Pfab Ferdinand, Brown Alexandra Lynne, Detmer A Raine, Baxter Ethan C, Moeller Holly V, Cunning Ross, Nisbet Roger M
Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, CA 93106, USA.
Daniel P. Haerther Center for Conservation and Research, G. Shedd Aquarium, 1200 S. DuSable Lake Shore Drive, Chicago, IL 60605, USA.
Conserv Physiol. 2022 May 5;10(1):coac026. doi: 10.1093/conphys/coac026. eCollection 2022.
Dynamic Energy Budget models relate whole organism processes such as growth, reproduction and mortality to suborganismal metabolic processes. Much of their potential derives from extensions of the formalism to describe the exchange of metabolic products between organisms or organs within a single organism, for example the mutualism between corals and their symbionts. Without model simplification, such models are at risk of becoming parameter-rich and hence impractical. One natural simplification is to assume that some metabolic processes act on 'fast' timescales relative to others. A common strategy for formulating such models is to assume that 'fast' processes equilibrate immediately, while 'slow' processes are described by ordinary differential equations. This strategy can bring a subtlety with it. What if there are multiple, interdependent fast processes that have multiple equilibria, so that additional information is needed to unambiguously specify the model dynamics? This situation can easily arise in contexts where an organism or community can persist in a 'healthy' or an 'unhealthy' state with abrupt transitions between states possible. To approach this issue, we offer the following: (a) a method to unambiguously complete implicitly defined models by adding hypothetical 'fast' state variables; (b) an approach for minimizing the number of additional state variables in such models, which can simplify the numerical analysis and give insights into the model dynamics; and (c) some implications of the new approach that are of practical importance for model dynamics, e.g. on the bistability of flux dynamics and the effect of different initialization choices on model outcomes. To demonstrate those principles, we use a simplified model for root-shoot dynamics of plants and a related model for the interactions between corals and endosymbiotic algae that describes coral bleaching and recovery.
动态能量预算模型将整个生物体的过程（如生长、繁殖和死亡）与亚生物体的代谢过程联系起来。它们的许多潜力源于形式主义的扩展，以描述生物体之间或单个生物体内器官之间代谢产物的交换，例如珊瑚与其共生体之间的共生关系。如果不进行模型简化，此类模型有变得参数过多从而不实用的风险。一种自然的简化方法是假设某些代谢过程相对于其他过程在“快速”时间尺度上起作用。制定此类模型的一个常见策略是假设“快速”过程立即达到平衡，而“缓慢”过程则由常微分方程描述。这种策略可能会带来一个微妙之处。如果存在多个相互依赖的快速过程且具有多个平衡点，以至于需要额外信息来明确指定模型动态会怎样？这种情况很容易出现在生物体或群落可以处于“健康”或“不健康”状态且状态之间可能发生突然转变的背景中。为了解决这个问题，我们提供以下内容：(a) 一种通过添加假设的“快速”状态变量来明确完成隐式定义模型的方法；(b) 一种最小化此类模型中额外状态变量数量的方法，这可以简化数值分析并深入了解模型动态；以及 (c) 新方法对模型动态具有实际重要性的一些影响，例如通量动态的双稳性以及不同初始化选择对模型结果的影响。为了证明这些原理，我们使用了一个简化的植物根 - 茎动态模型以及一个描述珊瑚白化和恢复的珊瑚与内共生藻类相互作用的相关模型。
