Statistical detection of density dependent parameter variation in growth curve models

Growth curve models are widely employed to analyze and interpret the dynamics of biological, ecological, epidemiological, and industrial processes. A fundamental challenge in growth modeling lies in the assumption of constant parameters, which may not reflect realistic growth mechanisms. While recent studies have developed methods to detect time-dependent parameter variation, the possibility of density-dependent changes, where model parameters vary as a function of population size or system state, has received limited statistical attention. Motivated by empirical evidence and theoretical developments in ecological modeling, this paper presents a novel statistical methodology for detecting density-dependent variation in growth model parameters. The proposed framework extends the interval-specific rate parameter (ISRP) estimation technique based on localized maximum likelihood methods to determine whether parameter variation is driven by population density. The method is validated through simulation experiments and applied to three real-world datasets: population growth data in the United States, cumulative COVID-19 cases in Germany, and a bio-ethanol production system. The results show that incorporating density-dependent parameter variation substantially improves model fit and captures nuanced system dynamics often overlooked in traditional approaches. This work provides a robust statistical foundation for identifying and quantifying density-regulated effects in growth models and offers broad applicability across domains where dynamic systems are influenced by feedback from population or system size.