ABSTRACT The ordinary least squares (OLS) can be affected by errors associated with heteroscedasticity and outliers, and extreme points can influence the regression parameters. Methods based on the median rather than on the mean and variance are more resistant to outliers and extreme points. These methods could be used to obtain regression parameter estimates that reflect more accurately the genuine relationship between the Y and X variables, leading to better identification of outliers and extreme points by comparing the slopes and intercepts of both methods. The Theil-Sen (TS) regression computes all possible pairwise slopes and determines the median of slopes as the regression slope. Here, we illustrated the potential use of TS and frequently used robust regression (RR) techniques to single linear regression using synthetic datasets and a practical problem in animal science. Three synthetic datasets were created assuming the normal distribution of Y and X values: one was free of outliers, while the other two had one or two clusters of outliers but the same X values. The TS, OLS, and RR had nearly identical regression parameter estimates for the dataset without synthetic outliers. However, the intercept and slope estimates by the OLS method differed considerably from the TS and RR methods when one or two clusters of outliers were included. The TS approach could be used to indirectly determine the presence of outliers or extreme points by comparing the 95 % confidence interval of the TS and OLS parameter estimates.

Abstract The present study determined the relationship between body mass index (BMI) and chemical components in Pelibuey ewes. The BMI was determined in 28 ewes. At slaughter, internal organs and blood were weighed, then were mixed and grounded. The half-carcasses were dissected into subcutaneous and intermuscular fat, muscle, and bone. The muscle and fat of each animal were ground together, and one sample of the mixture was taken. The carcass and viscera samples were freeze-dried and further analysed for crude protein (CP), fat (F), and ash (A). The relationship between BMI and body composition were estimated using correlation coefficients (r) and regression models. The r between BMI and carcass crude protein and visceral crude protein were 0.51 and 0.48, respectively (p < 0.001), and between BMI and carcass F and visceral F were 0.82 and 0.71, respectively (p < 0.0001). The r2 of the models relating to BMI and body chemical components ranged from 0.62 to 0.97. There was a quadratic relationship between total body CP, and A. The chemical carcass components (CP, F, and carcass energy [CE]) showed a linear relationship with BMI, with an r2 ranging from 0.67 to 0.96. It was concluded that BMI could be used as predictors of body chemical composition in non-pregnant and non-lactating Pelibuey ewes. The use of empty body weight for calculating BMI yielded more accurate estimates of the chemical components of the body of adult sheep.

Resumen El presente estudio tuvo como objetivo determinar la relación entre el índice de masa corporal (IMC) y los componentes químicos del cuerpo en ovejas Pelibuey. El IMC se determinó en 28 ovejas. Al sacrificio, se pesaron los órganos internos y la sangre de cada oveja y posteriormente se mezclaron y molieron. Las medias canales se diseccionaron en grasa subcutánea e intermuscular, músculo y hueso. El músculo y la grasa de cada animal se mezclaron y molieron, y se tomó una muestra. Las muestras de canal y vísceras se liofilizaron y se analizaron para proteína cruda (PC), grasa (G) y cenizas (C). Las relaciones entre el IMC y la composición corporal se estimaron mediante coeficientes de correlación (r) y modelos de regresión. Los r entre el IMC y la PC de canal y la PC visceral fueron 0.51 y 0.48, respectivamente (p < 0.001), y entre el IMC y la G en canal y la G visceral fueron 0.81 y 0.71, respectivamente (p < 0.0001). El r2 de los modelos que relacionan el IMC y la composición química del cuerpo variaron de 0.62 a 0.97. Se encontró una relación cuadrática entre la PC y la C total del cuerpo. Los componentes químicos de la canal (CP, G y energía de la canal [EC]) mostraron una relación lineal con el IMC, con un r2 entre 0.67 y 0.96. Por lo tanto, el IMC puede usarse como un predictor moderadamente preciso de la composición corporal en ovejas de pelo no gestantes y no lactantes. El uso del peso vivo vacío para calcular el IMC (IMCc) generó estimaciones más precisas de los componentes químicos del cuerpo en ovejas adultas.

ABSTRACT Tannins represent one of the most abundant polyphenolic compounds in plants. Tannins exist as a multitude of chemically unique entities in nature. The most commonly occurring tannins are typically divided into two major classes based on chemical structure: hydrolysable (HT) or condensed tannins (CT). Hydrolysable tannins are esters of gallic or ellagic acid linked to a polyol core, typically glucose. Condensed tannins or proanthocyanidins consist of flavan-3-ol subunits linked together to form oligomers and polymers. Both HT and CT are defined as astringent, medium-to-high-molecular weight polyphenolic compounds that characteristically bind and precipitate soluble proteins. The objective of this paper was to present recent advances in CT-ruminant interactions, the limitations associated with understanding and using CT in ruminant animal production, and future needs for research to further advance our knowledge of the role of CT in optimization of ruminant animal production. Condensed tannins pose some anti-nutritional problems to ruminants due to their astringent property that reduces feed intake and, consequently, animal performance. Ruminants can, however, tolerate CT by slowly adapting the ruminal microbes to the toxic effects of CT and by releasing CT-binding salivary proteins. The protein-binding ability of CT has some benefits to the ruminant due to complexes formed with essential amino acids, preventing their degradation in the rumen, but releasing them in the lower gut for absorption by the animal. Recent data have suggested increased N retention when CT is given to growing animals. There are potential benefits of using CT and HT for anthelmintic purposes due to their ability to inhibit egg hatching and larval motility of gastrointestinal nematode parasites, especially in small ruminants. Condensed tannins also bind to minerals (Al, Ca, Co, Cu, Fe, Mg, Mn, P, and Zn). Although studies with ruminants have been contradictory, it has been reported that because the CT-metal ion complex is stable over a wide pH range, CT may reduce the bioavailability of minerals. Methane mitigation by feeding CT might be the most impactful benefit for ruminant production. Many empirical equations have been developed to predict ruminal methane emissions, but very few have included CT. Future research should focus on the improvement of methodology to assess CT biological activity, interaction with other plant-specialized metabolites, and associated physiological and nutritional impacts on ruminants.