145 resultados para Third age


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ENGLISH: The spawning of Pacific northern bluefin tuna, Thunnus thynnus, takes place only in the western Pacific Ocean (WPO), but substantial numbers of the juveniles migrate to the eastern Pacific Ocean (EPO), where they remain for several months, or longer, and the.n return to the WPO. Lengthfrequency and tagging data show that many bluefin arrive in the EPO as 1-and 2-year olds, and remain there for one or two fishing seasons before returning to the WPO. The proportion of the fish which make the west-to-east migration varies among years. The numbers of 1-, 2-, 3-, 4, and >4 –year olds in the catches of the EPO are estimated for most years of the 1952-1991 period. SPANISH: EI desove del atun aleta azul del norte del Pacifico, Thunnus thynnus, ocurre solamente en el Océano Pacifico occidental (WPO), pero números substanciales de los juveniles migran al Océano Pacifico oriental (OPO), donde permanecen unos meses, 0 mas, antes de regresar al WPO. Datos de marcado y frecuencia de talla indican que muchos aletas azules llegan al OPO a 1 o 2 anos de edad, y permanecen alIi una 0 dos temporadas de pesca antes de regresar al WPO. La proporcion de los peces que migra del oeste al este varia entre anos. Se estima el numero de peces de 1, 2, 3, 4, Y>4 anos de edad en las capturas del OPO para la mayoria de los anos del periodo de 1952-1991. (PDF contains 40 pages.)

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The FIDAWOG workshop held from 29 March to 1 April 1999 in Jinja was the third major stock assessment workshop attended by most of the participants during the project. It followed two workshops, each of which lasted three weeks, held in 1998.

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The age and growth of Mugil cephalus was investigated in Bonny Estuary, Nigeria, from January, 1995 to December, 1996. Length-weight relationships were isometric with length exponents of 2.84 (males), 2.90 (females) and 2.88 (overall). Modal length at age were 12.0cm, 20.9cm, 25.0cm, 28.4cm and 30.2cm TL for ages 0+, 1+, 2+, 3+ and 4+ respectively. Corresponding total weights were 20.01g, 78.93g, 173.12g, 217.61g and 247.50g, respectively. Asymptotic length (Lo) was estimated 33.2cm TL, asymptotic weight (W sub(o)) was 484g, growth coefficient K=0.55847 super(-1) and hypothetical age at zero length To = 0.152yr. Longevity, Tmax, was 5.0yr, length and weight growth performance indices were Q super(1)=2.79 and Q = 1.44, respectively. Total mortality, natural mortality and fishing mortality were z = 1.02yr super(-1), M=0.607yr super(-1) and F=O. 3129yr super(-1), respectively. The exploitation ratio E was 0.4048 and exploitation rate U = 0.2302yr super(-1)

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The rate of sea level change has varied considerably over geological time, with rapid increases (0.25 cm yr-1) at the end of the last ice age to more modest increases over the last 4,000 years (0.04 cm yr-1; Hendry 1993). Due to anthropogenic contributions to climate change, however, the rate of sea level rise is expected to increase between 0.10 and 0.25 cm year-1 for many coastal areas (Warrick et al. 1996). Notwithstanding, it has been predicted that over the next 100 years, sea levels along the northeastern coast of North Carolina may increase by an astonishing 0.8 m (0.8 cm yr-1); through a combination of sea-level rise and coastal subsidence (Titus and Richman 2001; Parham et al. 2006). As North Carolina ranks third in the United States with land at or just above sea level, any additional sea rise may promote further deterioration of vital coastal wetland systems. (PDF contains 4 pages)

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English: Food selection of first-feeding yellowfin tuna larvae was studied in the laboratory during October 1992. The larvae were hatched from eggs obtained by natural spawning of yellowfin adults held in sea pens adjacent to Ishigaki Island, Okinawa Prefecture, Japan. The larvae were fed mixed-prey assemblages consisting of size-graded wild zooplankton and cultured rotifers. Yellowfin larvae were found to be selective feeders during the first four days of feeding. Copepod nauplii dominated the diet numerically, by frequency of occurrence and by weight. The relative importance of juvenile and adult copepods (mostly cyclopoids) in the diet increased over the 4-day period. Rotifers, although they comprised 31 to 40 percent of the available forage, comprised less than 2.1 percent of the diet numerically. Prey selection indices were calculated taking into account the relative abundances of prey, the swimming speeds of yellowfin larvae and their prey, and the microscale influence of turbulence on encounter rates. Yellowfin selected for copepod nauplii and against rotifers, and consumed juvenile and adult copepods in proportion to their abundances. Yellowfin larvae may select copepod nauplii and cyclopoid juveniles and adults based on the size and discontinuous swimming motion of these prey. Rotifers may not have been selected because they were larger or because they exhibit a smooth swimming pattern. The best initial diet for the culture of yellowfin larvae may be copepod nauplii and cyclopoid juveniles and adults, due to the size, swimming motion, and nutritional content of these prey. If rotifers alone are fed to yellowfin larvae, the rotifers should be enriched with a nutritional supplement that is high in unsaturated fatty acids. Mouth size of yellowfin larvae increases rapidly within the first few days of feeding, which minimizes limitations on feeding due to prey size. Although yellowfin larvae initiate feeding on relatively small prey, they rapidly acquire the ability to add relatively large, rare prey items to the diet. This mode of feeding may be adaptive for the development of yellowfin larvae, which have high metabolic rates and live in warm mixed-layer habitats of the tropical and subtropical Pacific. Our analysis also indicates a strong potential for the influence of microscale turbulence on the feeding success of yellowfin larvae. --- Experiments designed to validate the periodicity of otolith increments and to examine growth rates of yellowfin tuna larvae were conducted at the Japan Sea-Farming Association’s (JASFA) Yaeyama Experimental Station, Ishigaki Island, Japan, in September 1992. Larvae were reared from eggs spawned by captive yellowfin enclosed in a sea pen in the bay adjacent to Yaeyama Station. Results indicate that the first increment is deposited within 12 hours of hatching in the otoliths of yellowfin larvae, and subsequent growth increments are formed dailyollowing the first 24 hours after hatching r larvae up to 16 days of age. Somatic and otolith gwth ras were examined and compared for yolksac a first-feeding larvae reared at constant water tempatures of 26�and 29°C. Despite the more rapid develo of larvae reared at 29°C, growth rates were nnificaifferent between the two treatments. Howeve to poor survival after the first four days, it was ssible to examine growth rates beyond the onset of first feeding, when growth differences may become more apparent. Somatic and otolith growth were also examined for larvae reared at ambient bay water temperatures during the first 24 days after hatching. timates of laboratory growth rates were come to previously reported values for laboratory-reared yelllarvae of a similar age range, but were lower than growth rates reported for field-collected larvae. The discrepancy between laboratory and field growth rates may be associated with suboptimal growth conditions in the laboratory. Spanish: Durante octubre de 1992 se estudió en el laboratorio la seleccalimento por larvaún aleta amarillmera alimentación. Las larvas provinieron de huevos obtenidosel desove natural de aletas amarillas adultos mantenidos en corrales marinos adyacentes a la Isla Ishigaki, Prefectura de Okinawa (Japón). Se alimentó a las larvas con presas mixtas de zooplancton silvestre clasificado por tamaño y rotíferos cultivados. Se descubrió que las larvas de aleta amarilla se alimentan de forma selectiva durante los cuatro primeros días de alimentación. Los nauplios de copépodo predominaron en la dieta en número, por frecuencia de ocurrencia y por peso. La importancia relativa de copépodos juveniles y adultos (principalmente ciclopoides) en la dieta aumentó en el transcurso del período de 4 días. Los rotíferos, pese a que formaban del 31 al 40% del alimento disponible, respondieron de menos del 2,1% de la dieta en número. Se calcularon índices de selección de presas tomando en cuenta la abundancia relativa de las presas, la velocidad de natación de las larvas de aleta amarilla y de sus presas, y la influencia a microescala de la turbulencia sobre las tasas de encuentro. Los aletas amarillas seleccionaron a favor de nauplios de copépodo y en contra de los rotíferos, y consumieron copépodos juveniles y adultos en proporción a su abundancia. Es posible que las larvas de aleta amarilla seleccionen nauplios de copépodo y ciclopoides juveniles y adultos con base en el tamaño y movimiento de natación discontinuo de estas presas. Es posible que no se hayan seleccionado los rotíferos a raíz de su mayor tamaño o su patrón continuo de natación. Es posible que la mejor dieta inicial para el cultivo de larvas de aleta amarilla sea nauplios de copépodo y ciclopoides juveniles y adultos, debido al tamaño, movimiento de natación, y contenido nutritivo de estas presas. Si se alimenta a las larvas de aleta amarilla con rotíferos solamente, se debería enriquecerlos con un suplemento nutritivo rico en ácidos grasos no saturados. El tamaño de la boca de las larvas de aleta amarilla aumenta rápidamente en los primeros pocos días de alimentación, reduciendo la limitación de la alimentación debida al tamaño de la presa. Pese a que las larvas de aleta amarilla inician su alimentación con presas relativamente pequeñas, se hacen rápidamente capaces de añadir presas relativamente grandes y poco comunes a la dieta. Este modo de alimentación podría ser adaptivo para el desarrollo de larvas de aleta amarilla, que tienen tasa metabólicas altas y viven en hábitats cálidos en la capa de mezcla en el Pacífico tropical y subtropical. Nuestro análisis indica también que la influencia de turbulencia a microescala es potencialmente importante para el éxito de la alimentación de las larvas de aleta amarilla. --- En septiembre de 1992 se realizaron en la Estación Experimental Yaeyama de la Japan Sea- Farming Association (JASFA) en la Isla Ishigaki (Japón) experimentos diseñados para validar la periodicidad de los incrementos en los otolitos y para examinar las tasas de crecimiento de las larvas de atún aleta amarilla. Se criaron las larvas de huevos puestos por aletas amarillas cautivos en un corral marino en la bahía adyacente a la Estación Yaeyama. Los resultados indican que el primer incremento es depositado menos de 12 horas después de la eclosión en los otolitos de las larvas de aleta amarilla, y que los incrementos de crecimiento subsiguientes son formados a diario a partir de las primeras 24 horas después de la eclosión en larvas de hasta 16 días de edad. Se examinaron y compararon las tasas de crecimiento somático y de los otolitos en larvas en las etapas de saco vitelino y de primera alimentación criadas en aguas de temperatura constante entre 26°C y 29°C. A pesar del desarrollo más rápido de las larvas criadas a 29°C, las tasas de crecimiento no fueron significativamente diferentes entre los dos tratamientos. Debido a la mala supervivencia a partir de los cuatro primeros días, no fue posibación, uando las diferencias en el crecimiento podrían hacerse más aparentes. Se examinó también el crecimiento somático y de los otolitos para larvas criadas en temperaturas de agua ambiental en la bahía durante los 24 días inmediatamente después de la eclosión. Nuestras estimaciones de las tasas de crecimiento en el laboratorio fueron comparables a valores reportados previamente para larvas de aleta amarilla de edades similares criadas en el laboratorio, pero más bajas que las tasas de crecimiento reportadas para larvas capturadas en el mar. La discrepancia entre las tasas de crecimiento en el laboratorio y el mar podría estar asociada con condiciones subóptimas de crecimiento en el lab

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English: We describe an age-structured statistical catch-at-length analysis (A-SCALA) based on the MULTIFAN-CL model of Fournier et al. (1998). The analysis is applied independently to both the yellowfin and the bigeye tuna populations of the eastern Pacific Ocean (EPO). We model the populations from 1975 to 1999, based on quarterly time steps. Only a single stock for each species is assumed for each analysis, but multiple fisheries that are spatially separate are modeled to allow for spatial differences in catchability and selectivity. The analysis allows for error in the effort-fishing mortality relationship, temporal trends in catchability, temporal variation in recruitment, relationships between the environment and recruitment and between the environment and catchability, and differences in selectivity and catchability among fisheries. The model is fit to total catch data and proportional catch-at-length data conditioned on effort. The A-SCALA method is a statistical approach, and therefore recognizes that the data collected from the fishery do not perfectly represent the population. Also, there is uncertainty in our knowledge about the dynamics of the system and uncertainty about how the observed data relate to the real population. The use of likelihood functions allow us to model the uncertainty in the data collected from the population, and the inclusion of estimable process error allows us to model the uncertainties in the dynamics of the system. The statistical approach allows for the calculation of confidence intervals and the testing of hypotheses. We use a Bayesian version of the maximum likelihood framework that includes distributional constraints on temporal variation in recruitment, the effort-fishing mortality relationship, and catchability. Curvature penalties for selectivity parameters and penalties on extreme fishing mortality rates are also included in the objective function. The mode of the joint posterior distribution is used as an estimate of the model parameters. Confidence intervals are calculated using the normal approximation method. It should be noted that the estimation method includes constraints and priors and therefore the confidence intervals are different from traditionally calculated confidence intervals. Management reference points are calculated, and forward projections are carried out to provide advice for making management decisions for the yellowfin and bigeye populations. Spanish: Describimos un análisis estadístico de captura a talla estructurado por edad, A-SCALA (del inglés age-structured statistical catch-at-length analysis), basado en el modelo MULTIFAN- CL de Fournier et al. (1998). Se aplica el análisis independientemente a las poblaciones de atunes aleta amarilla y patudo del Océano Pacífico oriental (OPO). Modelamos las poblaciones de 1975 a 1999, en pasos trimestrales. Se supone solamente una sola población para cada especie para cada análisis, pero se modelan pesquerías múltiples espacialmente separadas para tomar en cuenta diferencias espaciales en la capturabilidad y selectividad. El análisis toma en cuenta error en la relación esfuerzo-mortalidad por pesca, tendencias temporales en la capturabilidad, variación temporal en el reclutamiento, relaciones entre el medio ambiente y el reclutamiento y entre el medio ambiente y la capturabilidad, y diferencias en selectividad y capturabilidad entre pesquerías. Se ajusta el modelo a datos de captura total y a datos de captura a talla proporcional condicionados sobre esfuerzo. El método A-SCALA es un enfoque estadístico, y reconoce por lo tanto que los datos obtenidos de la pesca no representan la población perfectamente. Además, hay incertidumbre en nuestros conocimientos de la dinámica del sistema e incertidumbre sobre la relación entre los datos observados y la población real. El uso de funciones de verosimilitud nos permite modelar la incertidumbre en los datos obtenidos de la población, y la inclusión de un error de proceso estimable nos permite modelar las incertidumbres en la dinámica del sistema. El enfoque estadístico permite calcular intervalos de confianza y comprobar hipótesis. Usamos una versión bayesiana del marco de verosimilitud máxima que incluye constreñimientos distribucionales sobre la variación temporal en el reclutamiento, la relación esfuerzo-mortalidad por pesca, y la capturabilidad. Se incluyen también en la función objetivo penalidades por curvatura para los parámetros de selectividad y penalidades por tasas extremas de mortalidad por pesca. Se usa la moda de la distribución posterior conjunta como estimación de los parámetros del modelo. Se calculan los intervalos de confianza usando el método de aproximación normal. Cabe destacar que el método de estimación incluye constreñimientos y distribuciones previas y por lo tanto los intervalos de confianza son diferentes de los intervalos de confianza calculados de forma tradicional. Se calculan puntos de referencia para el ordenamiento, y se realizan proyecciones a futuro para asesorar la toma de decisiones para el ordenamiento de las poblaciones de aleta amarilla y patudo.

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The work discussed in this report deals with aspects of the ecology of Arctic charr (Salvelinus alpinus, L.). The main aims of the study were: (1) To assess the relative abundance of migrants entering the River Liza and Smithy Beck in the English Lake District). (2) To assess the degree of stream specificity. (3) To determine the period of residency in the streams. (4) To obtain a better understanding of migratory behaviour. (5) To determine the growth rate of mature fish. (6) To determine the morphometric and meristic attributes. In conjunction with this work a study was carried out to investigate the feasibility of using a video recording system to monitor the migration of charr in Smithy Beck.

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Maternal effects on the quality of progeny can have direct impacts on population productivity. Rockfish are viviparous and the oil globule size of larvae at parturition has been shown to have direct effects on time until starvation and growth rate. We sampled embryos and preparturition larvae opportunistically from 89 gravid quillback rockfish (Sebastes maliger) in Southeast Alaska. Because the developmental stage and sampling period were correlated with oil globule size, they were treated as covariates in an analysis of maternal age, length, and weight effects on oil globule size. Maternal factors were related to developmental timing for almost all sampling periods, indicating that older, longer, and heavier females develop embryos earlier than younger, shorter, or lighter ones. Oil globule diameter and maternal length and weight were statistically linked, but the relationships may not be biologically significant. Weight-specific fecundity did not increase with maternal size or age, suggesting that reproductive output does not increase more quickly as fish age and grow. Age or size truncation of a rockfish population, in which timing of parturition is related to age and size, could result in a shorter parturition season. This shortening of the parturition season could make the population vulnerable to fluctuating environmental conditions.

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The hypothesis that heavy fishing pressure has led to changes in the biological characteristics of the estuary cobbler (Cnidoglanis macrocephalus) was tested in a large seasonally open estuary in southwestern Australia, where this species completes its life cycle and is the most valuable commercial fish species. Comparisons were made between seasonal data collected for this plotosid (eeltail catfish) in Wilson Inlet during 2005–08 and those recorded with the same fishery-independent sampling regime during 1987–89. These comparisons show that the proportions of larger and older individuals and the catch rates in the more recent period were far lower, i.e., they constituted reductions of 40% for fish ≥430 mm total length, 62% for fish ≥4 years of age, and 80% for catch rate. In addition, total mortality and fishing-induced mortality estimates increased by factors of ~2 and 2.5, respectively. The indications that the abundance and proportion of older C. macrocephalus declined between the two periods are consistent with the perception of long-term commercial fishermen and their shift toward using a smaller maximum gill net mesh to target this species. The sustained heavy fishing pressure on C. macrocephalus between 1987–89 and 2005–08 was accompanied by a marked reduction in length and age at maturity of this species. The shift in probabilistic maturation reaction norms toward smaller fish in 2005–08 and the lack of a conspicuous change in growth between the two periods indicate that the maturity changes were related to fishery-induced evolution rather than to compensatory responses to reduced fish densities.

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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.

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Red bream (Beryx decadactylus) is a commercially important deep-sea benthopelagic fish with a circumglobal distribution on insular and continental slopes and seamounts. In the United States, small numbers are caught incidentally in the wreckfish (Polyprion americanus) fishery which operates off the southeastern coast, but no biological information exists for the management of the U.S. red bream population. For this study, otoliths (n=163) and gonads (n=161) were collected from commercially caught red bream between 2003 and 2008 to determine life history parameters. Specimens ranged in size from 410 to 630 mm fork length and were all determined to be mature by histological examination of the gonads. Females in spawning condition were observed from June through September, and reproductively active males were found year-round. Sectioned otoliths were difficult to interpret, but maximum age estimates were much higher than the 15 years previously reported for this species from the eastern North Atlantic based on whole-otolith analysis. Estimated ages ranged from 8 to 69 years, and a minimum lifespan of 49 years was validated by using bomb radiocarbon dating. Natural mortality was estimated at 0.06/yr. This study shows that red bream are longer lived and more vulnerable to overfishing than previously assumed and should be managed carefully to prevent overexploitation.

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Fish growth is commonly estimated from length-at-age data obtained from otoliths. There are several techniques for estimating length-at-age from otoliths including 1) direct observed counts of annual increments; 2) age adjustment based on a categorization of otolith margins; 3) age adjustment based on known periods of spawning and annuli formation; 4) back-calculation to all annuli, and 5) back-calculation to the last annulus only. In this study we compared growth estimates (von Bertalanffy growth functions) obtained from the above five methods for estimating length-at-age from otoliths for two large scombrids: narrow-barred Spanish mackerel (Scomberomorus commerson) and broad-barred king mackerel (Scomberomorus semifasciatus). Likelihood ratio tests revealed that the largest differences in growth occurred between the back-calculation methods and the observed and adjusted methods for both species of mackerel. The pattern, however, was more pronounced for S. commerson than for S. semifasciatus, because of the pronounced effect of gear selectivity demonstrated for S. commerson. We propose a method of substituting length-at-age data from observed or adjusted methods with back-calculated length-at-age data to provide more appropriate estimates of population growth than those obtained with the individual methods alone, particularly when faster growing young fish are disproportionately selected for. Substitution of observed or adjusted length-at-age data with back-calculated length-at-age data provided more realistic estimates of length for younger ages than observed or adjusted methods as well as more realistic estimates of mean maximum length than those derived from backcalculation methods alone.

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This study documents validation of vertebral band-pair formation in spotted gully shark (Triakis megalopterus) with the use of fluorochrome injection and tagging of captive and wild sharks over a 21-year period. Growth and mortality rates of T. megalopterus were also estimated and a demographic analysis of the species was conducted. Of the 23 OTC (oxytetracycline) -marked vertebrae examined (12 from captive and 11 from wild sharks), seven vertebrae (three from captive and four from wild sharks) exhibited chelation of the OTC and fluoresced under ultraviolet light. It was concluded that a single opaque and translucent band pair was deposited annually up to at least 25 years of age, the maximum age recorded. Reader precision was assessed by using an index of average percent error calculated at 5%. No significant differences were found between male and female growth patterns (P>0.05), and von Bertalanffy growth model parameters for combined sexes were estimated to be L∞=1711.07 mm TL, k=0.11/yr and t0=–2.43 yr (n=86). Natural mortality was estimated at 0.17/yr. Age at maturity was estimated at 11 years for males and 15 years for females. Results of the demographic analysis showed that the population, in the absence of fishing mortality, was stable and not significantly different from zero and particularly sensitive to overfishing. At the current age at first capture and natural mortality rate, the fishing mortality rate required to result in negative population growth was low at F>0.004/ yr. Elasticity analysis revealed that juvenile survival was the principal factor in explaining variability in population growth rate.

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Preliminary validation of annual growth band deposition in vertebrae of great hammerhead shark (Sphyrna mokarran) was conducted by using bomb radiocarbon analysis. Adult specimens (n=2) were collected and thin sections of vertebral centra were removed for visual aging and use in radiocarbon assays. Vertebral band counts were used to estimate age, and year of formation was assigned to each growth band by subtracting estimated age from the year of capture. A total of 10 samples were extracted from growth bands and analyzed for Δ14C. Calculated Δ14C values from dated bands were compared to known-age reference chronologies, and the resulting patterns indicated annual periodicity of growth bands up to a minimum age of 42 years. Trends in Δ14C across time in individual specimens indicated that vertebral radiocarbon is conserved through time but that habitat and diet may inf luence Δ14C levels in elasmobranchs. Although the age validation reported here must be considered preliminary because of the small sample size and narrow age range of individuals sampled, it represents the first confirmation of age in S. mokarran, further illustrating the usefulness of bomb radiocarbon analysis as a tool for life history studies in elasmobranchs.

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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.