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.

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.

Trapping to monitor tephritid movement: Results, best practice, and assessment of alternatives

Movement of tephritid flies underpins their survival, reproduction, and ability to establish in new areas and is thus of importance when designing effective management strategies. Much of the knowledge currently available on tephritid movement throughout landscapes comes from the use of direct or indirect methods that rely on the trapping of individuals. Here, we review published experimental designs and methods from mark-release-recapture (MRR) studies, as well as other methods, that have been used to estimate movement of the four major tephritid pest genera (Bactrocera, Ceratitis, Anastrepha, and Rhagoletis). In doing so, we aim to illustrate the theoretical and practical considerations needed to study tephritid movement. MRR studies make use of traps to directly estimate the distance that tephritid species can move within a generation and to evaluate the ecological and physiological factors that influence dispersal patterns. MRR studies, however, require careful planning to ensure that the results obtained are not biased by the methods employed, including marking methods, trap properties, trap spacing, and spatial extent of the trapping array. Despite these obstacles, MRR remains a powerful tool for determining tephritid movement, with data particularly required for understudied species that affect developing countries. To ensure that future MRR studies are successful, we suggest that site selection be carefully considered and sufficient resources be allocated to achieve optimal spacing and placement of traps in line with the stated aims of each study. An alternative to MRR is to make use of indirect methods for determining movement, or more correctly, gene flow, which have become widely available with the development of molecular tools. Key to these methods is the trapping and sequencing of a suitable number of individuals to represent the genetic diversity of the sampled population and investigate population structuring using nuclear genomic markers or non-recombinant mitochondrial DNA markers. Microsatellites are currently the preferred marker for detecting recent population displacement and provide genetic information that may be used in assignment tests for the direct determination of contemporary movement. Neither MRR nor molecular methods, however, are able to monitor fine-scale movements of individual flies. Recent developments in the miniaturization of electronics offer the tantalising possibility to track individual movements of insects using harmonic radar. Computer vision and radio frequency identification tags may also permit the tracking of fine-scale movements by tephritid flies by automated resampling, although these methods come with the same problems as traditional traps used in MRR studies. Although all methods described in this chapter have limitations, a better understanding of tephritid movement far outweighs the drawbacks of the individual methods because of the need for this information to manage tephritid populations.

The complexities of knowing what it is you are trapping

The effectiveness of any trapping system is highly dependent on the ability to accurately identify the specimens collected. For many fruit fly species, accurate identification (= diagnostics) using morphological or molecular techniques is relatively straightforward and poses few technical challenges. However, nearly all genera of pest tephritids also contain groups of species where single, stand-alone tools are not sufficient for accurate identification: such groups include the Bactrocera dorsalis complex, the Anastrepha fraterculus complex and the Ceratitis FAR complex. Misidentification of high-impact species from such groups can have dramatic consequences and negate the benefits of an otherwise effective trapping program. To help prevent such problems, this chapter defines what is meant by a species complex and describes in detail how the correct identification of species within a complex requires the use of an integrative taxonomic approach. Integrative taxonomy uses multiple, independent lines of evidence to delimit species boundaries, and the underpinnings of this approach from both the theoretical speciation literature and the systematics/taxonomy literature are described. The strength of the integrative approach lies in the explicit testing of hypotheses and the use of multiple, independent species delimitation tools. A case is made for a core set of species delimitation tools (pre- and post-zygotic compatibility tests, multi-locus phylogenetic analysis, chemoecological studies, and morphometric and geometric morphometric analyses) to be adopted as standards by tephritologists aiming to resolve economically important species complexes. In discussing the integrative approach, emphasis is placed on the subtle but important differences between integrative and iterative taxonomy. The chapter finishes with a case study that illustrates how iterative taxonomy applied to the B. dorsalis species complex led to incorrect taxonomic conclusions, which has had major implications for quarantine, trade, and horticultural pest management. In contrast, an integrative approach to the problem has resolved species limits in this taxonomically difficult group, meaning that robust diagnostics are now available.