A prior for steepness in stock-recruitment relationships, based on an evolutionary persistence principle

Priors are existing information or beliefs that are needed in Bayesian analysis. Informative priors are important in obtaining the Bayesian posterior distributions for estimated parameters in stock assessment. In the case of the steepness parameter (h), the need for an informative prior is particularly important because it determines the stock-recruitment relationships in the model. However, specifications of the priors for the h parameter are often subjective. We used a simple population model to derive h priors based on life history considerations. The model was based on the evolutionary principle that persistence of any species, given its life history (i.e., natural mortality rate) and its exposure to recruitment variability, requires a minimum recruitment compensation that enables the species to rebound consistently from low critical abundances (Nc). Using the model, we derived the prior probability distributions of the h parameter for fish species that have a range of natural mortality, recruitment variabilities, and Nt values.

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

Estimated ages of red porgy (Pagrus pagrus) from fishery-dependent and fishery-independent data and a comparison of growth parameters

The red porgy, Pagrus pagrus, is an important reef fish in several offshore fisheries along the southeastern United States. We examined samples from North Carolina through southeast Florida from recreational (headboat) and commercial (hook and line) fisheries, as well as samples from a fishery-independent source. Red porgy attain a maximum age of at least 18 years and 733 mm total length. The weight-length relationship is represented by the ln-ln transformed equation: W = 8.85 × 10–6(L)3.06, where W = whole weight in grams, and L = total length in mm. The von Bertalanffy growth equation fitted to the most recent, back-calculated lengths from all the samples is Lt = 644(1 – e –0.15(t + 0.76)). Our study revealed a difference in mean length at age of red porgy from the three sources. Red porgy in fishery-independent collections were smaller at age than specimens examined from fishery-dependent sources. The difference in length-at-age may be related to gear selectivity and have important consequences in the assessment of fish stocks.

An increment technique for estimating growth parameters of tropical tunas, as applied to yellowfin tuna (Thunnus albacares)

ENGLISH: The rate of growth of tropical tunas has been studied by various investigators using diverse methods. Hayashi (1957) examined methods to determine the age of tunas by interpreting growth patterns on the bony or hard parts, but the results proved unreliable. Moore (1951), Hennemuth (1961), and Davidoff (1963) studied the age and growth of yellowfin tuna by the analysis of size frequency distributions. Schaefer, Chatwin and Broadhead (1961), and Fink (ms.), estimated the rate of growth of yellowfin tuna from tagging data; their estimates gave a somewhat slower rate of growth than that obtained by the study of length-frequency distributions. For the yellowfin tuna, modal groups representing age groups can be identified and followed for relatively long periods of time in length-frequency graphs. This may not be possible, however, for other tropical tunas where the modal groups may not represent identifiable age groups; this appears to be the case for skipjack tuna (Schaefer, 1962). It is necessary, therefore, to devise a method of estimating the growth rates of such species without identifying the year classes. The technique described in this study, hereafter called the "increment technique", employs the measurement of the change in length per unit of time, with respect to mean body length, without the identification of year classes. This technique is applied here as a method of estimating the growth rate of yellowfin tuna from the entire Eastern Tropical Pacific, and from the Commission's northern statistical areas (Areas 01-04 and 08) as shown in Figure 1. The growth rates of yellowfin tuna from Area 02 (Hennemuth, 1961) and from the northern areas (Davidoff, 1963) have been described by the technique of tracing modal progressions of year classes, hereafter termed the "year class technique". The growth rate analyses performed by both techniques apply to the segment of the population which is captured by tuna fishing vessels. The results obtained by both methods are compared in this report. SPANISH: La tasa del crecimiento de los atunes tropicales ha sido estudiada por varios investigadores quienes usaron diversos métodos. Hayashi (1957) examinó los métodos para determinar la edad de los atunes interpretando las marcas del crecimiento de las partes óseas o duras, pero los resultados no han demostrado eficacia. Moore (1951), Hennemuth (1961) y Davidoff (1963) estudiaron la edad y el crecimiento del atún aleta amarilla por medio del análisis de las distribuciones de la frecuencia de tamaños. Schaefer, Chatwin y Broadhead (1961) y Fink (Ms.), estimaron la tasa del crecimiento del atún aleta amarilla valiéndose de los datos de la marcación de los peces; ambos estimaron una tasa del crecimiento algo más lenta que la que se obtiene mediante el estudio de las distribuciones de la frecuencia de longitudes. Para el atún aleta amarilla, los grupos modales que representan grupos de edad pueden ser identificados y seguidos durante períodos de tiempo relativamente largos en los gráficos de la frecuencia de longitudes. Sin embargo, ésto puede no ser posible para otros atunes tropicales para los cuales los grupos modales posiblemente no representan grupos de edad identificables; este parece ser el caso para el barrilete (Schaefer, 1962). Consecuentemente, es necesario idear un método para estimar las tasas del crecimiento de las mencionadas especies sin necesidad de identificar las clases anuales. La técnica descrita en este estudio, en adelante llamada la "técnica incremental", emplea la medida del cambio en la longitud por unidad de tiempo, con respecto al promedio de la longitud corporal, sin tener que identificar las clases anuales. Esta técnica se aplica aquí como un método para estimar la tasa del crecimiento del atún aleta amarilla de todo el Pacífico Oriental Tropical, y de las áreas estadísticas norteñas de la Comisión (Areas 01-04 y 08), como se muestra en la Figura 1. Las tasas del crecimiento del atún aleta amarilla del Area 02 (Hennemuth, 1961) y de las áreas del norte (Davidoff, 1963), han sido descritas por medio de una técnica que consiste en delinear las progresiones modales de las clases anuales, en adelante llamada la "técnica de la clase anual". Los análisis de la tasa del crecimiento llevados a cabo por ambas técnicas se refieren al segmento de la población capturada por embarcaciones pesqueras de atún. Los resultados obtenidos por ambos métodos se comparan en este informe.

Growth of skipjack, Katsuwonus pelamis, and yellowfin, Thunnus albacares, tunas in the Eastern Pacific Ocean, as estimated from tagging data

ENGLISH: The average linear growth rate of skipjack in the eastern Pacific is less than 1 mm per day except for fish 375 to 424 mm in length at release. The growth rate shows a decrease with increasing length and increasing time at liberty. The growth rate of fish in the length range of about 43 to 57 cm is apparently more rapid in the eastern Pacific than in the western Pacific. Dsing data for the northeastern and southeastern Pacific combined, K and ~ were estimated to be 0.658 (on an annual basis) and 885 mm, respectively, by the ungrouped method and 0.829 and 846 mm, respectively, by the grouped method. Sensitivity analyses have shown however, that the estimates of these parameters are poorly determined by the sum of squares method used to derive them. Estimates of K and ~ for the eastern Pacific tend to be lower and higher, respectively, than those for the western Pacific. The average linear growth rate of yellowfin in the eastern Pacific is a little less than 1 mm per day for fish between about 25 and 100 cm in length at release. The growth appears to be most rapid in Area 2 (Revillagigedo Islands) and slowest in Areas 1 (Baja California), 5 (Central America- Colombia), and 6 (Ecuador-Peru). There is considerable variation in the growth rates of individual fish. The growth does not show a decrease with increasing length or increasing time at liberty so realistic estimates of the parameters of the von Bertalanffy or other similar equations cannot be calculated from these data. If realistic estimates of these parameters are to be secured larger fish must be tagged and released or many more long-term returns from fish to about 100 cm in length at release must be obtained. The growth patterns for the eastern Pacific, central Pacific and eastern Atlantic found by most other investigators differ from one another and from those found in the present study. Some of these differences may be real and others may be due to deficiencies in the data or the methods of analysis. Estimates obtained from tagging data are believed to be realistic provided the tags do not inhibit the growth of the fish. It appears that the growth rates of single- and double-tagged fish are the same; this indicates, though not unequivocally, that the tags do not inhibit the growth. SPANISH: La tasa media de crecimiento lineal del barrilete en el Pacífico oriental es inferior a lmm/día, excepto en el caso de peces de entre 375y 424mm de longitud de liberación. La tasa de crecimiento disminuye a medida que aumenta la longitud y el tiempo en libertad. La tasa de crecimiento de peces de entre unos 43 y 57 cm de longitud parece ser mayor en el Pacífico oriental que en el occidental. A partir de datos del Pacífico nororiental y suroriental combinados, se estimaron K y loo en 0.658 (anual) y 885mm, respectivamente, usando el método no agrupado, y 0.829 y 846mm, respectivamente, usando el método agrupado. Sin embargo, los análisis de sensitividad han demostrado que el método de suma de cuadrados utilizado para derivar las estimaciones de estos parámetros las determina con poca precisión. Las estimaciones de K y loo para el Pacífico oriental suelen ser inferiores y superiores, respectivamente, a los del Pacífico occidental. La tasa media de crecimiento lineal del aleta amarilla en el Pacífico oriental es ligeramente inferior a lmm/día para los peces de entre unos 25y 100cmde longitud de liberación. El crecimiento parece ser más rápido en el Area 2(Islas Revillagigedo),y más lento en las Areas 1(Baja California), 5 (Centroamérica-Colombia), y 6 (Ecuador-Perú). Las tasas de crecimiento de peces individuales varían considerablemente. El crecimiento no muestra una disminuciónconun aumento en la longitud o en el tiempo en libertad, y por consecuencia no se se pueden calcular estimaciones realistas de los parámetros de la ecuación de von Bertalanffy u otras ecuaciones similares a partir de estos datos. Para obtener estimaciones realistas de estos parámetros sería necesario marcar peces mayores u obtener muchas más devoluciones a largo plazo de marcas de peces de unos 100cm de longitud de liberación. Los patrones de crecimiento correspondientes al Pacífico oriental, Pacífico central, y Atlántico oriental descubiertos por la mayoría de los investigadores son diferentes entre síy también de los del presente estudio. Es posibleque algunas de estas diferencias sean verdaderas, mientras que otras se deban a faltas en los datos on en los métodos analíticos utilizados. Se considera que las estimaciones obtenidas a partir de los datos de marcado son realistas, suponiendo siempre que las marcas no impidan el crecimiento de los peces. Parece ser que las tasas de crecimiento de peces con una marca y con dos son idénticas, lo cual indica, aunque sin certeza total, que las marcas no ejercen tal efecto. (PDF contains 76 pages.)

Population parameters of small pelagic fishes caught off Tawi-Tawi, Philippines

Growth and mortality parameters, exploitation rates and annual recruitment patterns were estimated from monthly length-frequency samples for Sardinella longiceps, S. fimbriata, S. Albella, Decapterus macrosoma, Dipterygonatus balteatus, Rastrelliger faughni and Encrasicolina heteroloba. These results provide the first sets of stock parameter estimates for these species off Tawi-Tawi, Philippines. The growth parameters derived were found comparable with previous estimates available for the same species from other localities. Recruitment was noted to be year-round and bimodal. Estimates of fishing mortality and exploitation rate were found to be presently above appropriate levels.

Population parameters of Pennahia anea and Nibea maculata in the Palk Bay/Gulf of Mannar area, India

The population parameters of the two most abundant sciaenids comprising the trawl catch in the Palk Bay/Gulf of Mannar area are presented. The following parameters were estimated: 233 mm (L sub( infinity )), 1.26 yr super(1) (K), -0.08 yr (t sub(0)), 4.24 yr super(1) (Z) and 2.24 yr super(1)(M) for Pennahia anear, 284 mm (L sub( infinity )), 1.08 yr super(1) (K), -0.05 yr (t sub(0)), 4.41 yr super(1) (Z) and 1.92 yr super(1) for Nibea maculata. Length at first capture was 97 mm for P. anea and 124 mm for N. maculata. These lengths were noted to be less than the corresponding length at first maturity for both species. The exploitation rates (E) derived indicate that the two species are heavily fished, which may account for the decline in sciaenid catches from 1988 to 1992.

Biological parameters, body length-weight and length-height relationships for various species in Greek waters

Biological/fisheries parameters (L sub(oo) M, F) are presented for four fish species (Gadiculus argenteus; Gaidropsarus mediterraneous; Symphurus ligulatus; Lepidorhombus boscii) as well as body length-weight and length-height relationships for 11 and 12 fish species, respectively, estimated from trawl samples collected using three different cod-ends (stretched mesh size: 14 mm and 20 mm diamond-shaped and 20 mm square-shaped) during 1993-1994, in the western Aegean and North Euboikos Gulf, Greece. The fisheries paramaters, estimated from length-frequency using the ELEFAN approach and software, are discussed in the light of recent information on the selectivity of the presently used trawl cod-end (14 mm diamond shaped)

Age validation, growth, mortality, and additional population parameters of the goldband snapper (Pristipomoides multidens) off the Kimberley coast of northwestern Australia

Goldband snapper (Pristipomoides multidens) collected from commercial trap and line fishermen off the Kimberley coast of northwestern Australia were aged by examination of sectioned otoliths (sagittae).A total of 3833 P. multidens, 80–701 mm fork length (98–805 mm total length), were examined from commercial catches from 1995 to 1999. The oldest fish was estimated to be age 30+ years. Validation of age estimates was achieved with marginal increment analysis. The opaque and translucent zones were each formed once per year and are considered valid annual growth increments (the translucent zone was formed once per year between January and May). A strong link between water temperature and translucent zone formation was evident in P. multidens. The von Bertalanffy growth function was used to describe growth from length-at-age data derived from sectioned otoliths.

Seasonal growth of King George whiting (Sillaginodes punctata) estimated from length-at-age samples of the legal-size harvest

Samples of 11,000 King George whiting (Sillaginodes punctata) from the South Australian commercial and recreational catch, supplemented by research samples, were aged from otoliths. Samples were analyzed from three coastal regions and by sex. Most sampling was undertaken at fish processing plants, from which only fish longer than the legal minimum length were obtained. A left-truncated normal distribution of lengths at monthly age was therefore employed as model likelihood. Mean length-at-monthly-age was described by a generalized von Bertalanffy formula with sinusoidal seasonality. Likelihood standard deviation was modeled to vary allometrically with mean length. A range of related formulas (with 6 to 8 parameters) for seasonal mean length at age were compared. In addition to likelihood ratio tests of relative fit, model selection criteria were a minimum occurrence of high uncertainties (>20% SE), of high correlations (>0.9, >0.95, and >0.99) and of parameter estimates at their biological limits, and we sought a model with a minimum number of parameters. A generalized von Bertalanffy formula with t0 fixed at 0 was chosen. The truncated likelihood alleviated the overestimation bias of mean length at age that would otherwise accrue from catch samples being restricted to legal sizes.

Biological characteristics and determination of population dynamics parameters of Nemipterus japonicus in the coastal waters of Province Bushehr, Persian Gulf

This study was conducted to determine biological characteristics and population dynamics parameters of threadfin bream (Nemipterus japonicus) in Persian Gulf (Bushehr Province), during November 2006 and October 2007. The minimum and maximum specimens were 75-273 mm FL and their weight was 7.6 - 351.9 g. Based on the exponential relationship between fork length and weight, slope (b) for individuals, males and females was 2.987321, 2.992546 and 3.007314, respectively. The emptiness value (V) was 45.6% and it shows that N. japonicus is a moderate feeder. The results of Fp indicates that crustacean with 78.2% are main foods, mollusca (27.7%), fishes (20.7%), polychaeta (19.2%) and Foraminifera (11.7%) were identified as minor foods and phytoplanktons (9.9%), nematoda(8.0%), echinodermata (2.3%) and sea weeds (0.3%) were random foods. The reproduction studies showed the spawning season extended within 2 peaks, from April- May and September and main spawning occurs in spring season.The mean absolute and relative fecundities were 472388±42633 and 3817±293 (X±SE), respectively. The maximum, minimum and mean of oocyte diameter were 0.448, 0.022 and 0.221mm (SE=0.071), respectively.The fork length at 50% maturity estimated to be 20.25 cm for females. The growth coefficient (K) , length infinity (L∞ ) and ɸ' was estimated 0.42/yr , 34.17 cm and 2.69, respectively. The coefficient of total mortality, fishing mortality, natural mortality and E was 1.37, 0.43, 0.94 and 0.31, respectively.

The study of biological characteristics and determination of population dynamic parameters of sawtooth barracuda (Sphyraena putnamae) in the Persian Gulf (Hormozgun Province waters)

The biological characteristics and population dynamisms of Sphyraena putnamae, were studied in the northern Persian Gulf and Oman Sea restricted to Hormuzgan province waters within 13 months period, from November 2006 up to November 2007. Biometrical and anatomical measurements were carried out, and biological surveys were conducted on 486 specimens. On the other hand, the growth and mortality parameters were estimated by using 3096 samples. These samples were collected from 3 landings, namely Bandar Abbas, Bandar Lengeh and Bandar Jask. The measurements of the minimum and maximum Fork lengths and weights were 11.7 to 8.03 cm and 135.0 to 4140.0 g, respectively. The results indicated that this species, having the Relative Length of Gut, RLG=0.34±0.002, is strongly carnivorous (often fish-eater), proven by the fact that more than 98% of its stomach contents were fish pieces. Examining the changes in the index of stomach emptiness by the percentage of CV = 0.47% indicates that this fish is Moderate feeder. The level of feeding increased in March, before spawning and decreased in June and September, simultaneously with the spawning season. There are 2 peaks of reproduction or spawning seasons during the months of April-May and September, of which the prior is assumed as the main spawning. The sex ratio (M:F) was calculated 0.5:1.0(X2 =2.11), which did not show a significant difference with expected level of 1:1 (P>0.05). The average absolute and relative reproduction rates of Sphyraena putnamae is respectively as follows: 1866827.1±255448.9 and 1097.7±94.3. The highest and the lowest diameter of matured egg are from 200 to 750 μ, and its average diameter is 402.10 ± 0.190 μ. A parameter for Saw-tooth barracuda length measurement, Lm50, based on the Fork-length, was calculated as 54.01 cm. In other words, as far as the fisheries management is concerned, the fish whose lengths are less than 54.01 cm should not be caught. The calculated level of (R2) (correlations of total length & weight), indicated strong correlations between length and weight of this fish, and the obtained formula included W =0.007100 FL 2.9295 and reinforced this assumption. The “K” Index for this fish in 3 above mentioned landings (Jask, Bandar-Abbas and Bandar-Length) were 1.24, 0.37 and 0.46 per year, respectively and the FL index for the same landings were estimated as 129, 110 and 134 cm, respectively. The growth coefficient (MONRO) for the above mentioned regions were calculated as 3.601, 3.647 and 3.917, respectively; and in the surveyed regions there were no significant differences in populations. The Total mortality coefficient (Z) was calculated 0.76, 1.12 and 1.07 per year, the Natural mortality coefficient was 0.46, 0.63 and 0.70, and the Fishing mortality coefficient (rate) (F) was found to be 0.30, 0.49 and 0.37 per year. The value of the exploitation rate (E) is equal to 0.39 per year, indicating that this species is an under-exploited resource, and there is no excessive fishing pressure on the fish supply of this species in the afore-said regions. The highest level of exploitation was found for ‘Bandar Abbas’ fishing region and the lowest level of exploitation is in ‘Bandar Lengeh’ waters.

Population parameters of Oreochromis leucostictus from Lake Naivasha, Kenya

Length-frequency data collected from fish landings on Lake Naivasha were used to estimate the growth parameters: total mortality (Z), growth performance index (Ø’), exploitation rate and recruitment pattern in Oreochromis leucostictus. The asymptotic length (L∞) was 38 cm and K 0.48 yr -1 Z was estimated as 3.5 yr -1, M was 0.19 yr -1, F was 2.6 yr -1 and E of 0.74. Recruitment occurs throughout the year, with a peak in January to March, while entry into the fishery occurs at a mean length of 15.9 cm. Existing restriction on the maximum number of gill nets allowed per fishing licence (10 per boat) and a minimum mesh size (10 cm) in the lake are not adhered to. Poaching using illegal mesh size nets as small as 5 cm and use of more than 10 nets per boat are common in the lake.

Estimations, from tagging experiments, of mortality rates and other parameters respecting yellowfin and skipjack tuna

ENGLISH: In this paper, a method of analysis described by Gulland (1963) has been used to estimate the fishing mortality rates of tagged yellowfin and skipjack tuna for specific areas and years. Fishing mortality rates obtained for tagged tunas will also represent those for the entire population from which the tagged fishes were drawn, provided the assumptions used and corrections made for these analyses are valid. Total mortality rates of tagged fishes have also been computed. These are not assumed to be directly equivalent to the total mortality rates of the untagged populations,since tagged fishes are subject to additional types of attrition. These additional sources of mortality are also examined in this study. SPANISH: En el presente trabajo se ha usado un método de análisis descrito por Gulland (1963), para estimar las tasas de mortalidad de pesca de los atunes aleta amarilla y barrilete marcados en áreas y años específicos. Las tasas de mortalidad de pesca obtenidas en atunes marcados representarán también las de toda la población, de la cual fueron extraídos, previendo que las suposiciones usadas y las correcciones hechas para estos análisis sean válidas. Las tasas de mortalidad total de los peces marcados también han sido computadas. No se supone que éstas sean directamente equivalentes a las tasas de mortalidad total de las poblaciones no marcadas, ya que los peces marcados están sujetos también a otros tipos de pérdida. Estas otras causas de mortalidad son examinadas también en el presente estudio.