Estimation of the abundance of yellowfin tuna, Thunnus albacares, by age groups and regions within the Eastern Pacific Ocean

ENGLISH: Monthly estimates of the abundance of yellowfin tuna by age groups and regions within the eastern Pacific Ocean during 1970-1988 are made, using purse-seine catch rates, length-frequency samples, and results from cohort analysis. The numbers of individuals caught of each age group in each logged purse-seine set are estimated, using the tonnage from that set and length-frequency distribution from the "nearest" length-frequency sample(s). Nearest refers to the closest length frequency sample(s) to the purse-seine set in time, distance, and set type (dolphin associated, floating object associated, skipjack associated, none of these, and some combinations). Catch rates are initially calculated as the estimated number of individuals of the age group caught per hour of searching. Then, to remove the effects of set type and vessel speed, they are standardized, using separate weiznted generalized linear models for each age group. The standardized catch rates at the center of each 2.5 0 quadrangle-month are estimated, using locally-weighted least-squares regressions on latitude, longitude and date, and then combined into larger regions. Catch rates within these regions are converted to numbers of yellowfin, using the mean age composition from cohort analysis. The variances of the abundance estimates within regions are large for 0-, 1-, and 5-year-olds, but small for 1.5- to 4-year-olds, except during periods of low fishing activity. Mean annual catch rate estimates for the entire eastern Pacific Ocean are significantly positively correlated with mean abundance estimates from cohort analysis for age groups ranging from 1.5 to 4 years old. Catch-rate indices of abundance by age are expected to be useful in conjunction with data on reproductive biology to estimate total egg production within regions. The estimates may also be useful in understanding geographic and temporal variations in age-specific availability to purse seiners, as well as age-specific movements. SPANISH: Se calculan estimaciones mensuales de la abundancia del atún aleta amarilla por grupos de edad y regiones en el Océano Pacífico oriental durante 1970-1988, usando tasas de captura cerquera, muestras de frecuencia de talla, y los resultados del análisis de cohortes. Se estima el número de individuos capturados de cada grupo de edad en cada lance cerquero registrado, usando el tonelaje del lance en cuestión y la distribución de frecuencia de talla de la(s) muestra(s) de frecuencia de talla "más cercana/s)," "Más cercana" significa la(s) muestra(s) de frecuencia de talla más parecida(s) al lance cerquero en cuanto a fecha, distancia, y tipo de lance (asociado con delfines, con objeto flotante, con barrilete, con ninguno de éstos, y algunas combinaciones). Se calculan inicialmente las tasas de captura como el número estimado de individuos del grupo de edad capturado por hora de búsqueda. A continuación, para eliminar los efectos del tipo de lance y la velocidad del barco, se estandardizan dichas tasas, usando un modelo lineal generalizado ponderado, para cada grupo por separado. Se estima la tasa de captura estandardizada al centro de cada cuadrángulo de 2.5°-mes, usando regresiones de mínimos cuadrados ponderados localmente por latitud, longitud, y fecha, y entonces combinándolas en regiones mayores. Se convierten las tasas de captura dentro de estas regiones en números de aletas amarillas individuales, usando el número promedio por edad proveniente del análisis de cohortes. Las varianzas de las estimaciones de la abundancia dentro de las regiones son grandes para los peces de O, 1, Y5 años de edad, pero pequeñas para aquellos de entre 1.5 Y4 años de edad, excepto durante períodos de poca actividad pesquera. Las estimaciones de la tasa de captura media anual para todo el Océano Pacífico oriental están correlacionadas positivamente de forma significativa con las estimaciones de la abundancia media del análisis de las cohortes para los grupos de edad de entre 1.5 y 4 años. Se espera que los índices de abundancia por edad basados en las tasas de captura sean útiles, en conjunto con datos de la biología reproductiva, para estimar la producción total de huevos por regiones. Las estimaciones podrían asimismo ser útiles para la comprensión de las variaciones geográficas y temporales de la disponibilidad específica por edad a los barcos cerqueros, y también las migraciones específicas por edad. (PDF contains 35 pages.)

A-SCALA: an age-structured statistical catch-at-length analysis for assessing tuna stocks in the eastern tropical Pacific Ocean

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.

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 validation of great hammerhead shark (Sphyrna mokarran), determined by bomb radiocarbon analysis

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.

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).

An approach to estimate the natural mortality rate in fish stocks

A simple approach is introduced to estimate the natural mortality rate (M) of fish stocks. The approach is based on the age at maximum cohort biomass, or critical length (L*) concept. The ratio of the critical length to the asymptotic length ( = L*/L8) is relatively constant in 141 fish stocks at 0.62 (CV = 21.4 per cent) and the relationship M = 3K(1- )/ is derived and could be used to estimate M, where K is the growth coefficient of the von Bertalanffy growth function. Average values of are given for the various Families of fish in order to estimate M based on closely related species.

Can the age of the tropical species be determined by otolith measurement?: a study using Pristipomoides filamentosus (Pisces: Lutjanidae) from the Mahe Plateau, Seychelles

The sagittal otoliths of bluespot jobfish (Pristipomoides flamentosus) from the Mahe Plateau, Seychelles, were examined for growth rings using light microscopy. Banding with putative annual and monthly frequency were observed. Consistent age estimates were derived from each of the two patterns. The resulting length-at-age data were use t estimate the parameters K and t sub(0), viz: K=0.33, t sub(0) = 0.16 for males and K = 0.36, t sub(0) = 0.06 for females (using von Bertalanffy plots). Possible causes of the banding are discussed.

Effect of type of otolith and preparation technique on age estimation of larval and juvenile spot (Leiostomus xanthurus)

Otoliths of larval and juvenile fish provide a record of age, size, growth, and development (Campana and Neilson, 1985; Thorrold and Hare, 2002). However, determining the time of first increment formation in otoliths (Campana, 2001) and assessing the accuracy (deviation from real age) and precision (repeatability of increment counts from the same otolith) of increment counts are prerequisites for using otoliths to study the life history of fish (Campana and Moksness, 1991). For most fish species, first increment deposition occurs either at hatching, a day after hatching, or after first feeding and yolksac absorption (Jones, 1986; Thorrold and Hare, 2002). Increment deposition before hatching also occurs (Barkmann and Beck, 1976; Radtke and Dean, 1982). If first increment deposition does not occur at hatching, the standard procedure is to add a predetermined number to increment counts to estimate fish age (Campana and Neilson, 1985).

Age, growth, mortality, and radiometric age validation of gray snapper (Lutjanus griseus) from Louisiana

The gray snapper (Lutjanus griseus) is a temperate and tropical reef fish that is found along the Gulf of Mexico and Atlantic coasts of the southeastern United States. The recreational fishery for gray snapper has developed rapidly in south Louisiana with the advent of harvest and seasonal restrictions on the established red snapper (L. campechanus) fishery. We examined the age and growth of gray snapper in Louisiana with the use of cross-sectioned sagittae. A total of 833 specimens, (441 males, 387 females, and 5 of unknown sex) were opportunistically sampled from the recreational fishery from August 1998 to August 2002. Males ranged in size from 222 to 732 mm total length (TL) and from 280 g to 5700 g total weight (TW) and females ranged from 254 to 756 mm TL and from 340 g to 5800 g TW. Both edge analysis and bomb radiocarbon analyses were used to validate otolith-based age estimates. Ages were estimated for 718 individuals; both males and females ranged from 1 to 28 years. The von Bertalanffy growth models derived from TL at age were Lt = 655.4{1–e[–0.23(t)]} for males, Lt = 657.3{1–e[– 0.21(t)]} for females, and L t = 656.4{1–e[– 0.22 (t)]} for all specimens of known sex. Catch curves were used to produce a total mortality (Z) estimate of 0.17. Estimates of M calculated with various methods ranged from 0.15 to 0.50; however we felt that M= 0.15 was the most appropriate estimate based on our estimate of Z. Full recruitment to the gray snapper recreational fishery began at age 4, was completed by age 8, and there was no discernible peak in the catch curve dome.

Age and length composition of Columbia Basin chinook, sockeye, and coho salmon at Bonneville Dam in 2001

In 2001, representative samples of adult Columbia Basin chinook (Oncorhynchus tshawytscha), sockeye (O. nerka), and coho salmon (O. kisutch) populations at Bonneville Dam were collected. Fish were trapped, anesthetized, sampled for scales and biological data, revived, and then released adult migrating salmonids. Scales were examined to estimate age composition; the results contributed to an ongoing database for age class structure of Columbia Basin salmon populations. Based on scale analysis of chinook salmon, four-year-old fish (from brood year [BY] 1997) comprised 88% of the spring chinook, 67% of the summer chinook, and 42% of the Bright fall chinook salmon population. Five-year-old fish (BY 1996) comprised 9% of the spring chinook, 14% of the summer chinook, and 9% of the fall chinook salmon population. The sockeye salmon population at Bonneville was predominantly four-year-old fish (81%), with 18% returning as five-year-olds in 2001. The coho salmon population was 96% three-year-old fish (Age 1.1). Length analysis of the 2001 returns indicated that chinook salmon with a stream-type life history are larger (mean length) than the chinook salmon with an ocean-type life history. Trends in mean length over the sampling period for returning 2001 chinook salmon were analyzed. Chinook salmon of age classes 0.2 and 1.3 show a significant increase in mean length over time. Age classes 0.1, 0.3, 0.4, 1.1, 1.2, and 1.4 show no significant change over time. A year class regression over the past 12 years of data was used to predict spring, summer, and Bright fall chinook salmon population sizes for 2002. Based on three-year-old returns, the relationship predicts four-year-old returns of 132,600 (± 46,300, 90% predictive interval [PI]) spring chinook and 44,200 (± 11,700, 90% PI) summer chinook salmon for the 2002 runs. Based on four-year-old returns, the relationship predicts five-year-old returns of 87,800 (± 54,500, 90% PI) spring, 33,500 (± 11,500, 90% PI) summer, and 77,100 (± 25,800, 90% PI) Bright fall chinook salmon for the 2002 runs. The 2002 run size predictions should be used with caution; some of these predictions are well beyond the range of previously observed data.

Age and length composition of Columbia Basin chinook, sockeye, and coho salmon at Bonneville Dam in 2000

In 2000, representative samples of adult Columbia Basin chinook (Oncorhynchus tshawytscha), sockeye (O. nerka), and coho salmon (O. kisutch), populations were collected at Bonneville Dam. Fish were trapped, anesthetized, sampled for scales and biological data, allowed to revive, and then released. Scales were examined to estimate age composition and the results contribute to an ongoing database for age class structure of Columbia Basin salmon populations. Based on scale analysis, four-year-old fish (from brood year (BY) 1996) were estimated to comprise 83% of the spring chinook, 31% of the summer chinook, and 32% of the upriver bright fall chinook salmon population. Five-year-old fish (BY 1995) were estimated to comprise 2% of the spring chinook, 26% of the summer chinook, and 40% of the fall chinook salmon population. Three-year-old fish (BY 1997) were estimated to comprise 14% of the spring chinook, 42% of the summer chinook, and 17% of the fall chinook salmon population. Two-year-olds accounted for approximately 11% of the fall chinook population. The sockeye salmon population sampled at Bonneville was predominantly four-year-old fish (95%), and the coho salmon population was 99.9% three-year-old fish (Age 1.1). Length analysis of the 2000 returns indicated that chinook salmon with a stream-type life history are larger (mean length) than the chinook salmon with an ocean-type life history. Trends in mean length over the sampling period were also analysis for returning 2000 chinook salmon. Fish of age classes 0.2, 1.1, 1.2, and 1.3 have a significant increase in mean length over time. Age classes 0.3 and 0.4 have no significant change over time and age 0.1 chinook salmon had a significant decrease in mean length over time. A year class regression over the past 11 years of data was used to predict spring and summer chinook salmon population sizes for 2001. Based on three-year-old returns, the relationship predicts four-year-old returns of 325,000 (± 111,600, 90% Predictive Interval [PI]) spring chinook and 27,800 (± 29,750, 90% PI) summer chinook salmon. Based on four-year-old returns, the relationship predicts five-year-old returns of 54,300 (± 40,600, 90% PI) spring chinook and 11,000 (± 3,250, 90% PI) summer chinook salmon. The 2001 run size predictions used in this report should be used with caution, these predictions are well beyond the range of previously observed data.

Age and length composition of Columbia Basin chinook, sockeye, and coho salmon at Bonneville Dam in 2002

In 2002, representative samples of migrating Columbia Basin chinook (Oncorhynchus tshawytscha), sockeye (O. nerka), and coho salmon (O. kisutch) adult populations were collected at Bonneville Dam. Fish were trapped, anesthetized, sampled for scales and biological data, revived, and then released. Scales were examined to estimate age composition; the results contributed to an ongoing database for age class structure of Columbia Basin salmon populations. Based on scale analysis of chinook salmon, four-year-old fish (from brood year [BY] 1998) comprised 86% of the spring chinook, 51% of the summer chinook, and 51% of the bright fall chinook salmon population. Five-year-old fish (BY 1997) comprised 13% of the spring chinook, 43% of the summer chinook, and 11% of the bright fall chinook salmon population. The sockeye salmon population at Bonneville was predominantly five-year-old fish (55%), with 40% returning as four-year-olds in 2002. For the coho salmon population, 88% of the population was three-year-old fish of age class 1.1, while 12% were age class 1.0. Length analysis of the 2002 returns indicated that chinook salmon with a stream-type life history are larger (mean length) at age than the chinook salmon with an ocean-type life history. Trends in mean length over the sampling period for returning 2002 chinook salmon were analyzed. Chinook salmon of age classes 1.2 and 1.3 show a significant increase in mean length over the duration of the migration. A year class regression over the past 14 years of data was used to predict spring, summer, and bright fall chinook salmon population sizes for 2003. Based on three-year-old returns, the relationship predicts four-year-old returns of 54,200 (± 66,600, 90% predictive interval [PI]) spring chinook, 23,800 (± 19,100, 90% PI) summer, and 169,100 (± 139,500, 90% PI) bright fall chinook salmon for the 2003 runs. Based on four-year-old returns, the relationship predicts five-year-old returns of 36,300 (± 35,400, 90% PI) spring, 63,800 (± 10,300, 90% PI) summer, and 91,100 (± 69,400, 90% PI) bright fall chinook salmon for the 2003 runs. The 2003 run size predictions should be used with caution; some of these predictions are well beyond the range of previously observed data.

Age and growth of the estuarine dolphin (Sotalia guianensis) (Cetacea, Delphinidae) on the Paraná Coast, southern Brazil

Teeth of 71 estuarine dolphins (Sotalia guianensis) incidentally caught on the coast of Paraná State, southern Brazil, were used to estimate age. The oldest male and female dolphins were 29 and 30 years, respectively. The mean distance from the neonatal line to the end of the first growth layer group (GLG) was 622.4 ±19.1 μm (n=48). One or two accessory layers were observed between the neonatal line and the end of the first GLG. One of the accessory layers, which was not always present, was located at a mean of 248.9 ±32.6 μm (n=25) from the neonatal line, and its interpretation remains uncertain.The other layer, located at a mean of 419.6 ±44.6 μm (n=54) from the neonatal line, was always present and was first observed between 6.7 and 10.3 months of age. This accessory layer could be a record of weaning in this dolphin. Although no differences in age estimates were observed between teeth sectioned in the anterior-posterior and buccal-lingual planes, we recommend sectioning the teeth in the buccal-lingual plane in order to obtain on-center sections more easily. We also recommend not using teeth from the most anterior part of the mandibles for age estimation. The number of GLGs counted in those teeth was 50% less than the number of GLGs counted in the teeth from the median part of the mandible of the same animal. Although no significant difference (P>0.05) was found between the total lengths of adult male and female estuarine dolphins, we observed that males exhibited a second growth spurt around five years of age. This growth spurt would require that separate growth curves be calculated for the sexes. The asymptotic length (TL∞), k, and t0 obtained by the von Bertalanffy growth model were 177.3 cm, 0.66, and –1.23, respectively, for females and 159.6 cm, 2.02, and –0.38, respectively, for males up to five years, and 186.4 cm, 0.53 and –1.40, respectively, for males older than five years. The total weight (TW)/total length (TL) equations obtained for male and female estuarine dolphins were TW = 3.156 × 10−6 × TL 3.2836 (r=0.96), and TW = 8.974 × 10−5 × TL 2.6182 (r=0.95), respectively.

Age and growth of Hawaiian seaturtles (Chelonia mydas): an analysis based on skeletochronology

Skeletochronological data on growth changes in humerus diameter were used to estimate the age of Hawaiian green seaturtles ranging from 28.7 to 96.0 cm straight carapace length. Two age estimation methods, correction factor and spline integration, were compared, giving age estimates ranging from 4.1 to 34.6 and from 3.3 to 49.4 yr, respectively, for the sample data. Mean growth rates of Hawaiian green seaturtles are 4–5 cm/yr in early juveniles, decline to a relatively constant rate of about 2 cm/yr by age 10 yr, then decline again to less than 1 cm/yr as turtles near age 30 yr. On average, age estimates from the two techniques differed by just a few years for juvenile turtles, but by wider margins for mature turtles. The spline-integration method models the curvilinear relationship between humerus diameter and the width of periosteal growth increments within the humerus, and offers several advantages over the correction-factor approach.

Age and growth of the swordfish (Xiphias gladius L.) in the waters around Taiwan determined from anal-fin rays

Age and growth of the swordfish (Xiphias gladius) in Taiwan waters was studied from counts of growth bands on cross sections of the second ray of the first anal fin. Data on lower jaw fork length and weight, and samples of the anal fin of male and female swordfish were collected from three offshore and coastal tuna longline fishing ports on a monthly basis between September 1997 and March 1999. In total, 685 anal fins were collected and 627 of them (293 males and 334 females) were aged successfully. The lower jaw fork lengths of the aged individuals ranged from 83.4 to 246.6 cm for the females and from 83.3 to 206 cm for the males. The radii of the fin rays and growth bands on the cross sections were measured under a dissecting microscope equipped with an image analysis system. Trends in the monthly marginal increment ratio indicated that growth bands formed once a year. Thus, the age of each fish was deter-mined from the number of visible growth bands. Two methods were used to estimate and compare the standard and the generalized von Bertalanffy growth parameters for both males and females. The nonlinear least square estimates of the generalized von Bertalanffy growth parameters in method II, in which a power function was used to describe the relationship between ray radius and LJFL, were recommended as most acceptable. There were significant differences in growth parameters between males and females. The growth parameters estimated for females were the following: asymptotic length (L∞) = 300.66 cm, growth coefficient (K) = 0.040/yr, age at zero length (t0) = –0.75 yr, and the fitted fourth parameter (m) = –0.785. The growth parameters estimated for males were the following: asymptotic length (L∞) = 213.05 cm, growth coefficient (K) = 0.086/yr, age at zero length (t0) = –0.626 yr, and the fitted fourth parameter (m) = –0.768.