Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Implications of gain functions in fisheries management

The appealing concept of optimal harvesting is often used in fisheries to obtain new management strategies. However, optimality depends on the objective function, which often varies, reflecting the interests of different groups of people. The aim of maximum sustainable yield is to extract the greatest amount of food from replenishable resources in a sustainable way. Maximum sustainable yield may not be desirable from an economic point of view. Maximum economic yield that maximizes the profit of fishing fleets (harvesting sector) but ignores socio-economic benefits such as employment and other positive externalities. It may be more appropriate to use the maximum economic yield that which is based on the value chain of the overall fishing sector, to reflect better society's interests. How to make more efficient use of a fishery for society rather than fishing operators depends critically on the gain function parameters including multiplier effects and inclusion or exclusion of certain costs. In particular, the optimal effort level based on the overall value chain moves closer to the optimal effort for the maximum sustainable yield because of the multiplier effect. These issues are illustrated using the Australian Northern Prawn Fishery.

Efficient designs for sampling and subsampling in fisheries research based on ranked sets

Sampling strategies are developed based on the idea of ranked set sampling (RSS) to increase efficiency and therefore to reduce the cost of sampling in fishery research. The RSS incorporates information on concomitant variables that are correlated with the variable of interest in the selection of samples. For example, estimating a monitoring survey abundance index would be more efficient if the sampling sites were selected based on the information from previous surveys or catch rates of the fishery. We use two practical fishery examples to demonstrate the approach: site selection for a fishery-independent monitoring survey in the Australian northern prawn fishery (NPF) and fish age prediction by simple linear regression modelling a short-lived tropical clupeoid. The relative efficiencies of the new designs were derived analytically and compared with the traditional simple random sampling (SRS). Optimal sampling schemes were measured by different optimality criteria. For the NPF monitoring survey, the efficiency in terms of variance or mean squared errors of the estimated mean abundance index ranged from 114 to 199% compared with the SRS. In the case of a fish ageing study for Tenualosa ilisha in Bangladesh, the efficiency of age prediction from fish body weight reached 140%.

A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

A simple method for estimating growth parameters from multiple length-frequency data in presence of continuous recruitment

The extended recruitment season for short-lived species such as prawns biases the estimation of growth parameters from length-frequency data when conventional methods are used. We propose a simple method for overcoming this bias given a time series of length-frequency data. The difficulties arising from extended recruitment are eliminated by predicting the growth of the succeeding samples and the length increments of the recruits in previous samples. This method requires that some maximum size at recruitment can be specified. The advantages of this multiple length-frequency method are: it is simple to use; it requires only three parameters; no specific distributions need to be assumed; and the actual seasonal recruitment pattern does not have to be specified. We illustrate the new method with length-frequency data on the tiger prawn Penaeus esculentus from the north-western Gulf of Carpentaria, Australia.

Growth curves with time-dependent explanatory variables

A class of growth models incorporating time-dependent factors and stochastic perturbations are introduced. The proposed model includes the existing growth models used in fisheries as special cases. Particular attention is given to growth of a population (in average weight or length) from which observations are taken randomly each time and the analysis of tag-recapture data. Two real data sets are used for illustration: (a) to estimate the seasonal effect and population density effect on growth of farmed prawn (Penaeus monodon) from weight data and (b) to assess the effect of tagging on growth of barramundi (Lates calcarifer)

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Effects of fish density distribution and effort distribution on catchability

The effects of fish density distribution and effort distribution on the overall catchability coefficient are examined. Emphasis is also on how aggregation and effort distribution interact to affect overall catch rate [catch per unit effort (cpue)]. In particular, it is proposed to evaluate three indices, the catchability index, the knowledge parameter, and the aggregation index, to describe the effectiveness of targeting and the effects on overall catchability in the stock area. Analytical expressions are provided so that these indices can easily be calculated. The average of the cpue calculated from small units where fishing is random is a better index for measuring the stock abundance. The overall cpue, the ratio of lumped catch and effort, together with the average cpue, can be used to assess the effectiveness of targeting. The proposed methods are applied to the commercial catch and effort data from the Australian northern prawn fishery. The indices are obtained assuming a power law for the effort distribution as an approximation of targeting during the fishing operation. Targeting increased catchability in some areas by 10%, which may have important implications on management advice.

Analysing commercial catch and effort data from a penaeid trawl fishery: A comparison of linear models, mixed models, and generalised estimating equations approaches

Statistical methods are often used to analyse commercial catch and effort data to provide standardised fishing effort and/or a relative index of fish abundance for input into stock assessment models. Achieving reliable results has proved difficult in Australia's Northern Prawn Fishery (NPF), due to a combination of such factors as the biological characteristics of the animals, some aspects of the fleet dynamics, and the changes in fishing technology. For this set of data, we compared four modelling approaches (linear models, mixed models, generalised estimating equations, and generalised linear models) with respect to the outcomes of the standardised fishing effort or the relative index of abundance. We also varied the number and form of vessel covariates in the models. Within a subset of data from this fishery, modelling correlation structures did not alter the conclusions from simpler statistical models. The random-effects models also yielded similar results. This is because the estimators are all consistent even if the correlation structure is mis-specified, and the data set is very large. However, the standard errors from different models differed, suggesting that different methods have different statistical efficiency. We suggest that there is value in modelling the variance function and the correlation structure, to make valid and efficient statistical inferences and gain insight into the data. We found that fishing power was separable from the indices of prawn abundance only when we offset the impact of vessel characteristics at assumed values from external sources. This may be due to the large degree of confounding within the data, and the extreme temporal changes in certain aspects of individual vessels, the fleet and the fleet dynamics.

Does the size of subsamples taken from multispecies trawl catches affect estimates of catch composition and abundance?

Although subsampling is a common method for describing the composition of large and diverse trawl catches, the accuracy of these techniques is often unknown. We determined the sampling errors generated from estimating the percentage of the total number of species recorded in catches, as well as the abundance of each species, at each increase in the proportion of the sorted catch. We completely partitioned twenty prawn trawl catches from tropical northern Australia into subsamples of about 10 kg each. All subsamples were then sorted, and species numbers recorded. Catch weights ranged from 71 to 445 kg, and the number of fish species in trawls ranged from 60 to 138, and invertebrate species from 18 to 63. Almost 70% of the species recorded in catches were "rare" in subsamples (less than one individual per 10 kg subsample or less than one in every 389 individuals). A matrix was used to show the increase in the total number of species that were recorded in each catch as the percentage of the sorted catch increased. Simulation modelling showed that sorting small subsamples (about 10% of catch weights) identified about 50% of the total number of species caught in a trawl. Larger subsamples (50% of catch weight on average) identified about 80% of the total species caught in a trawl. The accuracy of estimating the abundance of each species also increased with increasing subsample size. For the "rare" species, sampling error was around 80% after sorting 10% of catch weight and was just less than 50% after 40% of catch weight had been sorted. For the "abundant" species (five or more individuals per 10 kg subsample or five or more in every 389 individuals), sampling error was around 25% after sorting 10% of catch weight, but was reduced to around 10% after 40% of catch weight had been sorted.

Subsampling multi-species trawl catches from tropical northern Australia: Does it matter which part of the catch is sampled?

Subsampling is a common method for estimating the abundance of species in trawl catches. However, the accuracy of subsampling in representing the total catch has not been assessed. To estimate one possible source of bias due to subsampling, we tested whether the position on trawler sorting trays from which subsamples were taken affected their ability to represent species in catches. This was done by sorting catches into 10 kg subsamples and comparing subsamples taken from different positions on the sorting tray. Comparisons were made after species were grouped into three categories of abundance, either 'rare', 'common' or 'abundant'. A generalised linear model analysis showed that taking subsamples from different positions on the sorting tray had no major effect on estimating the total numbers or weights of fish or invertebrates, or the total number of fish or invertebrate taxa, recorded in each position. Some individual taxa showed differences between positions on the sorting tray (11.5% of taxa ina three-position design; 25% in a five-position design). But consistent and meaningful patterns in the position of these taxa on the sorting tray could only be seen for the pony fish Leiognathus moretoniensis and the saucer scallop Amusium pleuronectes. Because most bycatch laxa are well mixed throughout the catch, subsamples can be taken from any position on trawler sorting trays without introducing bias.

A generalized estimating equations approach for analysis of the impact of new technology on a trawl fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988-96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.

A maximum-likelihood method for estimating natural mortality and catchability coefficient from catch-and-effort data

A simple stochastic model of a fish population subject to natural and fishing mortalities is described. The fishing effort is assumed to vary over different periods but to be constant within each period. A maximum-likelihood approach is developed for estimating natural mortality (M) and the catchability coefficient (q) simultaneously from catch-and-effort data. If there is not enough contrast in the data to provide reliable estimates of both M and q, as is often the case in practice, the method can be used to obtain the best possible values of q for a range of possible values of M. These techniques are illustrated with tiger prawn (Penaeus semisulcatus) data from the Northern Prawn Fishery of Australia.