Efficient approximation of global population dynamic models through statistical inference using local data

Biological growth curves are pivotal in predicting natural growth across disciplines, typically analyzed using nonlinear least squares or maximum likelihood methods. Bhowmick et al. (2014) introduced the interval-specific rate of parameters (ISRP) for growth equations, improving the estimation of relative growth rate (RGR) and model selection accuracy. Despite its effectiveness, computing these model-specific RGR estimates involves complex calculations and lacks explicit expressions for many nonlinear models. Also, for highly nonlinear models and non-monotonic data where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. So, the need for a more efficient computation method for ISRP remains a significant challenge in growth studies. In this article, we propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. Our study underscores the importance of an efficient ISRP computation technique, providing a more stable, unbiased, and normally distributed estimator. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. Both simulation studies and real data analysis have been carried out to validate the proposed estimation process. Additionally, its applicability to non-monotonic growth profiles and its robustness in handling highly non-linear growth equations highlight its versatility. We also developed a web application GpEM-R which is freely available for researchers and practitioners to analyze growth data.