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.

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

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Integrating methods for determining length-at-age to improve growth estimates for two large scombrids

Fish growth is commonly estimated from length-at-age data obtained from otoliths. There are several techniques for estimating length-at-age from otoliths including 1) direct observed counts of annual increments; 2) age adjustment based on a categorization of otolith margins; 3) age adjustment based on known periods of spawning and annuli formation; 4) back-calculation to all annuli, and 5) back-calculation to the last annulus only. In this study we compared growth estimates (von Bertalanffy growth functions) obtained from the above five methods for estimating length-at-age from otoliths for two large scombrids: narrow-barred Spanish mackerel (Scomberomorus commerson) and broad-barred king mackerel (Scomberomorus semifasciatus). Likelihood ratio tests revealed that the largest differences in growth occurred between the back-calculation methods and the observed and adjusted methods for both species of mackerel. The pattern, however, was more pronounced for S. commerson than for S. semifasciatus, because of the pronounced effect of gear selectivity demonstrated for S. commerson. We propose a method of substituting length-at-age data from observed or adjusted methods with back-calculated length-at-age data to provide more appropriate estimates of population growth than those obtained with the individual methods alone, particularly when faster growing young fish are disproportionately selected for. Substitution of observed or adjusted length-at-age data with back-calculated length-at-age data provided more realistic estimates of length for younger ages than observed or adjusted methods as well as more realistic estimates of mean maximum length than those derived from backcalculation methods alone.

Ontogenetic patterns and temperature-dependent growth rates in early life stages of Pacific cod (Gadus macrocephalus)

Pacific cod (Gadus macrocephalus) is an important component of fisheries and food webs in the North Pacific Ocean and Bering Sea. However, vital rates of early life stages of this species have yet to be described in detail. We determined the thermal sensitivity of growth rates of embryos, preflexion and postflexion larvae, and postsettlement juveniles. Growth rates (length and mass) at each ontogenetic stage were measured in three replicate tanks at four to five temperatures. Nonlinear regression was used to obtain parameters for independent stage-specific growth functions and a unified size- and temperature-dependent growth function. Specific growth rates increased with temperature at all stages and generally decreased with increases in body size. However, these analyses revealed a departure from a strict size-based allometry in growth patterns, as reduced growth rates were observed among preflexion larvae: the reduction in specific growth rate between embryos and free-swimming larvae was greater than expected based on body size differences. Growth reductions in the preflexion larvae appear to be associated with increased metabolic rates and the transition from endogenous to exogenous feeding. In future studies, experiments should be integrated across life transitions to more clearly define intrinsic ontogenetic and size-dependent growth patterns because these are critical for evaluations of spatial and temporal variation in habitat quality.

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.

Age structure, growth and mortality estimates of an endemic Ptychobarbus dipogon (Regan, 1905) (Cyprinidae: Schizothoracinae) in the Lhasa River, Tibet

Ptychobarbus dipogon is an endemic fish in the Yarlung Tsangpo River, but its biology is poorly known. We sampled 582 specimens (total length, TL, between 70.6 and 593.0 mm) from April 2004 to August 2006 in the Lhasa River, Tibet. We estimated ages based on the counts of alternating opaque and translucent zones (annuli) in thin transverse sections of lapilli otoliths. Ages ranged from 1(+) to 23(+) years for males and 1(+) to 44(+) for females. The observed 44(+) years was the oldest reported for schizothoracine fishes. Females attained a larger size than males. The TL weight relationship was W=7.12 x 10(-6)TL(3.006) for combined sexes. The growth parameters fitted von Bertalanffy growth functions were L-infinity = 598.66 mm, k=0.0898 year(-1), t(0)=-0.7261 year and W-infinity = 1585.38 g for females and L-infinity = 494.23mm, k=0.1197 year(-1), t(0)=-0.7296 year and W-infinity = 904.88g for males. The longevities of 32.7 year for females and 24.3 year for males were similar to the observed ages. Using an empirical model we estimated the instantaneous rate of total mortality (Z) at 0.28 per year in the lower reaches. Z in the upper and middle stocks was close to the M because of unexploited or lightly exploited stock. Protracted longevity, slow growth, low natural mortality and large body size were typical characteristics of P. dipogon. The current declining trend of P. dipogon could be prevented by altering fishing regulations.

Age and growth of Schizopygopsis younghusbandi younghusbandi in the Yarlung Zangbo River in Tibet, China

Schizopygopsis younghusbandi younghusbandi is an endemic species whose distribution is restricted to the middle reaches of the Yarlung Zangbo River, being one of the most important commercial fishes in this area. Age and growth of 606 specimens captured between October 2002 and April 2005 were studied. The range in standard length (L) was 65.7-387.3 mm and total weight (W) was 3.3-772.0 g. The relationship between L and W was W=0.000909L(2.2493) for males and W=0.000259L(2.4781) for females. Age, determined from anal scales and lapillus otoliths, ranged from 3 to 18 years. The parameters of von Bertalanffy growth functions, estimated by back-calculated length, were L-infinity = 442.7mm L, k=0.0738 year(-1) and t(0)=-1.4 year for males, and L-infinity = 471.4mm L, k=0.0789 year(-1) and t(0)=0.2 year for females. Males and females exhibited statistically significant differences in growth. chi(2)-test indicated that von Bertalanffy growth functions could well describe the growth of S. y. younghusbandi. The longevities were 39.2 and 38.2 years for males and females, respectively. Growth inflexion points were 10.2 and 12.0 years for males and females, respectively, but 84.8% of the captures were at the smaller ages. So conservation and management schemes for this population should be considered urgently. In addition, we found that populations from the upstream of the Lhasa River, the downstream of the Lhasa River and the middle reaches of the Yarlung Zangbo River showed statistically significant differences in growth patterns.

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (112), mean square error (MSE) were calculated using language of technical computing package Matlab(R), 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike's Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R(2), lower MSE and A/C Finally, the parameters A, B and k were adjusted in Matlab(R) 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

Growth curves for Macrobrachium rosenbergii in semi-intensive culture in Brazil

Four 0.02-ha earthen ponds at the UNESP Aquaculture Center, Jaboticabal, São Paulo, Brazil, were stocked with newly metamorphosed Macrobrachium rosenbergii post-larvae at 1.5 animals/m2. After 8 mo, prawn density at harvest ranged from 0.3/ m2 to 0.8/m2. Growth curves were determined for each population using von Bertalanffy growth functions. Asymptotic maximum length and asymptotic maximum weight increased as final population size decreased indicating that a strong density effect on prawn growth occurs in semi-intensive culture, even when populational density varies within a small range of less than 1 animal/m2.

Growth curves for ostriches (Struthio camelus) in a Brazilian population

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)