Mathematical models to describe the growth curves of Vietnamese Ri chicken

Abstract Ri chicken is the most popular backyard chicken breed in Vietnam, but little is known about the growth curve of this breed. This study compared the performances of models with three parameters (Gompertz, Brody, and Logistic) and models containing four parameters (Richards, Bridges, and Janoschek) for describing the growth of Ri chicken. The bodyweight of Ri chicken was recorded weekly from week 1 to week 19. Growth models were fitted using minpack.lm package in R software and Akaikes information criterion (AIC), Bayesian information criterion (BIC), and root mean square error (RMSE) were used for model comparison. Based on these criteria, the models having four parameters showed better performance than the ones with three parameters, and the Richards model was the best one for males and females. The lowest and highest value of asymmetric weights () were obtained by Bridges and Brody models for each of sexes, respectively. Age and weight estimated by the Richard model were 8.46 and 7.51 weeks and 696.88 and 487.58 g for males and for females, respectively. Differences in the growth curves were observed between males and female chicken. Overall, the results suggested using the Richards model for describing the growth curve of Ri chickens. Further studies on the genetics and genomics of the obtained growth parameters are required before using them for the genetic improvement of Ri chickens.

Resumo O frango Ri é a raça de frango de quintal mais popular do Vietnã, mas pouco se sabe sobre a curva de crescimento dessa raça. Este estudo comparou o desempenho de modelos com três parâmetros (Gompertz, Brody e Logistic) e modelos contendo quatro parâmetros (Richards, Bridges e Janoschek) para descrever o crescimento do frango Ri. O peso corporal do frango Ri foi registrado semanalmente da semana 1 à semana 19. Os modelos de crescimento foram ajustados usando o pacote minpack.lm no software R e o critério de informação de Akaike (AIC); critério de informação bayesiano (BIC) e erro quadrático médio (RMSE) foram usados para comparação de modelos. Com base nesses critérios, os modelos com quatro parâmetros apresentaram melhor desempenho do que os com três parâmetros, sendo o modelo de Richards o melhor para homens e mulheres. O menor e o maior valor dos pesos assimétricos () foram obtidos pelos modelos Bridges e Brody para cada um dos sexos, respectivamente. A idade e o peso estimados pelo modelo de Richard foram de 8,46 e 7,51 semanas e 696,88 e 487,58 g para homens e mulheres, respectivamente. Diferenças nas curvas de crescimento foram observadas entre frangos machos e fêmeas. No geral, os resultados sugeriram o uso do modelo de Richards para descrever a curva de crescimento de frangos Ri. Mais estudos sobre a genética e genômica dos parâmetros de crescimento obtidos são necessários antes de usá-los para o melhoramento genético de frangos Ri.

Bone Growth and Meat Quality of Quails Submitted to Different Lighting Programs

The present study was executed to evaluate the effect of lighting programs for meat quails on their bone growth and development. A total of 1500 sexed European quails (Coturnix coturnix coturnix) were distributed using a completely randomized design in a 2 × 3 factorial arrangement, with two sexes and three lighting programs (natural, intermittent, and continuous) with five replicates of 50 quails. The lighting programs were applied in the period from 7 to 49 d of age. Weekly slaughterings were performed to remove the tibiotarsus and femur and subsequently determine weight, length, dry and mineral matter content. The growth and deposition curves of dry and mineral matter in the bones were obtained using the Gompertz model. There was no significant interaction between lighting programs and sex for the estimates of the Gompertz curve parameters of all variables studied. There was an effect of the lighting programs only on the time needed to reach the maximum deposition rate of the growth curve and dry and mineral matter deposition. Females showed higher weight and deposition of mineral matter at maturity, and took longer to reach the maximum deposition rate value for these variables. There was influence of the lighting programs on resistance and bone deformity of the tibiotarsus. For quails raised in the tropical region, a natural or intermittent lighting program must be used, as it does not compromise the development of bones and assures bone quality.(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)

Mathematical models to describe the growth curves of Vietnamese Ri chicken / Modelos matemáticos para descrever as curvas de crescimento do frango Ri vietnamita

Ri chicken is the most popular backyard chicken breed in Vietnam, but little is known about the growth curve of this breed. This study compared the performances of models with three parameters (Gompertz, Brody, and Logistic) and models containing four parameters (Richards, Bridges, and Janoschek) for describing the growth of Ri chicken. The bodyweight of Ri chicken was recorded weekly from week 1 to week 19. Growth models were fitted using minpack.lm package in R software and Akaike’s information criterion (AIC), Bayesian information criterion (BIC), and root mean square error (RMSE) were used for model comparison. Based on these criteria, the models having four parameters showed better performance than the ones with three parameters, and the Richards model was the best one for males and females. The lowest and highest value of asymmetric weights (α) were obtained by Bridges and Brody models for each of sexes, respectively. Age and weight estimated by the Richard model were 8.46 and 7.51 weeks and 696.88 and 487.58 g for males and for females, respectively. Differences in the growth curves were observed between males and female chicken. Overall, the results suggested using the Richards model for describing the growth curve of Ri chickens. Further studies on the genetics and genomics of the obtained growth parameters are required before using them for the genetic improvement of Ri chickens.

O frango Ri é a raça de frango de quintal mais popular do Vietnã, mas pouco se sabe sobre a curva de crescimento dessa raça. Este estudo comparou o desempenho de modelos com três parâmetros (Gompertz, Brody e Logistic) e modelos contendo quatro parâmetros (Richards, Bridges e Janoschek) para descrever o crescimento do frango Ri. O peso corporal do frango Ri foi registrado semanalmente da semana 1 à semana 19. Os modelos de crescimento foram ajustados usando o pacote minpack.lm no software R e o critério de informação de Akaike (AIC); critério de informação bayesiano (BIC) e erro quadrático médio (RMSE) foram usados para comparação de modelos. Com base nesses critérios, os modelos com quatro parâmetros apresentaram melhor desempenho do que os com três parâmetros, sendo o modelo de Richards o melhor para homens e mulheres. O menor e o maior valor dos pesos assimétricos (α) foram obtidos pelos modelos Bridges e Brody para cada um dos sexos, respectivamente. A idade e o peso estimados pelo modelo de Richard foram de 8,46 e 7,51 semanas e 696,88 e 487,58 g para homens e mulheres, respectivamente. Diferenças nas curvas de crescimento foram observadas entre frangos machos e fêmeas. No geral, os resultados sugeriram o uso do modelo de Richards para descrever a curva de crescimento de frangos Ri. Mais estudos sobre a genética e genômica dos parâmetros de crescimento obtidos são necessários antes de usá-los para o melhoramento genético de frangos Ri.

Mathematical models to describe the growth curves of Vietnamese Ri chicken / Modelos matemáticos para descrever as curvas de crescimento do frango Ri vietnamita

Ri chicken is the most popular backyard chicken breed in Vietnam, but little is known about the growth curve of this breed. This study compared the performances of models with three parameters (Gompertz, Brody, and Logistic) and models containing four parameters (Richards, Bridges, and Janoschek) for describing the growth of Ri chicken. The bodyweight of Ri chicken was recorded weekly from week 1 to week 19. Growth models were fitted using minpack.lm package in R software and Akaikes information criterion (AIC), Bayesian information criterion (BIC), and root mean square error (RMSE) were used for model comparison. Based on these criteria, the models having four parameters showed better performance than the ones with three parameters, and the Richards model was the best one for males and females. The lowest and highest value of asymmetric weights (α) were obtained by Bridges and Brody models for each of sexes, respectively. Age and weight estimated by the Richard model were 8.46 and 7.51 weeks and 696.88 and 487.58 g for males and for females, respectively. Differences in the growth curves were observed between males and female chicken. Overall, the results suggested using the Richards model for describing the growth curve of Ri chickens. Further studies on the genetics and genomics of the obtained growth parameters are required before using them for the genetic improvement of Ri chickens.(AU)

O frango Ri é a raça de frango de quintal mais popular do Vietnã, mas pouco se sabe sobre a curva de crescimento dessa raça. Este estudo comparou o desempenho de modelos com três parâmetros (Gompertz, Brody e Logistic) e modelos contendo quatro parâmetros (Richards, Bridges e Janoschek) para descrever o crescimento do frango Ri. O peso corporal do frango Ri foi registrado semanalmente da semana 1 à semana 19. Os modelos de crescimento foram ajustados usando o pacote minpack.lm no software R e o critério de informação de Akaike (AIC); critério de informação bayesiano (BIC) e erro quadrático médio (RMSE) foram usados para comparação de modelos. Com base nesses critérios, os modelos com quatro parâmetros apresentaram melhor desempenho do que os com três parâmetros, sendo o modelo de Richards o melhor para homens e mulheres. O menor e o maior valor dos pesos assimétricos (α) foram obtidos pelos modelos Bridges e Brody para cada um dos sexos, respectivamente. A idade e o peso estimados pelo modelo de Richard foram de 8,46 e 7,51 semanas e 696,88 e 487,58 g para homens e mulheres, respectivamente. Diferenças nas curvas de crescimento foram observadas entre frangos machos e fêmeas. No geral, os resultados sugeriram o uso do modelo de Richards para descrever a curva de crescimento de frangos Ri. Mais estudos sobre a genética e genômica dos parâmetros de crescimento obtidos são necessários antes de usá-los para o melhoramento genético de frangos Ri.(AU)

Mathematical models to describe the growth curves of Vietnamese Ri chicken / Modelos matemáticos para descrever as curvas de crescimento do frango Ri vietnamita

Abstract Ri chicken is the most popular backyard chicken breed in Vietnam, but little is known about the growth curve of this breed. This study compared the performances of models with three parameters (Gompertz, Brody, and Logistic) and models containing four parameters (Richards, Bridges, and Janoschek) for describing the growth of Ri chicken. The bodyweight of Ri chicken was recorded weekly from week 1 to week 19. Growth models were fitted using minpack.lm package in R software and Akaike's information criterion (AIC), Bayesian information criterion (BIC), and root mean square error (RMSE) were used for model comparison. Based on these criteria, the models having four parameters showed better performance than the ones with three parameters, and the Richards model was the best one for males and females. The lowest and highest value of asymmetric weights (α) were obtained by Bridges and Brody models for each of sexes, respectively. Age and weight estimated by the Richard model were 8.46 and 7.51 weeks and 696.88 and 487.58 g for males and for females, respectively. Differences in the growth curves were observed between males and female chicken. Overall, the results suggested using the Richards model for describing the growth curve of Ri chickens. Further studies on the genetics and genomics of the obtained growth parameters are required before using them for the genetic improvement of Ri chickens.

Resumo O frango Ri é a raça de frango de quintal mais popular do Vietnã, mas pouco se sabe sobre a curva de crescimento dessa raça. Este estudo comparou o desempenho de modelos com três parâmetros (Gompertz, Brody e Logistic) e modelos contendo quatro parâmetros (Richards, Bridges e Janoschek) para descrever o crescimento do frango Ri. O peso corporal do frango Ri foi registrado semanalmente da semana 1 à semana 19. Os modelos de crescimento foram ajustados usando o pacote minpack.lm no software R e o critério de informação de Akaike (AIC); critério de informação bayesiano (BIC) e erro quadrático médio (RMSE) foram usados ​​para comparação de modelos. Com base nesses critérios, os modelos com quatro parâmetros apresentaram melhor desempenho do que os com três parâmetros, sendo o modelo de Richards o melhor para homens e mulheres. O menor e o maior valor dos pesos assimétricos (α) foram obtidos pelos modelos Bridges e Brody para cada um dos sexos, respectivamente. A idade e o peso estimados pelo modelo de Richard foram de 8,46 e 7,51 semanas e 696,88 e 487,58 g para homens e mulheres, respectivamente. Diferenças nas curvas de crescimento foram observadas entre frangos machos e fêmeas. No geral, os resultados sugeriram o uso do modelo de Richards para descrever a curva de crescimento de frangos Ri. Mais estudos sobre a genética e genômica dos parâmetros de crescimento obtidos são necessários antes de usá-los para o melhoramento genético de frangos Ri.

Effect of supplementation of ewes in the final third of gestation on the development of their lambs

This study examined the effect of different supplementation strategies for ewes in the last third of gestation, kept on a deferred Brachiaria brizantha cv. Marandu pasture, on their performance and the growth curve of their lambs. A total of 54 ewes, of no defined breed, with an average weight of 41.10±3.10 kg, were used in a completely randomized design, divided into three groups (18 ewes per treatment). In total, 61 lambs were born, 28 females and 33 males, with 3.70±0.55 and 3.68±0.69 kg birth weight, respectively. Treatments were as follows: multiple mixture ad libitum, concentrate supplement at 0.4% live weight (LW), and concentrate supplement at 0.8% LW. Average daily weight gain (ADG, g/animal/day) and total weight gain (TWG, kg/animal) were evaluated in ewes and lambs. Reproductive efficiency indices were measured in the ewes and biometric variables in the lambs. The ADG and TWG of ewes in the last third of gestation were higher in animals supplemented at 0.8% LW. Reproductive efficiency results were superior in ewes supplemented at 0.4% LW. The effect of ewe supplementation on lamb growth curve as estimated by the Gompertz model did not reveal differences between the curves of lambs born to ewes that received supplementation at 0.4 and 0.8% LW. However, supplementing ewes with a multiple mixture induced a reduction in the growth curve parameters of their lambs. The use of concentrated supplementation, at levels of 0.4 and 0.8% of LW, provides greater productive and reproductive performance for ewes and lambs.(AU)

Fit and genetic parameters of the growth curve of Polled Nellore cattle / Ajuste e parâmetros genéticos da curva de crescimento em bovinos da raça Nelore Mocho

This study was undertaken to compare different non-linear models for fitting growth curves of Polled Nellore animals as well as to estimate genetic parameters for the components of the growth curve. The study involved body weight-age data of 6,717 Polled Nellore cattle from birth to 650 days of age, which belonged to the Brazilian Association of Zebu Breeders (ABCZ), corresponding to the period from 1980 to 2011. Four non-linear models (Brody, Bertalanffy, Logistic, and Gompertz) were fitted and compared by the adjusted coefficient of determination (R2adj), mean absolute deviation of residuals (MAD), root mean square error (RMSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC). To estimate the genetic parameters and genetic values of asymptotic weight (A), integration constant (B), and maturation rate (K), the Bayesian inference method was adopted. The Brody model showed the lowest values of MAD, RMSE, AIC, and BIC and the highest R2adj. Heritability estimates for parameters A, B, and K were 0.11, 0.16, and 0.30, respectively, whereas genetic correlations were 0.01 (A-B), -0.91 (A-K), and 0.24 (B-K). The Brody model provided the best fit. The K parameter shows enough genetic variability for selection in the herd. Heavier animals in adulthood tend to exhibit lower growth rates. Despite the low heritability estimate of parameter A, there were genetic gains, indicating that selection is being efficient on asymptotic weight.(AU)

O objetivo deste estudo foi comparar diferentes modelos não lineares para o ajuste das curvas de crescimento de animais da raça Nelore Mocho e estimar os parâmetros genéticos para os componentes da curva de crescimento. Foram utilizados dados de peso corporal-idade do nascimento aos 650 dias de idades de 6.717 bovinos da raça Nelore Mocho, pertencentes à Associação Brasileira de Criadores de Zebu (ABCZ), referentes ao período de 1980 e 2011. Quatro modelos não lineares (Brody, Bertalanffy, Logístico e Gompertz) foram ajustados e comparados pelo coeficiente de determinação ajustado (R2adj), desvio médio absoluto dos resíduos (DMA), raiz quadrada do quadrado médio do resíduo (RMSE), critério de informação de Akaike (AIC) e o critério de informação bayesiano (BIC). Para estimativas dos parâmetros genéticos e valores genéticos do peso assintótico (A), constante de integração (B) e taxa de maturação (K), utilizou-se o método de inferência Bayesiana. O modelo Brody apresentou os menores valores de DMA, RMSE, AIC e BIC e o maior R2adj. As estimativas de herdabilidade foram 0,11; 0,16 e 0,30 para os parâmetros A, B e K, respectivamente, enquanto as correlações genéticas foram de 0,01 (A-B), -0,91 (A-K) e 0,24 (B-K). Constatou-se que o modelo Brody forneceu o melhor ajuste. O parâmetro K apresenta variabilidade genética suficiente para seleção no rebanho. Animais com maior peso na idade adulta tendem a apresentar menores taxas de crescimento. Apesar da baixa estimativa de herdabilidade do parâmetro A, observou-se ganhos genéticos, indicando que a seleção está sendo eficiente sobre o peso assintótico.(AU)

Choice of non-linear models to determine the growth curve of meat-type quail / Escolha de modelos não-lineares para determinar a curva de crescimento de codornas de corte

The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.(AU)

Objetivou-se, neste estudo, comparar modelos não lineares ajustados às curvas de crescimento de codornas para determinar qual modelo que melhor descreve o crescimento de codornas e verificar a similaridade dos modelos analisando as estimativas dos parâmetros. Para as análises foram utilizados os dados peso e idade de codornas européias de corte (Coturnix coturnix coturnix) proveniente de três linhagens, em um esquema fatorial 2x4, instalado em um delineamento inteiramente casualizado, com dois níveis de energia metabolizável e quatro níveis de proteína bruta, com seis repetições. Os modelos não lineares utilizados foram: Brody, Von Bertalanffy, Richards, Logístico e Gompertz. Para a escolha do melhor modelo utilizou-se o Coeficiente de Determinação Ajustado, o Percentual de Convergência, o Quadrado Médio do Resíduo, o Teste de Durbin-Watson, o Critério de informação Akaike e o Critério de informação Bayesiano como avaliadores da qualidade do ajuste. Utilizou-se a análise de agrupamento para verificar, baseado nas estimativas médias dos parâmetros, a similaridades entre os modelos. Entre os modelos estudados, o Richard foi o mais adequado para descrever as curvas de crescimento. Os modelos Logístico e Richards foram considerados similares nas análises sem distinção de linhagem, bem como nas análises das Linhagem 1, 2 e 3.(AU)

Kleiber ratios and growth curves of African Black and Red Neck ostrich breeds and their crossbreeds / Razão Kleiber e curva de crescimento para raças de avestruzes African Black e Red Neck e seus cruzamentos

The selection of animals with lower production costs can be achieved by using feed efficiency and growth curve information. Kleiber ratio (KR) is an alternative option for discriminating against the animals that have the greatest weight gain about their final weight. Alternative feed efficiency and growth curves for ostriches of the African Black (AB) and Red Neck (RN) breeds and their crossbreeds (CB) were investigated using KR and Gompertz equation. Univariate and multivariate analyses were used. The highest adult weight was identified in the RN and CB. AB was more precocious than the RN and CB individuals. Only AB animals reached 75% of their mature weight at one year of age. At 180 days, AB showed better KR. AB was different from the others, mainly for KR at 90 days and 180 days. Considering multivariate analysis, AB animals were different from the others, regardless of sex, mainly for KR at 90 days and KR at 180 days. Other subgroups separated the animals by sex. In a market preferring animals of minor structure (smaller cuts) and greater precocity, it would be suitable to opt for AB. When animals with greater body structure (larger cuts) are desired, males RN and CR is the best option, however, it will be slaughtered with greater age and lower value for KR (may generate a bigger production cost ). It is possible to obtain animals with precocity and high KR, being well represented by the AB breed.(AU)

A seleção de animais com custos de produção mais baixos pode ser alcançada usando a eficiência alimentar e informações da curva de crescimento. A razão de Kleiber (KR) é uma alternativa para discriminar os animais que apresentam maior ganho de peso em relação ao peso final. Eficiência alimentar alternativa e curvas de crescimento para avestruzes das raças African Black (AB) e Red Neck (RN) e seus cruzamentos (CB) foram investigadas usando a equação de KR e Gompertz. Análises univariadas e multivariadas foram utilizadas. O maior peso adulto foi observado no RN e no CB. AB foi mais precoce do que os indivíduos RN e CB. Apenas animais AB atingiram 75% de seu peso adulto até um ano de idade. Aos 180 dias, AB tem maior KR. AB foi diferente dos demais, principalmente para KR aos 90 dias e 180 dias. Considerando a análise multivariada, os animais AB diferiram dos demais, independente do sexo, principalmente pelos seguintes parâmetros: KR aos 90 dias, KR aos 180 dias. Outros subgrupos separaram os animais por sexo. Em um mercado que prefere animais de menor estrutura corporal (cortes menores) e maior precocidade, seria adequado optar pela AB. Para animais com maior estrutura corporal (cortes maiores), os machos RN e CR são a melhor opção, porém, serão abatidos com maior idade e menor valor para KR (pode gerar um maior custo de produção). É possível obter animais com precocidade e alto KR, sendo bem representados pelo AB.(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.(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.

Performance, Growth Curves and Carcass Yield of Four Strains of Broiler Chicken

The objective of this study was to evaluate the performance, carcass yield and growth curves of different commercial strains of broiler chicken. 2400 day-old chicks, males and females of the Cobb500, RossAp95, Hubbard Flex and a new Francesa line were used. The birds were distributed in a completely randomized design in a factorial arrangement 4x2 (line x sex), forming eight treatments with 10 replicates each. The birds were fed with the same diet. Feed intake, weight gain and feed conversion were determined. At 42 days, it was determined at the request of carcass and cuts of each lineage. The Gompertz model was applied to a growth curve for each line. The RossAP95 line shows the best performance results. Growth curves showed lower sexual dimorphism in the Hubbard Flex line. The Hubbard Flex strain presented higher thigh yield and a Cobb500 genetics the higher breast yield. Based on the results found it was observed that the RossAP95 performed better. Hubbard Flex line exhibits the least sexual dimorphism. The Cobb500 have better yield for breast and as Hubbard Flex birds greater thigh yield.(AU)

Performance, Growth Curves and Carcass Yield of Four Strains of Broiler Chicken

The objective of this study was to evaluate the performance, carcass yield and growth curves of different commercial strains of broiler chicken. 2400 day-old chicks, males and females of the Cobb500, RossAp95, Hubbard Flex and a new Francesa line were used. The birds were distributed in a completely randomized design in a factorial arrangement 4x2 (line x sex), forming eight treatments with 10 replicates each. The birds were fed with the same diet. Feed intake, weight gain and feed conversion were determined. At 42 days, it was determined at the request of carcass and cuts of each lineage. The Gompertz model was applied to a growth curve for each line. The RossAP95 line shows the best performance results. Growth curves showed lower sexual dimorphism in the Hubbard Flex line. The Hubbard Flex strain presented higher thigh yield and a Cobb500 genetics the higher breast yield. Based on the results found it was observed that the RossAP95 performed better. Hubbard Flex line exhibits the least sexual dimorphism. The Cobb500 have better yield for breast and as Hubbard Flex birds greater thigh yield.

Mathematical models to describe the growth curves of white-egg layers / Modelos matemáticos para descrever curvas de crescimento de poedeiras leves

The aim of this study was to compare mathematical models describing growth curves of white-egg layers at different population densities. To fit the models, 4,000 growing white-egg layers were utilized. The experimental design was completely randomized, with population densities of 71, 68, 65, 62, and 59 birds per cage in the starter phase and 19, 17, 15, 13, and 11 birds per cage in the grower phase, with 10 replicates each. Birds were weighed weekly to determine the average body weight and the weight gain. Gompertz and Logistic models were utilized to estimate their growth. The data analysis was carried out using the PROC NLMIXED procedure of the SAS® statistical computer software to estimate the parameters of the equation because mixed models were employed. The mean squared error, the coefficient of determination, and Akaikes information criterion were used to evaluate the quality of fit of the models. The studied models converged for the description of the growth of the birds at the different densities studied, showing that they were appropriate for estimating the growth of white-egg layers housed at different population densities. The Gompertz model showed a better fit than the Logistic model.(AU)

Esta pesquisa teve por objetivo comparar modelos matemáticos para descrever curva de crescimento de poedeiras leves em diferentes densidades populacional, por meio de equações de modelos de crescimento.Para o ajuste dos modelos foram utilizadas 4000 poedeiras leves em crescimento. O delineamento utilizado foi o inteiramente casualizado nas densidades populacional de 71, 68, 65, 62 e 59 aves por gaiola na fase de cria e de 19, 17, 15, 13 e 11 aves por gaiola na fase de recria, com dez repetições cada.Semanalmente, as aves foram pesadas para determinação do peso corporal médio e o ganho de peso. Para estimar o crescimento das aves foram utilizados os modelos de Gompertz e Logistic. A análise dos dados foi realizada pelo procedimento PROC NLMIXED do programa computacional estatísticoSAS®, para estimar os parâmetros da equação por se tratar de modelos mistos. O quadrático médio do erro, o coeficiente de determinação e o critério de informação de Akaike foram utilizados na avaliação da qualidade do ajuste dos modelos. Os modelos estudados atingiram a convergência para a descrição do crescimento das aves nas diferentes densidades estudadas, adequados para estimar o crescimento corporal das aves com alto grau de confiabilidade. Os modelos estimaram o crescimento de poedeiras leves, alojadas em diferentes densidades populacional, em que o modelo de Gompertz apresentou melhores ajustes em comparação ao Logistic.(AU)

Use of modified Richards model to predict isothermal and non-isothermal microbial growth

Mathematical models are often used to predict microbial growth in food products. An important class of these models involves the adaptation of classical sigmoid functions, such as the Gompertz and logistic functions. This study aimed to validate the use of the modified Richards model in various situations, which have not previously been tested. The model was obtained through solving a system of two differential equations and could be applied to both isothermal and non-isothermal environments. To test and validate this model, we used published datasets containing data for the growth of Pseudomonas spp. in fish products. The results obtained after fitting the model showed that it could be effectively used to describe and predict the Pseudomonas growth curves under various temperature regimens. However, the influence of the shape parameter on the growth curve is an issue that needs further evaluation.(AU)

Analysis of growth curves in different lineages of Caipira broiler type / Análise de curvas de crescimento em diferentes linhagens de frangos de corte tipo Caipira

The objective of this work was to identify, by means of different statistical criteria the idealnonlinear regression model to describe the growth curve of three lineages of caipira broiler for meatproduction. A total of 90 birds were used, being 30 birds from each of the following lineages: Pescoço Pelado,Carijó and Pesadão Vermelho. The individual body weight of broilers (1, 7, 14, 21,28, 35, 42, 49, 56, 63, 70,77, 84 and 91 days of age) was collected weekly for determination of growth curves by means of Modelsvon Bertalanffy, Gompertz, Logistic, Richards and Brody. The parameters of Brody model did notconverge to the weight of strains. The model that better adjusted to the data was Logistic.(AU)

Objetivou-se com este trabalho identificar, por meio de diferentes critérios estatísticos, omodelo de regressão não linear mais adequado para descrever a curva de crescimento de três linhagens defrangos caipira para produção de carne. Utilizaram-se 90 aves caipiras, sendo 30 aves de cada uma dasseguintes linhagens: Pescoço Pelado, Carijó e Pesadão Vermelho. Foi coletado semanalmente o pesocorporal individual dos frangos (1, 7, 14, 21,28, 35, 42, 49, 56, 63, 70, 77, 84 e 91 dias de idade) paradeterminação das curvas de crescimento por meio dos modelos Von Bertalanffy, Gompertz, Logístico,Richards e Brody. Os parâmetros do modelo Brody não convergiram, sendo então não adequado paradescrever o peso dessas linhagens. O modelo que melhor se ajustou aos dados foi o Logístico.(AU)

Analysis of growth curves in different lineages of Caipira broiler type / Análise de curvas de crescimento em diferentes linhagens de frangos de corte tipo Caipira

The objective of this work was to identify, by means of different statistical criteria the idealnonlinear regression model to describe the growth curve of three lineages of caipira broiler for meatproduction. A total of 90 birds were used, being 30 birds from each of the following lineages: Pescoço Pelado,Carijó and Pesadão Vermelho. The individual body weight of broilers (1, 7, 14, 21,28, 35, 42, 49, 56, 63, 70,77, 84 and 91 days of age) was collected weekly for determination of growth curves by means of Modelsvon Bertalanffy, Gompertz, Logistic, Richards and Brody. The parameters of Brody model did notconverge to the weight of strains. The model that better adjusted to the data was Logistic.

Objetivou-se com este trabalho identificar, por meio de diferentes critérios estatísticos, omodelo de regressão não linear mais adequado para descrever a curva de crescimento de três linhagens defrangos caipira para produção de carne. Utilizaram-se 90 aves caipiras, sendo 30 aves de cada uma dasseguintes linhagens: Pescoço Pelado, Carijó e Pesadão Vermelho. Foi coletado semanalmente o pesocorporal individual dos frangos (1, 7, 14, 21,28, 35, 42, 49, 56, 63, 70, 77, 84 e 91 dias de idade) paradeterminação das curvas de crescimento por meio dos modelos Von Bertalanffy, Gompertz, Logístico,Richards e Brody. Os parâmetros do modelo Brody não convergiram, sendo então não adequado paradescrever o peso dessas linhagens. O modelo que melhor se ajustou aos dados foi o Logístico.

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)