AgroReg: main regression models in agricultural sciences implemented as an R Package

Regression analysis is highly relevant to agricultural sciences since many of the factors studied are quantitative. Researchers have generally used polynomial models to explain their experimental results, mainly because much of the existing software perform this analysis and a lack of knowledge of other models. On the other hand, many of the natural phenomena do not present such behavior; nevertheless, the use of non-linear models is costly and requires advanced knowledge of language programming such as R. Thus, this work presents several regression models found in scientific studies, implementing them in the form of an R package called AgroReg. The package comprises 44 analysis functions with 66 regression models such as polynomial, non-parametric (loess), segmented, logistic, exponential, and logarithmic, among others. The functions provide the coefficient of determination (R2), model coefficients and the respective p-values from the t-test, root mean square error (RMSE), Akaike's information criterion (AIC), Bayesian information criterion (BIC), maximum and minimum predicted values, and the regression plot. Furthermore, other measures of model quality and graphical analysis of residuals are also included. The package can be downloaded from the CRAN repository using the command: install.packages("AgroReg"). AgroReg is a promising analysis tool in agricultural research on account of its user-friendly and straightforward functions that allow for fast and efficient data processing with greater reliability and relevant information.

Nonlinear models for soil moisture sensor calibration in tropical mountainous soils

Electromagnetic sensors are widely used to monitor soil water content (θ); however, site-specific calibrations are necessary for accurate measurements. This study compares regression models used for calibration of soil moisture sensors and investigates the relation between soil attributes and the adjusted parameters of the specific calibration equations. Undisturbed soil samples were collected in the A and B horizons of two Ultisols and two Inceptisols from the Mantiqueira Range in Southeastern Brazil. After saturation, the Theta Probe ML2X was used to obtain the soil dielectric constant (ε). Several readings were made, ranging from saturation to oven-dry. After each reading, the samples were weighted to calculate θ (m³ m-³). Fourteen regression models (linear, linearized, and nonlinear) were adjusted to the calibration data and checked for their residue distribution. Only the exponential model with three parameters met the regression assumptions regarding residue distribution. The stepwise regression was used to obtain multiple linear equations to estimate the adjusted parameters of the calibration model from soil attributes, with silt and clay contents providing the best relations. Both the specific and the general calibrations performed well, with RMSE values of 0.02 and 0.03 m³ m-³, respectively. Manufacturer calibration and equations from the literature were much less accurate, reinforcing the need to develop specific calibrations.

Sexual dimorphism and morphometrics in two populations of the neotropical freshwater turtle Mesoclemmys vanderhaegei (Testudines, Chelidae) / Dimorfismo sexual e morfometria em duas populações do quelônio aquático neotropical Mesoclemmys vanderhaegei (Testudines, Chelidae)

As commonly observed in turtles, sexual size dimorphism (SSD) is pronounced in the Neotropical freshwater turtle Mesoclemmys vanderhaegei (Bour, 1973), a species in which females are usually larger than males. We studied SSD in two populations of M. vanderhaegei from the Brazilian Cerrado savannah, based on 245 specimens captured between November 2010 and August 2013. The carapace length of the largest male was 201 mm (9.15% shorter than that of the largest female, 220 mm). The mean sizes of males and females did not differ in the two populations. However, a comparison of eight selected morphological variables revealed that the size distribution pattern differed between the populations. Using model selection, seven out of 34 morphometric variables - from the head, plastron, bridge, and tail - were selected as the most suitable ones to distinguish between males and females. The pattern of SSD found in M. vanderhaegei is similar to that found in other chelonian species and may be the result of natural selection rather than ecological factors, since individuals of both sexes use the same habitats.

Como comumente observado em quelônios, dimorfismo sexual em tamanho (SSD) é pronunciado em Mesoclemmys vanderhaegei (Bour, 1973), uma espécie de quelônio Neotropical de água doce onde as fêmeas são geralmente maiores que os machos. Nós estudamos SSD em duas populações de M. vanderhaegei no Cerrado brasileiro, com base em 245 espécimes capturados entre novembro de 2010 e agosto de 2013. O comprimento da carapaça do maior macho foi de 201 mm (9,15% menor que o comprimento da maior fêmea, 220 mm). Os tamanhos médios de fêmeas e machos não diferiram nas duas populações. No entanto, uma comparação de oito variáveis morfológicas revelou que o padrão de distribuição de tamanhos diferiu entre as populações. Usando a seleção de modelos, sete das 34 variáveis morfométricas - incluindo medidas da cabeça, plastrão, ponte e cauda - foram selecionadas como as mais adequadas para distinguir fêmeas e machos. O padrão de SSD encontrado em M. vanderhaegei é similar ao encontrado em outras espécies de quelônios e pode ser o resultado de seleção natural ao invés de fatores ecológicos, uma vez que indivíduos de ambos os sexos usam os mesmos habitats.

Sexual dimorphism and morphometrics in two populations of the Neotropical freshwater turtle Mesoclemmys vanderhaegei (Testudines, Chelidae)

ABSTRACT As commonly observed in turtles, sexual size dimorphism (SSD) is pronounced in the Neotropical freshwater turtle Mesoclemmys vanderhaegei (Bour, 1973), a species in which females are usually larger than males. We studied SSD in two populations of M. vanderhaegei from the Brazilian Cerrado savannah, based on 245 specimens captured between November 2010 and August 2013. The carapace length of the largest male was 201 mm (9.15% shorter than that of the largest female, 220 mm). The mean sizes of males and females did not differ in the two populations. However, a comparison of eight selected morphological variables revealed that the size distribution pattern differed between the populations. Using model selection, seven out of 34 morphometric variables - from the head, plastron, bridge, and tail - were selected as the most suitable ones to distinguish between males and females. The pattern of SSD found in M. vanderhaegei is similar to that found in other chelonian species and may be the result of natural selection rather than ecological factors, since individuals of both sexes use the same habitats.

RESUMO Como comumente observado em quelônios, dimorfismo sexual em tamanho (SSD) é pronunciado em Mesoclemmys vanderhaegei (Bour, 1973), uma espécie de quelônio Neotropical de água doce onde as fêmeas são geralmente maiores que os machos. Nós estudamos SSD em duas populações de M. vanderhaegei no Cerrado brasileiro, com base em 245 espécimes capturados entre novembro de 2010 e agosto de 2013. O comprimento da carapaça do maior macho foi de 201 mm (9,15% menor que o comprimento da maior fêmea, 220 mm). Os tamanhos médios de fêmeas e machos não diferiram nas duas populações. No entanto, uma comparação de oito variáveis morfológicas revelou que o padrão de distribuição de tamanhos diferiu entre as populações. Usando a seleção de modelos, sete das 34 variáveis morfométricas - incluindo medidas da cabeça, plastrão, ponte e cauda - foram selecionadas como as mais adequadas para distinguir fêmeas e machos. O padrão de SSD encontrado em M. vanderhaegei é similar ao encontrado em outras espécies de quelônios e pode ser o resultado de seleção natural ao invés de fatores ecológicos, uma vez que indivíduos de ambos os sexos usam os mesmos habitats.

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)

Evaluation of Bayesian models for analysis of crude protein requirement for pigs of Brazilian Piau breed

We evaluated the inclusion of information on genetic relationship into the analysis of crude protein requirement in diets for pigs of Brazilian Piau breed, using Bayesian inference. The animals were assigned to treatments in a completely randomized design in factorial scheme 4 × 2 (crude protein levels × sex) with 12 repetitions per treatment. The evaluations were carried out in the initial, growing and finishing phases, and after slaughter. The traits evaluated were feed conversion (FC), backfat thickness (BF), daily weight gain (DWG), daily feed intake (DFI) and some carcass cuts. Three models were considered to evaluate the inclusion of information on genetic relationship into the analysis: Model I, a simple linear model; Model II, the same effects of Model I with addition of the independent random effect of animal; and Model III, the same effects of Model II, but including the genetic relationship between the animals. Model III presented the best fit and was considered for later inferences. Crude protein (CP) levels did not significantly influence any of the evaluated traits. The effect of sex was significant only for the growing phase, while its interaction with protein levels presented an opposite result for all evaluated traits. Additionally, CP levels of 10.2 %, 9.6 % and 9.0 % can be used in diets for pigs of Brazilian Piau breed in the initial, growing and finishing phases, respectively.

Evaluation of Bayesian models for analysis of crude protein requirement for pigs of Brazilian Piau breed

We evaluated the inclusion of information on genetic relationship into the analysis of crude protein requirement in diets for pigs of Brazilian Piau breed, using Bayesian inference. The animals were assigned to treatments in a completely randomized design in factorial scheme 4 × 2 (crude protein levels × sex) with 12 repetitions per treatment. The evaluations were carried out in the initial, growing and finishing phases, and after slaughter. The traits evaluated were feed conversion (FC), backfat thickness (BF), daily weight gain (DWG), daily feed intake (DFI) and some carcass cuts. Three models were considered to evaluate the inclusion of information on genetic relationship into the analysis: Model I, a simple linear model; Model II, the same effects of Model I with addition of the independent random effect of animal; and Model III, the same effects of Model II, but including the genetic relationship between the animals. Model III presented the best fit and was considered for later inferences. Crude protein (CP) levels did not significantly influence any of the evaluated traits. The effect of sex was significant only for the growing phase, while its interaction with protein levels presented an opposite result for all evaluated traits. Additionally, CP levels of 10.2 %, 9.6 % and 9.0 % can be used in diets for pigs of Brazilian Piau breed in the initial, growing and finishing phases, respectively.(AU)

Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences / Método gerador de modelos de crescimento e decrescimento obtidos a partir de equações diferenciais aplicado as ciências agrárias

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.(AU)

O objetivo deste trabalho é propor um método gerador de modelos de crescimento e decrescimento por meio de equações diferenciais, bem como apresentar um modelo a partir do método proposto, compará-lo entre os modelos matemáticos não lineares clássicos seguintes, Logístico, Von Bertalanffy, Brody, Gompertz, e Richards e identificar aquele que representa melhor a curva média de crescimento. Para isso, foram utilizados dados de caprino (SRD - Sem Raça Definida) e de ovinos da raça Santa Inês oriundos, respectivamente, dos trabalhos de Cavalcante et al. (2013) e Sarmento et al. (2006a). A qualidade de ajuste foi medida por meio do quadrado médio do resíduo (QMR), critério de informação de Akaike (AIC), critério de informação Bayesiano (BIC), desvio médio absoluto (DMA) e coeficiente de determinação ajustado . Os parâmetros dos modelos (?, peso à idade adulta; ?, uma constante de integração; ?, parâmetro de forma sem interpretação biológica; k, taxa de maturação; e m, ponto de inflexão) foram estimados pelo método de mínimos quadrados utilizando o algoritmo de Levenberg-Marquardt por meio do Software IBM SPSS Statistics 1.0. Observou-se que o modelo Proposto foi superior aos outros modelos para o estudo das curvas de crescimento de caprinos e ovinos de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.(AU)

Modeling habitat suitability of the invasive clam Corbicula fluminea in a Neotropical shallow lagoon, southern Brazil / Modelagem da adequabilidade de habitat do bivalve invasor Corbicula fluminea em uma lagoa rasa Neotropical

This study aimed to model the habitat suitability for an invasive clam Corbicula fluminea in a coastal shallow lagoon in the southern Neotropical region (30.22, 50.55). The lagoon (19km2, maximum deep 2.5m) was sampled with an Ekman dredge in an orthogonal matrix comprising 84 points. At each sampling point, were obtained environmental descriptors as depth, organic matter content (OMC), average granulometry (Avgran), and the percentage of sand (Pcsand). Prediction performance of Generalized Linear Models (GLM), Generalized Additive Models (GAM) and Boosted Regression Tree (BRT) were compared. Also, niche overlapping with other native clam species (Castalia martensi, Neocorbicula limosa and Anodontites trapesialis) was examined. A BRT model with 1400 trees was selected as the best model, with cross-validated correlation of 0.82. The relative contributions of predictors were Pcsand-42.6%, OMC-35.8%, Avgran-10.9% and Depth-10.8%. Were identified that C. fluminea occur mainly in sandy sediments with few organic matter, in shallow areas nor by the shore. The PCA showed a wide niche overlap with the native clam species C. martensi, N. limosa and A. trapesialis.(AU)

O objetivo de deste estudo foi modelar a adequabilidade de habitat do bivalve invasor Corbicula fluminea em uma lagoa costeira na região Neotropical (30.22, 50.55). A lagoa (19km2, 2,5 m de profundidade máxima) foi amostrada com uma draga Ekman em uma matriz ortogonal compreendendo 84 pontos. Em cada ponto de amostragem foram obtidos descritores ambientais como a profundidade, teor de matéria orgânica (OMC), granulometria média (Avgran), e a percentagem de areia (Pcsand). O poder preditivo dos métodos Modelos Lineares Generalizados (GLM), Modelos Aditivos Generalizados (GAM) e Boosted Regression Trees (BRT) foram comparados. Além disso, a sobreposição de nicho com espécies de moluscos nativos (Castalia martensi, Neocorbicula limosa e Anodontites trapesialis) foi examinada. Um modelo BRT com 1.400 árvores foi selecionado como o melhor modelo, com correlação da validação cruzada de 0,82. As contribuições relativas dos preditores foram Pcsand-42,6%, OMC-35,8%, Avgran-10,9% e profundidade-10,8%. Foi demonstrado que C. fluminea está associada a sedimentos arenosos com pouca matéria orgânica, em áreas rasas próximo às margens. A PCA mostrou uma ampla sobreposição de nicho com as espécies de moluscos nativos C. martensi, N. limosa e A. trapesialis.(AU)

Modeling habitat suitability of the invasive clam Corbicula fluminea in a Neotropical shallow lagoon, southern Brazil

Abstract This study aimed to model the habitat suitability for an invasive clam Corbicula fluminea in a coastal shallow lagoon in the southern Neotropical region (30.22, 50.55). The lagoon (19km2, maximum deep 2.5m) was sampled with an Ekman dredge in an orthogonal matrix comprising 84 points. At each sampling point, were obtained environmental descriptors as depth, organic matter content (OMC), average granulometry (Avgran), and the percentage of sand (Pcsand). Prediction performance of Generalized Linear Models (GLM), Generalized Additive Models (GAM) and Boosted Regression Tree (BRT) were compared. Also, niche overlapping with other native clam species (Castalia martensi, Neocorbicula limosa and Anodontites trapesialis) was examined. A BRT model with 1400 trees was selected as the best model, with cross-validated correlation of 0.82. The relative contributions of predictors were Pcsand-42.6%, OMC-35.8%, Avgran-10.9% and Depth-10.8%. Were identified that C. fluminea occur mainly in sandy sediments with few organic matter, in shallow areas nor by the shore. The PCA showed a wide niche overlap with the native clam species C. martensi, N. limosa and A. trapesialis.

Resumo O objetivo de deste estudo foi modelar a adequabilidade de habitat do bivalve invasor Corbicula fluminea em uma lagoa costeira na região Neotropical (30.22, 50.55). A lagoa (19km2, 2,5 m de profundidade máxima) foi amostrada com uma draga Ekman em uma matriz ortogonal compreendendo 84 pontos. Em cada ponto de amostragem foram obtidos descritores ambientais como a profundidade, teor de matéria orgânica (OMC), granulometria média (Avgran), e a percentagem de areia (Pcsand). O poder preditivo dos métodos Modelos Lineares Generalizados (GLM), Modelos Aditivos Generalizados (GAM) e Boosted Regression Trees (BRT) foram comparados. Além disso, a sobreposição de nicho com espécies de moluscos nativos (Castalia martensi, Neocorbicula limosa e Anodontites trapesialis) foi examinada. Um modelo BRT com 1.400 árvores foi selecionado como o melhor modelo, com correlação da validação cruzada de 0,82. As contribuições relativas dos preditores foram Pcsand-42,6%, OMC-35,8%, Avgran-10,9% e profundidade-10,8%. Foi demonstrado que C. fluminea está associada a sedimentos arenosos com pouca matéria orgânica, em áreas rasas próximo às margens. A PCA mostrou uma ampla sobreposição de nicho com as espécies de moluscos nativos C. martensi, N. limosa e A. trapesialis.

Modelling the growth of tambaqui, Colossoma macropomum (Cuvier, 1816) in floodplain lakes: model selection and multimodel inference / Modelagem do crescimento do tambaqui (Colossoma macropomum Cuvier, 1816): seleção de modelos e inferência multimodelos

The tambaqui, Colossoma macropomum, is one of the most commercially valuable Amazonian fish species, and in the floodplains of the region, they are caught in both rivers and lakes. Most growth studies on this species to date have adjusted only one growth model, the von Bertalanffy, without considering its possible uncertainties. In this study, four different models (von Bertalanffy, Logistic, Gompertz and the general model of Schnüte-Richards) were adjusted to a data set of fish caught within lakes from the middle Solimões River. These models were adjusted by non-linear equations, using the sample size of each age class as its weight. The adjustment evaluation of each model was based on the Akaike Information Criterion (AIC), the variation of AIC between the models (i) and the evidence weights (wi). Both the Logistic (i = 0.0) and Gompertz (i = 1.12) models were supported by the data, but neither of them was clearly superior (wi, respectively 52.44 and 29.95%). Thus, we propose the use of an averaged-model to estimate the asymptotic length (L). The averaged-model, based on Logistic and Gompertz models, resulted in an estimate of L=90.36, indicating that the tambaqui would take approximately 25 years to reach average size.(AU)

O tambaqui, Colossoma macropomum, é uma das espécies de peixes amazônicos de maior valor comercial, sendo capturado em rios e lagos da planície alagável da região. Até o presente, a maioria dos estudos sobre essa espécie tem ajustado um único modelo de crescimento, o de von Bertalanffy, sem considerer as possíveis incertezas associadas ao uso do modelo. Neste estudo, quatro modelos diferentes (von Bertalanffy, Logístico, Gompertz e o modelo geral de Schnüte-Richards) foram ajustados a um conjunto de dados de peixes capturados no interior de lagos situados no médio Solimões. Esses modelos foram ajustados por equações não lineares e o número de tambaquis em cada classe de tamanho foi usado como peso no ajuste. A avaliação do ajuste de cada modelo foi baseada no Critério de Informação de Akaike (AIC), na diferença do AIC entre os modelos (i) e nos pesos de evidência (wi). Tanto o modelo Logístico (i = 0,0) como o de Gompertz (i = 1,12) foram suportados pelos dados, mas nenhum deles foi claramente superior (wi, respectivamente, de 52,44 e 29,95%). Assim, é proposto o uso de um modelo médio para estimar o comprimento assintótico (L). O modelo médio, baseado nos modelos Logístico e de Gompertz, resultou em uma estimativa de L = 90,36 e indicou que o tambaqui levaria aproximadamente 25 anos para atingir esse tamanho.(AU)

Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences / Método gerador de modelos de crescimento e decrescimento obtidos a partir de equações diferenciais aplicado as ciências agrárias

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

O objetivo deste trabalho é propor um método gerador de modelos de crescimento e decrescimento por meio de equações diferenciais, bem como apresentar um modelo a partir do método proposto, compará-lo entre os modelos matemáticos não lineares clássicos seguintes, Logístico, Von Bertalanffy, Brody, Gompertz, e Richards e identificar aquele que representa melhor a curva média de crescimento. Para isso, foram utilizados dados de caprino (SRD - Sem Raça Definida) e de ovinos da raça Santa Inês oriundos, respectivamente, dos trabalhos de Cavalcante et al. (2013) e Sarmento et al. (2006a). A qualidade de ajuste foi medida por meio do quadrado médio do resíduo (QMR), critério de informação de Akaike (AIC), critério de informação Bayesiano (BIC), desvio médio absoluto (DMA) e coeficiente de determinação ajustado . Os parâmetros dos modelos (?, peso à idade adulta; ?, uma constante de integração; ?, parâmetro de forma sem interpretação biológica; k, taxa de maturação; e m, ponto de inflexão) foram estimados pelo método de mínimos quadrados utilizando o algoritmo de Levenberg-Marquardt por meio do Software IBM SPSS Statistics 1.0. Observou-se que o modelo Proposto foi superior aos outros modelos para o estudo das curvas de crescimento de caprinos e ovinos de acordo com a metodologia e condições em que foi desenvolvido o presente estudo.