difficult problem, and there is currently no systematic, accurate analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using lattice Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely, restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka-Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka-Volterra model and its May-Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a more thorough and deeper understanding of coarse graining in spatially extended stochastic reaction-diffusion systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters, with a focus on ecological systems. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.
随机反应扩散模型被用于描述许多复杂的物理、生物、社会和生态系统。描述此类系统中大规模、长时间动力学的宏观反应速率是有效的、依赖尺度的重整化参数，这些参数需要通过实验测量或借助微观模型进行计算。在随机反应扩散系统的蒙特卡罗模拟中，特定事件发生的微观概率用作输入控制参数。为了使任何计算机模拟的结果与在宏观尺度上进行的观测或实验相匹配，需要在定义蒙特卡罗算法的微观概率与实验测量的宏观反应速率之间建立映射。找到涌现的宏观速率对微观概率（受特定相互作用规则约束）的函数依赖性是一个非常困难的问题，目前尚无系统、准确的解析方法来实现这一目标。因此，我们引入一种直接的数值方法，即使用晶格蒙特卡罗模拟，通过直接获取每个模拟时间步发生的事件数量的计数统计来评估宏观反应速率。我们的技术首先在已充分理解的基本示例上进行测试，即受限出生过程、扩散限制的双粒子凝聚以及双物种对湮灭动力学。接下来，我们利用由此获得的经验，研究在更复杂的模型系统中，微观算法概率如何粗粒化为有效的宏观速率，例如用于捕食者 - 猎物竞争与共存的洛特卡 - 沃尔泰拉模型，以及捕捉具有循环优势模式的种群动态的石头 - 剪刀 - 布或循环洛特卡 - 沃尔泰拉模型及其梅 - 伦纳德变体。从而，我们对空间扩展的随机反应扩散系统中的粗粒化以及相关微观和宏观模型参数之间的非平凡关系有了更全面、深入的理解，重点是生态系统。所提出的技术通常应提供一种有用的方法，使蒙特卡罗模拟结果能更好地拟合实验或观测数据。
