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.
Keywords: dynamic modeling; model calibration; parameter estimation; parameter identification; practical identifiability; structural identifiability.
When modeling biological systems, one major step of the modeling exercise is connecting the theory (the model) with the reality (the data). Such a connection passes through the resolution of the parameter identification (model calibration) problem, which aims at finding a set of parameters that best fits the variables predicted by the model to the data. Traditionally, the parameter identification step is often addressed like a downstream process (after data collection). Using this traditional approach, the modeler has minimal room for maneuvering to improve the model’s accuracy. This paper discusses the benefits of adopting an upstream approach (before data collection) during the model construction phase. This approach capitalizes on the identifiability analysis, a powerful tool seldom applied in dynamic models of the animal science domain, likely because of the lack of awareness or the specialized mathematical technicalities involved in the identifiability analysis. In this paper, we illustrate that the modeling community in animal science can easily integrate identifiability analysis in their model developments following a practitioner approach taking advantage of a variety of freely available software tools dedicated to identifiability testing.
© The Author(s) 2023. Published by Oxford University Press on behalf of the American Society of Animal Science.