Cross-sectional and longitudinal method for describing growth curve of rabbits / Método transversal e longitudinal para descrição da curva de crescimento de coelhos

Rabbit farming is an activity with high growth potential due to its easy handling, high prolificacy, low polluting impact, and easy adaptability to family farming systems, producing meat of high biological value. Therefore, the aim of this work was to evaluate, using von Bertalanffy's nonlinear model, growth curves of weight as a function of age in 'Flemish Giant Rabbits' and 'New Zealand White' crossbred rabbits. Two different data collections were used: the longitudinal method and the cross-sectional method. The experiment was carried out at the Federal University of Lavras, located in the municipality of Lavras, Minas Gerais, Brazil, where 10 crossbred rabbits were evaluated, and animals were weighed from 0 to 150 days of age. Both methods proved to be adequate to describe the development of rabbits and the cross-sectional method proved to be an adequate alternative to obtention of growth curves, saving time in data collection and showing consistent estimates.

A cunicultura é uma atividade com alto potencial de crescimento devido à facilidade em seu manejo e à alta prolificidade, por apresentar baixo impacto poluidor, por se enquadrar bem em sistemas próprios de agricultura familiar, além de produzir carne de alto valor biológico. Diante disso, o objetivo deste trabalho foi avaliar, por meio do modelo não linear de von Bertalanffy, curvas de crescimento de coelhos mestiços de Gigante de Flandres e Nova Zelândia Branco, utilizando-se dois métodos distintos da coleta dos dados: o método longitudinal e o método transversal, a fim de estimar o crescimento do peso em função da idade. O experimento foi realizado na Universidade Federal de Lavras, situado no município de Lavras, Minas Gerais, Brasil. Foram avaliados 10 coelhos mestiços, cuja pesagem foi realizada de 0 a 150 dias de idade. Os dois métodos se mostraram adequados para descrever o crescimento de coelhos, e o método transversal se revelou uma boa alternativa, com ganho de tempo na coleta dos dados e apresentando estimativas consistentes.

Bayesian modeling of the coffee tree growth curve / Modelagem bayesiana da curva de crescimento do cafeeiro

When modeling growth curves, it should be considered that longitudinal data may show residual autocorrelation, and, if this characteristic is not considered, the results and inferences may be compromised. The Bayesian approach, which considers priori information about studied phenomenon has been shown to be efficient in estimating parameters. However, as it is generally not possible to obtain marginal distributions analytically, it is necessary to use some method, such as the weighted resampling method, to generate samples of these distributions and thus obtain an approximation. Among the advantages of this method, stand out the generation of independent samples and the fact that it is not necessary to evaluate convergence. In this context, the objective of this work research was: to present the Bayesian nonlinear modeling of the coffee tree height growth, irrigated and non-irrigated (NI), considering the residual autocorrelation and the nonlinear Logistic, Brody, von Bertalanffy and Richard models. Among the results, it was found that, for NI plants, the Deviance Information Criterion (DIC) and the Criterion of density Predictive Ordered (CPO), indicated that, among the evaluated models, the Logistic model is the one that best describes the height growth of the coffee tree over time. For irrigated plants, these same criteria indicated the Brody model. Thus, the growth of the non-irrigated and irrigated coffee tree followed different growth patterns, the height of the non-irrigated coffee tree showed sigmoidal growth with maximum growth rate at 726 days after planting and the irrigated coffee tree starts its development with high growth rates that gradually decrease over time.

Na modelagem de curvas de crescimento deve-se considerar que dados longitudinais podem apresentar autocorrelação residual, sendo que, se tal característica não é considerada, os resultados e inferências podem ser comprometidos. A abordagem bayesiana, que considera informações à priori sobre o fenômeno em estudo tem se mostrado eficiente na estimação de parâmetros. No entanto, como geralmente não é possível obter as distribuições marginais de forma analítica, faz-se necessário a utilização de algum método, como o método de reamostragem ponderada, para gerar amostras dessas distribuições e assim obter uma aproximação para as mesmas. Dentre as vantagens desse método, destaca-se a geração de amostras independentes e o fato de não ser necessário avaliar convergência. Diante desse contexto, o objetivo deste trabalho foi apresentar a modelagem não linear bayesiana do crescimento em altura de plantas do cafeeiro, irrigadas e não irrigadas (NI), considerando a autocorrelação residual e os modelos não lineares Logístico, Brody, von Bertalanffy e Richards. Em vista dos resultados, verificou-se que, para as plantas NI, o DIC e CPOc, indicaram que, dentre os modelos avaliados, o modelo Logístico é o que melhor descreve o crescimento em altura do cafeeiro ao longo do tempo. E, para as plantas irrigadas, esses mesmos critérios indicaram o modelo Brody. Assim, o crescimento da planta do cafeeiro não irrigado e irrigado seguiram padrões de crescimento distintos, a altura do cafeeiro não irrigado apresentou crescimento sigmoidal com taxa máxima de crescimento aos 726 dias após o plantio, já o cafeeiro irrigado inicia seu desenvolvimento com altas taxas de crescimento que vão diminuindo aos poucos com o tempo.

How temperature variation affects white-rot fungi mycelial growth dynamics: a nonlinear mixed models approach.

This study aimed to model mycelial growth in a factorial experiment with two species of white rot fungi growing at five temperatures. The nonlinear models evaluated were logistic, Gompertz, Weibull and von Bertalanffy. The adjustments were performed first by evaluating the fixed and mixed-effects models with random effects, added to the fixed parameters. Then, the best adjusted model was improved by an adequated covariance structure, and dummy variables were added to the parameters asymptote (α) and abscissa of the inflection point (ß) in the model in order to verify the effect of the experiment factors, species and temperatures on the regression parameters. The criteria used to compare models were residual variance and Akaike information criterion. Gompertz and von Bertalanffy mixed-effects models were better adjusted. The parameters differed between species. Moreover, the linear and quadratic effects of temperature evaluated in each species were significant. The models were reparametrized in order to consider two parameters of interest: velocity (µ) at the inflection point and lag time (λ). The maximum growth velocity was obtained at 25.4 °C by S. ostrea, while T. villosa was achieved at 30.5 °C; both fungi suffered less lag time by increasing the temperature.

Evaluation of non-linear models for growth curve in Brazilian tropical goats.

In the present study, 1060 body weight-age records were measured on 300 Canindé goats. The records were collected from Rio Grande do Norte state, North-eastern part of Brazil, and used for evaluation of non-linear models (Brody, Von Bertalanffy, Logistic, and Gompertz) describing growth curve in goats. The non-linear models were compared applying mean squared error of prediction (MSEP), mean squared residue (MSR), mean absolute deviation (MAD), adjusted coefficient of determination (R2aj), and convergence percentage (%C) for determining the most appropriate model describing the growth curve in Canindé goats. The absolute growth rate (AGR) was estimated based on the adjusted model as a function of time to describe the growth rate of the animals, and the effect of sex on the curve parameters was assessed. The Brody model was the most indicated to represent the average growth curve of Canindé goats. Furthermore, the growth curves estimated by the models under study show that the Brody model displayed the best fit, indicating a greater association between observed and estimated weights, suggesting that it can be used to describe the growth behavior and development of the animals analyzed of both sexes.

Nonlinear mixed effects models for comparing growth curves for Guzerá cattle / Modelos não lineares mistos para comparar curvas de crescimento de bovinos da raça Guzerá

The objective of the present work was to evaluate the accuracy of the fitted Gompertz and von Bertalanffy models for male and female Guzerá cattle, respectively. Four production regions in Northeast Brazil were included in the models as a fixed effect, and the animals were included as a random effect. In addition, the coefficients of the growth models in the production regions were compared. The accuracy of the fit equations was assessed with the Akaike information criterion, Bayesian information criterion, mean absolute deviation, mean squared error, and coefficient of determination. Confidence intervals were used for comparing the production regions. The Guzerá males in the Gado-Algodão and Serra Geral da Bahia production regions were statistically equal in asymptotic weight, and the animals in the Itapetinga-Valadares and Mata-Agreste regions had equivalent maturity rates. The Guzerá females in the Itapetinga-Valadares and Serra Geral da Bahia regions had the same asymptotic weight. The maturity rates in Itapetinga-Valadares were equal to those estimated for Mata-Agreste and Serra Geral da Bahia. The inclusion of the fixed effect of the production region and the random effect of the animals in the models improved the fit quality and increased the possibility of generating growth curves for each region.(AU)

O objetivo do presente trabalho foi avaliar a acurácia dos modelos Gompertz e Von Bertalanffy ajustados, respectivamente, para machos e fêmeas da raça Guzerá, sendo incorporado nos modelos o efeito fixo de quatro regiões de produção do nordeste brasileiro e efeito aleatório de animal, além de comparar os coeficientes dos modelos de crescimento entre regiões de produção. A acurácia das equações ajustadas foi avaliada por meio do critério de informação de Akaike, critério de informação Bayesiano, desvio médio absoluto, erro quadrático médio e o coeficiente de determinação. Para comparar as regiões de produção foram utilizados intervalos de confiança. Verificou-se que machos da raça Guzerá das regiões de produção Gado-Algodão e Serra Geral da Bahia possuem peso assintótico estatisticamente igual, enquanto que a taxa de maturidade é equivalente para animais das regiões Itapetinga-Valadares e Mata-Agreste. As fêmeas da raça Guzerá das regiões de Itapetinga-Valadares e Serra Geral da Bahia possuem o mesmo peso assintótico. A taxa de maturidade em Itapetinga-Valadares é igual a estimada para Mata-Agreste e Serra Geral da Bahia. Ao incluir o efeito fixo de região de produção e aleatório de animal nos modelos, houve melhora na qualidade de ajuste e a possibilidade de gerar curvas de crescimento para cada região.(AU)

Nonlinear mixed effects models for comparing growth curves for Guzerá cattle / Modelos não lineares mistos para comparar curvas de crescimento de bovinos da raça Guzerá

The objective of the present work was to evaluate the accuracy of the fitted Gompertz and von Bertalanffy models for male and female Guzerá cattle, respectively. Four production regions in Northeast Brazil were included in the models as a fixed effect, and the animals were included as a random effect. In addition, the coefficients of the growth models in the production regions were compared. The accuracy of the fit equations was assessed with the Akaike information criterion, Bayesian information criterion, mean absolute deviation, mean squared error, and coefficient of determination. Confidence intervals were used for comparing the production regions. The Guzerá males in the Gado-Algodão and Serra Geral da Bahia production regions were statistically equal in asymptotic weight, and the animals in the Itapetinga-Valadares and Mata-Agreste regions had equivalent maturity rates. The Guzerá females in the Itapetinga-Valadares and Serra Geral da Bahia regions had the same asymptotic weight. The maturity rates in Itapetinga-Valadares were equal to those estimated for Mata-Agreste and Serra Geral da Bahia. The inclusion of the fixed effect of the production region and the random effect of the animals in the models improved the fit quality and increased the possibility of generating growth curves for each region.

O objetivo do presente trabalho foi avaliar a acurácia dos modelos Gompertz e Von Bertalanffy ajustados, respectivamente, para machos e fêmeas da raça Guzerá, sendo incorporado nos modelos o efeito fixo de quatro regiões de produção do nordeste brasileiro e efeito aleatório de animal, além de comparar os coeficientes dos modelos de crescimento entre regiões de produção. A acurácia das equações ajustadas foi avaliada por meio do critério de informação de Akaike, critério de informação Bayesiano, desvio médio absoluto, erro quadrático médio e o coeficiente de determinação. Para comparar as regiões de produção foram utilizados intervalos de confiança. Verificou-se que machos da raça Guzerá das regiões de produção Gado-Algodão e Serra Geral da Bahia possuem peso assintótico estatisticamente igual, enquanto que a taxa de maturidade é equivalente para animais das regiões Itapetinga-Valadares e Mata-Agreste. As fêmeas da raça Guzerá das regiões de Itapetinga-Valadares e Serra Geral da Bahia possuem o mesmo peso assintótico. A taxa de maturidade em Itapetinga-Valadares é igual a estimada para Mata-Agreste e Serra Geral da Bahia. Ao incluir o efeito fixo de região de produção e aleatório de animal nos modelos, houve melhora na qualidade de ajuste e a possibilidade de gerar curvas de crescimento para cada região.

Describing the growth curve of local turkey using non-linear models / Descripción de la curva de crecimiento de pavos locales usando modelos no lineales

ABSTRACT Objective. Determine the best non-linear model to fit the growth curve of local turkeys managed under confinement in Michoacan, Mexico. Material and methods. Twenty-four and 43 female and male turkeys, reared under commercial conditions were given commercial feed. Birds were weighed weekly from hatch to 29 weeks of age. The Gompertz, Brody, Richards, von Bertalanffy and Logistic models were chosen to describe the age-weight relationship. Results. The best fitting model was selected based on the multiple determination coefficient (R2), the Akaike information criterion (AIC) and visual analysis of the observed and predicted curves. In both female and male, von Bertalanffy was the best model. The highest estimates of parameter A (mature weight) for both females and males were obtained with the von Bertalanffy model followed by the Gompertz and Logistic. The estimates of A were higher for males than for females. The highest estimates of parameter k (rate of maturity) for both females and males were, in decreasing order, for the Logistic, Gompertz, and von Bertalanffy models. k values for female turkeys was higher than for males. The age at the point of inflection (ti) and body weight at the age of point of inflection (WI) varied with the model used. The largest values of TI and WI corresponded to the Logistic model. Between sexes, the largest TI and WI values corresponded to males. Conclusions. The best models to describe turkey growth was the von Bertalanffy because it present the highest R2 and lowest AIC values.

RESUMEN Objetivo. Determinar el modelo no lineal que mejor ajuste la curva de crecimiento de pavos locales criados en confinamiento. Material y métodos. Veinticuatro y 43 pavos hembras y machos, respectivamente, criados en confinamiento fueron alimentados con dietas comerciales. Cada animal se pesó desde el nacimiento hasta la semana 29 de edad. Los modelos de Gompertz, Brody, Richards, von Bertalanffy y Logístico fueron elegidos para describir la relación edad-peso. El mejor modelo se seleccionó con base en el coeficiente de determinación (R2), el criterio de información de Akaike (AIC) y el análisis visual de las curvas observadas y predichas. Resultados. El mejor ajuste (machos y hembras) correspondió al modelo von Bertalanffy. El más alto valor del parámetro A (edad a la madurez), para hembras y machos correspondió al modelo von Bertalanffy, seguido de Gompertz y Logístico. El estimador A fue mayor para machos que hembras. El mayor valor del parámetro k (tasa de madurez), para hembras y machos, variaron según el modelo utilizado. Los valores de k fueron más altos para hembras que para machos. La edad al punto de inflexión (T:) y peso vivo al punto de inflexión (W:) también variaron de un modelo a otro. Los valores más altos de T, y Wj correspondieron al modelo Logístico. Entre sexos, los valores mayores de T: y WI correspondieron a los machos. Conclusiones. El mejor modelo que describió la curva de crecimiento de los pavos locales fue el de von Bertalanffy.

Ecology of the growth of Anolis nebulosus (Squamata: Dactyloidae) in a seasonal tropical environment in the Chamela region, Jalisco, Mexico.

Juvenile growth rates are thought to be restricted by available food resources. In animals that grow throughout the year, such as tropical lizards, growth is therefore predicted to be faster during the rainy season. We test this prediction using a population of Anolis nebulosusby describing the growth trajectories of both sexes using nonlinear regression models, and we then correlate the growth rates of individuals with food available in the environment, precipitation, and temperature. The Von Bertalanffy model fits the growth rates of the females better, while the logistic-by-length model fits the males better. According to both models, the males grew faster than females, reaching slightly smaller sizes at adulthood. Males reached sexual maturity when 35 mm long, at an age of seven months, and females matured at 37 mm (SVL), taking nine months to reach this size. In 1989, juvenile males and females grew more in both seasons (rainy and dry) than adults; for 1990, there were no differences by season or between age classes. These results are interesting since in the 1989 and 1990 rainy seasons, practically the same orders of prey and the greatest abundance of prey available in the environment were registered. A possible explanation could be that predation was more intense in 1990 than in 1989. There is little evidence that food, temperature, and humidity affect growth rates of A. nebulosus, refuting our predictions. This is mainly due to the low variation in growth observed in 1990. Therefore we think that the growth of this species reflects a complex combination of ecological and genetic factors.

Age, growth and mortality of white grunt caught in Pernambuco state, Brazil / Idade, crescimento e mortalidade de Haemulon plumierii capturada no estado de Pernambuco, Brasil

The aim of the present study was to measure the primary growth parameters and to estimate the mortality of the white grunt Haemulon plumierii in the state of Pernambuco, Brazil. Sagittal otoliths were collected monthly from May 2013 to April 2014 from three different commercial fishing landings along the coast of Pernambuco. A total of 333 individuals measuring 10.5 to 32.2 cm total length were caught. The total length distributions were different between locations. The weight-length relationships and the von Bertalanffy equations were statistically different between the three fishing sites. The weight-length relationship indicated negative allometric growth, therefore the von Bertalanffy equation for pooled sexes was TL(t) = 31.1[1-e(-0.1 (t +4.57))]. The maximum observed age was 21 years and the mortality rate was 0.21 year-1. The conducted analysis indicates a species with long life cycle and slow growth. Small reef fish with slow movement, such as the white grunt, are susceptible to fishing efforts, environmental factors and degradation, which affect growth and mortality. Therefore, we suggest an assessment of the status of the stock.

O objetivo do presente estudo foi estimar os primeiros parâmetros de crescimento e mortalidade de Biquara Haemulon plumierii no estado de Pernambuco, Brasil. Os otólitos sagittae foram coletados mensalmente de maio de 2013 a abril de 2014 a partir de desembarques da pesca comercial ao longo da costa de Pernambuco. O total de 333 indivíduos medindo 10,5 a 32,2 cm foram capturados. As distribuições de frequência de comprimento foram diferentes entre as áreas. Consequentemente, as relações peso-comprimento foram diferentes entre as áreas, bem como os parâmetros de von Bertalanffy. A relação peso-comprimento indicou crescimento alométrico negativo. Portanto, a equação de von Bertalanffy para sexos agrupados foi TL(t) = 31.1[1-e(-0.1 (t +4.57))]. A idade máxima observada foi 21 anos e a mortalidade total foi 0,21 ano-1. As análises conduzidas indicam uma espécie com ciclo de vida longa e crescimento lento. Pequenos peixes recifais de pouca movimentação, como a biquara, são susceptíveis ao esforço pesqueiro, fatores ambientais e degradação, que afetam o crescimento e a mortalidade. Portanto, sugerimos uma avaliação do status atual do estoque.

Age, growth and mortality of white grunt caught in Pernambuco state, Brazil / Idade, crescimento e mortalidade de Haemulon plumierii capturada no estado de Pernambuco, Brasil

The aim of the present study was to measure the primary growth parameters and to estimate the mortality of the white grunt Haemulon plumierii in the state of Pernambuco, Brazil. Sagittal otoliths were collected monthly from May 2013 to April 2014 from three different commercial fishing landings along the coast of Pernambuco. A total of 333 individuals measuring 10.5 to 32.2 cm total length were caught. The total length distributions were different between locations. The weight-length relationships and the von Bertalanffy equations were statistically different between the three fishing sites. The weight-length relationship indicated negative allometric growth, therefore the von Bertalanffy equation for pooled sexes was TL(t) = 31.1[1-e(-0.1 (t +4.57))]. The maximum observed age was 21 years and the mortality rate was 0.21 year-1. The conducted analysis indicates a species with long life cycle and slow growth. Small reef fish with slow movement, such as the white grunt, are susceptible to fishing efforts, environmental factors and degradation, which affect growth and mortality. Therefore, we suggest an assessment of the status of the stock.(AU)

O objetivo do presente estudo foi estimar os primeiros parâmetros de crescimento e mortalidade de Biquara Haemulon plumierii no estado de Pernambuco, Brasil. Os otólitos sagittae foram coletados mensalmente de maio de 2013 a abril de 2014 a partir de desembarques da pesca comercial ao longo da costa de Pernambuco. O total de 333 indivíduos medindo 10,5 a 32,2 cm foram capturados. As distribuições de frequência de comprimento foram diferentes entre as áreas. Consequentemente, as relações peso-comprimento foram diferentes entre as áreas, bem como os parâmetros de von Bertalanffy. A relação peso-comprimento indicou crescimento alométrico negativo. Portanto, a equação de von Bertalanffy para sexos agrupados foi TL(t) = 31.1[1-e(-0.1 (t +4.57))]. A idade máxima observada foi 21 anos e a mortalidade total foi 0,21 ano-1. As análises conduzidas indicam uma espécie com ciclo de vida longa e crescimento lento. Pequenos peixes recifais de pouca movimentação, como a biquara, são susceptíveis ao esforço pesqueiro, fatores ambientais e degradação, que afetam o crescimento e a mortalidade. Portanto, sugerimos uma avaliação do status atual do estoque.(AU)

Factors affecting estimates of size at age and growth in grey triggerfish Balistes capriscus from the northern Gulf of Mexico.

Growth zones in dorsal spines of grey triggerfish Balistes capriscus from the northern Gulf of Mexico were utilized to estimate growth and examine factors that may affect estimates of size at age. Age was estimated from dorsal-spine sections of 4687 individuals sampled from U.S. waters during 2003-2013, including both fishery-independent (n = 1312) and fishery-dependent (n = 3375) samples. Ninety-six per cent (n = 4498) of these sections were deemed suitable for ageing; average per cent error between two independent readers was 10·8%. Fork length (LF ) ranged from 65 to 697 mm and age estimates from 0 to 14 years. Both sex and sample source (fishery-independent v. recreational) significantly affected estimated size at age for 2-6 year-old fish. Data were pooled between sources to fit sex-specific von Bertalanffy growth functions. Results for the female model were L∞ = 387 mm LF , k = 0·52 year-1 and t0 = 0·01 year, while for males L∞ = 405 mm LF , k = 0·55 year-1 and t0 = 0·02 year. These results were significantly different between sexes and indicate clear sexual dimorphism. Thus, growth should be modelled separately by sex when examining population parameters or conducting stock assessment modelling. The positive bias in estimates of size at age computed for recreational v. fishery-independent samples also has clear implications for stock assessment as growth functions computed with fishery-dependent samples would tend to overestimate stock productivity.

Age and growth of Zapteryx brevirostris (Elasmobranchii: Rhinobatidae) in southern Brazil

Age and growth studies are fundamental to successful fisheries management. Zapteryx brevirostris (Müller & Henle, 1841) is distributed off the Brazilian continental shelf and this species is assessed as "Vulnerable" in the Red List of the International Union for the Conservation of Nature (IUCN). Thus, the objective of this study was to present previously unknown information about the age and growth of Z. brevirostris that can be used for its management, conservation, and fisheries. A total of 162 specimens were sampled, with total lengths (TL) varying between 35.7 cm and 56 cm. The vertebrae were embedded in resin, sectioned in cuts with 0.5 mm thickness and the growth bands of the vertebrae were read under a light microscope. In the studied area, Z. brevirostris ages were estimated from 4 to 10 years according to vertebrae patterns. The species reaches its maximum asymptotic size (Linf) around 56 cm (56 cm for females and 50.37 cm for males). This is the first estimate of age and growth for a species of the Zapteryx genus, and the results support the hypothesis that this ray requires future management conservation, particularly due to its slow growth rate and consequent susceptibility to overexploitation.(AU)

Estudos de idade e crescimento são fundamentais para o sucesso da gestão pesqueira. Zapteryx brevirostris (Müller & Henle, 1841) distribui-se pela plataforma continental brasileira, sendo classificada como "Vulnerável" no livro vermelho da IUCN (International Union for the Conservation of Nature). Assim, o objetivo deste estudo foi apresentar informações previamente desconhecidas sobre a idade e o crescimento de Z. brevirostris que podem ser utilizados para sua gestão, conservação e pescas. No total foram amostrados 162 espécimes, com comprimento total (CT) variando de 35.7 cm a 56 cm. As vértebras foram incluídas em resina e seccionadas num corte com cerca de 0.5 mm de espessura, e as bandas de crescimento das vértebras foram lidas com microscópio de luz transmitida branca. Na área estudada, Z. brevirostris possui idades estimadas entre os 4 a 10 anos de idade, de acordo com seu padrão de vértebras. A espécie atinge seu Linf (comprimento máximo assintótico) em torno dos 56 cm (56 cm para fêmeas e 50.37 cm para machos). Essa é a primeira estimativa dos parâmetros de idade e crescimento para uma espécie do gênero Zapteryx, e os resultados obtidos corroboram a hipótese de que a espécie requer uma gestão de conservação adequada, devido sobretudo à sua lenta taxa de crescimento e consequente suscetibilidade à sobre-exploração.(AU)

Age and growth of Zapteryx brevirostris (Elasmobranchii: Rhinobatidae) in southern Brazil

Age and growth studies are fundamental to successful fisheries management. Zapteryx brevirostris (Müller & Henle, 1841) is distributed off the Brazilian continental shelf and this species is assessed as "Vulnerable" in the Red List of the International Union for the Conservation of Nature (IUCN). Thus, the objective of this study was to present previously unknown information about the age and growth of Z. brevirostris that can be used for its management, conservation, and fisheries. A total of 162 specimens were sampled, with total lengths (TL) varying between 35.7 cm and 56 cm. The vertebrae were embedded in resin, sectioned in cuts with 0.5 mm thickness and the growth bands of the vertebrae were read under a light microscope. In the studied area, Z. brevirostris ages were estimated from 4 to 10 years according to vertebrae patterns. The species reaches its maximum asymptotic size (Linf) around 56 cm (56 cm for females and 50.37 cm for males). This is the first estimate of age and growth for a species of the Zapteryx genus, and the results support the hypothesis that this ray requires future management conservation, particularly due to its slow growth rate and consequent susceptibility to overexploitation.(AU)

Estudos de idade e crescimento são fundamentais para o sucesso da gestão pesqueira. Zapteryx brevirostris (Müller & Henle, 1841) distribui-se pela plataforma continental brasileira, sendo classificada como "Vulnerável" no livro vermelho da IUCN (International Union for the Conservation of Nature). Assim, o objetivo deste estudo foi apresentar informações previamente desconhecidas sobre a idade e o crescimento de Z. brevirostris que podem ser utilizados para sua gestão, conservação e pescas. No total foram amostrados 162 espécimes, com comprimento total (CT) variando de 35.7 cm a 56 cm. As vértebras foram incluídas em resina e seccionadas num corte com cerca de 0.5 mm de espessura, e as bandas de crescimento das vértebras foram lidas com microscópio de luz transmitida branca. Na área estudada, Z. brevirostris possui idades estimadas entre os 4 a 10 anos de idade, de acordo com seu padrão de vértebras. A espécie atinge seu Linf (comprimento máximo assintótico) em torno dos 56 cm (56 cm para fêmeas e 50.37 cm para machos). Essa é a primeira estimativa dos parâmetros de idade e crescimento para uma espécie do gênero Zapteryx, e os resultados obtidos corroboram a hipótese de que a espécie requer uma gestão de conservação adequada, devido sobretudo à sua lenta taxa de crescimento e consequente suscetibilidade à sobre-exploração.(AU)

The invariance of production per unit of food consumed in fish populations.

The amount of biomass production per unit of food consumed (P/Q) represents an important quantity in ecosystem functioning, because it indicates how efficient a population transforms ingested food into biomass. Several investigations have noticed that P/Q remains relatively constant (or invariant) across fish population that feed at the same food-type level (carnivorous/herbivorous). Nevertheless, theoretical explanation for this invariant is still lacking. In this paper, we demonstrate that P/Q remains invariant across fish populations with stable-age distribution. Three key assumptions underpin the P/Q invariant: (1) the ratio between natural mortality M and von Bertalanffy growth parameter k (M/k ratio) should remain invariant across fish populations; (2) a parameter defining the fraction of ingested food available for growth needs to remain constant across fish that feed at the same trophic level; (3) third, the ratio between length at age 0 ([Formula: see text]) and asymptotic length ([Formula: see text]) should be constant across fish populations. The influence of these assumptions on the P/Q estimates were numerically assessed considering fish populations of different lifespan. Numerical evaluations show that the most critical condition highly relates to the first assumption, M/k. Results are discussed in the context of the reliability of the required assumption to consider the P/Q invariant in stable-age distributed fish populations.

Age structure and growth of the rough scad, Trachurus lathami (Teleostei: Carangidae), in the Southeastern Brazilian Bight

The rough scad, Trachurus lathami Nichols, 1920, is a small pelagic species distributed along the West Atlantic coast. It is most abundant in the Southern Brazil (28°30’-34°S) and in the Southeastern Brazilian Bight (SEBB, 22°-28°30’S). The rough scad is fished by purse seines, which main target is the Brazilian sardine, Sardinella brasiliensis (Steindachner, 1879). Age and growth are vital to understand the life cycle of a species, to fishery management and ecosystem modeling. This study aimed to assess the age and growth of T. lathami, to identify its age structure in the SEBB, and to evaluate what causes the wide differences among Trachurus species in terms of body size and growth parameters. Data available on T. lathami was attained between 2008 and 2010 from surveys at SEBB. A total of 278 whole otoliths of T. lathami, total length between 27 mm and 208 mm, were analyzed and compared with the only other source of otolith data, from 1975. Three blind readings were performed and assessed using traditional methods to study fish age and growth. Zero up to eight rings were found, each ring corresponding to one year in the life of an individual of this species. The von Bertalanffy growth model parameters were L∞ = 211.90 mm and K = 0.319 year-1. The results of the analyses have shown similarities between 1975 and 2008-2010, indicating that the otolith development, the growth pattern and the age structure remained stable. T. lathami is the smallest species of Trachurus and it has the highest growth rates among them. This is probably related to the different temperatures where larvae/juvenile and adult grow, to the absence of a strong fishing pressure and to decadal population variability.

Age structure and growth of the rough scad, Trachurus lathami (Teleostei: Carangidae), in the Southeastern Brazilian Bight

The rough scad, Trachurus lathami Nichols, 1920, is a small pelagic species distributed along the West Atlantic coast. It is most abundant in the Southern Brazil (28°30-34°S) and in the Southeastern Brazilian Bight (SEBB, 22°-28°30S). The rough scad is fished by purse seines, which main target is the Brazilian sardine, Sardinella brasiliensis (Steindachner, 1879). Age and growth are vital to understand the life cycle of a species, to fishery management and ecosystem modeling. This study aimed to assess the age and growth of T. lathami, to identify its age structure in the SEBB, and to evaluate what causes the wide differences among Trachurus species in terms of body size and growth parameters. Data available on T. lathami was attained between 2008 and 2010 from surveys at SEBB. A total of 278 whole otoliths of T. lathami, total length between 27 mm and 208 mm, were analyzed and compared with the only other source of otolith data, from 1975. Three blind readings were performed and assessed using traditional methods to study fish age and growth. Zero up to eight rings were found, each ring corresponding to one year in the life of an individual of this species. The von Bertalanffy growth model parameters were L∞ = 211.90 mm and K = 0.319 year-1. The results of the analyses have shown similarities between 1975 and 2008-2010, indicating that the otolith development, the growth pattern and the age structure remained stable. T. lathami is the smallest species of Trachurus and it has the highest growth rates among them. This is probably related to the different temperatures where larvae/juvenile and adult grow, to the absence of a strong fishing pressure and to decadal population variability.(AU)

Individual, spatial and inter-sex variation in somatic growth: a study of Piaractus mesopotamicus (Characiformes: Serrasalmidae), a long-distance freshwater Neotropical migratory fish

Growth is a fundamental biological process, driven by multiple endogenous (intra-individual) and exogenous (environmental) factors that maintain individual fitness and population stability. The current study aims to assess whether individual, spatial (headwaters and floodplains) and inter-sex variation occurs in the growth of Piaractus mesopotamicus in the Cuiabá River basin. Samples were collected monthly from July 2006 to July 2007, at two areas in the Cuiabá River basin (headwaters and floodplain). Three growth models (individuals; individuals and sex factors; individuals and areas factors) were developed and compared the fish growth parameters using Akaike information criterion (AIC). The best fit to the length-at-age data was obtained by a model that considered individual variation and sex. The theoretical maximum average length ( L∞ ) was 64.99 cm for females, and 63.23 cm for males. Females showed a growth rate (k) of 0.230 yr-1and males of 0.196 yr-1. Thus, could be concluded that individual variability and sex were the main sources of variation in P. mesopotamicus somatic growth parameters.(AU)

O crescimento é um processo biológico fundamental, impulsionado por múltiplos fatores endógenos (intra-individual) e exógenos (ambientais) que mantém o fitness individual e a estabilidade populacional. Este trabalho tem como objetivo avaliar se ocorre variação individual, espacial (região de cabeceira e planície de inundação) e entre sexo no crescimento de Piaractus mesopotamicus na bacia do rio Cuiabá. Amostragens foram realizadas mensalmente entre julho de 2006 a julho de 2007, em duas áreas da bacia do rio Cuiabá (região de cabeceira e planície de inundação). Três modelos de crescimento (indivíduos, indivíduos e sexo como fator, indivíduos e área como fator) foram elaborados e comparados os parâmetros de crescimentos dos peixes com base no critério de Informação de Akaike (AIC). O melhor ajuste aos dados de comprimento na idade data foi obtido pelo modelo que considerou a variação individual e o sexo. O comprimento médio máximo teórico ( L∞ ) das fêmeas foi 64,99 cm e para os machos 63,23 cm. O coeficiente de crescimento (k) médio foi de 0,230 yr-1 e 0,196 yr-1, respectivamente para fêmeas e machos. Portanto, pode-se concluir que variabilidade individual e sexo foram as principais origem de variação dos parâmetros de crescimento somático de P. mesopotamicus.(AU)

Growth of the silverside Atherinella brasiliensis in a subtropical estuary with some insights concerning the weight-length relationship

ABSTRACT Specimens of Brazilian silverside (Atherinella brasiliensis, n=9672) with a length range of 1.5 to 14.2 cm were captured in the intertidal areas of the Estuarine Complex of Paranaguá, Brazil, between August 2010 and July 2011. The species' weight-length relationship was represented by the equation W=0.00533 L3.136 with a slightly positive allometry (b>3) and could be divided into two growth stanzas: W = W1 + W2; Stanza 1: W1= SW. (0.005239 L3.152); Stanza 2: W2= (1 - SW). (0.000699 L3.913); Switch-Function: SW = [1 + e1.204 (L - 11.66)]-1. The breakpoint between the first and second stanza (11.66 cm) matches published values for the estimated size at first maturity of adult females. Frequency distributions indicate that the species is present in the shallow areas of the Estuarine Complex of Paranaguá during all phases of its ontogenetic development, with the recruitment of juveniles taking place between October and November. Modal displacement was monitored throughout 12 months. The von Bertalanffy growth model and longevity was estimated as follow: asymptotic length (L∞) of 17.5 cm, growth coefficient (K) of 0.89 (year-1) and longevity (A95) of 3.33 years. We present some considerations with regard to the general methodology for adjusting weight-length relationships.

Individual, spatial and inter-sex variation in somatic growth: a study of Piaractus mesopotamicus (Characiformes: Serrasalmidae), a long-distance freshwater Neotropical migratory fish

Growth is a fundamental biological process, driven by multiple endogenous (intra-individual) and exogenous (environmental) factors that maintain individual fitness and population stability. The current study aims to assess whether individual, spatial (headwaters and floodplains) and inter-sex variation occurs in the growth of Piaractus mesopotamicus in the Cuiabá River basin. Samples were collected monthly from July 2006 to July 2007, at two areas in the Cuiabá River basin (headwaters and floodplain). Three growth models (individuals; individuals and sex factors; individuals and areas factors) were developed and compared the fish growth parameters using Akaike information criterion (AIC). The best fit to the length-at-age data was obtained by a model that considered individual variation and sex. The theoretical maximum average length ( L∞ ) was 64.99 cm for females, and 63.23 cm for males. Females showed a growth rate (k) of 0.230 yr-1and males of 0.196 yr-1. Thus, could be concluded that individual variability and sex were the main sources of variation in P. mesopotamicus somatic growth parameters.(AU)

O crescimento é um processo biológico fundamental, impulsionado por múltiplos fatores endógenos (intra-individual) e exógenos (ambientais) que mantém o fitness individual e a estabilidade populacional. Este trabalho tem como objetivo avaliar se ocorre variação individual, espacial (região de cabeceira e planície de inundação) e entre sexo no crescimento de Piaractus mesopotamicus na bacia do rio Cuiabá. Amostragens foram realizadas mensalmente entre julho de 2006 a julho de 2007, em duas áreas da bacia do rio Cuiabá (região de cabeceira e planície de inundação). Três modelos de crescimento (indivíduos, indivíduos e sexo como fator, indivíduos e área como fator) foram elaborados e comparados os parâmetros de crescimentos dos peixes com base no critério de Informação de Akaike (AIC). O melhor ajuste aos dados de comprimento na idade data foi obtido pelo modelo que considerou a variação individual e o sexo. O comprimento médio máximo teórico ( L∞ ) das fêmeas foi 64,99 cm e para os machos 63,23 cm. O coeficiente de crescimento (k) médio foi de 0,230 yr-1 e 0,196 yr-1, respectivamente para fêmeas e machos. Portanto, pode-se concluir que variabilidade individual e sexo foram as principais origem de variação dos parâmetros de crescimento somático de P. mesopotamicus.(AU)

Modelos não-lineares para a estimativa da produção de tomate do tipo cereja / Nonlinear models for estimating cherry tomato yield

RESUMO: Os objetivos do trabalho foram ajustar modelos de regressão não-linear para a estimativa da produção de frutos de tomate tipo cereja e identificar o tamanho da parcela com melhor poder de explicação e ajuste dos modelos, utilizando dois ensaios de uniformidade em estufa plástica. Os modelos ajustados foram o logístico e o de von Bertalanffy, para peso médio de frutos, número médio de frutos e de cachos acumulado nas múltiplas colheitas e com diferentes tamanhos de parcela. Os modelos apresentaram estimativas semelhantes entre si e as mesmas estimativas dos parâmetros em todos os casos de tamanho de parcela. Os modelos de regressão não-linear estudados descrevem satisfatoriamente o comportamento da produção de frutos de tomate tipo cereja cultivado em estufa plástica. Parcela constituída de duas plantas para ensaios em estufa plástica de 250m2 e de três plantas em estufa plástica de 200m2 proporcionam bom poder de explicação nas estimativas dos parâmetros dos modelos.

ABSTRACT: The aim of this paper was to test nonlinear regression models for estimating the cherry tomato production and to identify the plot size with better fitting quality and adjustment of the models, using two uniformity trials in greenhouse. The logistic and von Bertalanffy models were used on variables, as the means fruit weight, the means number of fruits and bunches accumulated in the multiple harvests and with different plot sizes. The models presented similar estimates for all parameters in all plot sizes studied. The nonlinear models adequately describe the behavior of the production of cherry tomato fruits cultivated in greenhouse. Plots constituted by two and three plants, respectively in trials with greenhouse of 250 m2 and 200 m2, provide a good fitting quality in the models adjustment.