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.

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

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.

Growth curves with explanatory variables and estimation of the effect of tagging

The von Bertalanffy growth model is extended to incorporate explanatory variables. The generalized model includes the switched growth model and the seasonal growth model as special cases, and can also be used to assess the tagging effect on growth. Distribution-free and consistent estimating functions are constructed for estimation of growth parameters from tag-recapture data in which age at release is unknown. This generalizes the work of James (1991, Biometrics 47 1519-1530) who considered the classical model and allowed for individual variability in growth. A real dataset from barramundi (Lates calcarifer) is analysed to estimate the growth parameters and possible effect of tagging on growth.

Harvest strategy evaluation to optimise the sustainability and value of the Queensland scallop fishery. Queensland scallop fishery - FRDC Project No 2006/024 Final Report

Objective 1. Measure spatial and temporal trawl frequency of scallop grounds using VMS data. This will provide a relative measure of how often individual undersized scallops are caught and put through a tumbler 2. Estimate discard mortality and growth rates for saucer scallops using cage experiments. 3. Evaluate the current management measures, in particular the seasonal closure, rotational closure and seasonally varying minimum legal sizes using stock assessment and management modeling models. Recommend optimal range of management measures to ensure long-term viability and value of the Scallop fishery based on a formal management strategy evaluation. Outcomes acheived to date: 1. Improved understanding of the survival rates of discarded sub-legal scallops; 2. Preliminary von Bertalanffy growth parameters using data from tagged-and-released scallops; 3. Changing trends in vessels and fishing gear used in the Queensland scallop fishery and their effect on scallop catch rates over time using standardised catch rates quantified; 4. Increases in fishing power of vessels operating in the Queensland scallop fishery quantified; 5. Trawl intensity mapped and quantified for all Scallop Replenishment Areas; 6. Harvest Strategy Evaluations completed.

Latitudinal and seasonal effects on growth of the Australian eastern king prawn (Melicertus plebejus)

The growth of the Australian eastern king prawn (Melicertus plebejus) is understood in greater detail by quantifying the latitudinal effect. The latitudinal effect is the change in the species’ growth rate during migration. Mark–recapture data (N = 1635, latitude 22.21°S–34.00°S) presents northerly movement of the eastern king prawn, with New South Wales prawns showing substantial average movement of 140 km (standard deviation: 176 km) north. A generalized von Bertalanffy growth model framework is used to incorporate the latitudinal effect together with the canonical seasonal effect. Applying this method to eastern king prawn mark–recapture data guarantees consistent estimates for the latitudinal and seasonal effects. For M. plebejus, it was found that growth rate peaks on 25 and 29 January for males and females, respectively; is at a minimum on 27 and 31 July, respectively; and that the shape parameter, k (per year), changes by –0.0236 and –0.0556 every 1 degree of latitude south increase for males and females, respectively.

Spatial variation in life history reveals insight into connectivity and geographic population structure of a tropical estuarine teleost: king threadfin, Polydactylus macrochir

Understanding the life history of exploited fish species is not only critical in developing stock assessments and productivity models, but has a dual function in the delineation of connectivity and geographical population structure. In this study, patterns in growth and length and age at sex change of Polydactylus macrochir, an ecologically and economically important protandrous estuarine teleost, were examined to provide preliminary information on the species' connectivity and geographic structure across northern Australia. Considerable variation in life history parameters was observed among the 18 locations sampled. Both unconstrained and constrained (t(0) = 0) estimates of von Bertalanffy growth function parameters differed significantly among all neighbouring locations with the exception of two locations in Queensland's east coast and two in Queensland's Gulf of Carpentaria waters, respectively. Comparisons of back-calculated length-at-age 2 provided additional evidence for growth differences among some locations, but were not significantly different among locations in the south-eastern Gulf of Carpentaria or on Queensland's east coast. The length and age at sex change differed markedly among locations, with fish from the east coast of Australia changing sex from males to females at significantly greater lengths and ages than elsewhere. Sex change occurred earliest at locations within Queensland's Gulf of Carpentaria, where a large proportion of small, young females were recorded. The observed differences suggest that P. macrochir likely form a number of geographically and/or reproductively distinct groups in Australian waters and suggest that future studies examining connectivity and geographic population structure of estuarine fishes will likely benefit from the inclusion of comparisons of life history parameters. (C) 2012 Elsevier B.V. All rights reserved.

Long-term variation of tropical rock lobster panulirus ornatus (decapoda, palinuridae) growth inTorres Strait, Australia

This analysis of all carapace length measurements collected between 1989 and 2009, during scientific surveys, describes the variation of tropical rock lobster, Panulirus ornatus, somatic growth in Torres Strait. Multiple models of carapace length frequency distributions were compared by maximum likelihood to determine which hypotheses were most supported by the data. The best model assumed sex and cohort-specific Von Bertalanffy's parameters. These estimates are consistent with results derived from tagging data collected in the 1980s and provide new information on parameters' uncertainty. In the past two decades, growth rates have fluctuated inter-annually without displaying any distinctive trend. Associated uncertainties are large, suggesting that sampling will need to be intensified in order to detect an effect of climate change.

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).

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected. (C) 2013 Elsevier B.V. All rights reserved.

Growth in the Asian elephant

Records of captive Asian elephants (Elephas maximus) were used to derive parameters of the von Bertalanffy function for growth in height, body weight and circumference of tusks with age. There was some evidence for a post-pubertal secondary growth spurt in both male and female elephants. Domestic elephants which were born in captivity or captured at a young age also showed a reduced growth in height in both the sexes and in body weight in males compared to wild elephants. Aspects of allometric growth such as height-body weight relationship are examined. The height was twice the circumference of front foot throughout the life span, indicating an isometric relationship.

Evaluación del rendimiento pesquero potencial de la República Argentina: III. Edad y crecimiento de peces 1

Age and growth of populations of three fish species from sixteen lakes and reservoirs situated in the Patagonian Andean and the Patagonian Plateau Region (Argentina) were studied. They included two native species, the Patagonian smallmouth perch. (Percichthys trucha) and the Patagonian silverside (Patagonina hatcheri) and the introduced rainbow trout (Oncorhynchus mykiss). For the three species backcalculated lenght at age was obtained from scale readings. Von Bertalanffy growth curves were usually adjusted to data. For the three species, faster growth was related with lake productivity. (Document contains 38 pages.)

Recovery and status of shortnose sturgeon in the Hudson River

Shortnose sturgeon (Acipenser brevirostrum), an endangered species, has experienced a several-fold increase in abundance in the Hudson River in recent decades. This population growth followed a substantial improvement in water quality during the 1970s to a large portion (c. 40%) of the species' summertime nursery area. Age structure and growth were investigated to evaluate the hypothesis that improvements in water quality stimulated population recovery through increased survival of young of the year juveniles. Specimens were captured using gill nets bi-monthly from November 2003 to November 2004 (n = 596). Annuli in fin spine sections were used to generate estimates of sturgeon age. Based upon a marginal increment analysis, annuli were determined to form at an annual rate. Age determinations yielded a catch composed of age 5-30 years for sizes 49-105cm Total Length (n = 554). Individual growth rate (von Bertalanffy coefficients: TL, = 1045mm, K = 0.07) for the population was similar to previous growth estimates within the Hudson River as well as proximal estuaries. Hindcast year-class strengths, based upon a recent stock assessment (Bain et al. 2000) and corrected for gill net mesh selectivity and cumulative mortality indicated high recruitments (28,000-43,000 yearlings)during 1986-1992, which were preceded and succeeded by c.5-year periods of lower recruitment (5,000-1 5,000 yearlings). Recruitment patterns were corroborated by trends in shortnose sturgeon bycatch from a Hudson utilities-sponsored monitoring program. Results indicated that Hudson River shortnose sturgeon abundance increased due to the formation of several strong year-classes occurring about five years subsequent to improved water quality in important nursery and forage habitats in the upper Hudson River estuary. (PDF contains 108 pages.)

Population dynamics of the skipjack tuna (Katsuwonus pelamis) of the Eastern Pacific Ocean

ENGLISH: Catches of skipjack tuna supporting major fisheries in parts of the western, central and eastern Pacific Ocean have increased in recent years; thus, it is important to examine the dynamics of the fishery to determine man's effect on the abundance of the stocks. A general linear hypothesis model was developed to standardize fishing effort to a single vessel size and gear type. Standardized effort was then used to compute an index of abundance which accounts for seasonal variability in the fishing area. The indices of abundance were highly variable from year to year in both the northern and southern areas of the fishery but indicated a generally higher abundance in the south. Data from 438 fish tagged and recovered in the eastern Pacific Ocean were used to compute growth curves. A least-squares technique was used to estimate the parameters of the von Bertalanffy growth function. Two estimates of the parameters were made by analyzing the same data in different ways. For the first set of estimates, K= 0.819 on an annual instantaneous basis and L= 729 mm; for the second, K = 0.431 and L=881. These compared well with estimates derived using the Chapman-Richards growth function, which includes the von Bertalanffy function as a special case. It was concluded that the latter function provided an adequate empirical fit to the skipjack data since the more complicated function did not significantly improve the fit. Tagging data from three cruises involving 8852 releases and 1777 returns were used to compute mortality rates during the time the fish were in the fishery. Two models were used in the analyses. The best estimates of the catchability coefficient (q) in the north and south were 8.4 X 10- 4 and 5.0 X 10- 5 respectively. The other loss rate (X), which included losses due to emigration, natural mortality and mortality due to carrying a tag, was 0.14 on an annual instantaneous basis for both areas. To detect the possible effect of fishing on abundance and total yield, the relation between abundance and effort and between total catch and effort was examined. It was found that at levels of intensity observed in the fishery, fishing does not appear to have had any measurable effect on the stocks. It was concluded therefore that the total catch could probably be increased by substantially increasing total effort beyond the present level, and that the fluctuations in abundance are fishery-independent. The estimates of growth, mortality and fishing effort were used to compute yield-per-recruitment isopleths for skipjack in both the northern and southern areas. For a size at first entry of about 425 mm, the yield per recruitment was calculated at 3 pounds in the north and 1.5 pounds in the south. In both areas it would be possible to increase the yield per recruitment by increasing fishing effort. It was not possible to assess potential production of the skipjack stocks fished in the eastern Pacific, except to note that the fishery had not affected their abundance and that they were certainly under-exploited. It was concluded that the northern and southern stocks could support increased harvests, especially the latter. SPANISH: Las capturas de atún barrilete que sostienen las pesquerías principales de la parte occidental, central y oriental del Océano Pacífico han aumentado en los últimos años; así que es importante examinar la dinámica de la pesquería para determinar el efecto que pueda tener sobre la abundancia de los stocks. Se desarrolló un modelo hipotético, lineal para standardizar el esfuerzo de pesca a un solo tamaño de barco y tipo de arte. Luego se usó el esfuerzo standardizado para computar un índice de la abundancia que pueda dar razón de la variabilidad estacional en el área de pesca. Los índices de la abundancia variaron mucho de un año a otro tanto en el área septentrional como en el área meridional de la pesquería, pero indicaron una abundancia generalmente superior en el sur. Se emplearon los datos de 438 peces marcados y recuperados en el Océano Pacífico oriental para computar las curvas de crecimiento. Una técnica de mínimos cuadrados fue usada para estimar los parámetros de la función de crecimiento de van Bertalanffy. Se hicieron dos estimativos de los parámetros mediante el análisis de los mismos datos, de diferente manera. Para el primer juego de estimativos, K=0.819 sobre una base anual instantánea y L∞=729 mm; para el segundo, K=0.431 y L∞=881. Estos se correlacionaron bien con los estimativos obtenidos usando la función de crecimiento de Chapman-Richards, que incluye la de von Bertalanffy como un caso especial. Se decidió que la última función proveía un ajuste empírico, adecuado a los datos del barrilete, ya que la función más complicada no mejoró significativamente el ajuste. Los datos de marcación de tres cruceros incluyendo 8852 liberaciones y 1777 retornos, fueron usados para computar las tasas de mortalidad durante el tiempo en que los peces estuvieron en la pesquería. Se usaron dos modelos en los análisis. Los mejores estimativos del coeficiente de capturabilidad (q) en el norte y en el sur fueron 8.4 X 10-4 y 5.0 X 10-5 , respectivamente. La otra tasa de pérdida (X), la cual incluyó pérdidas debidas a la emigración, mortalidad natural y mortalidad debida a llevar una marca, fue 0.14 sobre una base anual instantánea para las dos áreas. Con el fin de descubrir el efecto que posiblemente pueda tener la pesca sobre la abundancia y el rendimiento total, se examinó la relación entre la abundancia y el esfuerzo y entre la captura total y el esfuerzo. Se encontró que a los niveles de la intensidad observada en la pesquería, la pesca no parece haber tenido ningún efecto perceptible en los stocks. Por lo tanto se decidió que mediante un aumento substancial del esfuerzo total, más allá del nivel actual, la captura total probablemente podría aumentarse, y que las fluctuaciones de la abundancia son independientes de la pesquería. Los estimativos del crecimiento, mortalidad y esfuerzo de pesca fueron usados para computar las isopletas del rendimiento por recluta del barrilete, tanto en las áreas del norte como del sur. Para una talla de primera entrada de unos 425 mm, el rendimiento por recluta fue calculado en 3 libras en el norte y 1.5 libras en el sur. En ambas áreas sería posible aumentar el rendimiento por recluta mediante un aumento del esfuerzo de pesca. No fue posible determinar la producción potencial de los stocks del barrilete pescado en el Pacífico oriental, excepto para observar que la pesquería no ha afectado su abundancia y que ciertamente se encuentran subexplotados. Se concluyó que los stocks norte y sur pueden soportar un aumento en el rendimiento, especialmente este último. (PDF contains 274 pages.)

The age and growth of the tongue sole Cynoglossus canariensis (Steind 1882)

The geometric mean regression equation for the weight; length relationship of Cynoglossus canariensis was W = 0.0025 L super(3.1770). The Von Bertalanffy constants Woo, Loo, K, and to were 507.5852 g, 47.3683 cm, 0.3333 and 0.1397 for males and 839.0753 g, 54.4720 cm, 0.3062 and 0.1737 for females. Total mortality coefficient Z ranged from 0.6482 and 0.8021