The main objective of this study is to examine the relationship between inflation, unemployment and economic growth in terms of the Phillips, Okun and Aggregate supply curves. In this regard, we use nonlinear smooth transition autoregressive methods during the period from 1380 to 1393. The results show that A) Based on the Terasvirta Test, the Phillips curve follows the nonlinear logistic model; the Okun curve follows the exponential nonlinear model and the aggregate supply follows the linear model. B) The Phillips model follows two regimes; in the down regime, the relationship between inflation and unemployment is positive and in the up regime, this is a negative relationship. C) The Okun model follows two regimes that, in down regime, has a negative relationship between economic growth and unemployment; but in up regime, the relationship between economic growth and unemployment is positive. D) The relationship between economic growth and inflation is positive.

In this study, it was aimed at estimating of the growth curve in Raeini Cashmere goats. For drawing growth curve, records of weight-age data of 6765 female and male goats were individually fitted to Brody, Von Bertalanffy, Verhulst, Logistic and Gompertz growth models. The growth models were compared using the coefficient of determination (R2), residual mean square error (MSE), Akaike’s information criterion (AIC) and a number of interations. Among all nonlinear models, the highest R2 and the smallest AIC, MSE values and number of interations were calculated by Brody function for both sexes. Moreover, males have higher A (weight at maturity) and B parameters than females and have a lower K parameter (rate of maturity) than females. As the Brody growth curve, female adult live weight was lower than males, because sex factor significantly influences on live weight. The range of inflection point 4.80 and 7.89 for females, 5.86 and 9.55 for males, respectively. The lowest of an inflection point in both sexes estimated for Von Bertalanffy model, and highest inflection point estimated for logistic in both sexes. The lowest and highest of inflection age in both sexes estimated for Von Bertalanffy and Verhulst models, respectively. In conclusion according to the results of this study, the nonlinear Brody growth model seems to be the most appropriate to adjust the growth curve of the Raeini Cashmere goats.

Extended Abstract Background: A growth curve describes body weight changes over time or age using mathematical parameters that are capable of biological interpretation. Today, several growth curves, including Logistic, Richards, Gompertz, Von Bertalanffy, and Brody curves, are used to describe growth in animals and plants. These curves include parameters that can be considered new traits. Regression coefficients and growth parameters play an important role in decision-making for management, feeding, breeding, and genetic improvement programs; however, these growth rates vary depending on the breed, individual, and environment. Since the growth of different animals has different growth curves, the process of selecting growth curve models is necessary to determine which one works best under the study conditions. Growth curve parameters are heritable, and the shape of the growth curve can be changed and growth can be improved through selection. The parameter A in the growth curve indicates the asymptotic weight at which the animal reaches the maximum weight of its period. The parameter B is the time-scale parameter (integration constant), which describes the time for an individual to reach its maximum growth rate, characterizing the first part of growth before the point of inflection. The k coefficient is the mature growth rate that characterizes the second part of the growth in which the growth rate decreases until the individual reaches the asymptotic or mature weight (A). This study aims to investigate and determine the best function that represents the growth pattern of dairy calves from birth to weaning to use this information in managing dairy calves and commercial purposes. Methods: In this research, the weight data of 45 dairy calves were used to compare the performance of non-linear models in growth curve analysis and to identify the best growth pattern. The studied non-linear models included logistic, Richards, Gompertz, von Bertalanffy, and Brody models. The non-linear models were fitted using the non-linear least squares (NLIN) procedure of SAS software. The best model was selected using goodness of fit statistics, including the coefficient of determination (R2), root mean of square error (RMSE), and the Akaike information criterion (AIC). Results: All investigated non-linear functions were fully fitted. Based on the goodness of fit statistics, the highest value of R2 and the lowest values for AIC and RMSE criteria belonged to the logistic model, which was therefore selected as the best model for modeling the growth curve in Holstein calves. Based on this model, the asymptotic weight was estimated at 85.18 kg. The highest asymptotic weight (A) (final weight of the experiment) in this study was estimated according to the Gomperts model (85.39 kg). The highest and lowest values of parameter B belonged to logistic and Gompertz models. The highest and lowest values of parameter K were estimated using Richards and logistic models. The highest and lowest correlations between the observed data and the predicted data were obtained using the logistic (95.9%) and Richards (94.9%) non-linear functions, respectively. In a literature review, the best models differ based on the breed and geographic location where the modeling takes place. Genetic diversity within and between breeds, selection, and breeding methods and criteria, the management system, and environmental conditions influence the difference in growth patterns and the definition of the best model. Conclusion: In total, five non-linear models of the growth curve were investigated and studied in Holstein calves. According to the results, the logistic model showed the best description of the growth curve for calves and was selected as the best model. Therefore, this model can be used to determine the management strategies and the optimum weaning age in Holstein dairy calves. The absolute growth rate reflects the increase in body weight from birth to the point where growth reaches a maximum, which corresponds to the peak point, and subsequently decreases to values close to zero when the individual reaches maximum weight (asymptotic weight). Due to the short lactation period and continued growth in weaned calves, the growth curve cannot reach a plateau during weaning. Therefore, the conventional mathematical equations used may not be suitable for growth patterns and for describing weight gain in relation to pre-weaning age. Therefore, non-linear functions that describe a non-sigmoid growth curve may have the potential to better match growth data in dairy calves at weaning.

Understanding the genomics aspect of curve variable allows for the combination of genomic regions of such model-based variables from multiple measurements into a few biologically meaningful variables. With this motivation, the aim of the current study was a model-based quantitative trait loci (QTL) detection for growth curve variables in Ghezel fat-tailed sheep. We tested the following items during research: 1) Determining the best nonlinear growth models using six nonlinear equations (Von Bertalanffy, Gompertz, Logistic, Richards, Weibull and Brody) according to 24905 obtained data sets collected from the Ghezel Sheep Breeding Center, Iran, during the 1994-2013 period,2) Conducted partial genome scan to identify significant QTl controlling best growth model parameters in Ghezel sheep using three half-sib families (Family size=25-50) and 8 microsatellite markers distributed on ovine chromosome 1. In addition, QTL effects for two paternal half-sibs using two models, individual families and across families were calculated. Molecular data were analyzed using SAS and GridQTL programs. Observed results demonstrated the Brody model was the best growth model for growth data according to the lower values of RMSE, AIC and BIC and generally greater values of R2adj than other models. Thus, Brody model parameters (A, B, and C) were sub-jected to further QTL analysis. Also, our observation identified one significant QTL between the markers INRA11-CSSM004 associated with Brody model A variable (maturity) located in 123 CM in chromosome 1 (P<0. 01). Analyses using more families and advance massive genotyping tools will be useful to confirm or to reject these findings.

Background and Objectives: Strategies should be considered to increase the growth and production of sheep meat in Iran. Weight prediction of sheep helps to determine the optimal time for slaughter as well as the appropriate feeding program. Weight prediction can be investigated using mathematical models describing growth. The purpose of this study was to evaluate the performance artificial neural networks in predicting the weight of Moghani sheeps during the growth period of the animal up to one year of age. Materials and Methods: In this study, the information related to the weight characteristics of 10726 Moghani sheep from birth to one year old, which were collected during the years 1989 to 2016 in the breeding station of Moghani sheep located in Jafarabad Moghan, Ardabil province, was used. To more investigate the growth curve, a multi-layer perceptron artificial neural network accompanied by the backpropagation algorithm was used in this research. Transfer functions such as tangent axon, sigmoid axon, and hyperbolic linear tangent and training algorithms such as momentum, gradient descent, and Levenberg–Marquardt algorithm were used to design the multi-layer perceptron neural network. After fitting nonlinear models and artificial neural network, goodness-of-fit indices including coefficient of determination R2, MSE and MAE were used to select the best model. Results: The results of this study showed that in the artificial neural network, with three input variables (sex, recording season and age), the hyperbolic axon tangent function and training algorithm of gradient descent was the best performance, with the explanation coefficient, the average square squares, and the average absolute error of 0. 919, 602. 60 and 3. 50, respectively. In the artificial neural network with four input variables (sex, recording season, birth type and age), 1 hidden layer, axon stimulus function, and momentum learning algorithm, had the best performance so that the explanation coefficient, average error squares, and the an absolute error were 0. 923, 123/864 and 2864/864, respectively. In the artificial neural network with five input variables (Sex, season of recording, type of birth, age of mother at birth and age of animal), 1 hidden layer, axon hyperbolic linear tangent stimulus function, and Levenberg–Marquardt algorithm, explanation coefficient, the average square squares, and the mean of the absolute error were 0. 928, 0 and 2. 754, respectively. Conclusion: The results of this study showed that the artificial neural network model used in this research, with very high accuracy, has the ability to predict the weight of Moghani sheep during the animal's growth period up to one year of age. So that the correlation coefficients in using three, four and five input variables to predict the weight of Moghani sheep were 0. 95, 0. 96 and 0. 96, respectively.