The Growth Pattern of Brazilian Canela-Preta Chickens with Different Plumages Reared in Two Rearing Systems

Growth pattern is essential for economically efficient poultry production. In this study, we aimed to describe the growth curve of chickens of the Canela-Preta breed reared in two different rearing systems, considering their different plumage colors. Initially, 204 one-day-old male and female chicks were randomly distributed in confinement and semi-confinement (102 animals in each system) without separation by gender. The animals were individually identified by wing and foot plastic brands and were weighted every seven days. The body weight and age records were used to estimate the growth curves of the following factors using the Richards model: plumage color, gender, and rearing system. The likelihood ratio test was used to verify the equality of parameters and identify nonlinear models to compare the growth patterns of the evaluated groups. The growth pattern of Canela-Preta chickens changed as a function of gender, plumage color, and rearing system. Females with black plumage, black and gold hens, and males with black and white plumage showed greater sensitivity to changes in rearing systems. Within-breed selection strategies for specific colors can improve the use of growth pattern differences, improving production efficiency. Semi-confinement is suitable for rearing Canela-Preta chickens with any plumage color, as these animals meet the free-range poultry niche market requirements.(AU)

Growth curves of broilers fed different nutritional relationships using the Gompertz model

The study aimed to evaluate performance and growth curves of broilers fed different nutritional relations. A total of 1,440 Cobb-500 male day-old chicks were assigned to eight treatments in a 2 x 2 x 2 factorial arrangement with six replicates of 30 birds each. The main factors were nutritional density (control and high), lysine source (HCl and sulfate), and calcium pidolate (presence and absence). Analyses were made for body weight gain (BWG), and feed conversion rate (FCR) at 21, and 42 days of age. The growth curves were adjusted by weighing a bird per plot every three days. Data for BWG were tested by ANOVA to evaluatethe effects of treatments and their interactions at 5% significance, and the Gompertz model was adjusted by NLS. Birds fed a high nutritional density had higher BWG and lower FCR. Calcium pidolate and different sources of lysine did not influence the FCR of broilers, however a triple interaction was evidenced for BWG at 1 to 42 days of age. The day with maximum gain adjusted by Gompertz of all treatments was at the 32ndday of age and the maximum weight (A) was around 5.85 kg.(AU)

Growth predictability models in Mangalarga marchador horses / Modelos de previsibilidade de crescimento em cavalos Mangalarga marchador

This study evaluated the suitability of the Brody, logistic, and quadratic response plateau models to describe chest and cannon girth data obtained cross-sectionally in Mangalarga Marchador horses, in order to select the best model and predict the growth and maturity of males and females of this breed. Data were collected from 230 horses aged 6 to 176 months, divided by sex and age (16 age classes). The studied models were compared according to each quality evaluator by computing the adjusted coefficient of determination (R²adj) and residual standard deviation (RSD) with R statistical software. The chest girths obtained by the models ranged from 172.06 (males) to 181.50 cm (females) (Brody), 172.51 (males) to 181.89 cm (females) (logistic), and 177.67 (males) to 183.09 cm (females) (plateau). For cannon girth, the values were 18.18 (females) to 19.33 cm (males) (Brody), 18.11 (females) to 19.41 cm (males) (logistic), and 18.70 (females) to 19.40 cm (males) (plateau). The logistic model was best suited to describe the growth in chest girth of male and female Mangalarga Marchador horses. For cannon girth growth, the model best suited for males was the logistic model, and the one best suited for females was the Brody model.

RESUMO: O objetivo deste estudo foi avaliar o ajuste dos modelos Brody, Logístico e Platô de resposta quadrática aos dados de perímetros torácico e de canela em equinos Mangalarga Marchador obtidos pelo método transversal, a fim de selecionar o melhor modelo e predizer sobre o crescimento e a maturidade de machos e fêmeas desta raça. Foram utilizados dados de 230 equinos de seis a 176 meses de idade que foram divididos por sexo e em 16 classes de idade. Os modelos estudados foram comparados segundo os avaliadores de qualidade: coeficiente de determinação ajustado (R²adj) e desvio padrão residual (DPR), utilizando-se o software estatístico R. Os perímetros torácicos obtidos pelos modelos variaram de 172,06 a 181,50 cm (Brody), 172,51 a 181,89 cm (Logístico) e 183,09 a 177,67 cm (Platô) para fêmeas e machos, respectivamente. Para o perímetro de canela os valores variaram de 18,18 a 19,33 cm (Brody), 18,11 a 19,41 cm (Logístico) e 18,70 a 19,40 cm (Platô) para fêmeas e machos, respectivamente. O modelo logístico é mais indicado para expressar o crescimento em perímetro torácico de machos e fêmeas da raça Mangalarga Marchador. Já para a variável perímetro de canela, o modelo mais indicado para os machos foi o modelo Logístico e para as fêmeas o modelo de Brody.

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.

Polymorphism in the BIEC2-808543 locus and its association with growth curve in Brasileiro de Hipismo horse breed

Our objective was to evaluate whether the single nucleotide polymorphism (SNP) BIEC2-808543, identified in some horse breeds, also occurs in the Brasileiro de Hipismo (BH) breed. In addition, we verified if this SNP is related to the growth curve profile of these animals for the variables body mass, height at withers, and height at croup, using nonlinear mixed models. For the DNA isolation, we collected blood samples from 167 young BH horses. We obtained the genotypes of these animals using the polymerase chain reaction-restriction fragment length polymorphism technique. For the association studies of this polymorphism with the growth curve in foals, we selected three traits: body mass, height at withers, and height at croup. Polymorphism C/T exists in BH horses and is significantly associated with the evaluated traits. Animals that presented the TT genotype were smaller and lighter when compared with animals of the CT and CC genotypes. By the Akaike information criterion, the model that best described the growth curve for the body mass variable is the Brody model associated with the power of the mean variance function. For the height at withers variable, the best-fit model was von Bertalanffy, adjusted without polymorphism effect in parameter b, associated with the asymptotic variance. For the height at croup trait, the model that best described the growth curve was Brody model, associated with asymptotic variance. This polymorphism represents a good molecular marker. Nonlinear models are promising for describing growth curves in horses, particularly by the possibility of associating SNP effects to model parameters.

Influence of caprine arthritis encephalitis on milk production and quality along the lactation curve in primiparous dairy goats / Influência da artrite encefalite caprina na produção e qualidade do leite ao longo da curva de lactação em cabras leiteiras primíparas

The aim of this study was to examine the influence of caprine arthritis encephalitis (CAE) on the production of milk and its components (protein, fat and total solids) along the lactation curve of primiparous goats. The study was developed using a database from the years 2014 to 2018. Sixty-one animals were subjected to the serological test for CAE, whose result indicated that 42 were seropositive and 19 seronegative, and milk production and quality data were compiled. To adjust the curve for production of milk, fat, protein and total solids during lactation, the following nonlinear model developed by Wood (1967) was used: Y = atb e-ct, where Y represents the observations of milk, fat, protein or total solid production at time t; a is the parameter associated with the initial production; b is the parameter associated with the rate of rise in production until the peak; c is the parameter associated with the rate of decline of the lactation curve; and t is the representative time of the day in milk. The parameters were compared by the confidence interval considering 95% probability. Peak production was calculated using the following formula: a(b/c)b e-b. There was no statistical difference (p > 0.05) between seropositive and seronegative primiparous goats for initial production and the rates of rise and decline of the parameters of milk, fat, protein and total solid production. However, at their peak, these variables were 26, 27, 23 and 23% higher, respectively, in the seronegative goats than in their seropositive counter parts. In conclusion, CAE does not affect milk production or the production of fat, protein and total solids along the lactation curve, but seropositive goats produce less milk and respective components at the peak of the lactation curve than seronegative goats.

Objetivou-se avaliar a influência da artrite encefalite caprina (CAE) sobre a produção leiteira e seus constituintes (proteína, gordura e sólidos totais) ao longo da curva de lactação de cabras primíparas. O estudo foi realizado a partir do banco de dados dos anos de 2014 a 2018. Foram utilizados um total de 61 animais, todos submetidos ao teste de sorologia para CAE, sendo 42 cabras soropositivas e 19soronegativas, e os dados foram compilados de produção e qualidade do leite. Para o ajuste da curva para a produção de leite, gordura, proteína e sólidos totais ao longo da lactação foi utilizado o modelo não linear de Wood (1967): Y = atb e-ct, no qual: Y representa as observações de produção de leite, gordura, proteína ou sólidos totais no tempo t, a é o parâmetro associado à produção inicial, b é o parâmetro associado à taxa de ascensão da produção até o pico, c é o parâmetro associado à taxa declínio da curva de lactação e t é o tempo representativo do dia em lactação. Os parâmetros foram comparados pelo intervalo de confiança considerando 95% de probabilidade. A produção no pico foi calculada pela fórmula: a(b/c)b e-b. Não houve diferença estatística (p > 0,05) entre cabras primíparas soropositivas e soronegativas para a produção inicial, taxa de ascensão e taxa de declínio dos parâmetros para a produção de leite, de gordura, de proteína e de sólidos totais. Porém a produção no pico das variáveis em cabras soronegativas foi de26%, 27%, 23% e 23%, respectivamente, mais altas que em soropositivas. Conclui-se que a CAE não afeta a produção leiteira, bem como a produção de gordura, proteína e sólidos totais ao longo da curva de lactação, entretanto cabras soropositivas têm menor produção de leite e de seus componentes no pico da curva de lactação em relação às soronegativas.

Influence of caprine arthritis encephalitis on milk production and quality along the lactation curve in primiparous dairy goats / Influência da artrite encefalite caprina na produção e qualidade do leite ao longo da curva de lactação em cabras leiteiras primíparas

The aim of this study was to examine the influence of caprine arthritis encephalitis (CAE) on the production of milk and its components (protein, fat and total solids) along the lactation curve of primiparous goats. The study was developed using a database from the years 2014 to 2018. Sixty-one animals were subjected to the serological test for CAE, whose result indicated that 42 were seropositive and 19 seronegative, and milk production and quality data were compiled. To adjust the curve for production of milk, fat, protein and total solids during lactation, the following nonlinear model developed by Wood (1967) was used: Y = atb e-ct, where Y represents the observations of milk, fat, protein or total solid production at time t; a is the parameter associated with the initial production; b is the parameter associated with the rate of rise in production until the peak; c is the parameter associated with the rate of decline of the lactation curve; and t is the representative time of the day in milk. The parameters were compared by the confidence interval considering 95% probability. Peak production was calculated using the following formula: a(b/c)b e-b. There was no statistical difference (p > 0.05) between seropositive and seronegative primiparous goats for initial production and the rates of rise and decline of the parameters of milk, fat, protein and total solid production. However, at their peak, these variables were 26, 27, 23 and 23% higher, respectively, in the seronegative goats than in their seropositive counter parts. In conclusion, CAE does not affect milk production or the production of fat, protein and total solids along the lactation curve, but seropositive goats produce less milk and respective components at the peak of the lactation curve than seronegative goats.(AU)

Objetivou-se avaliar a influência da artrite encefalite caprina (CAE) sobre a produção leiteira e seus constituintes (proteína, gordura e sólidos totais) ao longo da curva de lactação de cabras primíparas. O estudo foi realizado a partir do banco de dados dos anos de 2014 a 2018. Foram utilizados um total de 61 animais, todos submetidos ao teste de sorologia para CAE, sendo 42 cabras soropositivas e 19soronegativas, e os dados foram compilados de produção e qualidade do leite. Para o ajuste da curva para a produção de leite, gordura, proteína e sólidos totais ao longo da lactação foi utilizado o modelo não linear de Wood (1967): Y = atb e-ct, no qual: Y representa as observações de produção de leite, gordura, proteína ou sólidos totais no tempo t, a é o parâmetro associado à produção inicial, b é o parâmetro associado à taxa de ascensão da produção até o pico, c é o parâmetro associado à taxa declínio da curva de lactação e t é o tempo representativo do dia em lactação. Os parâmetros foram comparados pelo intervalo de confiança considerando 95% de probabilidade. A produção no pico foi calculada pela fórmula: a(b/c)b e-b. Não houve diferença estatística (p > 0,05) entre cabras primíparas soropositivas e soronegativas para a produção inicial, taxa de ascensão e taxa de declínio dos parâmetros para a produção de leite, de gordura, de proteína e de sólidos totais. Porém a produção no pico das variáveis em cabras soronegativas foi de26%, 27%, 23% e 23%, respectivamente, mais altas que em soropositivas. Conclui-se que a CAE não afeta a produção leiteira, bem como a produção de gordura, proteína e sólidos totais ao longo da curva de lactação, entretanto cabras soropositivas têm menor produção de leite e de seus componentes no pico da curva de lactação em relação às soronegativas.(AU)

Curva de crescimento em altura na cernelha de equinos da raça Mangalarga Marchador considerando-se heterocedasticidade / Growth curve for height at withers of Mangalarga Marchador horses with heterocedasticity

Objetivou-se, com este estudo, avaliar o ajuste dos modelos de Brody, Gompertz, Logístico e Von Bertalanffy aos dados de altura na cernelha de equinos Mangalarga Marchador, ponderando pelo inverso da variância, a fim de selecionar o melhor modelo e predizer sobre o crescimento e a maturidade dos animais dessa raça. Foram utilizados dados de 230 equinos dos seis aos 176 meses de idade, os quais foram divididos por sexo e em 16 classes de idade. Os modelos estudados foram comparados segundo os avaliadores de qualidade: coeficiente de determinação (R2); desvio padrão residual (DPR) e critério de informação de Akaike (AIC). A estimação dos parâmetros dos modelos foi realizada pelo método de mínimos quadrados ponderado no software R. Todos os modelos avaliados se mostraram adequados para descrever a curva de crescimento em ambos os sexos. Perante os avaliadores utilizados, o modelo Logístico foi o mais adequado para descrever as curvas de crescimento em altura na cernelha nos dois sexos da raça Mangalarga Marchador. Observou-se também um crescimento acelerado nos primeiros meses de idade. Os animais machos atingiram uma altura adulta maior, porém as fêmeas são mais precoces, pois apresentaram maior estimativa para o índice de maturidade.(AU)

This work aimed to evaluate the fit of models Brody, Gompertz, Logistic and Von Bertalanffy to height at the withers of Mangalarga Marchador horses, weighed by the inverse of variance, in order to select the best model and predict growth and maturity of this breed pf animals. We used data of 230 equines from 06 to 176 months of age who were divided by sex and 16 age classes. The models were compared according to the quality assessors: coefficient of determination (R2); residual standard deviation (RSD) and Akaike information criteria (AIC). The estimation of the parameters from models was performed by the weighted least squares method in Software R. All models evaluated were suitable to describe the growth curve in both sexes. In view of the evaluators used, the logistic model was the most suitable to describe the growth curves in withers height in both sexes for the race Mangalarga Marchador. A strong growth at first age was also observed. The males reached a greater adult height, but females did so sooner, because they presented higher estimates for the maturity index.(AU)

Curva de crescimento em altura na cernelha de equinos da raça Mangalarga Marchador considerando-se heterocedasticidade / Growth curve for height at withers of Mangalarga Marchador horses with heterocedasticity

Objetivou-se, com este estudo, avaliar o ajuste dos modelos de Brody, Gompertz, Logístico e Von Bertalanffy aos dados de altura na cernelha de equinos Mangalarga Marchador, ponderando pelo inverso da variância, a fim de selecionar o melhor modelo e predizer sobre o crescimento e a maturidade dos animais dessa raça. Foram utilizados dados de 230 equinos dos seis aos 176 meses de idade, os quais foram divididos por sexo e em 16 classes de idade. Os modelos estudados foram comparados segundo os avaliadores de qualidade: coeficiente de determinação (R2); desvio padrão residual (DPR) e critério de informação de Akaike (AIC). A estimação dos parâmetros dos modelos foi realizada pelo método de mínimos quadrados ponderado no software R. Todos os modelos avaliados se mostraram adequados para descrever a curva de crescimento em ambos os sexos. Perante os avaliadores utilizados, o modelo Logístico foi o mais adequado para descrever as curvas de crescimento em altura na cernelha nos dois sexos da raça Mangalarga Marchador. Observou-se também um crescimento acelerado nos primeiros meses de idade. Os animais machos atingiram uma altura adulta maior, porém as fêmeas são mais precoces, pois apresentaram maior estimativa para o índice de maturidade.(AU)

This work aimed to evaluate the fit of models Brody, Gompertz, Logistic and Von Bertalanffy to height at the withers of Mangalarga Marchador horses, weighed by the inverse of variance, in order to select the best model and predict growth and maturity of this breed pf animals. We used data of 230 equines from 06 to 176 months of age who were divided by sex and 16 age classes. The models were compared according to the quality assessors: coefficient of determination (R2); residual standard deviation (RSD) and Akaike information criteria (AIC). The estimation of the parameters from models was performed by the weighted least squares method in Software R. All models evaluated were suitable to describe the growth curve in both sexes. In view of the evaluators used, the logistic model was the most suitable to describe the growth curves in withers height in both sexes for the race Mangalarga Marchador. A strong growth at first age was also observed. The males reached a greater adult height, but females did so sooner, because they presented higher estimates for the maturity index.(AU)

Growth and yield models for eucalyptus stands obtained by differential equations

ABSTRACT: The main purpose of this study was to assess nonlinear models generated by integrating the basal area growth rate to estimate the growth and yield of forest stands. The database was collected from permanent sample units, in Paraopeba county, in the state of Minas Gerais, Brazil. The stands were represented by Eucalyptus camaldulensis × Eucalyptus urophylla hybrid trees, with 3 × 3 meters of spacing. The data were divided into two groups: fitting and validating databases. Two nonlinear models (Strategy A and Strategy B) were developed using differential equations to estimate the basal area growth and yield of the sample units. The logistic model was fitted to estimate the volumetric yield as a function of age, site index and basal area. The efficiency of the systems generated by logistic model and models obtained by differential equations (Strategy A and Strategy B) was also compared to the efficiency of the system estimated by the Clutter model (Strategy C). The projection models used to estimate basal area obtained by differential equations were compatible with forest growth and yield, and the logistic model with covariates was compatible with volumetric growth and yield. Strategy A and Strategy B generated different thinning and harvesting options for different site indices, which is biologically consistent.

Growth and yield models for eucalyptus stands obtained by differential equations

ABSTRACT: The main purpose of this study was to assess nonlinear models generated by integrating the basal area growth rate to estimate the growth and yield of forest stands. The database was collected from permanent sample units, in Paraopeba county, in the state of Minas Gerais, Brazil. The stands were represented by Eucalyptus camaldulensis × Eucalyptus urophylla hybrid trees, with 3 × 3 meters of spacing. The data were divided into two groups: fitting and validating databases. Two nonlinear models (Strategy A and Strategy B) were developed using differential equations to estimate the basal area growth and yield of the sample units. The logistic model was fitted to estimate the volumetric yield as a function of age, site index and basal area. The efficiency of the systems generated by logistic model and models obtained by differential equations (Strategy A and Strategy B) was also compared to the efficiency of the system estimated by the Clutter model (Strategy C). The projection models used to estimate basal area obtained by differential equations were compatible with forest growth and yield, and the logistic model with covariates was compatible with volumetric growth and yield. Strategy A and Strategy B generated different thinning and harvesting options for different site indices, which is biologically consistent.(AU)

Growth Patterns of Two Chinese Native Goose Breeds

To study the development rules of Chinese native geese, two breeds, Shitou and Sichuan White geese were analyzed from 0 to 12 weeks of age. The growth curves were fitted with commonly used four kinds of nonlinear models (Logistic, Gompertz, Von Bertalanffy and Richards). The results showed that the growth curves were appropriately fitted with all four models but the Logistic and Richards both had the best fitting with growth curve (R2>0.99). Analyzing the fitting parameters of the Logistic and Richards, we found that male Shitou had the highest adult body weight while Sichuan White female had the lowest weight. In Shitou breed, Shape parameter Predicted with Richards model was corresponded with Gompertz curve, while in Sichuan breed it was in between Gompertz and Bertalanffy. Growth parameters predicted with Logistic model was much more closed to observed value as compared others. So overall logistic was the best model to analyze the growth curve in Chinese native goose and Shitou goose had excellent growth performance when compared to Sichuan White.(AU)

Growth Patterns of Two Chinese Native Goose Breeds

To study the development rules of Chinese native geese, two breeds, Shitou and Sichuan White geese were analyzed from 0 to 12 weeks of age. The growth curves were fitted with commonly used four kinds of nonlinear models (Logistic, Gompertz, Von Bertalanffy and Richards). The results showed that the growth curves were appropriately fitted with all four models but the Logistic and Richards both had the best fitting with growth curve (R2>0.99). Analyzing the fitting parameters of the Logistic and Richards, we found that male Shitou had the highest adult body weight while Sichuan White female had the lowest weight. In Shitou breed, Shape parameter Predicted with Richards model was corresponded with Gompertz curve, while in Sichuan breed it was in between Gompertz and Bertalanffy. Growth parameters predicted with Logistic model was much more closed to observed value as compared others. So overall logistic was the best model to analyze the growth curve in Chinese native goose and Shitou goose had excellent growth performance when compared to Sichuan White.

Growth curves in meat-type and laying quail: a Bayesian perspective / Curvas de crescimento em codornas de corte e postura: uma perspectiva Bayesiana

The aim of this study was to assess the goodness of fit for nonlinear models, using the best model to describe body growth curves, comparing the parameters obtained for gender and one meat-type (Coturnix coturnix coturnix) and two laying (Coturnix coturnix japonica) quail strains, as well as nesting via MCMC (Markov chain Monte Carlo processes) methods under a Bayesian approach. A total of 1,350 one-day-old mixed quail were used: 400 of meat-type, 450 of yellow laying, and 500 of red laying strains distributed in a completely randomized design with three treatments (each treatment corresponded to one strain) and five replications. The experimental period consisted of 1 to 42 days of age. At 21 days of age, quail sexing was performed by means of sexual dimorphism, being individually identified at one day of age with numbered rings, allowing determining growth curves by gender. Birds were reared in a conventional system, fed ad libitum with diets formulated to meet nutritional requirements. Body weight was determined weekly and assessed using nonlinear models: Logistic, Brody, Von Bertalanffy, and Gompertz, whose parameters were estimated under a Bayesian approach via MCMC algorithm by means of BRugs package from the software R. DIC (Deviance Information Criterion) criterion was used to select the best nonlinear model, i.e. the lower the DIC value is, the better the model goodness of fit to thedata. Gompertz model was better adjusted to the data regardless the gender or strain. Meat-type quailhad the highest asymptotic weights and the highest age at which growth rate was maximum, followedby red and yellow strains. All nestings presented significant differences (p < 0.05) between gender forcontrasted parameters. Meat-type, yellow, and red females presented values significantly (p < 0.05)higher for asymptotic weight (370, 203, and 215 g, respectively) when compared to males (274, 131,and 143 g, respectively), which were earlier in body growth.

O objetivo deste trabalho foi avaliar a qualidade de ajuste dos modelos não lineares aos dados, utilizando o melhor modelo para descrever as curvas de crescimento corporal, comparando os parâmetros obtidos para gênero e uma linhagem de codornas de corte (Coturnix coturnix coturnix) e duas de postura (Coturnix coturnix japonica), bem como o aninhamento, via método MCMC (Cadeias de Markov em processos de Monte Carlo), sob o enfoque Bayesiano. Foram utilizadas 1.350 codornas mistas, com um dia de idade, sendo: 400 da linhagem de corte, 450 de postura amarela e 500 de postura vermelha, distribuídas por um delineamento inteiramente casualizado, com três tratamentos (cada tratamento corresponde a uma linhagem) e cinco repetições. O período experimental foi de 1 a 42 dias de idade. Aos 21 dias de idade foi realizada a sexagem por dimorfismo sexual, sendo que elas foram identificadas individualmente com um dia com anilhas numeradas, possibilitando a determinação das curvas de crescimento por gênero. As aves foram criadas em um sistema convencional, alimentadas ad libitum com rações formuladas para atender às exigências nutricionais. O peso corporal foi determinado semanalmente e avaliados por meio dos modelos não lineares: Logístico, Brody, Von Bertalanffy e Gompertz. Para a seleção domelhor modelo não linear utilizou-se o critério DIC (Deviance Information Criterion), em que quantomenor o valor de DIC, melhor é a qualidade do ajuste do modelo aos dados. Gompertz melhor se ajustouaos dados, independentemente do gênero ou linhagem. As codornas de corte tiveram os maiores pesosassintóticos e a maior idade em que a taxa de crescimento é máxima, seguido pela vermelha e amarela.Todos aninhamentos apresentaram diferenças significativas (p < 0,05) entre gênero para os parâmetroscontrastados. As fêmeas de corte, amarela e vermelha apresentaram valores significativamente (p <0,05) maiores para o peso assintótico (370, 203 e 215 g, respectivamente), comparados aos...

Growth curves in meat-type and laying quail: a Bayesian perspective / Curvas de crescimento em codornas de corte e postura: uma perspectiva Bayesiana

The aim of this study was to assess the goodness of fit for nonlinear models, using the best model to describe body growth curves, comparing the parameters obtained for gender and one meat-type (Coturnix coturnix coturnix) and two laying (Coturnix coturnix japonica) quail strains, as well as nesting via MCMC (Markov chain Monte Carlo processes) methods under a Bayesian approach. A total of 1,350 one-day-old mixed quail were used: 400 of meat-type, 450 of yellow laying, and 500 of red laying strains distributed in a completely randomized design with three treatments (each treatment corresponded to one strain) and five replications. The experimental period consisted of 1 to 42 days of age. At 21 days of age, quail sexing was performed by means of sexual dimorphism, being individually identified at one day of age with numbered rings, allowing determining growth curves by gender. Birds were reared in a conventional system, fed ad libitum with diets formulated to meet nutritional requirements. Body weight was determined weekly and assessed using nonlinear models: Logistic, Brody, Von Bertalanffy, and Gompertz, whose parameters were estimated under a Bayesian approach via MCMC algorithm by means of BRugs package from the software R. DIC (Deviance Information Criterion) criterion was used to select the best nonlinear model, i.e. the lower the DIC value is, the better the model goodness of fit to thedata. Gompertz model was better adjusted to the data regardless the gender or strain. Meat-type quailhad the highest asymptotic weights and the highest age at which growth rate was maximum, followedby red and yellow strains. All nestings presented significant differences (p < 0.05) between gender forcontrasted parameters. Meat-type, yellow, and red females presented values significantly (p < 0.05)higher for asymptotic weight (370, 203, and 215 g, respectively) when compared to males (274, 131,and 143 g, respectively), which were earlier in body growth.(AU)

O objetivo deste trabalho foi avaliar a qualidade de ajuste dos modelos não lineares aos dados, utilizando o melhor modelo para descrever as curvas de crescimento corporal, comparando os parâmetros obtidos para gênero e uma linhagem de codornas de corte (Coturnix coturnix coturnix) e duas de postura (Coturnix coturnix japonica), bem como o aninhamento, via método MCMC (Cadeias de Markov em processos de Monte Carlo), sob o enfoque Bayesiano. Foram utilizadas 1.350 codornas mistas, com um dia de idade, sendo: 400 da linhagem de corte, 450 de postura amarela e 500 de postura vermelha, distribuídas por um delineamento inteiramente casualizado, com três tratamentos (cada tratamento corresponde a uma linhagem) e cinco repetições. O período experimental foi de 1 a 42 dias de idade. Aos 21 dias de idade foi realizada a sexagem por dimorfismo sexual, sendo que elas foram identificadas individualmente com um dia com anilhas numeradas, possibilitando a determinação das curvas de crescimento por gênero. As aves foram criadas em um sistema convencional, alimentadas ad libitum com rações formuladas para atender às exigências nutricionais. O peso corporal foi determinado semanalmente e avaliados por meio dos modelos não lineares: Logístico, Brody, Von Bertalanffy e Gompertz. Para a seleção domelhor modelo não linear utilizou-se o critério DIC (Deviance Information Criterion), em que quantomenor o valor de DIC, melhor é a qualidade do ajuste do modelo aos dados. Gompertz melhor se ajustouaos dados, independentemente do gênero ou linhagem. As codornas de corte tiveram os maiores pesosassintóticos e a maior idade em que a taxa de crescimento é máxima, seguido pela vermelha e amarela.Todos aninhamentos apresentaram diferenças significativas (p < 0,05) entre gênero para os parâmetroscontrastados. As fêmeas de corte, amarela e vermelha apresentaram valores significativamente (p <0,05) maiores para o peso assintótico (370, 203 e 215 g, respectivamente), comparados aos...(AU)

Growth curves on females of the Caracu breed / Curvas de crescimento de fêmeas da raça Caracu

The objective of the study was to analyze nonlinear models that best fit the growth of Caracu cows. The experiment was conducted at the Instituto de Zootecnia, Centro APTA Bovinos de Corte, Sertãozinho, SP. Data of weight at birth to 63 months of age, from 500 females of the Caracu breed were used. The mean weight at birth (BW), weaning weight (W7), weight at 26 months (W26) and weight at 63 months (W63) were, respectively, 32 kg, 198 kg, 354 kg and 488 kg, providing an average daily gain (ADG) of 0.241 kg/day. The nonlinear models used were: Brody, Von Bertalanffy, Logistic and Gompertz. All of the models tended to describe accordingly the growth curve of these animals, but, according to the mean square residual and coefficient of determination adopted to select the most appropriate model, Brody showed the best fit. All models presented a high and negative correlation between the A and k parameters, indicating that the most precocious animals are less likely to reach elevated weights at 63 months of age. The effect of year of birth significantly affected (P 0.01) the parameters A and k, concluding that the animal selection based on growth traits favored the increase of mature weight and growth precocity over the generations.

O objetivo do estudo foi analisar os modelos não-lineares que melhores se ajustam ao crescimento de fêmeas da raça Caracu. O experimento foi conduzido no Instituto de Zootecnia, Centro APTA Bovinos de Corte, Sertãozinho, SP. Dados de peso ao nascimento até os 63 meses de idade de 500 fêmeas da raça Caracu foram utilizados. A media de peso ao nascer (PN), peso a desmama (P7), peso aos 26 meses (P26) e peso aos 63 meses (P63) foram, respectivamente, de 32 kg, 198 kg, 354 kg e 488 kg, fornecendo um ganho médio diário (GMD) de 0,241 kg/dia. Os modelos não-lineares utilizados foram: Brody, Von Bentarlanffy, Logístico e Gompertz. Todos os modelos descreveram adequadamente a curva de crescimento destes animais, porém de acordo com o quadrado médio do resíduo e coeficiente de determinação, adotados para escolha do modelo mais apropriado, Brody mostrou o melhor ajuste. Todos os modelos apresentaram alta e negativa correlação entre os parâmetros A e k, indicando que animais mais precoces possuem menor probabilidade de atingir pesos mais elevados aos 63 meses de idade. O efeito de ano de nascimento afetou significativamente (P 0,01) os parâmetros A e k, sugerindo que a seleção dos animais com base em características de crescimento favoreceu o aumento do peso adulto e a precocidade, com o passar das gerações.

Growth curves for Ile de France female sheep raised in feedlot / Curvas de crescimento de fêmeas da raça Ile de France criadas em confinamento

The objective of the present study was to analize the non-linear models that best fit the growth of ewes Ile de France. The experiment was conducted in school farm Capão da Onça, located in city of Ponta Grossa - PR and so, were used data on weight at birth to 210 days of age of 34 females of the breed Ile de France. The animals showed mean weight at birth (PN) of 4,58 kilograms, weaning weight (P60) of 19,58 kilograms and weight at 210 days (P210) equal to 43,18 kilograms, providing daily weight gain (GMD) equal to 0,183 kg/day. The non-linear models used were: Brody, Von Bentarlanffy, Logístic and Gompertz, presenting results, respectively, of 33.5453; 33.7120; 33.6714 and 33.8836 for Error Mean Square (EMS) and 0.9650; 0.8302; 0.9649 and 0.9647 for coefficient of determination (R2). All models tended to describe accordingly the curve of animals growth, but, according to the methods adopted to select the most appropriate model, Von Bertarlanffy showed the best fit. All models presented high and negative correlation between the A and k parameters, indicating that the most precocious animals are less likely to reach elevated weights for 210 days of age.(AU)

O objetivo do presente trabalho foi analisar os modelos não lineares que melhor se ajustam ao crescimento de fêmeas da raça Ile de France. O experimento foi conduzido na Fazenda Escola Capão da Onça, localizada no município de Ponta Grossa - PR e para tanto, foram utilizados dados de peso ao nascimento até os 210 dias de idade de 34 fêmeas da raça Ile de France. Os animais apresentaram médias de peso ao nascer (PN) de 4,58 kg, peso a desmama (P60) de 19,58 kg e peso aos 210 dias (P210) igual a 43,18 kg, proporcionando ganho de peso médio diário do nascimento aos 210 dias (GMD) igual a 0,183 kg/dia. Os modelos não lineares utilizados foram: Brody, Von Bentarlanffy, Logístico e Gompertz, apresentando resultados, respectivamente, de 33,5453; 33,7120; 33,6714 e 33,8836 para o Quadrado Médio do Resíduo (QMR) e de 0,9650; 0,8302; 0,9649 e 0,9647 para o Coeficiente de Determinação (R2). Todos os modelos tenderam a descrever adequadamente a curva de crescimento destes animais, porém, de acordo com os métodos adotados para escolha do modelo mais adequado, Von Bertarlanffy apresentou o melhor ajuste. Todos os modelos demonstraram correlação alta e negativa entre os parâmetros A e k, indicando que animais mais precoces possuem menor probabilidade de atingir pesos mais elevados aos 210 dias de idade.(AU)

Inflection and stability points of diphasic logistic analysis of growth

Growth functions with inflection points following a diphasic model, can be adjusted by two approaches using segmented regression or the sum of two functions. In both cases, there are two functions, one for each phase, with inflection and stability points. However, when they are summed, the result is a new function and the points of inflection and stability are different from those obtained from using each function individually. A method to determine these points in a diphasic logistics sum of functions is suggested and the results obtained from fitting the models to eucalyptus growth data showed a better fit of the logistic diphasic sum as compared with segmented regression and monophasic logistic models.

Inflection and stability points of diphasic logistic analysis of growth

Growth functions with inflection points following a diphasic model, can be adjusted by two approaches using segmented regression or the sum of two functions. In both cases, there are two functions, one for each phase, with inflection and stability points. However, when they are summed, the result is a new function and the points of inflection and stability are different from those obtained from using each function individually. A method to determine these points in a diphasic logistics sum of functions is suggested and the results obtained from fitting the models to eucalyptus growth data showed a better fit of the logistic diphasic sum as compared with segmented regression and monophasic logistic models.(AU)

AVALIAÇÃO DO CRESCIMENTO DE FRANGOS CAIPIRAS ECÓTIPOS CANELUDO DO CATOLÉ

Objetivou-se avaliar as equações dos modelos de regressão não-lineares de Brody, Gompertz, von Bertalanffy, logístico e exponencial para descrever a curva de crescimento de aves caipiras Ecotipos Caneludo do Catolé. Para tal, foram analisadas 900 observações do peso corporal de 150 aves caipiras não sexados, mensuradas ao 1, 30, 60, 90, 120 e 150 dias de idade, pertencentes ao Laboratório Experimental de Avicultura da Universidade Estadual do Sudoeste da Bahia, Campus de Itapetinga. Os parâmetros dos modelos foram estimados por meio de verossimilhança restrita ponderada pela variância e pela estrutura de correlação do tipo autoregressiva. Foi considerado o critério de Informação de Akaike (AIC) e o Critério Bayesiano de Schwarz (BIC) para avaliar a qualidade do ajuste dos modelos. A taxa de crescimento máxima foi estimada, por meio da primeira derivada da equação de Gompertz. Os intervalos de confiança de cada parâmetro foram obtidos considerando-se um = 0,05. Todas as análises foram feitas por meio do software R-3.6.1. Apenas os modelos de Gompertz, logístico e exponencial convergiram com os dados. Segundo o critério AIC e BIC, o modelo Gompertz foi considerado o melhor modelo. Logo, as estimativas dos parâmetros A, b e k foram de 12,4 kg, 5,655 e 0,009 dia-1 respectivamente. A taxa de crescimento absoluta em função da idade, foi observada aos 150 dias de idade com estimativa de 0,03639 kg/dia. Recomenda-se o modelo de Gompertz para ajustar curvas de crescimento de ecótipos Caneludo do Catolé.

The objective was to evaluate the equations of the nonlinear regression models of Brody, Gompertz, von Bertalanffy, logistic and exponential to describe the growth curve of free-range birds Caneludo do Catolé Ecotypes. For this purpose, 900 body weight observations of 150 non-sexed free-range birds were analyzed, measured at 1, 30, 60, 90, 120 and 150 days of age, belonging to the Experimental Poultry Laboratory of the State University of Southwest Bahia, Campus de Itapetinga. The parameters of the models were estimated by means of restricted likelihood weighted by the variance and by the autoregressive correlation structure. The Akaike Information criterion (AIC) and the Schwarz Bayesian Criterion (BIC) were used to assess the quality of the models' fit. The maximum growth rate was estimated using the derivative of the Gompertz equation. The confidence intervals for each parameter were obtained considering = 0.05. Only the Gompertz, logistic and exponential models converged with the data. According to the AIC and BIC criteria, the Gompertz model was considered the best model. Therefore, the estimates for parameters A, b and k were 12,4 kg, 5,655 and 0,009 day-1 respectively. The absolute growth rate as a function of age was observed at 150 days of age with an estimate of 0,03639 kg / day. The Gompertz model is recommended to adjust growth curves of Caneludo do Catolé ecotypes.