1. There has been a recent demand for forecasting in ecology, particularly in the field of ecosystem management. Empirical dynamic modelling (EDM), an equation‐free nonlinear forecasting method, is receiving growing attention, but it requires long time series to produce accurate predictions. Though most ecological time series are short, spatial replicates are often available. Here we explore how utilizing available spatial data can improve our ability to forecast ecological dynamics.
2. There are several ways to incorporate spatial information into EDM and not all have been applied in ecology. We compare spatial EDM approaches used in ecology and physics and introduce a flexible Bayesian model that makes use of prior movement information.
3. We test these methods on simulated data generated with three population dynamics models with varying levels of complexity, time series length, spatial symmetry and heterogeneity. Adding spatial data generally improves accuracy, though the best method depends on the spatial process. We applied the methods to empirical fisheries data, highlighting the complexity of real population dynamics.
4. Leveraging spatial data is an effective way to overcome the problem of short ecological time series. Since the best forecasting method depends on the underlying dynamics, we suggest that users apply several in concert and that this may be useful in identifying spatial heterogeneity in dynamics.

中文翻译：

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利用空间信息预测非线性生态动力学

1. 最近对生态学，特别是在生态系统管理领域的预测有需求。经验动态建模（EDM）是一种无方程式的非线性预测方法，正受到越来越多的关注，但需要长时间序列才能产生准确的预测。尽管大多数生态时间序列都很短，但通常可以进行空间复制。在这里，我们探索如何利用可用的空间数据来提高我们预测生态动力学的能力。
2. 有几种方法可以将空间信息合并到EDM中，但并非所有方法都已应用于生态学中。我们比较了生态学和物理学中使用的空间EDM方法，并介绍了一种利用先前运动信息的灵活贝叶斯模型。
3. 我们在具有三种不同复杂度，时间序列长度，空间对称性和异质性的种群动力学模型生成的模拟数据上测试了这些方法。尽管最佳方法取决于空间过程，但是添加空间数据通常可以提高准确性。我们将这些方法应用于经验渔业数据，突出了实际种群动态的复杂性。
4. 利用空间数据是克服生态时间序列短的有效方法。由于最佳的预测方法取决于基本动力学，因此我们建议用户共同应用几种预测方法，这对于确定动力学中的空间异质性可能很有用。