Modeling complex systems in animal science: A pedagogical framework for new researchers

ABSTRACT Mathematical modeling is a systematic process that involves identifying key variables and understanding how they interact. This review provides a comprehensive pedagogical framework for new researchers in animal science modeling, addressing the critical gap between general modeling theory and domain-specific applications. While modeling typically begins with conceptualization using visual aids such as causal loop diagrams, stock and flow diagrams, mind maps, and flowcharts to organize relationships among variables, there is a notable lack of resources that effectively bridge theoretical concepts with practical applications in animal science. This process allows scientists to build simplified representations of complex systems while providing structured guidance specifically tailored to biological systems. Modelers must balance simplicity and complexity to maintain functionality while reflecting real-world systems. Simple models, though limited, offer greater usability and interpretability, while complex models can become challenging to apply practically. After translation to mathematical form and computer code, models undergo rigorous parameterization with real-world data, evaluation against independent datasets, and sensitivity analyses. Models challenge our understanding, reveal knowledge gaps, and guide research. By embracing an iterative approach to model development—in which refinement and improvement are continuous—researchers can develop models that are not only accurate and predictive, but also practical and usable in addressing real-world challenges. This continuous development cycle, evaluation, and application ensures that models remain relevant and capable of evolving alongside scientific knowledge and technology advancements.