Dynamical Ising model of spatially coupled ecological oscillators
Dynamical Ising model of spatially coupled ecological oscillators
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DOI：
10.1098/rsif.2020.0571
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发表时间：
2020-10-28
影响因子：
3.9
通讯作者：
Hastings, Alan
中科院分区：
文献类型：
--
作者：
Nareddy, Vahini Reddy;Machta, Jonathan;Hastings, Alan
短程相互作用的长程同步是生物和物理系统中常见的模式，其中许多系统在同步点上具有一组共同的“通用”属性。常见的耦合振子生物系统被证明是伊辛普适类的成员，这意味着非常简单的伊辛模型复制了这些系统在平稳性上的某些空间统计。这一观察是有用的，因为它揭示了空间模式的哪些方面独立于控制局部动态的细节而出现，从而加深了对生物同步的理解，并为生物同步提供了一个更简单的基线模型。然而，在许多情况下，一个系统的动态比他们的静态空间属性更感兴趣。在这里，我们问一个动态伊辛模型是否可以复制生态系统的普遍和非普遍的功能，使用噪声耦合集合种群模型与两个周期的动态作为一个案例研究。标准的伊辛模型做出了不切实际的动力学预测，但具有记忆的伊辛模型通过使用额外的参数来反映局部动力学保持其振荡相位的趋势来纠正这一点。通过拟合伊辛模型的两个参数与记忆模拟生态动态，我们评估伊辛和生态模型之间的对应关系，在他们的几个功能（同步和异步动态之间的参数空间中的临界边界的位置，局部相变的概率和预测未来动态的能力）。我们发现，伊辛模型与记忆是合理的好，在代表这些属性的生态集合种群。这些模型之间的对应关系为简单而著名的伊辛类模型创造了潜力，使其成为理解复杂生物系统的有价值的工具。
Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of 'universal' properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system's dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.