Stochastic growth models for analyzing crustacean data

Foo, Chuan Hui and Wang, You-Gan (2013). Stochastic growth models for analyzing crustacean data. In: J. Piantadosi, R. S. Anderssen and J. Boland, Proceedings: MODSIM2013, 20th International Congress on Modelling and Simulation. 20th International Congress on Modelling and Simulation (MODSIM 2013), Adelaide, SA, Australia, (566-572). 1-6 December 2103.

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Author Foo, Chuan Hui
Wang, You-Gan
Title of paper Stochastic growth models for analyzing crustacean data
Conference name 20th International Congress on Modelling and Simulation (MODSIM 2013)
Conference location Adelaide, SA, Australia
Conference dates 1-6 December 2103
Proceedings title Proceedings: MODSIM2013, 20th International Congress on Modelling and Simulation
Journal name 20Th International Congress On Modelling and Simulation (Modsim2013)
Place of Publication Canberra, ACT, Australia
Publisher Modelling and Simulation Society of Australia and New Zealand
Publication Year 2013
Sub-type Fully published paper
ISBN 9780987214331
Editor J. Piantadosi
R. S. Anderssen
J. Boland
Start page 566
End page 572
Total pages 7
Language eng
Abstract/Summary The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed form crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as “jumps” (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e.g. red curve in Figure 1).
Keyword Subordinator
Discontinuous growth trajectories
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status UQ
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Document type: Conference Paper
Collection: School of Mathematics and Physics
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Created: Tue, 20 Jan 2015, 10:44:23 EST by You-Gan Wang on behalf of Mathematics