CPUE standardisation and the construction of indices of stock abundance in a spatially varying fishery using general linear models

Construction of annual indices of stock abundance based on catch and effort data remains central to many fisheries’ assessments. While the use of more advanced statistical methods has helped catch rates to be standardised against many explanatory variables, the changing spatial characteristics of most fisheries data sets provide additional challenges for constructing reliable indices of stock abundance. After reviewing the use of general linear models to construct indices of annual stock abundance, potential biases which can arise due to the unequal and changing nature of the spatial distribution of fishing effort are examined and illustrated through the analysis of simulated data. Finally, some options are suggested for modelling catch rates in unfished strata and for accounting for the uncertainties in the stock and fishery dynamics which arise in the interpretation of spatially varying catch rate data.     

Use of individual types of fishing effort in analyzing catch and effort data by use of a generalized linear model

Fishing effort is a function of many (continuous) variables which fishers can manipulate. However, when catch and fishing effort data are analysed using a generalized linear model, individual types of fishing effort usually enter as a composite quantity. But not all quantities can be combined into a composite quantity. Use of such data this way generally leads to a loss of information and incurs a model bias. In this paper, I analyse catch and effort data for the blue swimmer crab off South Australia by a direct use of individual types of fishing effort to extract a relative index of biomass, and use the concept of homogeneous functions to present some of the results. I also give formulae for choosing a combination of different types of fishing effort to effect a specified level of catch in both absolute and relative terms. Assuming that catch follows an independent gamma, normal, negative binomial, or Poisson distribution, fitting of a generalized linear model with a log-link function to the commercial catch and effort data suggests that: (1) the exploitable biomass remained relatively constant from 1 July 1983 to 30 June 1996; (2) the relative instantaneous rate of fishing mortality of a particular sex and age (if gear selectivity was constant over time) slightly increased over time; (3) a 1% increase in the number of days fished gave about 0.85% increase in catch whereas a 1% increase in the number of people on a boat led to only about a 0.45% increase in catch. This implies that use of a composite measure of fishing effort such as boat days and man days when analysing catch and effort data is inappropriate for this fishery. Although a generalized linear model may be a reasonable first-order approximation, catch and effort data are best interpreted through a process model.     

Predicting the age of fish using general and generalized linear models of biometric data: A case study of two estuarine finfish from New South Wales, Australia

Direct ageing of fish can be a laborious and expensive task when age estimates from a large population are required, and often involves a degree of subjectivity. This study examined the application of general and generalized linear models that predict the age of fish from a range of efficiently and objectively measured covariates. The data sampled were from yellowfin bream (Acanthopagrus australis (Sparidae) (Owen, 1853)) and sand whiting (Sillago ciliata (Sillaginidae) Cuvier, 1829) populations from New South Wales, Australia. The covariates evaluated in the models were fish length, otolith weight, sex and location (the estuary from which the fish were sampled). Akaike Information Criteria were used for model selection and residual plots of the final models revealed a satisfactory fit to the observations. The best fitting model for each species included all covariates. An additional investigation considered whether general and generalized linear models that predict age from two different categories of biometric information outperform age-length keys with respect to subsequent estimates of total mortality from catch-curve analysis. The two categories of biometric information differed in the ease and cost with which the information could be collected. The first category only included fish length and location as covariates, whilst the second category also included otolith weight and sex. It was found that traditional age-length keys outperformed the predictive models that estimated age from only fish length and location, because the results from the models were prone to significant bias. However, when otolith weight and sex were added as covariates to the predictive models, some of them, including a generalized linear model with a Poisson-distributed response variable, performed similarly to the age-length key. Given that otolith weight and the sex of fish are cheaper to quantify than age from a sectioned otolith in many situations, general or generalized linear models may represent a cheaper and faster method of estimating mortality compared to age-length keys. Such models can also easily incorporate the influence of spatial, temporal and demographic variation.