Least Squares Estimation Principle and its Geometrical Interpretation

pdf contains 14 pages)

Proceedings of the Eighteenth International Sea Turtle Symposium, 3-7 March 1998, Mazatlán, Sinaloa, Mexico

For the first time in its history, the International Symposium on Sea Turtle Biology and Conservation migrated to a site outside of the United States. Thus the Eighteenth edition was hosted by the Mazatlán Research Unit of the Instituto de Ciencias del Mar y Limnología of the Mexican National Autonomous University (UNAM) in Mazatlán, Sinaloa (Mexico) where it was held from 3-7, March, 1998. Above all, our symposium is prominent for its dynamism and enthusiasm in bringing together specialists from the world´s sea turtle populations. In an effort to extend this philosophy, and fully aware of how fast the interest in sea turtles has grown, the organizers paid special attention to bring together as many people as possible. With the tremendous efforts of the Travel Committee and coupled with a special interest by the Latin American region´s devotees, we managed to get 653 participants from 43 countries. The number of presentations increased significantly too, reaching a total of 265 papers, ranging from cutting-edge scientific reports based on highly sophisticated methods, to the experiences and successes of community-based and environmental education programs. A priority given by this symposium was the support and encouragement for the construction of "bridges" across cultural and discipline barriers. We found success in achieving a multinational dialogue among interest groups- scientists, resource managers, decision makers, ngo's, private industry. There was a broad representation of the broad interests that stretch across these sectors, yet everyone was able to listen and offer their own best contribution towards the central theme of the Symposium: the conservation of sea turtles and the diversity of marine and coastal environments in which they develop through their complicated and protracted life cycle. Our multidisciplinary approach is highly important at the present, finding ourselves at a cross roads of significant initiatives in the international arena of environmental law, where the conservation of sea turtles has a key role to play. Many, many people worked hard over the previous 12 months, to make the symposium a success. Our sincerest thanks to all of them: Program committee: Laura Sarti (chair), Ana Barragán, Rod Mast, Heather Kalb, Jim Spotilla, Richard Reina, Sheryan Epperly, Anna Bass, Steve Morreale, Milani Chaloupka, Robert Van Dam, Lew Ehrhart, J. Nichols, David Godfrey, Larry Herbst, René Márquez, Jack Musick, Peter Dutton, Patricia Huerta, Arturo Juárez, Debora Garcia, Carlos Suárez, German Ramírez, Raquel Briseño, Alberto Abreu; Registration and Secretary: Jane Provancha (chair), Lupita Polanco; Informatics: Germán Ramírez, Carlos Suárez; Cover art: Blas Nayar; Designs: Germán Ramírez, Raquel Briseño, Alberto Abreu. Auction: Rod Mast; Workshops and special meetings: Selina Heppell; Student prizes: Anders Rhodin; Resolutions committee: Juan Carlos Cantú; Local organizing committee: Raquel Briseño, Jane Abreu; Posters: Daniel Ríos and Jeffrey Semminoff; Travel committee: Karen Eckert (chair), Marydele Donnelly, Brendan Godley, Annette Broderick, Jack Frazier; Student travel: Francisco Silva and J. Nichols; Vendors: Tom McFarland and J. Nichols; Volunteer coordination: Richard Byles; Latin American Reunión: Angeles Cruz Morelos; Nominations committee: Randall Arauz, Colleen Coogan, Laura Sarti, Donna Shaver, Frank Paladino. Once again, Ed Drane worked his usual magic with the Treasury of the Symposium Significant financial contributions were generously provided by government agencies. SEMARNAP (Mexico´s Ministry of Environment, Natural Resources and Fisheries) through its central office, the Mazatlán Regional Fisheries Research Center (CRIP-Mazatlán) and the National Center for Education and Capacity Building for Sustainable Development (CECADESU) contributed to the logistics and covered the costs of auditoria and audiovisual equipment for the Symposium, teachers and their hotels for the Community Development and Environmental Education workshop in the 5th Latin American Sea Turtle Specialists; DIF (Dept of Family Affairs) provided free accomodation and food for the more than 100 participants in the Latin American Reunion. In this Reunion, the British Council-Mexico sponsored the workshop on the Project Cycle. The National Chamber of the Fisheries Industry (CANAINPES) kindly sponsored the Symposium´s coffee breaks. Personnel from the local Navy (Octave Zona Naval) provided invaluable aid in transport and logistics. The Scientific Coordination Office from UNAM (CICUNAM) and the Latin American Biology Network (RELAB) also provided funding. Our most sincere recognition to all of them. In the name of this Symposium´s compilers, I would like to also express our gratitude to Wayne Witzell, Technical Editor for his guidance and insights and to Jack Frazier for his help in translating and correcting the English of contributions from some non-native English speakers. Many thanks to Angel Fiscal and Tere Martin who helped with the typing in the last, last corrections and editions for these Proceedings. To all, from around the world, who generously helped make the 18th Symposium a huge success, shared their experiences and listened to ours, our deepest gratitude! (PDF contains 316 pages)

Relationship between fish size and otolith length for 63 species of fishes from the Eastern North Pacific Ocean

Otoliths commonly are used to determine the taxon, age, and size of fishes. This information is useful for population management, predator-prey studies, and archaeological research. The relationship between the length of a fish and the length of its otoliths remains unknown for many species of marine fishes in the Pacific Ocean. Therefore, the relationships between fish length and fish weight, and between otolith length and fish length, were developed for 63 species of fishes caught in the eastern North Pacific Ocean. We also summarized similar relationships for 46 eastern North Pacific fish species reported in the literature. The relationship between fish length and otolith length was linear, and most of the variability was explained by a simple least-squares regression (r 2 > 0.700 for 45 of 63 species). The relationship between otolith length and fish length was not significantly different between left and right otoliths for all but one fish species. Images of otoliths from 77 taxa are included to assist in the identification of species. (PDF file contains 38 pages.)

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

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

Nigerian fisheries development, challenges and opportunities of the 1980's

With the momentum generated in Nigeria under the Green Revolution Programme to make the country self-sufficient in food, the fishing industry is poised for very rapid development. It is however, realized that there is no quick magic formula for this development, which has to be preceded by careful planning, evaluation of resources, development of necessary management and technical personnel, introduction of appropriate technology and identification of priorities and the needs of the industry. This paper attempts to focus attention on the possibilities and priorities for the development of fisheries in Nigeria during this decade and spells out the role of the agencies in the country connected with fisheries to bring about this development

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.)

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.)

Results from RV Utafiti research cruises

Monthly fish surveys were made from 1997-1999 in the Kenyan waters of Lake Victoria in order to estimate the magnitude of fisheries resources. Sample sites were defined using GPS while thirty minute hauls in alternate grid squares were made. Demersal fish biomass was estimated using the swept area method, while for trawling two different trawl nets were used. Collected fish was sorted into species, measured (TL) and weighed. Smaller fish were mixed on deck and sub-samples taken. Sexual maturity stages of fish were also observed. Areas with consistency high catches were located outside major urban and riverine influence where most artisanal fishermen were concentrated. Very low catches were obtained from areas that had recently been covered by water hyacinth Eichhornia crassipes

Biologie de Penaeus duorarum notialis en Côte d'Ivoire. 5 - Nouvelle étude de la croissance

Von Bertalanffy's growth curve parameters K, L∞ and t'o have been estimated for female Penaeus duorarum by modal progression analysis, using the "successive maximums method" of Gheno and Le Guen (1968) for the polymodal size frequency curves analysis and the Tomlinson and Abrahamson's least squares method for parameters computations. For the male the authors used an original method to get an age/length key. The parameters were calculated by Gulland's graphical method (1969).

Biologie de Ethmalosa fimbriata (Bowdich) en Côte d'Ivoire. 2 - Étude de la croissance en lagune par la méthode de Petersen

Ethmalosa growth curves (calculated by the least squares method) were determined from weekly samplings in Ebrié Lagoon. In order to obtain more accurate results than with a modal decomposition, the author used directly the modal values of the samples. One-year-old ethmalosa is about 15 cm long (fork length). For older fish, growth data seem to be disturbed by migrations: fish measuring >25 cm do not appear in the lagoon. Ethmalosa would spend the first year of its life in the lagoon, where it hatches and reproduces, and would migrate to the sea during its second year.

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-weight relationship of fishes from Yemen waters (Gulf of Aden and Red Sea)

The data for this study were gathered between 1993 and 1996 on board commercial trawlers from Somalia, China and Yemen and also from the research vessel Ibn Magid belonging to the Marine Science and Resources Research Centre, Aden, Republic of Yemen. Fish were identified using the FAO species identification literature. All fish were measured to the nearest mm (total length) and weighed to the nearest g. Sex was determined by dissection after the length and weight had been measured. The length-weight relationships were calculated using least-squares regression on log-transformed data and the parameters of the relationship of the form of W=aL super(b) are summarized. Maximum and minimum size of fish sampled are also given. Common names and recent changes in nomenclature were taken from ICLARM's FishBase.

Length-weight relationship of marine fishes from southern Brazil

The relationship between length (L) and weight (W) was estimated for 80 species belonging to 50 families of marine fishes from the shelf and upper slope of southern Brazil (lat. 28°S - 34°S). Sample sizes (n) for different species ranged from 11 to 14 741 specimens collected from commercial landings and research surveys. The fit of the equations (W=aLb) with a and b parameters estimated from regular and functional regression (of log-transformed weight and length data) as well as from a non-linear iterative process using the quasi-Newton algorithm were compared. The non-linear method gave the most accurate estimates in terms of residual sum of squares. Differences were less than 2.3% for n>500 compared with predictive regressions and 1.5% compared with functional regressions. No difference was observed between both predictive and functional regressions. Determination coefficients (r2) increased with sample size, and the highest r2 were obtained for 50

Blue Crab, Callinectes sapidus, Retention Rates in Different Trap Meshes

Percent escapements of blue crabs, Callinectes sapidus, by size and sex were determined for commercially available 38.1 mm square and hexagonal meshes and for five experimental squares. Commercial trap mesh sizes retained excessive numbers of sublegal blue crabs. Based on the criteria of maximizing sublegal crab escapement without an unacceptable loss of legal blue crabs, the 44.4 mm square (as measured from the inside of adjacent corners) was optimum and superior to either trap mesh used by fishermen.

An evaluation of back-calculation methodology using simulated otolith data

I simulated somatic growth and accompanying otolith growth using an individual-based bioenergetics model in order to examine the performance of several back-calculation methods. Four shapes of otolith radius-total length relations (OR-TL) were simulated. Ten different back-calculation equations, two different regression models of radius length, and two schemes of annulus selection were examined for a total of 20 different methods to estimate size at age from simulated data sets of length and annulus measurements. The accuracy of each of the twenty methods was evaluated by comparing the back-calculated length-at-age and the true length-at-age. The best back-calculation technique was directly related to how well the OR-TL model fitted. When the OR-TL was sigmoid shaped and all annuli were used, employing a least squares linear regression coupled with a log-transformed Lee back-calculation equation (y-intercept corrected) resulted in the least error; when only the last annulus was used, employing a direct proportionality back-calculation equation resulted in the least error. When the OR-TL was linear, employing a functional regression coupled with the Lee back-calculation equation resulted in the least error when all annuli were used, and also when only the last annulus was used. If the OR-TL was exponentially shaped, direct substitution into the fitted quadratic equation resulted in the least error when all annuli were used, and when only the last annulus was used. Finally, an asymptotically shaped OR-TL was best modeled by the individually corrected Weibull cumulative distribution function when all annuli were used, and when only the last annulus was used.