RESUMO: O objetivo deste estudo foi avaliar o ajuste dos modelos Brody, Logístico e Platô de resposta quadrática aos dados de perímetros torácico e de canela em equinos Mangalarga Marchador obtidos pelo método transversal, a fim de selecionar o melhor modelo e predizer sobre o crescimento e a maturidade de machos e fêmeas desta raça. Foram utilizados dados de 230 equinos de seis a 176 meses de idade que foram divididos por sexo e em 16 classes de idade. Os modelos estudados foram comparados segundo os avaliadores de qualidade: coeficiente de determinação ajustado ( R adj 2) e desvio padrão residual (DPR), utilizando-se o software estatístico R. Os perímetros torácicos obtidos pelos modelos variaram de 172,06 a 181,50 cm (Brody), 172,51 a 181,89 cm (Logístico) e 183,09 a 177,67 cm (Platô) para fêmeas e machos, respectivamente. Para o perímetro de canela os valores variaram de 18,18 a 19,33 cm (Brody), 18,11 a 19,41 cm (Logístico) e 18,70 a 19,40 cm (Platô) para fêmeas e machos, respectivamente. O modelo logístico é mais indicado para expressar o crescimento em perímetro torácico de machos e fêmeas da raça Mangalarga Marchador. Já para a variável perímetro de canela, o modelo mais indicado para os machos foi o modelo Logístico e para as fêmeas o modelo de Brody.

ABSTRACT: This study evaluated the suitability of the Brody, logistic, and quadratic response plateau models to describe chest and cannon girth data obtained cross-sectionally in Mangalarga Marchador horses, in order to select the best model and predict the growth and maturity of males and females of this breed. Data were collected from 230 horses aged 6 to 176 months, divided by sex and age (16 age classes). The studied models were compared according to each quality evaluator by computing the adjusted coefficient of determination ( R adj 2) and residual standard deviation (RSD) with R statistical software. The chest girths obtained by the models ranged from 172.06 (males) to 181.50 cm (females) (Brody), 172.51 (males) to 181.89 cm (females) (logistic), and 177.67 (males) to 183.09 cm (females) (plateau). For cannon girth, the values were 18.18 (females) to 19.33 cm (males) (Brody), 18.11 (females) to 19.41 cm (males) (logistic), and 18.70 (females) to 19.40 cm (males) (plateau). The logistic model was best suited to describe the growth in chest girth of male and female Mangalarga Marchador horses. For cannon girth growth, the model best suited for males was the logistic model, and the one best suited for females was the Brody model.

ABSTRACT The objective of this study was to evaluate the accuracy of the following six body weight (BW) estimation methods in Campolina (CAM) horses: A - weight tape placed at three different positions on the animal’s thorax; B - Crevat and Quetelet’s formula; C - Hall’s formula; D - Hintz and Griffiths’s table; E - Santos’s table; and F - Cintra’s formula. A total of 380 CAM horses were separated according to sex, age class, and gestational stage and evaluated. To determine their accuracy, weights measured on a scale and weight estimates of the six methods were compared by paired t-test, mean prediction error (MPE), and coefficient of determination (R2), using R software. The predictive capacity of method F was lower in the 6-12 months age class, so this formula is not indicated. The BW was overestimated compared with the actual weight by methods A (with weight tape placed in position 3) and B and underestimated by method C. Methods D and E accurately estimated BW of CAM horses. Correction factors are required to accurately estimate BW in this breed using methods B and C. Method A with the weight tape placed in position 2 is the most accurate for predicting BW, including pregnant female horses, and can, therefore, be considered the most suitable method for estimating BW of CAM horses.

RESUMO: O objetivo deste estudo foi avaliar os modelos logístico e platô de resposta quadrática na descrição do crescimento de equinos da raça Mangalarga Marchador identificando o que melhor descreve o crescimento das variáveis altura de cernelha e comprimento corporal. Foram utilizados dados de 230 equinos de 6 a 176 meses de idade que foram divididos por sexo e em 16 classes de idade. Toda a parte computacional envolvida foi realizada utilizando-se o software estatístico R. O modelo logístico foi o mais indicado para expressar o crescimento em altura na cernelha e comprimento corporal de machos e fêmeas da raça Mangalarga Marchador. Foi criada uma tabela de valores referência para estas medidas ao longo da idade com base no intervalo de confiança dos parâmetros deste modelo. Estimativas das alturas de cernelha adultas obtidas pelo modelo logístico variaram de 144 a 154 cm nos machos e de 143 a 151 cm para fêmeas. Já em comprimento corporal os valores adultos variaram de 146 a 156 cm nos machos e 143 a 156 cm para fêmeas. As fêmeas apresentam maior precocidade do que os machos para atingir a estabilidade em ambas variáveis estudadas.

ABSTRACT: This study aimed to evaluate the logistic and quadratic response plateau models to describe the growth of Mangalarga Marchador horses to identify the model that best describes growth for the variables height at withers and body length. Data were used from 230 horses aged 6 to 176 months, divided by sex and 16 age classes. All computational work was performed using R statistical software. The logistic model was the best suited to express growth in height at withers and body length of male and female Mangalarga Marchadors aged 6 to 176 months. This allowed creating a table of reference values for these measurements over time based on the confidence interval of the model parameters. Estimates of height at withers obtained by the logistic model ranged from 144 to 154 cm in adult males and from 143 to 151 cm in adult females. For body length, values ranged from 146 to 156 cm in adult males and 143 to 156 cm in adult females. Females achieved stability in both height at withers and body length at earlier ages than did males.

Resumo: O objetivo deste trabalho foi avaliar o desenvolvimento de características morfométricas de equinos Mangalarga Marchador por meio de modelos não lineares. Utilizou-se o método transversal para coletar dados de altura da cernelha (AC), comprimento corporal (CC) e perímetros torácico (PT) e de canela (PC) de 200 cavalos (75 machos e 125 fêmeas não gestantes), com idade entre 6 e 153 meses. Os parâmetros dos modelos não lineares de Brody, de Gompertz, logístico e de Von Bertalanffy foram estimados com uso do programa R. A comparação e a seleção dos modelos foi realizada por meio do coeficiente de determinação, do desvio-padrão residual e do critério de informação de Akaike corrigido. Nas fêmeas adultas, AC, CC, PT e PC variaram entre 146,45-148,34, 148,59-151,64, 179,07-182,88 e 18,25-18,76 cm, respectivamente. Nos machos, AC, CC e PC variaram entre 148,55-151,80, 150,77-154,88 e 18,95-19,41 cm, respectivamente. O modelo logístico é o mais indicado para expressar o crescimento em AC em machos e fêmeas, bem como em CC e PC em machos, enquanto o de Brody é o melhor preditor de AC, CC, PT e PC em fêmeas. O aumento nos valores das medidas morfométricas é mais rápido e homogêneo entre as idades de 6 a 24 meses, e estabiliza-se aos 60 meses em ambos os sexos.

Abstract: The objective of this work was to evaluate the development of the morphometric characteristics of Mangalarga Marchador horses through nonlinear models. The transversal method was used to collect data on height at the withers (HW), body length (BL), and thoracic (TP) and cannon (CP) perimeters from 200 horses (75 males and 125 non-pregnant females), aged between 6 and 153 months. The parameters of the Brody, Gompertz, logistic, and von Bertalanffy nonlinear models were estimated using the R software. Models were compared and selected using the coefficient of determination, the residual standard deviation, and the corrected Akaike information criterion. For adult females, HW, BL, TP, and CP ranged between 146.45-148.34, 148.59-151.64, 179.07-182.88, and 18.25-18.76 cm, respectively. For males, HW, BL, and CP ranged between 148.55-151.80, 150.77-154.88, and 18.95-19.41 cm, respectively. The logistic model best expresses growth in HW for males and females, as well as in BL and CP for males, whereas the Brody model is the best predictor for HW, BL, TP, and CP for females. The increase in the values of the morphometric measurements is more rapid and homogeneous between the ages of 6 and 24 months, stabilizing at 60 months in both sexes.

ABSTRACT The objective was to evaluate the accuracy of six body weight (BW) estimating methods in Mangalarga Marchador horses (MM) (n = 318): method A - tape placements at three different positions around the thoracic girth; B - Crevat and Quetelec's formula; C - Hall's formula; D - Hintz and Griffiths’ table; E - Santos’ table; and F - Cintra's formula. For additional analyses, gender, age, and gestational stage were considered. Estimated average BW was compared to the actual scale weight by the paired T test, mean predicted error, and determination coefficient. In the general population, methods A (position 3), B, and C estimated BW that were different from that of the scale. Method A, at positions 1 and 2, was more accurate in predicting the scale weight results compared with all other methods. For pregnant mares, the tape in positions 1 and 2 in method A did not differ from those of the scale. Method A in positions 1 and 2 and the table (method E) may be used to estimate the BW of males and females of different ages and/or gestational stages. To use Methods B and C, correction factors are necessary to precisely estimate the body weights in this breed.

RESUMO: O estudo sobre curvas de crescimento animal com base em modelos não lineares tem sido utilizado para análise do crescimento e desenvolvimento de diversas espécies. Neste trabalho objetivou-se avaliar o ajuste dos modelos Brody, Gompertz, Logístico e vonBertalanffy a dados transversais de peso vivo de equinos Mangalarga Marchador, a fim de selecionar o melhor modelo e predizer sobre o crescimento e a maturidade de machos e fêmeas desta raça. Foram pesados 214 equinos, sendo 94 machos e 120 fêmeas não gestantes, com idade variando entre seis e 153 meses. A estimação dos parâmetros dos modelos foi realizada pelo método de mínimos quadrados, utilizando o processo iterativo de Gauss-Newton, seguindo rotinas do Software R. Os modelos foram comparados pelos critérios: coeficiente de determinação (R²); desvio padrão residual (DPR); critério de informação de Akaike corrigido (AICc). O peso adulto, estimado pelos modelos, variou entre 431kg e 439kg para os machos e entre 416kg e 420kg para fêmeas. O método transversal de obtenção de dados pode ser aplicado no estudo de curvas de crescimento. O modelo de vonBertalanffy foi o mais eficiente para expressar o crescimento nos machos, enquanto que para as fêmeas, o modelo Brody se mostrou mais apropriado. As fêmeas Mangalarga Marchador são mais precoces que os machos para atingir o peso vivo adulto.

ABSTRACT: The analysis of the growth and development of various species has been done using the growth curves of the specific animal based on non-linear models. The objective of the current study was to evaluate the fit of the Brody, Gompertz, Logistic and von Bertalanffy models to the cross-sectional data of the live weight of the MangalargaMarchador horses to identify the best model and make accurate predictions regarding the growth and maturity in the males and females of this breed. The study involved recording the weight of 214 horses, of which 94 were males and 120 were non-pregnant females, between 6 and 153 months of age. The parameters of the model were estimated by employing the method of least squares, using the iteratively regularized Gauss-Newton method and the R software package. Comparison of the models was done based on the following criteria: coefficient of determination (R²); Residual Standard Deviation (RSD); corrected Akaike Information Criterion (AICc). The estimated weight of the adult horses by the models ranged between 431kg and 439kg for males and between 416kg and 420kg for females. The growth curves were studied using the cross-sectional data collection method. For males the von Bertalanffymodel was found to be the most effective in expressing growth, while in females the Brody model was more suitable. The MangalargaMarchador females achieve adult body weight earlier than the males.