Productividad y curvas de crecimiento usando modelos no lineales en un cruce de ovino de pelo colombiano x pelibuey

Los ovinos criollos de pelo (OCP) desarrollaron ventajas adaptativas al climática tropical, que le permiten tener resistencia a enfermedades, alta fertilidad y prolificidad; sin embargo, se reportan pocas investigaciones sobre la productividad de los OCP en sistemas asociados al cultivo de la caña, lo que hace necesario realizar investigaciones, que permitan fomentar sus atributos. El objetivo del presente trabajo fue analizar la productividad y el desarrollo corporal de un cruce de OCP, mediante parámetros productivos y curvas de crecimiento. Se utilizaron 180 animales de partos simples y múltiples; se registró el peso al nacimiento (PN), al destete (PD), a los 210 días (PAJ210) y las ganancias diarias predestete (GDPRE) y posdestete (GDPOS). Los datos, se analizaron mediante estadística descriptiva, con un GLM, con los efectos sexo (S), tipo de nacimiento (TN), número de partos (NP) y época de nacimiento (EPONAC). Se emplearon los modelos no lineales Gompertz, Logístico, Brody, Richards y Von Bertalanffy, en 1.455 registros de pesos, a diferentes edades, para realizar las curvas de crecimiento. Los análisis, se efectuaron con el paquete estadístico SAS. Se consideraron los coeficientes R2, AIC y BIC, obtenidos por el método de Gauss-Newton, para seleccionar el modelo de mejor ajuste. Los machos presentaron mayores promedios en las variables PN, PD, PAJ210 y GDPOS. El TN afectó todas las variables; el PN y las GDPOS fueron afectadas por el NP y, la EPONAC, afectó PN, las GDPRE, el PAJ210 y las GDPOS. El modelo de mejor ajuste para las curvas de crecimiento fue la de Richards.

The creole hair sheep (CHS) developed adaptive advantages to the tropical climate, which allow them to have resistance to diseases, high fertility and prolificacy. Currently, there is little research on the productivity of CHS in systems associated with the cultivation of sugarcane, which makes it necessary to carry out research to promote its attributes. The purpose of this research was to analyze the productivity and body development of a crossing of CHS, using production parameters and growth curves.180 animals of single and multiple births were used; the follow weight was recorded: at birth (WB), at weaning (WW); at 210 days (W210), and furthermore, daily gains of pre-weaning (WDPRE) and post-weaning (WPPOS) were recorded. The data were analyzed using descriptive statistics with a GLM with the effects sex (S), type of birth (TB), number of births (NB) and period of birth (PB). The non-linear models Gompertz, Logistic, Brody, Richards and Von Bertalanffy were used in 1455 records of weights at different ages to perform growth curves. All analyzes were performed with the SAS statistical package. The R2, AIC and BIC coefficients obtained by the Gauss-Newton method were considered to select the best fit model. The males presented higher averages in the variables WB, WW, W210) and WPOS. The TB affected all the variables; The WB and the WPPOS were affected by the NB and the PB affected the WB, the WDPRE, the W210 and the WPPOS. The best fit model for the growth curves was of Richards.

Estimation of lactation curves of Gyr cattle and some associated production parameters in the Colombian low tropic

Background: The Gyr breed is widely used in Colombian low tropic dairy production systems. During the last 10 years, the Asociación Colombiana de Criadores de Ganado Cebú† ASOCEBU, has been leading a dairy milk control program which led to the creation of a dataset that permits to carry out the first analysis of milk yield in Gyr cattle in the country using records from several herds. Objectives: To study milk production dynamics of Gyr cattle in the Colombian low tropic through the estimation of lactation curves and four derived production parameters: total milk yield between 5 and 305 days (TMY305), peak milk yield (PMY), days at peak (DP) and persistency (P). Methods: 13,798 daily milk yield records from 1,510 cows performing in 103 herds were used; the total number of lactations was 2,480. Four models were considered: Wood, Wiltmink, Papajcsik & Bordero, and a second-degree polynomial. Mean square error, mean absolute error, mean square error of prediction, Akaike and Bayesian information criteria were used to select the model better describing each lactation using the majority rule, that is, the model selected by most criteria was the chosen one. The shape of each fitted lactation curve was checked using basic results from calculus which permitted the classification of the estimated curves into two groups: typical and atypical; only typical functions were used to compute the four aforementioned production parameters. Results: The second-order polynomial was the model most frequently selected, while the Papajcsik & Bordero model had the lowest frequency. Average TMY305, PMY, DP and P were 3,489.86 kg, 17.28 kg, 57.17 days, and 0.83, respectively, with coefficients of variation: 0.27, 0.21, 0.41, and 0.16. Conclusions: This study permitted to identify individuals with outstanding phenotypic performance. To the best of our knowledge, this is the first study of this kind involving thousands of lactations from Gyr cows performing in several regions of Colombian low tropic.

Antecedentes: La raza Gyr es ampliamente utilizada en las lecherías de trópico bajo en Colombia. Durante los últimos 10 años, la Asociación Colombiana de Criadores de Ganado Cebú ASOCEBU, ha liderado un programa de control lechero que generó una base de datos que permite llevar a cabo el primer análisis de producción de leche de la raza Gyr en el país, considerando individuos de varias fincas. Objetivos: Caracterizar la dinámica de producción de leche de ganado Gyr en el trópico bajo colombiano mediante la estimación de curvas de lactancia y cuatro parámetros de producción derivados: producción total entre 5 y 305 días (TMY305), pico de lactancia (PMY), días al pico (DP) y persistencia (P) Métodos: Se utilizaron 13.798 registros de producción diaria de leche de 1.510 vacas provenientes de 103 fincas, el total de lactancias fue 2.480. Se consideraron cuatro modelos: Wood, Wiltmink, Papajcsik & Bordero, y un polinomio de segundo grado. Los criterios usados para elegir el modelo que mejor describió cada lactancia fueron: error cuadrático medio, error absoluto medio, error cuadrático medio de predicción, criterio de información de Akaike y criterio de información Bayesiano. Se utilizó el criterio de mayoría, esto es, el modelo seleccionado fue aquel elegido por más criterios. La forma de cada una de las curvas de lactancia estimadas fue chequeada utilizando resultados básicos del cálculo, esto permitió clasificar las curvas estimadas en dos grupos: típicas y atípicas; solamente las curvas típicas fueron empleadas para calcular los cuatro parámetros antes mencionados. Resultados: El polinomio de segundo grado fue el modelo que se seleccionó con mayor frecuencia, mientras que el modelo Papajcsik & Bordero tuvo la menor frecuencia. Los promedios para TMY305, PMY, DP y P fueron 3.489,86 kg, 17,28 kg, 57,17 días, y 0,83, respectivamente, con coeficientes de variación 0,27, 0,21, 0,41 y 0,16 Conclusiones: Este estudio permitió identificar individuos con desempeño fenotípico sobresaliente. De acuerdo al estado del arte, este es el primer estudio de este tipo que considera miles de lactancias de vacas Gyr provenientes de varias regiones del trópico bajo colombiano.

Antecedentes: Gir é uma raça Bos indicus amplamente utilizada em sistemas de produção leiteira no trópico baixo Colombiano. A Asociación Colombiana de Criadores de Ganado CebúASOCEBU, lidera um programa de controle de leite nos últimos 10 anos, o que permitiu à coleta de um conjunto de dados para realizar a primeira análise de produção de leite em bovinos Gir no país com informações de vários rebanhos. Objetivo: Estudar a dinâmica da produção de leite por meio da estimativa das curvas de lactação e quatro parâmetros de produção derivados: produção total de leite entre 5 e 305 dias (TMY305), produção de leite no pico de lactação (PMY), dias em produção de leite no pico de lactação (DP) e persistência (P). Métodos: Foram utilizados 13.798 registros de produção diária de leite de 1.510 vacas de 103 fazendas , totalizando 2.480 lactações. Foram considerados quatro modelos: Wood, Wiltmink, Papajcsik & Bordero e um polinômio de segundo grau. Para selecionar o modelo que melhor descreve cada lactação foram utilizados os seguintes critérios: erro quadrado médio, erro absoluto médio, e erro quadrado médio de predição. O modelo selecionado pela maioria dos parâmetros, de acordo com os critérios de informação de Akaike e Bayesiano, foi o escolhido. A forma de cada curva de lactação ajustada foi verificada utilizando os resultados básicos do cálculo, isso permitiu classificar as curvas estimadas em dois grupos: típico e atípico, e apenas funções típicas foram utilizadas para calcular os quatro parâmetros de produção acima mencionados Resultados: O polinômio de segunda ordem foi o modelo mais frequentemente selecionado, enquanto o modelo Papajcsik & Bordero apresentou a menor frequência. A média de TMY305, PMY, DP e P foram 3.489,86 kg, 17,28 kg, 57,17 d e 0,83, respectivamente, com coeficientes de variação de 0,27, 0,21, 0,41 e 0,16. Conclusões: Este estudo permitiu identificar indivíduos com excelente desempenho fenotípico. De acordo com a literatura atual, este é o primeiro estudo envolvendo milhares de lactações de vacas Gir em várias regiões do trópico baixo colombiano.

Analysis on epidemiological characteristics of hand foot mouth disease and the influence of meteorological factors on its incidence in Beijing / 公共卫生与预防医学

Objective To study the epidemic characteristics of hand foot mouth disease (HFMD) and the influence of meteorological factors on the incidence of HFMD in Beijing from 2010 to 2019, and to provide scientific evidence for the warning, prediction, prevention and control of HFMD. Methods Descriptive statistical analysis was conducted to analyze the epidemic characteristics of HFMD in Beijing from 2010 to 2019 using R4.0.2 software, and the relationship between meteorological factors such as daily average temperature, daily average relative humidity, daily average precipitation, daily average air pressure, and daily average wind speed and HFMD incidence from 2015 to 2019 was analyzed by using distribution lag nonlinear model. Results In 2010-2019, a total of 324 864 HFMD cases were reported in Beijing, with an average incidence rate of 155.10/100,000. May to July was the annual peak of HFMD. The average daily temperature, relative humidity and precipitation were positively correlated with the incidence of HFMD (Rs=0.66, 0.45 and 0.24, P=0.0000, 0.0000 and 0.0000, respectively). The average daily wind speed and pressure were negatively correlated with the incidence of HFMD (Rs=-0.14 and -0.3, P=2.22×10-9 and 0.0000, respectively). The RR was the highest when the air temperature was 25℃ and at the lag of 10 day, which was 1.41 (95%CI:1.12-1.77). Humid weather conditions were the risk factors of HFMD, and the influence time was relatively long. The RR was the highest when the relative humidity was 84.5% and the lag was 15 days, which was 1.51 (95%CI:1.34-1.70). When daily average wind speed was 3m/s, and the lag was 14 days, the RR was the highest, which was 1.22 (95%CI:0.86-1.73). The RR was the highest when the daily average pressure was 842.5 hPa and the lag was 5 day, which was 1.20 (95%CI:0.66-2.07). When the daily average precipitation was 166.5 mm and the lag was 7 days, the RR was the highest, which was 4.37 (95%CI:1.61-11.84). When the above meteorological conditions were met, the risk of HFMD was the highest. Conclusion Meteorological factors such as daily average temperature, daily average relative humidity, daily average precipitation, daily average pressure and daily average wind speed are closely related to the incidence of HFMD, which is nonlinear and has certain lag. It can be used to predict the risk and epidemic intensity of HFMD, and to provide a scientific basis for the prevention and control, early warning, and prediction of infectious diseases.

Analysis on association between incidence of hand foot and mouth disease and meteorological factors in Xiamen, 2013-2017 / 中华流行病学杂志

Objective@#To study the influence of meteorological factors on the incidence of hand foot and mouth disease (HFMD) in Xiamen, Fujian province, and provide scientific evidence for the early warning, prediction, prevention and control of HFMD.@*Methods@#Correlation analysis and distribution lag nonlinear models (DLNM) analysis of meteorological factors such as daily average pressure, daily average relative humidity, daily average temperature and sunshine hours and the incidence of HFMD in Xiamen during 2013 to 2017 were conducted by using R3.4.3 software.@*Results@#A total of 36 464 cases of HFMD were reported in Xiamen during 2013-2017, and the incidence showed an upward trend (F=40.359, P=0.008). The daily average relative humidity, daily average temperature and sunshine hours were positively correlated with the incidence of HFMD (r>0), and the daily average site pressure was negatively correlated with the incidence of HFMD (r<0). In the case of a lag of 0-5 days, when the daily average pressure of the station was higher than 1 005 hPa, the risk of HFMD gradually increased with the increase of air pressure, and the risk of disease decreased with the increase of lag days. The risk was highest when air pressure was 1 017 hPa and at the lag of 0 day (RR=1.14, 95%CI: 0.67-1.94). When the relative humidity was higher than 95%, the risk of HFMD gradually increased with the increase of relative humidity, and the lag time ranged from 0 day to 10 days, which was most obvious on the 4th and 5th days. The risk was highest when relative humidity was 100% and at the lag of 5 days (RR=1.32, 95%CI: 1.02-1.71). When the air temperature was >28 ℃ and <8 ℃, the risk of HFMD existed, but the lag time was inconsistent. The relative risk was highest during 15-20 days at low air temperature, and the lag time at high air temperature was mainly during 5-15 days. The risk was highest when air temperature was 28 ℃ and at the lag of 4 days (RR=1.10, 95%CI: 0.94-1.29). The sunshine time was >12 h and lag of 0-3 days was a risk factor for the incidence of HFMD. The risk was highest when sunshine time was 13 h and the lag of 0 day (RR=1.20, 95%CI: 1.05-1.36).@*Conclusion@#Meteorological factors such as daily average pressure, daily average relative humidity, daily average temperature and sunshine hours were associated with the incidence of HFMD with certain lag in Xiamen. So, it is suggested to use these data in the early warning system of HFMD.

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)

Modelagem hierárquica Bayesiana na avaliação de curvas de crescimento de suínos genotipados para o gene halotano / Hierarchical Bayesian modeling for the evaluation of growth curves of pigs genotyped for the halothane gene

Para avaliar a influência do gene halotano sobre a curva de crescimento de suínos, bem como sua interação com o sexo do animal, foi proposta uma modelagem hierárquica Bayesiana. Nesta abordagem, os parâmetros dos modelos não-lineares de crescimento (Logístico, Gompertz e von Bertalanffy) foram estimados conjuntamente com os efeitos de sexo e genótipos do gene halotano. Foram utilizados 344 animais F2(Comercial x Piau) pesados ao nascer, aos 21, 42, 63, 77, 105 e 150 dias. O modelo Logístico foi aquele que apresentou melhor qualidade de ajuste por apresentar menor DIC (Deviance Information Criterion) que os demais. As amostras das distribuições marginais a posteriori para as diferenças entre as estimativas dos parâmetros do modelo Logístico indicaram que o peso dos machos à idade adulta com genótipo heterozigoto (HalNn) foi superior ao dos homozigotos (HalNN). A título de comparação, também foi considerada a abordagem frequentista tradicional, baseada em dois passos distintos, a qual, por apresentar um menor poder de discernimento estatístico, não mostrou diferenças significativas.

A hierarchical Bayesian modeling was used to evaluate the influence of halothane gene and its interaction with sex on pig´s growth curves. Under this approach, the parameters from growth models (Logistic, Gompertz and von Bertalanffy) were estimated jointly with the effects of halothane gene and sex. A total of 344 F2 (Commercial x Piau) animals were weighted at birth, 21, 42, 63, 77, 105 and 150 days in life. The Logistic model has presented the best fit based on DIC (Deviance Information Criterion). Thus, the samples from marginal posterior distributions for the differences between the parameters estimates of Logistic model have indicated that the maturity weight of males with heterozygous genotypes (HalNn) was superior to males with homozygous genotypes (HalNN). In order to realize a comparison with the traditional methodology, the frequentist approach based on two distinct steps also was used, but there was not identified significant differences between growth curve parameter estimates from each group (combinations of halothane genotypes and sex).

Growth curve of female collared peccaries (Pecari tajacu) raised in captivity in the Brazilian Amazon Region / Curva de crescimento de fêmeas cateto (Pecari tajacu) criados em cativeiro na Amazônia Brasileira

This work aims to determine the most suitable nonlinear model to describe the growth of female collared peccaries (Pecari tajacu). The monthly records of the weight of 10 captive female collared peccaries over a period of two years in the Brazilian Amazon Region were used. The growth models used were the Von Bertalanffy, Brody, Gompertz and Logistic. The parameters were estimated by using the NLIN procedure from the SAS application. The criteria used to verify the adjustment of the models were: asymptotic standard deviation (ASD); coefficient of determination (R²); average absolute residual deviation (ARD) and the asymptotic rate (AR). The Brody model and the Logistic model estimated the highest (19.44kg) and the lowest (19.18kg) asymptotic weight (A), indicating the lowest (0.0070kg/day) and the highest (0.0121kg/day) maturation rate (K). These results and the coefficients of phenotypic correlation that varied from -0.75 and -0.47 confirmed the antagonistic nature between these parameters. The Brody model estimated the lower value for ARD, a limiting factor for describing the lowest value for AR through this model. The Brody model showed the best adjustment for AR, although the other models also showed a suitable adjustment to the weight data of said species/gender. Based on the AR obtained in this work, the Brody model is recommended for adjusting the growth curve of the female collared peccaries. Depending on the estimated values, especially for K, this trait can be included in a selection index.

Com o objetivo de ajustar modelos não-lineares, foram utilizados registros mensais do peso de 10 fêmeas de cateto (Pecari tajacu) coletados durante dois anos, no criatório do campo experimental Álvaro Adolfo da Embrapa Amazônia Oriental, Belém, PA. Utilizaram-se os modelos de Von Bertalanffy, Brody, Gompertz e Logístico. Os parâmetros foram estimados usando o procedimento NLIN do aplicativo SAS. Os critérios utilizados para verificar o ajuste dos modelos foram: desvio padrão assintótico (ASD); coeficiente de determinação (R²); desvio médio absoluto dos resíduos (ARD) e o índice assintótico (AR). Os modelos Brody e Logístico estimaram, respectivamente, o maior (19,44kg) e o menor (19,18kg) peso assintótico (A), caracterizando a menor (0,0064kg/dia) e a maior (0,0113kg/dia) taxa de maturação (K), haja vista a natureza antagônica entre estes parâmetros, comprovada pela correlação fenotípica variando entre -0,75 à -0,47. O modelo Brody estimou o menor valor para o ARD, fator limitante para caracterizar o menor valor para o AR por este modelo. Considerando o AR, o modelo Brody apresentou o melhor ajuste, contudo, pelos valores encontrados, os demais modelos também apresentaram ajuste adequando aos dados ponderais da referida espécie/sexo. Com base no AR adotado neste trabalho, recomenda-se o modelo Brody para ajustar a curva de crescimento de fêmeas de cateto (Pecari tajacu). Em razão dos valores estimados, sobretudo, para a K, essa característica pode ser incluída em um índice de seleção. Contudo, estudos com grupos mais representativos e criados em outras condições se faz oportuno.

Ajuste de modelos de platô de resposta via regressão isotônica / Response plateau models fitting via isotonic regression

Dentro do contexto nutricional, a suplementação de microminerais em rações para aves frequentemente é feita em quantidades superiores às exigidas na tentativa de assegurar o bom desempenho dos animais. Os experimentos do tipo dose resposta são muito comuns na determinação de níveis ótimos dos nutrientes na ração e contemplam a utilização de modelos de regressão para atingir tal objetivo. Porém, na análise de regressão usual, geralmente, não se usa uma informação a priori sobre uma possível relação de ordem na variável resposta. A regressão isotônica é um método de estimação por mínimos quadrados que gera estimativas que satisfazem a mesma ordenação dos dados. Na teoria da regressão isotônica, essa informação é utilizada de forma essencial e espera-se que a eficiência do ajuste seja aumentada quando se faz uso dela. Diante do exposto, o presente trabalho tem como objetivo utilizar uma metodologia de regressão isotônica, como uma forma alternativa para analisar dados de deposição de zinco (Zn) na tíbia de aves machos da linhagem Hubbard. No estudo, foram considerados os modelos de platô de resposta polinomial quadrático e não linear exponencial. Além desses modelos, também foi proposto o ajuste de um modelo logarítmico para os dados e a eficiência da metodologia foi avaliada por meio de um estudo de simulação Monte Carlo, considerando diferentes cenários para os valores paramétricos. A isotonização dos dados propiciou uma melhora em todos os avaliadores de qualidade de ajuste considerados no trabalho. Dentre os modelos utilizados, o logarítmico apresentou estimativas dos parâmetros mais coerentes com os valores relatados na literatura, para os dados de deposição de Zn na tíbia de aves machos.

Within the nutritional context, the supplementation of microminerals in bird food is often made in quantities exceeding those required in the attempt to ensure the proper performance of the animals. The experiments of type dosage x response are very common in the determination of levels of nutrients in optimal food balance and include the use of regression models to achieve this objective. Nevertheless, the regression analysis routine, generally, uses a priori information about a possible relationship between the response variable. The isotonic regression is a method of estimation by least squares that generates estimates which preserves data ordering. In the theory of isotonic regression this information is essential and it is expected to increase fitting efficiency. The objective of this work was to use an isotonic regression methodology, as an alternative way of analyzing data of Zn deposition in tibia of male birds of Hubbard lineage. We considered the models of plateau response of polynomial quadratic and linear exponential forms. In addition to these models, we also proposed the fitting of a logarithmic model to the data and the efficiency of the methodology was evaluated by Monte Carlo simulations, considering different scenarios for the parametric values. The isotonization of the data yielded an improvement in all the fitting quality parameters evaluated. Among the models used, the logarithmic presented estimates of the parameters more consistent with the values reported in literature.

Comparação entre modelos para predição do nitrogênio mineralizado: uma abordagem bayesiana / Comparison of the models for prediction of the mineralized nitrogen: a bayesian approach

Neste trabalho, desenvolveu-se uma abordagem bayesiana para predizer as quantidades de nitrogênio mineralizados por intermédio de modelos não lineares. Os modelos não lineares considerados para avaliar a dinâmica da mineralização do nitrogênio e para ilustrar o procedimento bayesiano foram: modelo de Cabrera, Marion, Stanford e Smith. A comparação dos modelos foi feita por meio do Fator de Bayes (FB) e do Critério de Informação Bayesiano (BIC). A inferência sobre os parâmetros realizou-se por intermédio do Amostrador de Gibbs e do Metropolis Hastings. O modelo de Cabrera (1993) foi o que proporcionou melhor qualidade de ajuste ao conjunto de dados de mineralização de nitrogênio, sendo seguido pelo modelo de Stanford & Smith (1972) e, por último, o de Marion et al. (1981).

In this work one developed a Bayesian approach to predict the amount of mineralized nitrogen through nonlinear models. The nonlinear models considered to evaluate the mineralization of organic nitrogen and to illustrate the Bayesian procedure were: models of Cabrera, Marion, Stanford and Smith. The comparison of the models was promoted through the Bayes Factor (FB) and Bayes Information Criterion (BIC). Inference on the parameters was carried out through the Gibbs Sampling and Metropolis Hastings. The model that provided better adjustment quality to the group of data was Cabrera's model (1993), followed by the model of Stanford & Smith (1972) and the last one by Marion et al. (1981).

Abordagem Bayesiana das curvas de crescimento de duas cultivares de feijoeiro / Bayesian approach in the growth curves of two cultivars of common bean

Neste trabalho foi utilizada a metodologia Bayesiana para ajustar o modelo não-linear logístico para dados de crescimento de duas cultivares de feijoeiro, "Neguinho" e "Carioca". O delineamento experimental utilizado foi o inteiramente casualizado, com vinte repetições, no esquema de parcelas subdivididas, sendo que os tratamentos principais foram constituídos pelas cultivares e as subparcelas foram constituídas por 17 períodos de avaliações, do plantio até aos 85 dias. A metodologia permitiu comparar as curvas de crescimentos sem utilizar a teoria assintótica e estes resultados mostraram um maior incremento em altura para a cultivar "Carioca".

In this paper the Bayesian methodology was used to fit the logistic nonlinear model to growth data of two common bean cultivars, 'Neguinho' and 'Carioca'. The experiment was a split plot under a completely randomized design with twenty replicates, being the main treatments constituted by cultivars and the sub plots constituted by seventeen periods of evaluations, from planting to 85 days. The methodology allowed comparing the growth curves without using the asymptotic theory, and these results showed a larger height increment for the 'Carioca' cultivar.