Accounting for individual variability in the von Bertalanffy growth model

Estimation of von Bertalanffy growth parameters has received considerable attention in fisheries research. Since Sainsbury (1980, Can. J. Fish. Aquat. Sci. 37: 241-247) much of this research effort has centered on accounting for individual variability in the growth parameters. In this paper we demonstrate that, in analysis of tagging data, Sainsbury's method and its derivatives do not, in general, satisfactorily account for individual variability in growth, leading to inconsistent parameter estimates (the bias does not tend to zero as sample size increases to infinity). The bias arises because these methods do not use appropriate conditional expectations as a basis for estimation. This bias is found to be similar to that of the Fabens method. Such methods would be appropriate only under the assumption that the individual growth parameters that generate the growth increment were independent of the growth parameters that generated the initial length. However, such an assumption would be unrealistic. The results are derived analytically, and illustrated with a simulation study. Until techniques that take full account of the appropriate conditioning have been developed, the effect of individual variability on growth has yet to be fully understood.

An extravariation model for improving confidence intervals of population size estimates from removal data

We propose a new model for estimating the size of a population from successive catches taken during a removal experiment. The data from these experiments often have excessive variation, known as overdispersion, as compared with that predicted by the multinomial model. The new model allows catchability to vary randomly among samplings, which accounts for overdispersion. When the catchability is assumed to have a beta distribution, the likelihood function, which is refered to as beta-multinomial, is derived, and hence the maximum likelihood estimates can be evaluated. Simulations show that in the presence of extravariation in the data, the confidence intervals have been substantially underestimated in previous models (Leslie-DeLury, Moran) and that the new model provides more reliable confidence intervals. The performance of these methods was also demonstrated using two real data sets: one with overdispersion, from smallmouth bass (Micropterus dolomieu), and the other without overdispersion, from rat (Rattus rattus).

Effect of individual variability on estimation of population parameters from length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock when there is individual variability in the von Bertalanffy growth parameter L-infinity and investigate the possible bias in the estimates when the individual variability is ignored. Three methods are examined: (i) the regression method based on the Beverton and Holt's (1956, Rapp. P.V. Reun. Cons. Int. Explor. Mer, 140: 67-83) equation; (ii) the moment method of Powell (1979, Rapp. PV. Reun. Int. Explor. Mer, 175: 167-169); and (iii) a generalization of Powell's method that estimates the individual variability to be incorporated into the estimation. It is found that the biases in the estimates from the existing methods are, in general, substantial, even when individual variability in growth is small and recruitment is uniform, and the generalized method performs better in terms of bias but is subject to a larger variation. There is a need to develop robust and flexible methods to deal with individual variability in the analysis of length-frequency data.

An improved Fabens method for estimation of growth parameters in the vonBertalanffy model with individual asymptotes

In the analysis of tagging data, it has been found that the least-squares method, based on the increment function known as the Fabens method, produces biased estimates because individual variability in growth is not allowed for. This paper modifies the Fabens method to account for individual variability in the length asymptote. Significance tests using t-statistics or log-likelihood ratio statistics may be applied to show the level of individual variability. Simulation results indicate that the modified method reduces the biases in the estimates to negligible proportions. Tagging data from tiger prawns (Penaeus esculentus and Penaeus semisulcatus) and rock lobster (Panulirus ornatus) are analysed as an illustration.

The impact of global positioning systems and plotters on fishing power in the northern prawn fishery, Australia

The impact of global positioning systems (GPS) and plotter systems on the relative fishing power of the northern prawn fishery fleet on tiger prawns (Penaeus esculentus Haswell, 1879, and P. semisulcatus de Haan, 1850) was investigated from commercial catch data. A generalized linear model was used to account for differences in fishing power between boats and changes in prawn abundance. It was found that boats that used a GPS alone had 4% greater fishing power than boats without a CPS. The addition of a plotter raised the power by 7% over boats without the equipment. For each year between the first to third that a fisher has been working with plotters, there is an additional 2 or 3% increase. It appears that when all boats have a GPS and plotter for at least 3 years, the fishing power of the fleet will increase by 12%. Management controls have reduced the efficiency of each boat and lowered the number of days available to fish, but this may not have been sufficient to counteract the increases. Further limits will be needed to maintain the desired levels of mortality.

The navigation and visualisation of environmental audio using zooming spectrograms

Acoustic recordings play an increasingly important role in monitoring terrestrial and aquatic environments. However, rapid advances in technology make it possible to accumulate thousands of hours of recordings, more than ecologists can ever listen to. Our approach to this big-data challenge is to visualize the content of long-duration audio recordings on multiple scales, from minutes, hours, days to years. The visualization should facilitate navigation and yield ecologically meaningful information prior to listening to the audio. To construct images, we calculate acoustic indices, statistics that describe the distribution of acoustic energy and reflect content of ecological interest. We combine various indices to produce false-color spectrogram images that reveal acoustic content and facilitate navigation. The technical challenge we investigate in this work is how to navigate recordings that are days or even months in duration. We introduce a method of zooming through multiple temporal scales, analogous to Google Maps. However, the “landscape” to be navigated is not geographical and not therefore intrinsically visual, but rather a graphical representation of the underlying audio. We describe solutions to navigating spectrograms that range over three orders of magnitude of temporal scale. We make three sets of observations: 1. We determine that at least ten intermediate scale steps are required to zoom over three orders of magnitude of temporal scale; 2. We determine that three different visual representations are required to cover the range of temporal scales; 3. We present a solution to the problem of maintaining visual continuity when stepping between different visual representations. Finally, we demonstrate the utility of the approach with four case studies.