Abstract

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly-encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long re-growth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand, and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding, and predicting biphasic population growth. The two key components of the framework are: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters; and, (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.