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 identifiability 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 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.

中文翻译：

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通过来自通用消费者资源随机动力学的种群数据对饲喂率进行失衡推断


统计模型在结构上通常是不可识别的，因为不同的参数集可以导致相同的模型结果。为了便于从数据中进行预测和参数推断，随机总体模型需要可识别，这意味着可以从大量模型观测中唯一地推断出模型参数。特别是，在消费者-资源动态中精确估计摄食率至关重要，因为消费者-资源过程是决定跨生态系统的生物质运输的核心。模型参数通常在平稳性时进行估计，因为在这种情况下，模型分析通常更容易。在这篇文章中，我们分析了多资源消费者资源模型中的参数冗余问题，表明模型的可识别性取决于动力学是否达到平稳性。准确地说，我们：（i） 使用生成函数分析计算捕食者丰度的稳态和非平衡概率分布，这使我们能够揭示参数冗余并进行适当的最大似然估计。（ii） 通过跟踪正在寻找或处理猎物的消费者的丰度进行计算机实验，然后将数据用于最大似然参数估计。（iii） 表明，当模型观测记录不平衡时，进料参数是真正可识别的，而如果仅在平稳性下进行采样，则只能从数据中推断出速率比率（即参数是冗余的）。我们讨论了在推断一般动力学模型参数时结果的含义。