Exploration of the relationship between somatic and otolith growth, and development of a proportionality-based back-calculation approach based on traditional growth equations

Back-calculation of lengths at ages prior to capture has been found to be a valuable tool for many fish studies. The approach relies on the relationship between fish length and measures of growth zones formed at validated, regular intervals in hard structures within the fish, such as otoliths. While it has been suggested that the inclusion of age in back-calculation procedures might improve the quality of the estimates that are produced, there are relatively few back-calculation approaches that have employed this variable, and it appears that none has made use of traditional growth curves when describing somatic and otolith growth. This thesis employed data for six teleost species with different biological characteristics to determine whether results of analyses were broadly applicable to a wide range of species. The performance of a new proportionality-based back-calculation approach based on a model of somatic and otolith growth that employs traditional forms of growth curves and assumes a bivariate distribution of deviations from these two growth curves was explored. The forms of the curves used to describe fish length and otolith size at capture were selected from a suite of traditional and flexible growth curves on the basis of Akaike Information Criteria for the fitted models. Coefficients of determination indicated good fits of the bivariate growth model for five of the six species. Deviations from the two growth curves were positively correlated and, for three of the six species, statistically significant. The accuracy and precision of predictions made using the fitted bivariate growth model were assessed by comparing predicted lengths at capture given both age and otolith radius, and predicted otolith radius at capture given both age and fish length, with the corresponding observed values for fish that were not included when fitting the model. The resulting measures of root mean square error (RMSE) for six fish species with different biological characteristics were compared with those obtained using the methods employed in a set of existing proportionality-based back-calculation approaches that also incorporated age when describing the relationship between fish length and otolith radius. Based on the results from this cross-validation, the RMSEs of predictions of fish length and otolith size of the new bivariate model were found typically to be equal to or better than those produced using the regression equations of the alternative approaches. The new bivariate growth model was extended to provide a proportionality-based back-calculation approach, with the option of constraining the growth curves to pass through a biological intercept, i.e., the length, otolith radius and age of recently-hatched larvae. Back-calculated estimates of lengths at ages prior to capture calculated for individuals from a population of Acanthopagrus butcheri using the bivariate growth model were compared with the estimates produced by other proportionality-based back-calculation approaches that employed age and with a constraint-based back-calculation approach that was known to have good performance. The resulting estimates of length at ages produced by the proportionality-based back-calculation approach developed using the bivariate growth model, when constrained to pass through the biological intercept for this species, were typically more consistent with mean observed lengths at corresponding ages than those of the alternative back-calculation approaches. In combination with the cross-validation results, these findings suggest that, for this population of A. butcheri, back-calculated lengths produced using the bivariate growth model are likely to be more reliable than those produced using the other back-calculation approaches. A common assumption of mixed effects models of otolith growth suggests that, through inclusion of a random effect for different fish, the growth rate of otolith of an individual fish relative to that of other fish will persist throughout life. It was proposed that, throughout the life of an individual from a selected population of A. butcheri, the sizes of its otolith remain in constant proportion to the average sizes of the otoliths of fish of the same ages. This hypothesis was investigated by exploring the extent to which the natural logarithms of the ratios of otolith size for individual fish to average otolith size from A. butcheri of the same age remained constant throughout life. Although, for individuals of this species, the hypothesis of constant proportionality with age was found to be invalid as the ratios of relative otolith size varied among different periods of life, these ratios became increasingly constant with increasing age. Other factors likely to affect predictions derived from the new back-calculation approach, such as length-dependent selection and level of fishing mortality, were explored using simulation. Results from this simulation suggest that, due to the cumulative effect of fishing mortality on survival, the mean age of fish of a given length or otolith size is likely to decrease as length-dependent fishing mortality increases for fish with larger lengths or otolith sizes, with the effect apparently less on otolith size than on fish length. Similarly, mean lengths for fish with otoliths of a given size and, to a lesser extent, mean otolith sizes for a given fish length, decreased with increasing fishing mortality for fish with larger lengths or otolith sizes. Mean otolith sizes at age of younger fish, however, appeared little affected by reduced selectivity. Although otolith size at age of older fish predicted by bivariate models fitted to simulated otolith sizes at capture appeared little affected by increasing fishing mortality, predicted fish lengths at age of older fish and fish lengths at otolith size of fish with larger otoliths decreased with increasing fishing mortality, with the magnitude and direction of the effect varying among species with different levels of fishing mortality. The model developed in this study provides a link between studies of somatic growth and investigations of the relationship between length and otolith size undertaken in traditional back-calculation approaches, thereby facilitating future investigation of factors affecting this relationship and, through this, improving our understanding of the influence of environmental factors on somatic and otolith growth.