Growth Models and Analysis of Crustacean Growth Data

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, however, 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´evy process — 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 maximum likelihood approach is constructed given that they are conditionally independent of each other. These two probability functions are subsequently integrated through a simulation technique. 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 realistic analyses that will undoubtedly be useful for environmental sustainability, marine crustacean industry, and future research.