Age- or length-based methods of growth estimation. What drives the choice?

Based upon a global comparison of over 400 fisheries, the Principal Components Analysis (PCA) methodology was used to identify factors affecting the choice of growth estimation methods. Of the six factors examined, the growth rate (K) and asymptotic length (L8) explained most of the variations. Financial resources, i.e., Gross National Product (GNP), and latitude were also important factors.

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected. (C) 2013 Elsevier B.V. All rights reserved.

Growth, mortality, and exploitation of the Engraulidae, with special reference to the anchoveta, Cetengraulis mysticetus, and the colorado, Anchoa naso, in the Eastern Pacific Ocean

ENGLISH: Growth and mortality data for Cetengraulis mysticetus, Anchoa naso, Engraulis mordax, E. ring ens, E. anchoita, E. encraslcbolus, E. japonicus, and E. australis were assembled and compared. Estimates of the coefficients of natural mortality, M, of E. anchoita and Ancboa naso were made from the maximum age of the former and from data for the other species. The relative yields per recruit at different fishing mortality rates and lengths at entry into the fishery were calculated for each species, using what are considered to be the best estimates and other likely values of K, a constant of growth, and M. The maximum yields per recruit are theoretically obtainable at very high fishing mortality rates, except when the length at entry is low relative to the asymptotic length. K and M may be positively related to the temperature and to each other, and if such is the case at higher temperatures greater fishing effort would be needed to attain the maximum yield per recruit. The applicability of the yield-per-recruit approach to the data is discussed, and suggestions for further research are made. SPANISH: Se reunieron y compararon los datos sobre el crecimiento y mortalidad correspondientes a Cetengraulis mysticetus, Anchoa naso, Engraulis mordax, E. ringens, E. anchoíta, E. encrasicbolus, E. japonicus y E. australls. Los estimativos de los coeficientes de la mortalidad natural, M, de E. anchoita y Anchoa naso se obtuvieron según la edad máxima de E. anchoita y según los datos de las otras especies. Se calculó para cada especie el rendimiento relativo por recluta a diferentes tasas de mortalidad por la pesca y a diferentes longitudes de entrada a la pesquería, empleándose lo que se considera que son los mejores estimativos y otros valores probables de K, una constante de crecímíento, y M. El rendimiento máximo por recluta se obtiene teóricamente a tasas muy altas de la mortalidad por la pesca con excepción de cuando la longitud a la entrada es baja en relación a la longitud asintótica. K y M pueden estar relacionadas positivamente a la temperatura y mutuamente, y si este es el caso a temperaturas más altas se necesitará un esfuerzo superior de pesca para obtener el rendimiento máximo por recluta. La aplicabilidad del enfoque a los datos rendimiento-por-recluta es discutido y se hacen sugerencias para otras investigaciones. (PDF contains 66 pages.)

Age and growth of Mugil cephalus (Linnaeus, 1758) (Perciformes: Mugilidae) in Bonny Estuary

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)

Age, growth, and reproduction of dolphinfish (Coryphaena hippurus) caught off the coast of North Carolina

Age, growth, and reproductive data were obtained from dolphinfish (Coryphaena hippurus, size range: 89 to 1451 mm fork length [FL]) collected between May 2002 and May 2004 off North Carolina. Annual increments from scales (n=541) and daily increments from sagittal otoliths (n=107) were examined; estimated von Bertalanffy parameters were L∞ (asymptotic length)=1299 mm FL and k (growth coefficient)=1.08/yr. Daily growth increments reduced much of the residual error in length-at-age estimates for age-0 dolphinfish; the estimated average growth rate was 3.78 mm/day during the first six months. Size at 50% maturity was slightly smaller for female (460 mm FL) than male (475 mm FL) dolphinfish. Based on monthly length-adjusted gonad weights, peak spawning occurs from April through July off North Carolina; back-calculated hatching dates from age-0 dolphinfish and prior reproductive studies on the east coast of Florida indicate that dolphinfish spawning occurs year round off the U.S. east coast and highest levels range from January through June. No major changes in length-at-age or size-at-maturity have occurred since the early 1960s, even after substantial increases in fishery landings.

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.

Observations on gillnet catches of Kariba tilapia, Oreochromis mortimeri from Bumi Basin of Lake Kariba, Zimbabwe

Gillnet catches of Oreochromis mortimeri (Trewavas) were studied in the Bumi Basin of Lake Kariba in 1988 and 1989. Total length (TL) was positively correlated with standard length (SL). The linear relationship between TL and SL was TL=1.91 + 1.22 SL (r super(2)=0.982). The relationship between SL and weight in g (W) was of the form W = 0.12 SL super(2.67). Maximum standard length (L sub(max)) was 33 cm and asymptotic length (L sub( infinity )) was 34.7 cm. Monthly ratios of male to female varied between 0.6:1 and 13:1. The mean ratio was 57.4% male: 42.6%female. Monthly condition factors varied between 3.19 and 5.11 in males, and between 3.18 and 5.14 in females. Catches were higher in 1989 compared to 1988 and possible reasons for these differences are discussed.

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 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.

Breeding, age and growth of the freshwater shark Wallago attu (Bloch and Schneider) from the Dhir Beel of the Brahmaputra Basin, Assam, India

The Dhir Beel, one of the major live beels of the Brahmaputra Basin, Assam, has an area of 689 ha and situated in Dhubri district of Assam. The dominance of freshwater shark, Wallago attu (8.10%) in the beel is a striking feature. Restricted breeding of W. attu once a year from June to September was observed. The mean observed length was 37.5, 65.0, 84.5 and 99.0 cm in the 6th, 12th, 18th and 24th months of age respectively. The length growth coefficient (K), the asymptotic length (L infinity ), and the arbitrary origin of the growth curve (t omicron ), for W. attu were estimated to be 0.054484 per month, 136.16 cm and 0.0355 month respectively. The calculated life span (T infinity ) of the fish is 123.86 months (about 10 years). The weight growth parameters were estimated where the monthly growth coefficient (K), the asymptotic weight (W infinity) and the arbitrary origin of the growth curve (t omicron) were found to be 0.0743 per month, 7636.92 gram and 0.431908 month respectively. The length-weight relationship follows the cube law.

Some aspects of population dynamics of juvenile hilsa shad (Tenualosa ilisha Ham.) from the Meghna river, Bangladesh

Population dynamics of the juvenile hilsa shad (Tenualosa ilisha) in the nursery ground of the Meghna River have been studied on the basis of the length cohort analysis of 8023 specimens. The growth parameters viz; asymptotic length (Lα), curvature character (K) and initial time (t0) were found to be 30.69 cm, 1.2 yrˉ¹ and 0.45 yrˉ¹ respectively. Curvature parameter indicates that jatka is a fast growth performer. The natural, fishing and total mortality were found to be 1.37 yrˉ¹, 1.41 yrˉ¹ and 2.78 yrˉ¹ respectively. Survival rate (S) was found to be 6.2%. A small difference was found between the age at first capture (Tc) and the recruitment age (Tr). Stocks of jatka seem to be overexploited and need to be conserved.