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

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.

Measurement errors in body size of sea scallops (Placopecten magellanicus) and their effect on stock assessment models

Body-size measurement errors are usually ignored in stock assessments, but may be important when body-size data (e.g., from visual sur veys) are imprecise. We used experiments and models to quantify measurement errors and their effects on assessment models for sea scallops (Placopecten magellanicus). Errors in size data obscured modes from strong year classes and increased frequency and size of the largest and smallest sizes, potentially biasing growth, mortality, and biomass estimates. Modeling techniques for errors in age data proved useful for errors in size data. In terms of a goodness of model fit to the assessment data, it was more important to accommodate variance than bias. Models that accommodated size errors fitted size data substantially better. We recommend experimental quantification of errors along with a modeling approach that accommodates measurement errors because a direct algebraic approach was not robust and because error parameters were diff icult to estimate in our assessment model. The importance of measurement errors depends on many factors and should be evaluated on a case by case basis.

Age validation, growth modeling, and mortality estimates for striped trumpeter (Latris lineata) from southeastern Australia: making the most of patchy data

Age estimates for striped trumpeter (Latris lineata) from Tasmanian waters were produced by counting annuli on the transverse section of sagittal otoliths and were validated by comparison of growth with known-age individuals and modal progression of a strong recruitment pulse. Estimated ages ranged from one to 43 years; fast growth rates were observed for the first five years. Minimal sexual dimorphism was shown to exist between length, weight, and growth characteristics of striped trumpeter. Seasonal growth variability was strong in individuals up to at least age four, and growth rates peaked approximately one month after the observed peak in sea surface temperature. A modified two-phase von Bertalanffy growth function was fitted to the length-at-age data, and the transition between growth phases was linked to apparent changes in physiological and life history traits, including offshore movement as fish approach maturity. The two-phase curve was found to represent the mean length at age in the data better than the standard von Bertalanffy growth function. Total mortality was estimated by using catch curve analysis based on the standard and two-phase von Bertalanffy growth functions, and estimates of natural mortality were calculated by using two empirical models, one based on longevity and the other based on the parameters L∞ and k from both growth functions. The interactions between an inshore gillnet fishery targeting predominately juveniles and an offshore hook fishery targeting predominately adults highlight the need to use a precautionary approach when developing harvest strategies.

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 Hawaiian seaturtles (Chelonia mydas): an analysis based on skeletochronology

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

Trend and growth analysis of marine fish production in Bangladesh

The study based on time series marine fish production data during the period of 1983-1984 to 2007-2008 in Bangladesh. For this growth analysis six deterministic time series models are considered. The estimated best fitting models are the cubic, quadratic and quadratic model is appropriate for industrial marine fish production, artisanal marine fish production and total marine fish production in Bangladesh respectively. The study attempts to provide forecasts of marine fish production in Bangladesh for the year of 2008-09 to 2012-13. The magnitude of instability in marine fish production was attempted by computing the coefficient of variation (CV) and the percentage deviation from three years moving average values. The study revealed that the total marine fish production was observed to be relatively stable (CV being 31.85%) compared to the artisanal marine fish production (CV being 32.04%) and industrial marine fish (CV being 47.20%). For the three components of marine fish production the growth rates were different over different time points. The variation of the growth rates in industrial marine fish production was -21.6% to 13.12%, in artisanal marine fish production was 2.39% to 5.29% and in total marine fish production was 11.23% to 24.85% during the study period.