基于一般消费者-资源随机动力学种群数据的非平衡摄食率推断
Out-of-equlibrium inference of feeding rates through population data from generic consumer-resource stochastic dynamics
AI总结：
本文研究多资源消费者-资源随机模型的参数可辨识性，通过生成函数解析概率分布并结合模拟最大似然估计，证明非平衡观测可唯一识别摄食率，而稳态采样仅能推断速率比值。
摘要：
统计模型通常在结构上不可辨识，因为不同的参数集合可能产生相同的模型结果。为了能够用于从数据进行预测和参数推断，随机种群模型必须具备可辨识性，这意味着可以从大量模型观测中唯一地推断出模型参数。特别地，精确估计消费者-资源动力学中的摄食率至关重要，因为消费者-资源过程决定着生物量在生态系统中的流动。模型参数通常在稳态下估计，因为此时模型分析往往更为容易。在本研究中，我们分析了多资源消费者-资源模型中的参数冗余问题，表明模型可辨识性取决于动力学是否已达到稳态。具体而言，我们：(i) 利用生成函数解析地计算捕食者丰度的稳态和非平衡概率分布，从而揭示参数冗余并进行恰当的最大似然估计；(ii) 通过追踪正在搜寻或处理猎物的消费者丰度开展计算机模拟实验，并将所得数据用于最大似然参数估计；(iii) 证明当模型观测在非平衡状态下记录时，摄食参数确实可辨识，而如果仅在稳态下采样，则只能从数据中推断速率的比值（即参数存在冗余）。我们还讨论了上述结果在推断一般动力学模型参数时的意义。
英文摘要：
Statistical models are often structurally unidentifiable, because different sets of parameters can lead to equal model outcomes. To be useful for prediction and parameter inference from data, stochastic population models need to be identifiable, this meaning that model parameters can be uniquely inferred from a large number of model observations. In particular, precise estimation of feeding rates in consumer-resource dynamics is crucial, because consumer-resource processes are central in determining biomass transport across ecosystems. Model parameters are usually estimated at stationarity, because in that case model analyses are often easier. In this contribution we analyze the problem of parameter redundancy in a multi-resource consumer-resource model, showing that model indentifiability depends on whether the dynamics have reached stationarity or not. To be precise, we: (i) Calculate the steady-state and out-of-equilibrium probability distributions of predator's abundances analytically using generating functions, which allow us to unveil parameter redundancy and carry out proper maximum likelihood estimation. (ii) Conduct \emph{in silico} experiments by tracking the abundance of consumers that are either searching for or handling prey, data then used for maximum likelihood parameter estimation. (iii) Show that, when model observations are recorded out of equilibrium, feeding parameters are truly identifiable, whereas if sampling is done solely at stationarity, only ratios of rates can be inferred from data (i.e., parameters are redundant). We discuss the implications of our results when inferring parameters of general dynamical models.
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