Crustaceans exhibit discontinuous growth as they shed hard shells periodically. Fundamentally, the growth of crustaceans is typically assessed through two key components, length increase after molting (LI) and time intervals between consecutive molts (TI). In this article, we propose a unified likelihood approach that combines a generalized additive model and a Cox proportional hazard model to estimate the parameters of LI and TI separately in crustaceans. This approach captures the observed discontinuity in individuals, providing a comprehensive understanding of crustacean growth patterns. Our study focuses on 75 ornate rock lobsters (Panulirus ornatus) off the Torres Strait in northeastern Australia. Through a simulation study, we demonstrate the effectiveness of the proposed models in characterizing the discontinuity with a continuous growth curve at the population level.
Keywords: Markov property; crustaceans; discontinuous; molt; unified likelihood approach.