Estimates of growth and comparisons of growth rates determined from length- and age-based models for populations of purple wrasse (Notolabrus fucicola)

Growth of a temperate reefa-ssociated fish, the purple wrasse (Notolabrus fucicola), was examined from two sites on the east coast of Tasmania by using age- and length-based models. Models based on the von Bertalanffy growth function, in the standard and a reparameterized form, were constructed by using otolith-derived age estimates. Growth trajectories from tag-recaptures were used to construct length-based growth models derived from the GROTAG model, in turn a reparameterization of the Fabens model. Likelihood ratio tests (LRTs) determined the optimal parameterization of the GROTAG model, including estimators of individual growth variability, seasonal growth, measurement error, and outliers for each data set. Growth models and parameter estimates were compared by bootstrap confidence intervals, LRTs, and randomization tests and plots of bootstrap parameter estimates. The relative merit of these methods for comparing models and parameters was evaluated; LRTs combined with bootstrapping and randomization tests provided the most insight into the relationships between parameter estimates. Significant differences in growth of purple wrasse were found between sites in both length- and age-based models. A significant difference in the peak growth season was found between sites, and a large difference in growth rate between sexes was found at one site with the use of length-based models.

Fishery resource surveys: beyond length-weight relationship models

Fisheries resource surveys are regular management tools for rational exploitation of commercial fisheries. In a growing number of cases, the use of these resource surveys has been largely restricted to assessment of the relative well being of fish stocks and the potential yields of such fisheries. This paper seeks to demonstrate that the data from such surveys can also be easily used to evaluate species diversity of such fisheries, both in terms of species richness and equitability of distribution. Using published data on two freshwater and two marine fisheries as case studies, Shannon-Wiener Diversity Function and Simpson's Index were computed for each of these fisheries. These biodiversity indices gave a deeper insight into the environmental status of each of these fisheries, beyond what the length-weight relationship models can reveal. Generally, while the marine fisheries showed more species richness, the freshwater fisheries apparently had more stable and equilibrated fish communities

Length-frequency estimation for yellowfin tuna (Thunnus albacares) caught by commercial fishing gear in the Eastern Pacific Ocean

ENGLISH: Methods of collecting samples for the purpose of estimating the numbers and weights of fish caught, by length interval, are described. Several models for two-stage sampling are described, and the equations for the estimators and their variances are given. The results from a brief simulation study are used to show the differences between estimates made with the different models. Estimators for the average weights of fish in the catch and their variances are also described. These average weights are used to provide improved estimates of the total annual catches of yellowfin taken from the eastern Pacific Ocean, east of 150°W, between 1955 and 1990. SPANISH: Se describen los métodos de recoger de muestreo para estimar el número o peso de peces capturados, por intervalo de talla. Se describen varios modelos para el muestreo de dos etapas, y se presentan las ecuaciones para los estimadores y sus varianzas. Se usan los resultados de un breve estudio de simulación para indicar las diferencias entre estimaciones realizadas con los distintosmodelos. También se describe un estimador para el peso promedio de peces en la captura y su varianza. Se usan estos estimadores para calcular estimaciones mejoradas de las capturas anuales totales de aleta amarilla tomadas del Océano Pacífico oriental, al este de 150°W, entre 1955 y 1990. (PDF contains 41 pages.)

An evaluation of length-frequency sampling procedures and subsequent data analysis for purse seine-caught yellowfin tuna in the Eastern Pacific Ocean

ENGLISH: A two-stage sampling design is used to estimate the variances of the numbers of yellowfin in different age groups caught in the eastern Pacific Ocean. For purse seiners, the primary sampling unit (n) is a brine well containing fish from a month-area stratum; the number of fish lengths (m) measured from each well are the secondary units. The fish cannot be selected at random from the wells because of practical limitations. The effects of different sampling methods and other factors on the reliability and precision of statistics derived from the length-frequency data were therefore examined. Modifications are recommended where necessary. Lengths of fish measured during the unloading of six test wells revealed two forms of inherent size stratification: 1) short-term disruptions of existing pattern of sizes, and 2) transition zones between long-term trends in sizes. To some degree, all wells exhibited cyclic changes in mean size and variance during unloading. In half of the wells, it was observed that size selection by the unloaders induced a change in mean size. As a result of stratification, the sequence of sizes removed from all wells was non-random, regardless of whether a well contained fish from a single set or from more than one set. The number of modal sizes in a well was not related to the number of sets. In an additional well composed of fish from several sets, an experiment on vertical mixing indicated that a representative sample of the contents may be restricted to the bottom half of the well. The contents of the test wells were used to generate 25 simulated wells and to compare the results of three sampling methods applied to them. The methods were: (1) random sampling (also used as a standard), (2) protracted sampling, in which the selection process was extended over a large portion of a well, and (3) measuring fish consecutively during removal from the well. Repeated sampling by each method and different combinations indicated that, because the principal source of size variation occurred among primary units, increasing n was the most effective way to reduce the variance estimates of both the age-group sizes and the total number of fish in the landings. Protracted sampling largely circumvented the effects of size stratification, and its performance was essentially comparable to that of random sampling. Sampling by this method is recommended. Consecutive-fish sampling produced more biased estimates with greater variances. Analysis of the 1988 length-frequency samples indicated that, for age groups that appear most frequently in the catch, a minimum sampling frequency of one primary unit in six for each month-area stratum would reduce the coefficients of variation (CV) of their size estimates to approximately 10 percent or less. Additional stratification of samples by set type, rather than month-area alone, further reduced the CV's of scarce age groups, such as the recruits, and potentially improved their accuracy. The CV's of recruitment estimates for completely-fished cohorts during the 198184 period were in the vicinity of 3 to 8 percent. Recruitment estimates and their variances were also relatively insensitive to changes in the individual quarterly catches and variances, respectively, of which they were composed. SPANISH: Se usa un diseño de muestreo de dos etapas para estimar las varianzas de los números de aletas amari11as en distintos grupos de edad capturados en el Océano Pacifico oriental. Para barcos cerqueros, la unidad primaria de muestreo (n) es una bodega de salmuera que contenía peces de un estrato de mes-área; el numero de ta11as de peces (m) medidas de cada bodega es la unidad secundaria. Limitaciones de carácter practico impiden la selección aleatoria de peces de las bodegas. Por 10 tanto, fueron examinados los efectos de distintos métodos de muestreo y otros factores sobre la confiabilidad y precisión de las estadísticas derivadas de los datos de frecuencia de ta11a. Se recomiendan modificaciones donde sean necesarias. Las ta11as de peces medidas durante la descarga de seis bodegas de prueba revelaron dos formas de estratificación inherente por ta11a: 1) perturbaciones a corto plazo en la pauta de ta11as existente, y 2) zonas de transición entre las tendencias a largo plazo en las ta11as. En cierto grado, todas las bodegas mostraron cambios cíclicos en ta11a media y varianza durante la descarga. En la mitad de las bodegas, se observo que selección por ta11a por los descargadores indujo un cambio en la ta11a media. Como resultado de la estratificación, la secuencia de ta11as sacadas de todas las bodegas no fue aleatoria, sin considerar si una bodega contenía peces de un solo lance 0 de mas de uno. El numero de ta11as modales en una bodega no estaba relacionado al numero de lances. En una bodega adicional compuesta de peces de varios lances, un experimento de mezcla vertical indico que una muestra representativa del contenido podría estar limitada a la mitad inferior de la bodega. Se uso el contenido de las bodegas de prueba para generar 25 bodegas simuladas y comparar los resultados de tres métodos de muestreo aplicados a estas. Los métodos fueron: (1) muestreo aleatorio (usado también como norma), (2) muestreo extendido, en el cual el proceso de selección fue extendido sobre una porción grande de una bodega, y (3) medición consecutiva de peces durante la descarga de la bodega. EI muestreo repetido con cada método y distintas combinaciones de n y m indico que, puesto que la fuente principal de variación de ta11a ocurría entre las unidades primarias, aumentar n fue la manera mas eficaz de reducir las estimaciones de la varianza de las ta11as de los grupos de edad y el numero total de peces en los desembarcos. El muestreo extendido evito mayormente los efectos de la estratificación por ta11a, y su desempeño fue esencialmente comparable a aquel del muestreo aleatorio. Se recomienda muestrear con este método. El muestreo de peces consecutivos produjo estimaciones mas sesgadas con mayores varianzas. Un análisis de las muestras de frecuencia de ta11a de 1988 indico que, para los grupos de edad que aparecen con mayor frecuencia en la captura, una frecuencia de muestreo minima de una unidad primaria de cada seis para cada estrato de mes-área reduciría los coeficientes de variación (CV) de las estimaciones de ta11a correspondientes a aproximadamente 10% 0 menos. Una estratificación adicional de las muestras por tipo de lance, y no solamente mes-área, redujo aun mas los CV de los grupos de edad escasos, tales como los reclutas, y mejoró potencialmente su precisión. Los CV de las estimaciones del reclutamiento para las cohortes completamente pescadas durante 1981-1984 fueron alrededor de 3-8%. Las estimaciones del reclutamiento y sus varianzas fueron también relativamente insensibles a cambios en las capturas de trimestres individuales y las varianzas, respectivamente, de las cuales fueron derivadas. (PDF contains 70 pages)

Length and sex effects on the spatial structure of catches of Pacific halibut (Hippoglossus stenolepis) on longline gear

Field experiments were conducted to test the hypotheses that Pacific halibut (Hippoglossus stenolepis) display small-scale spatial structure within longline catches, relative to other species and empty hooks, or within-species based on sex or length. Sequential hook-by-hook inventories, along with length and sex data, were taken at thirty-one survey stations. Two-dimensional spatial statistics were used to test for 1) aggregation, defined as the clustering of individuals within a given demographic of size or sex over small intervals of distance; and 2) segregation, defined as the sequential occurrence of individuals within a given demographic of size or sex, uninterrupted by other observations, irrespective of the distance between individuals. Statistically significant structure was detected within catches that is more commonly associated with fish length than sex. Significant spatial structuring occurred at 60% of all stations tested. Significant aggregation of halibut of legal length for commercial retention (≥82 cm) was detected at 44% of stations and aggregation of sublegal-size halibut was detected at 11%. Maleand female-based aggregations were observed at 22% and 11% of stations, respectively. Significant segregation of females was observed at 20% of stations, male segregation occurred at 8% of stations, and segregation by size at 16% of stations. Understanding small-scale spatial structure within longline catches may help us interpret changes in survey and commercial catch data. If structure is generated by behavior, then observed size-at-age or relative sex-ratios may be biased relative to underlying distributions. Although physical processes such as gape limitation should remain stable over the time, dynamic processes may be spatially and temporally variabl

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity.

Age and growth of spiny dogfish (Squalus acanthias) in the Gulf of Alaska: analysis of alternative growth models

Ten growth models were fitted to age and growth data for spiny dogfish (Squalus acanthias) in the Gulf of Alaska. Previous studies of spiny dogfish growth have all fitted the t0 formulation of the von Bertalanffy model without examination of alternative models. Among the alternatives, we present a new two-phase von Bertalanffy growth model formulation with a logistically scaled k parameter and which estimates L0. A total of 1602 dogfish were aged from opportunistic collections with longline, rod and reel, set net, and trawling gear in the eastern and central Gulf of Alaska between 2004 and 2007. Ages were estimated from the median band count of three independent readings of the second dorsal spine plus the estimated number of worn bands for worn spines. Owing to a lack of small dogfish in the samples, lengths at age of small individuals were back-calculated from a subsample of 153 dogfish with unworn spines. The von Bertalanffy, two-parameter von Bertalanffy, two-phase von Bertalanffy, Gompertz, two-parameter Gompertz, and logistic models were fitted to length-at-age data for each sex separately, both with and without back-calculated lengths at age. The two-phase von Bertalanffy growth model produced the statistically best fit for both sexes of Gulf of Alaska spiny dogfish, resulting in L∞ = 87.2 and 102.5 cm and k= 0.106 and 0.058 for males and females, respectively.

Age- and length-at-maturity of female arrowtooth flounder (Atheresthes stomias) in the Gulf of Alaska

Arrowtooth flounder (Atheresthes stomias) has had the highest abundance of any groundfish species in the Gulf of Alaska since the 1970s (Matarese et al., 2003; Turnock et al., 2005; Blood et al., 2007); however, commercial catches have been restricted because Pacific halibut (Hippoglossus stenolepis) are caught as bycatch in the fishery. Arrowtooth flounder plays a key role in the ecosystem because it is a dominant organism within the food web, both as an apex predator of fish and invertebrates, as well as an important prey for walleye pollock (Theragra chalcogramma; Aydin et al., 2002). Walleye pollock is the dominant groundfish in the Bering Sea, a principal groundfish in the Gulf of Alaska, and the primary prey for marine mammals. The distribution of arrowtooth flounder extends from Cape Navarin and the eastern Sea of Okhotsk in Russia, across the Bering Sea, Aleutian Islands, Gulf of Alaska, and south to the coast of central California (Shuntov, 1964; Britt and Martin, 2001; Chetvergov, 2001; Weinberg et al., 2002; Zenger, 2004). Because of the importance of arrowtooth flounder in the marine ecosystem of A laska, a maturity study of this species was undertaken to determine age-at-maturity, which is essential for age-based stock management models. Before these results, management has had to rely upon a length-at-maturity-based estimate (Zimmermann, 1997) to manage stocks in the Gulf of Alaska (GOA), Bering Sea, and Aleutian Islands. The central GOA was selected as the location for this maturity study Age- and length-at-maturity of female arrowtooth flounder (Atheresthes stomias) in the Gulf of Alaska because it contains approximately 70% of the total Gulf of Alaska arrowtooth flounder biomass (1.9×106 t, age 3 and older)— the highest percentage in the world (Shuntov, 1964; Britt and Martin, 2001; Weinberg et al., 2002; Wilderbuer and Nichol, 2006).

Natural mortality rate, annual fecundity, and maturity at length for Greenland halibut (Reinhardtius hippoglossoides) from the northeastern Pacific Ocean

Mortality, fecundity, and size at maturity are important life history traits, and their interactions determine the evolution of life history strategies (Roff, 1992; Stearns, 1992; Charnov, 2002). These same traits are also important for population dynamics models (Hunter et al., 1992; Clark, 1999). It is increasingly important to accurately determine Greenland halibut (Reinhardtius hippoglossoides) life history traits and to correctly assess the status of its stocks because low recruitment or low biomass estimates have led to catch restrictions in the Bering Sea and Aleutian Islands (Ianelli et al.1), the Northeastern Arctic (Ådlandsvik et al., 2004), and the Northwest Atlantic (Bowering and Nedreaas, 2000).

Parameterizing probabilities for estimating age-composition distributions for mixture models

When estimating parameters that constitute a discrete probability distribution {pj}, it is difficult to determine how constraints should be made to guarantee that the estimated parameters { pˆj} constitute a probability distribution (i.e., pˆj>0, Σ pˆj =1). For age distributions estimated from mixtures of length-at-age distributions, the EM (expectationmaximization) algorithm (Hasselblad, 1966; Hoenig and Heisey, 1987; Kimura and Chikuni, 1987), restricted least squares (Clark, 1981), and weak quasisolutions (Troynikov, 2004) have all been used. Each of these methods appears to guarantee that the estimated distribution will be a true probability distribution with all categories greater than or equal to zero and with individual probabilities that sum to one. In addition, all these methods appear to provide a theoretical basis for solutions that will be either maximum-likelihood estimates or at least convergent to a probability distribut

Length-girth relationships of Barbodes gonionotus and Hampala macrolepidota in the Jatiluhur reservoir, Indonesia

The length-girth relationships of Javanese carp (Barbodes gonionotus) and hampal carp (Hampala macrolepidota) in the Jatilujur Reservoir, Indonesia were examined. The equations derived from estimating the maximum girth of Javanese carp are G sub(m) = -1.19 + 0.80L, and for the hampal carp, G super(m) = -0.47 + 0.62L. Models relating head girth to total length are also given. The relationship between G sub(m) (maximum girth) of fish caught and gillnet mesh size is also briefly discussed.

Length-weight Relationships of Dolphinfish, Coryphaena hippurus, and Wahoo, Acanthocybium solandri: Seasonal Effects of Spawning and Possible Migration in the Central North Pacific

Weight-on-length (W-L) relationships for 2,482 dolphinfish, Coryphaena hippurus, and 1,161 wahoo, Acanthocybium solandri, were examined. Data on fork length, whole (round) weight, and sex were collected for dolphinfish at the Honolulu fish auction from March 1988 through November 1989. Unsexed weight and length data for wahoo were collected at the auction from July 1988 through November 1989. We also used sex specific weight and length data of 171 wahoo collected during 1977–1985 research cruises for analysis. Coefficients of W-L regressions were significantly different between the sexes for dolphinfish. Coefficients did not significantly differ between the sexes for wahoo based on research cruise data. In a general linear model evaluating month as a categorical factor, month was significant for female dolphinfish, male dolphinfish, and wahoo with sexes pooled. W-L and length-on-weight (L-W) relationships were fitted by nonlinear regression for all dolphinfish, female dolphinfish, male dolphinfish, and all wahoo sexes pooled. W-L relationships for monthly samples of female dolphinfish, male dolphinfish, and all wahoo with sexes pooled were also fitted by nonlinear regression. Predicted mean weight at length for wahoo was highest at the beginning of the spawning season in June and lowest after the spawning season in September. Maximum and minimum predicted mean weight at length for both sexes of dolphinfish did not correspond with the peak spawning period (March–May). Plausible migration models in conjunction with reproductive behavior were examined to explain the variability in monthly predicted mean weight at length for dolphinfish.

Morphometrics, length-weight relationship and condition of Rastrineobola argentea (Pellegrin 1904) in the Winam Gulf of Lake Victoria (Kenya)

Correlation between total length (TL), fork length (FL) and standard length (SL) of Raslrineobola argentea (pellegrin 1904) in the Winam Gulf of Lake Victoria indicate that FL = 0.92 TL - 0.74 and SL = 0.90 TL - 1.74. Length-weight relationship of log-transformed data shows that the slopes of the regression lines were 3.06 to 3.22 for juveniles, 2.70 to 3.05 for males and 3.24 to 3.71 for females. The slopes were significantly different between groups at at a =0.05. The Fulton's condition factor (K) was highest in December (1.019-1.073) and March/April (1.015-1.030) but lowest in June (1:00-1.025) for all stations. Significant differences between groups demands for the use of different growth models for juveniles, males and females especially for the von Bertalanffy growth equation which uses length-weight relationship. Observed cyclic viations in condition factor suggests two peak breeding seasons for this species in the Winam Gulf. The practical lmplications of these results in stock assessment using length-based fish stock assessment methods is briefly discussed.