Parameter estimation of laboratory-reared Panulirus ornatus

Abstract

In the fisheries study, fish growth is typically in an indeterminate fashion implying a continuous growth function occurs throughout the life. Most existing studies of fish trajectories are continuous; however, it is not true when modelling growth of the crustacean species with discontinuous growth paths. In this context, it is imperative to insure that a different type of model for describing absolute growth in crustaceans. Crustaceans must moult for them to grow. A moulting process is of periodical shedding of the exoskeleton and thus the crustacean growth is known to be a discontinuous process. The sudden growth of crustaceans through the moulting process makes the growth estimation more complex. To model the discontinuous growth, we consider stochastic approaches where the growth model only considers for a monotonically increasing function. To this end, we introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that enabling the individual variability and environmental perturbation to be included in modelling growth. A dataset in the laboratory setting (e.g. in an aquarium) is developed. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, where the growth parameters can be estimated through two inter-correlated variables, namely the intermoult periods and the moult increments. We propose a joint density function, consisting of the moult increments and the intermoult periods. Both of these variables are assumed to be conditionally independent based on the Markov property. In the four-year studies from 1995 to 1999, the growth rates for females and males are estimated averagely 0.307 mm year–1 and 0.205 mm year–1, respectively. Therefore, the growth parameters of moult increments and intermoult periods can be quantified individually. The corresponding functions will then be convoluted through a simulation approach to obtain a population mean curve for crustaceans.