Estimation of the growth curve parameters in Macrobrachium rosenbergii

Growth is one of the most important characteristics of cultured species. The objective of this study was to determine the fitness of linear, log linear, polynomial, exponential and Logistic functions to the growth curves of Macrobrachium rosenbergii obtained by using weekly records of live weight, total length, head length, claw length, and last segment length from 20 to 192 days of age. The models were evaluated according to the coefficient of determination (R2), and error sum off square (ESS) and helps in formulating breeders in selective breeding programs. Twenty full-sib families consisting 400 PLs each were stocked in 20 different hapas and reared till 8 weeks after which a total of 1200 animals were transferred to earthen ponds and reared up to 192 days. The R2 values of the models ranged from 56 – 96 in case of overall body weight with logistic model being the highest. The R2 value for total length ranged from 62 to 90 with logistic model being the highest. In case of head length, the R2 value ranged between 55 and 95 with logistic model being the highest. The R2 value for claw length ranged from 44 to 94 with logistic model being the highest. For last segment length, R2 value ranged from 55 – 80 with polynomial model being the highest. However, the log linear model registered low ESS value followed by linear model for overall body weight while exponential model showed low ESS value followed by log linear model in case of head length. For total length the low ESS value was given by log linear model followed by logistic model and for claw length exponential model showed low ESS value followed by log linear model. In case of last segment length, linear model showed lowest ESS value followed by log linear model. Since, the model that shows highest R2 value with low ESS value is generally considered as the best fit model. Among the five models tested, logistic model, log linear model and linear models were found to be the best models for overall body weight, total length and head length respectively. For claw length and last segment length, log linear model was found to be the best model. These models can be used to predict growth rates in M. rosenbergii. However, further studies need to be conducted with more growth traits taken into consideration

The von Bertalanffy growth curve: when a good fit is not good enough

The von Bertalanffy growth function is used for length based analysis of growth and mortality patterns for management of fisheries. However, certain fish have growth patterns that the VBGF may not be able to describe adequately.e.g. the Acanthurus lineatus in Samoa. In such cases a two phase VBGF may be a useful approach.

A note on application of hills procedure for growth-curve analysis of Indian major carp, Labeo rohita (Ham.), during the gonodal development period at Shillong, Meghalaya

The present study deals with the length increment data of 15 adult Labeo rohita (Ham.) over a period of five months by the applicatin of finite difference method at an altitude of 1496 m above mean sea level at Shilllong, Meghalaya.

Early postnatal growth of the spotted dolphin, Stenella attenuata, in the offshore Eastern Tropical Pacific.

Estimates of length at birth and early postnatal growth are made for the northern and southern populations of the offshore spotted dolphin in the offshore eastern tropical Pacific. Length at birth is estimated to be 85.4 cm for the northern population and 83.2 cm for the southern population. Analyses of series of monthly distributions of length revealed two cohorts born each year in the northern population, at least in the northern inshore part of its geographic range, but only one cohort born each year in the southern population. Growth curves fitted to the means of the monthly distributions of length gave estimates of length at 1 year of 126.2 and 132.6 cm and length at 2 years of 154.3 and 154.9 cm for the two cohorts in the northern population. and length at 1 year of 127.9 cm for the southern population. A growth curve fitted to lengths and ages (in dental growth layer groups) from the northern population gave estimates of lengths at 1 and 2 years of 123.0 and 143.0 cm, respectively.

Growth of yellowfin tuna, Thunnus albacares, in the Eastern Pacific Ocean based on otolith increments

ENGLISH: The growth of yellowfin tuna in the eastern Pacific is described in terms of several measurements taken from the fish and their otoliths (sagittae). Equations are also developed to predict age from the readily available dimensions of fork length and head length. The data for all of these relationships were obtained from a sample of 196 fish collected during 1977 through 1979 from purse seiners fishing north of the equator and east of 137°W. The fork-length range of the sample was 30-170 cm. The number of increments on a sagitta of each fish was used as a direct estimate of its age in days. The correspondence between increments and days has been validated for yellowfin in the length range of 40-110 cm. Circumstantial evidence indicates that the relationship also applies in the intervals of 0-40 cm and 110-170 cm. This circumstancial evidence was derived from: 1) literature on validated increments during early growth for other species, 2) knowledge that structures assumed to be daily increments on yellowfin otoliths have subsequently been validated in the corresponding zone on bluefin otoliths, and 3) a comparison of the growth curve based on increments to others obtained from length frequency modal analysis. Based on this information the age estimates over the entire size range of sampled fish are believed to be accurate. In addition to the general growth and age-predictive relationships, the major conclusions of the study are that: 1) Sexually dimorphic growth exists in terms of fork length, fish weight and the length of the otolith counting path for the entire data set. Examination of the data for 1977 and 1979 also revealed that the fork-length growth of each sex differed within years. 2) For combined sexes there were significant differences among the fork-length growth curves for yellowfin sampled in different years. 3) Yellowfin caught inshore (within 275 miles of the coast) were heavier than those caught offshore for fork lengths between 30 and 110 cm. The situation was reversed for lengths greater than 110 cm. 4) Back-calculated spawning months were distributed uniformly throughout the year in 1974 and 1977, but in 1975-1976 and 1978 spawning activity was apparently concentrated in the latter half of the year. SPANISH: El crecimiento del atún aleta amarilla en el Pacífico oriental se describe en términos de varias medidas obtenidas de peces y otolitos (sagita). Se formularon también ecuaciones para pronosticar la edad, según las dimensiones fácilmente disponibles de la longitud horquilla y longitud de la cabeza. Los datos de todas estas relaciones fueron obtenidos mediante una muestra de 196 peces recolectados desde 1977hasta 1979, en barcos cerqueros que estaban pescando al norte de la línea ecuatorial y al este de los 137°W. El intervalo de la longitud horquilla de la muestra fue de 30-170 cm. Se empleó el número de incrementos en la sagita de cada pez como un estimado directo de la edad en días. Se ha comprobado la relación entre los incrementos y los días en el intervalo de longitud de 40-110 cm del aleta amarilla. La evidencia circunstancial indica que se aplica también la relación a los intervalos de 0-40 cm y 110-170 cm. Esta evidencia circunstancial se dedujo: 1) de las publicaciones sobre incrementos comprobados de otras especies durante el primer crecimiento, 2) del conocimientoque las estructuras que se supone son incrementos diarios en los otolitos del aleta amarilla han sido comprobadas luego en la parte correspondiente de otolitos del aleta azul y 3) por una comparación de la curva de crecimiento, basada en incrementos relacionados a otras curvas obtenidas según el análisis modal frecuencia-talla. Se cree, basados en esta información, que las estimaciones de la edad sobre toda la amplitud de talla de los peces muestreados, es acertada. Además de la relación del crecimiento general y del pronóstico de la edad, las principales conclusiones de este estudio son: 1) En toda la serie de datos existe el crecimiento sexualmente dimórfico en términos de longitud horquilla, peso del pez y longitud del plano de conteo del otolito. El examen de los datos de 1977 y 1979, revelan también que el crecimiento longitud horquilla de cada sexo es diferente en los años. 2) En los sexos combinados hubo diferencias significativas entre las curvas de crecimiento longitud horquilla del aleta amarilla muestreado en diferentes años. 3) El aleta amarilla capturado cerca a la costa (en las primeras 275 millas) fue más pesado que el capturado en las aguas mar afuera, correspondiente a la longitud horquilla entre 30 y 110 cm. La situación fue inversa para tallas de más de 110 cm. 4) En 1974 y 1977, los meses retrocalculados del desove se distribuyeron uniformemente durante el año, pero en 1975-1976 y 1978, la actividad del desove se concentró aparentemente en el último semestre del año. (PDF contains 62 pages.)

Growth parameters for Lates niloticus (L.), Bagrus docmak (Forsskal), Oreochromis niloticus (L.), Clarias gariepinus (Burchell) and Synodontis species derived from tag returns

In a tagging experiment carried out in the Kenyan waters of Lake Victoria, an annual growth increment of 29 cm yr was obtained for Lates niloticus (L.). Growth parameters obtained using the von Bertalanffy model on the growth curve fitted by eye were L (inf.) = 122 cm yr and k = 0.26 yr. Data for other species tagged were inadequate to obtain meaningful results.

A note on the von Bertalanffy growth function concerning the allocation of surplus energy to reproduction

We propose an extended form of the von Bertalanffy growth function (VBGF), where the allocation of surplus energy to reproduction is considered. Any function can be used in our model to describe the ratio of energy allocation for reproduction to that for somatic growth. As an example, two models for energy allocation were derived: a step-function and a logistic function. The extended model can jointly describe growth in adult and juvenile stages. The change in growth rate between the two stages can be either gradual or steep; the latter gives a biphasic VBGF. The results of curve fitting indicated that a consideration of reproductive energy is meaningful for model extension. By controlling parameter values, our comprehensive model gives various growth curve shapes ranging from indeterminate to determinate growth. An increase in the number of parameters is unavoidable in practical applications of this new model. Additional information on reproduction will improve the reliability of model estimates.

Growth and seasonal recruitment of Octopus maya on Campeche Bank, Mexico

A study of growth and seasonal recruitment of the cephalopod Octopus maya on Campeche Bank, Mexico, was conducted, based on catch at size data sampled from 1983 to 1988. The parameters of a seasonally oscillating version of the von Bertalanffy growth function and total mortality estimates were obtained via the ELEFAN software. It was found that when recruitment occurs early in the year, the growth curve of the next year does not display seasonal oscillations, and conversely. Total mortality estimates ranged from Z = 2.6 to Z = 6.3/year.

Age, growth and mortality of the toadfish, Halobatrachus didactylus (Schneider, 1801) (Pisces: Batrachoididae), in the Bay of Cádiz (southwestern Spain)

Age, growth and mortality of the toadfish, Halobatrachus didactylus, were determined by examination of the whole sagittal otoliths of fish sampled in the Bay of Cádiz (southwestern Spain) from March 1999 to March 2000. A total of 844 specimens (425 males, 416 females, and 3 of indeterminate sex), ranging from 95 to 470 mm in total length were examined. Eighty-nine percent of the otoliths could be read allowing an age estimation. The opaque zone was formed between April and May coincident with the maximum reproductive peak, while the translucent zone formed mainly in summer-fall (June to December). Maximum ages for males and females were 12 and 10 years, respectively. The samples were dominated by 2- to 6-year-old specimens. Males matured at an age of approximately 2 years and females at 3 years. Fish total length and otolith radius were closely related. The von Bertalanffy growth curve was used to describe growth. The parameters were derived from back-calculated length-at-age. Significant differences in the growth parameters were found between sexes. Although the growth analysis revealed that this species is slow-growing, males reached larger sizes than females. Females appeared to experience higher natural mortality rates than males.

Modeling red sea urchin (Strongylocentrotus franciscanus) growth using six growth functions

The growth of red sea urchins (Strongylocentrotus franciscanus) was modeled by using tag-recapture data from northern California. Red sea urchins (n=211) ranging in test diameter from 7 to 131 mm were examined for changes in size over one year. We used the function Jt+1 = Jt + f(Jt) to model growth, in which Jt is the jaw size (mm) at tagging, and Jt+1 is the jaw size one year later. The function f(Jt), represents one of six deterministic models: logistic dose response, Gaussian, Tanaka, Ricker, Richards, and von Bertalanffy with 3, 3, 3, 2, 3, and 2 minimization parameters, respectively. We found that three measures of goodness of fi t ranked the models similarly, in the order given. The results from these six models indicate that red sea urchins are slow growing animals (mean of 7.2 ±1.3 years to enter the fishery). We show that poor model selection or data from a limited range of urchin sizes (or both) produces erroneous growth parameter estimates and years-to-fishery estimates. Individual variation in growth dominated spatial variation at shallow and deep sites (F=0.246, n=199, P=0.62). We summarize the six models using a composite growth curve of jaw size, J, as a function of time, t: J = A(B – e–Ct) + Dt, in which each model is distinguished by the constants A, B, C, and D. We suggest that this composite model has the flexibility of the other six models and could be broadly applied. Given the robustness of our results regarding the number of years to enter the fishery, this information could be incorporated into future fishery management plans for red sea urchins in northern California.

Age and growth of the bastard grunt (Pomadasys incisus: Haemulidae) inhabiting the Canarian archipelago, Northwest Africa

The bastard grunt (Pomadasys incisus) is one of the most abundant coastal demersal fishes inhabiting the Canary Islands. Age and growth were studied from samples collected between October 2000 and September 2001. Growth analysis revealed that this species is a fast growing and moderately short-lived species (ages up to seven years recorded). Length-at-age was described by the von Bertalanffy growth model (L∞=309.58 mm; k=0.220/year; t0=–1.865 year), the Schnute growth model (y1=126.66 mm; y2=293.50 mm; a=–0.426; b= 5.963), and the seasonalized von Bertalanffy growth model (L∞=309.93 mm; k=0.218/ year; t0= –1.896 year; C=0.555; ts=0.652). Individuals grow quickly in their first year, attaining approximately 60% of their maximum length; after the first year, their growth rate drops rapidly as energy is probably diverted to reproduction. The parameters of the von Bertalanffy weight growth curve were W∞=788.22 mm; k=0.1567/year; t0= –1.984 year. Fish total length and otolith radius were closely correlated, r2=0.912. A power relationship was estimated between the total length and the otolith radius (a=49.93; ν=0.851). A year’s growth was represented by an opaque and hyaline (translucent) zone—an annulus. Backcalculated lengths were similar to those predicted by the growth models. Growth parameters estimated from the backcalculated sizes at age were L∞=315.23 mm; k=0.217/year; and t0= –1.73 year.

Validated age and growth of the porbeagle shark (Lamna nasus) in the western North Atlantic Ocean

Growth parameters were estimated for porbeagle shark (Lamna nasus) in the northwest Atlantic Ocean on the basis of vertebral annuli. A total of 578 vertebrae was analyzed. Annuli were validated up to an age of 11 years by using vertebrae from recaptured oxytetracycline-injected and known-age sharks. Males and females grew at similar rates until the size of male sexual maturity, after which the relative growth of the males declined. The growth rate of the females declined in a similar manner at the onset of maturity. Growth curves were consistent with those derived from tag-recapture analyses (GROTAG) of 76 recaptured fish and those based on length-frequency methods with measurements from 13,589 individuals. Von Bertalanffy growth curve parameters (combined sexes) were L∞ = 289.4 cm fork length, K = 0.07 and t0 = –6.06. Maximum age, based on vertebral band pair counts, was 25 and 24 years for males and females, respectively. Longevity calculations, however, indicated a maximum age of 45 to 46 years in an unfished population.

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.

Age determination and age related factors in the teeth of Western North Atlantic bottlenose dolphins.

Teeth were taken from 120 bottlenose dolphins, Tursiops truncatus, which had stranded on the mid-Atlantic coast of the United States. The number of annual growth layer groups (GLGs) for each animal was used to construct a growth curve. The growth rate of coastal North Atlantic Ocean Tursiops is similar to other cetaceans in having a high initial rate of growth, with no differences in growth between females and males. In females, the first dentinal GLG is thickest and is followed by GLGs which become progressively narrower. In males, the second GLG is thicker than the first; GLGs beyond number two become progressively smaller but at a slower rate than in females. In males and females, the translucent layer makes up proportionally larger parts of the GLG as the animal ages, but in males the percent translucent layer remains constant at about 50% while in females it continues to increase up to about 70% of the GLG. These two factors, GLGs width and translucent layer width, indicate that the sex and age of the animal influence the deposition of GLGs. Incremental layers are also present, averaging 12 per GLG, and seem similar to incremental layers described in other marine mammals. A plot of the relationship of percent growth of the last GLG to time of death suggests that the deposition of GLGs is relatively constant, at least during the first half of the year, and that North Atlantic Ocean Tursiops give birth in the fall as well as in the spring. (PDF contains 31 pages.)