Pakistan Journal of Nutrition 12 (9): 865-869, 2013 ISSN 1680-5194 © Asian Network for Scientific Information, 2013 Corresponding Author: Muhammad Aman Ullah, Department of Statistics, Bahauddin Zakariya University, Multan 60800, Pakistan 865 Non-Linear Regression Models to Predict the Lamb and Sheep Weight Growth Muhammad Aman Ullah, Muhammad Amin and Muhammad Ansar Abbas Department of Statistics, Bahauddin Zakariya University, Multan 60800, Pakistan Abstract: The study of living organism growth is the hot issue now a days in biological sciences. In this research, we explore the descriptive analysis of Lamb and Sheep weight growth in Pakistan. Also the non- linear regression models are identified on the basis of model selection criteria’s for lamb and sheep weight growth prediction. From the analysis, we have found that for commercial sheep, spring born lambs and twin born lambs, the best model is the Von Bertalanffy model. While for predicting the weight of male commercial sheep, autumn born and single born lambs, the best model is the Brody model. Key words: Growth curve, sheep weight, lamb weight, non-linear regression modeling INTRODUCTION Growth of living cells, tissues, organs and organisms is a biological phenomenon and can be explained in terms of mathematical terms. Increase in number of cells and increase in size of cells results in overall increase in mass of living tissue. This increase is not always steady and linear but has some non-linear fashion. Therefore, it may be divided into phases to explain it. Many researcher defined growth in their own way. Growth, one of the most essential traits for animals, is defined as an increase in tissues and organs of the animals per unit time and effected by genetic and environmental factors (Tariq et al., 2011). The growth that has sigmoid form is explained reliably by non-linear growth models such as Gompertz, logistic, Richards, Weibull, Monomolecular, Brody and von Bertalanffy. Information about parameters of these non linear models enables researchers to obtain beneficial clues for selection studies. Growth is a trait of interest in the domestic complex subject which has been studied through many different approaches. A widely used approach is to fit growth data with mathematical equations or growth curve equations. Those functions are based on deterministic differential equations that seek a biological interpretation. Even though growth is a variable among individuals, it follows a well defined course in populations of animals with age. Generally; growth follows a sigmoid or s-shaped curve through the growth rate which varies with age. The rate slowly declines to zero reaching a plateau when the animal achieves mature weight (Arango and van Vleck, 2002). Different models have been developed by researchers for studying growth and other such attributes. For instance Benjamin Gompertz (1825) developed Gompertz model to calculate mortality rates. Today this model is most frequently applied to study biological growth. A gompertz curve or gompertz function is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and of a time period. Other important function is the Logistic curve. It was developed by Verhulst (1838) as a model for population growth. In this function inflection point is independent on measurement. It often applied for sigmoid growth where the inflection is located at approximately half of the ultimate value and is closely related to the Hubert Curve. In statistics, logistic regression (sometimes called the logistic model or logit model) is used for prediction of the probability of occurrence of an event by fitting data to a logistic function. It is a generalized linear model used for binomial regression. Bertalanffy model was developed by Bertalanffy (1957) as a model for body weight growth. The point of inflection is fixed at 8/27 or 29.63% of the maximum value. It is suitable for sigmoid growth with inflection points around 30% of the ultimate. In Brody curve the inflection points occurs between the two curves. It was derived by S. Brody as models for Piecewise growth process of exponential type. The increasing function is only valid in temporarily limited intervals and can be extrapolated. The decreasing function can be extrapolated and is suitable for monotonous decrease. Wildeus (1997) conducted the study to explore the growth performance of different breeds of sheep in US. Lancelot et al. (2000) explored the different factors which are affecting the growth sheep. They use multi-level modeling and have found that Age, litter-size, age xlitter- size, litter-sizextreatment and age xlitter-sizex treatment are the significant factors for growth of sheep. Lamb et al. (2008) fitted logistic, Gompertz, Richards and exponential models and linear regression models to describe the growth of two breeds of lambs from birth to slaughter. On the basis of model selection criteria’s R 2