Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects. However, simulating stochastic individual based models can be extremely demanding, especially when the sample size is large. Hence we propose an alternative simulation approach, whose computation cost is lower than the one of the classic stochastic algorithms. First, we describe how starting from the individual description of predator-prey dynamics, it is possible to derive the mean-field equations for the homogeneous and heterogeneous space cases. Then, we see that the new approach is able to preserve the order and that it converges to the mean-field solutions as the sample size increases. We show how to simulate the dynamics with the new approach, performing different numerical experiments in order to test its efficiency. Finally, we analyze the different nature of oscillations between mean-field and stochastic simulations underling how the new algorithm can be useful also to study the collective behaviours at the population level.

中文翻译：

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用于具有捕食者-猎物动力学的基于代理的模型的高效随机算法

捕食者-猎物系统的实验表明出现了长期循环。确定性模型通常无法捕捉这些行为，这些行为源于基于个体的动力学和随机效应的微观相互作用。但是，模拟基于随机个体的模型可能非常苛刻，尤其是在样本量很大的情况下。因此，我们提出了一种替代模拟方法，其计算成本低于经典随机算法之一。首先，我们描述了如何从捕食者-猎物动力学的个体描述出发，推导出均匀和异构空间情况的平均场方程。然后，我们看到新方法能够保持顺序，并且随着样本大小的增加它会收敛到平均场解。我们展示了如何使用新方法模拟动力学，执行不同的数值实验以测试其效率。最后，我们分析了平均场模拟和随机模拟之间振荡的不同性质，以说明新算法如何也可用于研究群体水平的集体行为。