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Growth Models and Analysis of Crustacean Growth Data

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Growth Models and Analysis of Crustacean Growth Data Growth Models and Analysis of Crustacean Growth Data Chuan Hui Foo B.Sc Edu (Hon), M.Sc (Hon) A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2017 School of Mathematics and Physics Abstract Crustaceans represent one of the most important fishery species in the world, both ecologically and economically. Understanding the growth pattern of these species is fundamental to their stock assessment and sustainability management. Unlike most other fishery species, crustaceans must shed their exoskeleton periodically in order to grow, a process known as `moulting'. As a result, their growth trajectories do not follow a linear pattern. Traditional growth models, how- ever, are based on continuous growth trajectories and thus are not appropriate for modellling stepwise growth in crustaceans. This thesis develops novel methodology for modelling discrete growth pattern in crustacean species. We introduce new stochastic growth models that incorporate discontinuous jumps, taking into account individual heterogeneity and environmental variability. There are two different settings, data from an artificial condition (tank data) and data from the natural environment (tag-recapture data). We propose new approaches for modelling the growth of crustaceans from each data type, respectively. A likelihood approach is constructed to estimate the parameters of our growth models. Our methodology addresses four major challenges in modelling crustacean growth. Firstly, as previously mentioned, crustacean growth is a discrete stepwise process and hence traditional models, which assumes continuous growth over time, is not appropriate for use. Secondly, growth patterns are significantly affected by individual variability. The process of moulting involves interaction between two major stochastic processes of growth, namely the intermoult period (the time interval between two successive moults) and the moult increment (the increase in size between moults). The former varies significantly according to individual factors, such as sexual maturity. In particular, adult females are required to moult more often than adult males in order to produce juveniles and thus have a shorter intermoult period. Moreover, in general, the intermoult period increases with size, whereas the moult increment decreases over time. Thirdly, intrinsic variations and environmental conditions can also influence growth patterns. Biologically, all individuals possess a different terminal size that is partly determined by their genetics. Such phenomena are commonly referred to as forms of intrinsic variation. Apart from these variations, environmental factors such as water temperature, population density and food availability are strongly associated with growth rate. For example, maturity rate varies with habitat conditions, changing with different tank settings and natural habitat parameters. Fourthly, further to the above, data obtained from the natural environment (tag-recapture data) are more challenging to analyse than those obtained from a laboratory environment (tank data). This is because the realisation of moult increments and the intermoult periods can be observed directly in the latter case, whereas the intermoult period is not available for tag-recapture data. In addition, conventional tag-recapture studies focus on `single recapture' data which may lead to misleading results and are prone to biases given that individual heterogeneities exist in the population. To account for the aforementioned issues including individual heterogeneity and environmental variability, we introduce a special case of L´evyprocess | a subordinator that allows for indefinitely small jumps to be incorporated into growth models. An appealing advantage of a subordinator-based model is that it can ensure a monotonic increase in growth, an important criterion for modelling lengthwise growth. Furthermore, we developed a novel methodology for analysing multiple recapture data, utilising a biologically realistic model that can efficiently describe the correlation between two consecutive moults, including the hidden variables with regard to data derived from multiple recaptures. To quantify growth parameters of moult increments as well as intermoult periods, a maxi- mum likelihood approach is constructed given that they are conditionally independent of each other. These two probability functions are subsequently integrated through a simulation tech- nique. Our analysis provides a more realistic growth model for crustaceans from which critical information can be deduced, including how often an individual moults and how large can a moult increment be. In addition, the rate at which a crustacean reaches asymptotic size, and the variability of individual asymptotic size can be determined via a mean population growth curve. This thesis has contributed novel methodologies for quantitative modelling of crustaceans growth under both tank and (single/multiple) recapture scenarios, providing much more realis- tic analyses that will undoubtedly be useful for environmental sustainability, marine crustacean industry, and future research. Declaration by author This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis. Publications during candidature Conference abstracts and presentations Chuan Hui, Foo and You-Gan, Wang (2013). Modelling growth data from crustaceans. Young Statisticians' Meeting (YSI). Hong Kong, 23-24 August. (Poster) Chuan Hui, Foo and You-Gan, Wang (2014). Estimation of molting growth parameters from reared lobsters. Applied Statistics and Public Policy Analysis Conference. Wagga Wagga, 11-12 December. (Oral presentation) Publications included in this thesis Chuan Hui, Foo and You-Gan, Wang (2013). Stochastic growth models for analyzing crus- tacean 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. Incorporated as Chapter 5 and Chapter 6. Contributor Statement of Contribution Author Foo Developed the idea (50%) Wrote the paper (100%) Data analysis (100%) Author Wang Developed the idea (50%) Edited paper (10%) Contributions by others to the thesis No contributions by others. Statement of parts of the thesis submitted to qualify for the award of another degree None. Acknowledgements Firstly, I would like to express my special appreciation and thanks to my principal advisor Prof. You-Gan Wang who skillfully guided me through the stormy seas of methodological and statistical challenges with his remarkable forbearance, demonstrating high level of scientific precision and intellectual rigor, and ensuring that I did not sink along the way. I could not have imagined having a better advisor and mentor for my Ph.D study. Thank you also to my associate advisor Prof. Geoffrey McLachlan for his generous support that he has provided over the years. I thank the Ministry of Higher Education (Malaysia) and the Sultan Idris Education University (UPSI) for their financial support during my candidature. I acknowledge the dedication and assistance of all fellow postgraduates in the School of Mathe- matics and Physics who engaged with me either formal or informal discussion of issues relating to my research studies. The journey to completion of this thesis was a memorable one. The challenges were daunting but stimulating, with peaks to be scaled and valleys to be crossed. All works could never have been accomplished successfully without the backing of key people in my life, who fuelled my motivation and determination to succeed. Above all, for their constant support, patience and understanding I acknowledge my family especially my beloved parents; for believing in me, showing me what is decent and supporting me spiritually throughout writing this thesis and my life in general. Keywords Crustacean, moult, von Bertalanffy growth function, subordinator, growth model, heterogeneity. Australian and New Zealand Standard Research
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