Non-linear models were analysed to describe both the biological and commercial growth curves of the Segureña sheep, one of the most important Spanish breeds. We evaluated Brody, von Bertalanffy, Verhulst, logistic and Gompertz models, using historical data from the National Association of Segureña Sheep Breeders (ANCOS). These records were collected between 2000 and 2013, from a total of 129 610 weight observations ranging from birth to adulthood. The aim of this research was to establish the mathematical behaviour of body development throughout this breed's commercial life (birth to slaughter) and biological life (birth to adulthood); comparison between both slopes gives important information regarding the best time for slaughter, informs dietary advice according to animals' needs, permits economical predictions of productions and, by using the curve parameters as selection criteria, enables improvements in growth characteristics of the breed. Models were fitted according to the non-linear regression procedure of statistical package SPSS version19. Model parameters were estimated using the Levenberg-Marquardt algorithm. Candidate models were compared using the determinative coefficient, mean square error, number of iterations, Akaike information coefficient and biological coherence of the estimated parameters. The von Bertalanffy and logistic models were found to be best suited to the biological and commercial growth curves, respectively, for both sexes. The Brody equation was found to be unsuitable for studying the commercial growth curve. Differences between the parameters in both sexes indicate a strong impact of sexual dimorphism on growth. This can emphasize the value of the highest growth rate for females, indicating that they reach maturity earlier.Keywords: growth, models, sex, sheep, Zootechny ImplicationsNon-linear models can be an option to establish the mathematical behaviour of body development throughout the life of the Segureña sheep breed. These models require lower computational and faster convergence than other methods. Moreover, in genetic evaluation programmes with large data sets, non-linear models are more advantageous. The results showed a strong impact of sexual dimorphism on growth.

The objectives of this study were to describe growth curve of Raeini Cashmere goat applying the Gompertz growth model and genetic evaluation of growth curve-related traits including model parameters of A, B and K, inflection age (IA) and inflection weight (IW) under animal model. The data used in this study, collected in Raeini Cashmere goat breeding station from 1997 to 2009 and were included 12,831 body weights records measured at birth, weaning, 6-months of age, 9-month of age and yearling of age. The Pearson's correlation coefficient between observed and predicted body weights was 0.98, which means that Gompertz model adequately described the growth curve in Raeini Cashmere goat. The estimated value for growth curve parameters of A, B and K were 17.97, 1.97 and 0.017, respectively. The weight and age at point of inflection were 6.63 kg and 52.94 days, respectively. Direct heritability estimates for A, B, K, IA and IW were low values of 0.14, 0.10, 0.03, 0.14 and 0.14, respectively. Low estimated values for direct heritability of the studied growth curve traits in Raeini Cashmere goat indicated that direct selection for these traits may not be useful in terms of achieving genetic change. Direct genetic correlations ranged from −0.76 (K-IW) to 0.98 (A-IW). Phenotypic correlation estimates were generally lower than the direct genetic ones and ranged from −0.30 (K-IW) to 0.69 (A-B and B-IA). IA and IW had high positive phenotypic (0.86) and genetic (0.99) correlations, implying IA and IW were highly correlated in terms of phenotypic and genetic effects. The studied growth curve parameters of Raeini Cashmere goat have shown low levels of additive genetic variation.

This paper studies the genetic importance of growth curve parameters and their relevance as selection criteria in breeding programmes of Segureño sheep. Logistic and Verhulst growth functions were chosen for their best fit to BW/age in this breed; the first showed the best general fit and the second the best individual fit. Live weights of 41 330 individuals from the historical archives of the National Association of Segureña Sheep Breeders were used in the analysis. The progeny of 1464 rams and 27 048 ewes were used to study the genetic and phenotypic parameters of growth curve parameters and derived traits. Reproductive management in the population consists in controlled natural mating inside every herd, with a minimum of 15% of the females fertilized by artificial insemination with fresh semen; with the purpose being the herd genetic connections, all herd genealogies are screened with DNA markers. Estimates of growth curve parameters from birth to 80 days were obtained for each individual and each function by the non-linear regression procedure using IBM SPSS statistics (version 21) with the Levenberg-Marquart estimation method. (Co)variance components and genetic parameters were estimated by using the REML/Animal model methodology. The heritability of mature weight was estimated as 0.41 ± 0.042 and 0.38 ± 0.021 with the logistic and Verhulst models, respectively, and the heritability of other parameters ranged from 0.41 to 0.62 and 0.37 to 0.61, with the models, respectively. A negative genetic correlation between mature weight and rate of maturing was found.

Seven non-linear growth models were compared in the Andalusian turkey, an endangered native breed. To this aim, turkeys were weekly weighted until they reached 35 weeks. The goodness-of-fit and flexibility criteria of Brody, Von Bertalanffy, Verhulst, Logistic, Gompertz, Richards, and Sinusoidal growth models were evaluated to quantify their ability to describe the biological growth curve. Goodness-of-fit criteria were assessed comparing the mean squared error (MSE) and adjusted determination coefficient (Pseudo-R 2 ), while the flexibility criteria of Akaike (AIC) and Bayesian information criteria (BIC) were evaluated to quantify the explanatory and predictive ability of the models tested. Afterward, all criteria were considered in a combined index to determine the most efficient model to describe and predict growth patterns. The best-fitting model for males growth was Logistic (MSE: 250,349.87; Pseudo-R 2 : 0.97) which also reported the best explanatory and predictive properties (AIC: 18,949.25; BIC: 18,963.24), while best goodnessof-fit criteria, explanatory and predictive capacity in females were reported for the Richards model (MSE: 144,432.45; Pseudo-R 2 : 0.95; AIC: 17,529.83; BIC: 17,549.02, respectively). Von Bertalanffy and Richards models underestimated the weight at early age stages, contrary to Logistic and Verhulst models. The asymptotic weight was higher in males than in females at all evaluated models, being 11,085.37 g for Logistic and 5,706.38 g for Richards, respectively. In conclusion, a marked sexual dimorphism is evident, with females reaching maturity earlier than males. The higher inflection point in males may enable their relatively easier commercial standardisation than in turkey hens. HIGHLIGHTSLogistic was the best fitting model for males' growth and Richards for females. Females reach maturity earlier than males with higher rates of maturity. Andalusian turkey breed shows an intense sexual dimorphism.

Feral and conventional growth performances were compared using Marismeña cattle as a model. Marismeña calves are commonly reared under feral conditions in one of the most important reserves of Europe (Doñana National Park, Spain). Data recording in these natural conditions faces compromises as animals are only handled once per year. This fact has to be saved to obtain efficient estimations for the biological growth curve of cattle reared under feral conditions. On the one hand, we assessed the inference of the theoretical influence of human management on cattle growth. On the other hand, we studied the fitness of the best growth curve, in both feral and conventional systems to use the physiological meaning of the parameters obtained from their study as selection criteria related to the adaptability of potential breeding males and females. Fitting of Brody's, von Bertalanffy, Verhulst, logistic, Gompertz and Richards' models was tested as these models are the most representative ones for cattle growth. In general, Brody's and Richards' models presented the best fitting values for the biological curve. According to the biological curve parameters, males and females presented asymptotic weights of 641.71 kg and 403.55 kg, respectively. As expected, the results of the commercial growth curve severely differed from those of the biological curve. The best fitting biological curve was not representative for cattle reared under commercial conditions. The logistic model was the best fitting one for feral females, Gompertz model for feral males, and Verhulst for intensive males and females, respectively. Seasonal oscillations in feeding may be responsible for the earlier achievement of the best performance in feral cattle (7 and 10 months for males and females, respectively), while such best performances were reached at 11 months in intensive calves, what becomes relevant for management and slaughtering decision-making. The study of the biological curve in Marismeña feral breed is very illustrative as this is the first time that feral cattle's growth is approached. Knowledge on the biological growth curve parameters could be used to interpret the strong relation between feral animals and their environment. This research could infer a model to quantify the effects of human management on livestock development, as feral resources offer unique opportunities to study domestic livestock without any human influence.