Université Paris-Saclay, INRAE, AgroParisTech, UMR Modélisation Systémique Appliquée aux Ruminants, 91120 Palaiseau, France.
Department of Animal Science, Texas A&M University, College Station, TX 77843-2471, USA.
J Anim Sci. 2023 Jan 3;101. doi: 10.1093/jas/skad320.
Constructing dynamic mathematical models of biological systems requires estimating unknown parameters from available experimental data, usually using a statistical fitting procedure. This procedure is usually called parameter identification, parameter estimation, model fitting, or model calibration. In animal science, parameter identification is often performed without analytic considerations on the possibility of determining unique values of the model parameters. These analytical studies are related to the mathematical property of structural identifiability, which refers to the theoretical ability to recover unique values of the model parameters from the measures defined in an experimental setup and use the model structure as the sole basis. The structural identifiability analysis is a powerful tool for model construction because it informs whether the parameter identification problem is well-posed (i.e., the problem has a unique solution). Structural identifiability analysis is helpful to determine which actions (e.g., model reparameterization, choice of new data measurements, and change of the model structure) are needed to render the model parameters identifiable (when possible). The mathematical technicalities associated with structural identifiability analysis are very sophisticated. However, the development of dedicated, freely available software tools enables the application of identifiability analysis without needing to be an expert in mathematics and computer programming. We refer to such a non-expert user as a practitioner for hands-on purposes. However, a practitioner should be familiar with the model construction and software implementation process. In this paper, we propose to adopt a practitioner approach that takes advantage of available software tools to integrate identifiability analysis in the modeling practice in the animal science field. The application of structural identifiability implies switching our regard of the parameter identification problem as a downstream process (after data collection) to an upstream process (before data collection) where experiment design is applied to guarantee identifiability. This upstream approach will substantially improve the workflow of model construction toward robust and valuable models in animal science. Illustrative examples with different levels of complexity support our work. The source codes of the examples were provided for learning purposes and to promote open science practices.
构建生物系统的动态数学模型需要根据可用的实验数据来估计未知参数,通常使用统计拟合程序。这个过程通常被称为参数识别、参数估计、模型拟合或模型校准。在动物科学中,参数识别通常是在没有对确定模型参数的唯一值的可能性进行分析考虑的情况下进行的。这些分析研究与结构可识别性的数学性质有关,结构可识别性是指从实验设置中定义的测量中恢复模型参数的唯一值并仅使用模型结构作为唯一基础的理论能力。结构可识别性分析是模型构建的有力工具,因为它可以告知参数识别问题是否有良好的定义(即,问题是否有唯一的解)。结构可识别性分析有助于确定需要采取哪些行动(例如,模型重新参数化、选择新的数据测量、改变模型结构)来使模型参数可识别(在可能的情况下)。与结构可识别性分析相关的数学技术非常复杂。然而,专用免费软件工具的开发使得可以在不需要成为数学和计算机编程专家的情况下应用可识别性分析。出于实际目的,我们将这样的非专家用户称为从业者。然而,从业者应该熟悉模型构建和软件实现过程。在本文中,我们建议采用从业者方法,利用可用的软件工具将可识别性分析集成到动物科学领域的建模实践中。结构可识别性的应用意味着将我们对参数识别问题的关注从数据收集后(下游过程)转换为数据收集前(上游过程),在这个过程中应用实验设计来保证可识别性。这种上游方法将大大改进模型构建的工作流程,使其在动物科学中建立稳健且有价值的模型。不同复杂程度的实例说明了我们的工作。为了促进开放科学实践,提供了示例的源代码以供学习。