Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long‐term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a logistic reaction component instead of a Malthusian component when population growth demonstrates asymptotic behavior. As a case study, we demonstrated that our model improves spatiotemporal abundance forecasts of sea otters in Glacier Bay, Alaska. Furthermore, we predicted spatially varying local equilibrium abundances as a result of environmentally driven diffusion and density‐regulated growth. Integrating equilibrium abundances over the study area in our application enabled us to infer the overall carrying capacity of sea otters in Glacier Bay, Alaska.

中文翻译：

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非线性反应扩散过程模型改进了对种群动态的推断

偏微分方程 (PDE) 是对生态过程的时空动态进行建模的有用工具。然而，随着生态过程的发展，我们需要能够适应随着收集新数据而变化的动态的统计模型。我们开发了一个模型，该模型将生态扩散方程和逻辑增长相结合，以表征在异质环境中建立长期平衡的种群的定殖过程。我们还开发了一种同质化策略，以在统计上放大 PDE 以加快计算速度，并采用分层框架来适应在不同空间尺度收集的多个数据源。当人口增长表现出渐近行为时，我们强调了使用逻辑反应分量而不是马尔萨斯分量的优势。作为案例研究，我们证明了我们的模型改进了阿拉斯加冰川湾海獭的时空丰度预测。此外，由于环境驱动的扩散和密度调节的生长，我们预测了空间变化的局部平衡丰度。在我们的应用程序中整合研究区域的平衡丰度使我们能够推断阿拉斯加冰川湾海獭的整体承载能力。