A genetic investigation of various growth models to describe growth of lambs of two contrasting breeds1

Abstract

This study compared the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter. Live BW records (n = 7559) from 240 Texel and 231 Scottish Blackface (SBF) lambs weighed at 2-wk intervals were modeled. Biologically relevant variables were estimated for each lamb from modified versions of the logistic, Gompertz, Richards, and exponential models, and from linear regression. In both breeds, all nonlinear models fitted the data well, with an average coefficient of determination (R2) of > 0.98. The linear model had a lower average R2 than any of the nonlinear models (< 0.94). The variables used to describe the best 3 models (logistic, Gompertz, and Richards) included estimated final BW (A); maximum ADG (B); age at maximum ADG (C); position of point of inflection in relation to A (D, for Richards only). The Richards and Gompertz models provided the best fit (average R2 = 0.986 to 0.989) in both breeds. Richards estimated an extra variable, allowing increased flexibility in describing individual growth patterns, but the Akaike's information criteria value (which weighs log-likelihood by number of parameters estimated) was similar to that of the Gompertz model. Variables A, B, C, and D were moderately to highly heritable in Texel lambs (h2 = 0.33 to 0.87), and genetic correlations between variables within-model ranged from -0.80 to 0.89, suggesting some flexibility to change the shape of the growth curve when selecting for different variables. In SBF lambs, only variables from the logistic and Gompertz models had moderate heritabilities (0.17 to 0.56), but with high genetic correlations between variables within each model (< -0.88 or > 0.92). Selection on growth variables seems promising (in Texel more than SBF), but high genetic correlations between variables may restrict the possibilities to change the growth curve shape. A random regression model was also fitted to the data to allow predictions of growth rates at relevant time points. Heritabilities for growth rates differed markedly at various stages of growth and between the 2 breeds (Texel: 0.14 to 0.74; SBF: 0.07 to 0.34), with negative correlations between growth rate at 60 d of age and growth rate at finishing. Following these results, future studies should investigate genetic relationships between relevant growth curve variables and other important production traits, such as carcass composition and meat quality.

Genetic evaluation of partial growth trajectory of Santa Inês breed using random regression models

“…Regarded to genetic correlations in this study, the results confirm what has been observed by other authors (Fischer et al, 2004(Fischer et al, , 2006Lambe et al;Sarmento et al, in press), that genetic correlations among weights at subsequent ages, close together, are high, tending to unity and the weights at younger ages are not under the same genetic control than those taken in later life.…”

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

“…Higher R 2 values (0.98 to 0.99) and MSE (2.1 to 3.2) were reported for Morkaraman and Awassi lambs (Topal et al, 2004). In the Scottish Blackface and Texel lambs, the value of R 2 ranged from 0.938 to 0.994 and AIC from 45.95 to 83.61 (Lambe et al, 2006).…”

“…of monthly weight from birth to 180 days of age, the level of significance of fixed effects, the coefficient of determination (R 2 ) and the coefficient of variation (CV) indicated by the proc GLM Fixed effect BW (889) W30 (864) W60 (831) W90 (778) W120 (728) W150 (594) W180 (590) Season of birth ** ** * ** ** ns ns Dry season (2420) 1.71 6 0.02 (390) The goodness of fit was assessed by using the higher R 2 , the lower MSE and AIC values (Brown et al, 1976;Akbas et al, 1999;Topal et al, 2004;Lambe et al, 2006). Even though the selected models provide a view of the predicted weight at fixed age, the parameters A, B and k of the significant effect of season of birth, sex of the lamb, the parity of dam, the type of birth and the year of birth on the observed weight, have been calculated separately (Matlab R , 2006) simulating specific slop of the selected growth curve.…”

“…In the Bergamasca sheep in Brazil (McManus et al, 2003), among the fitted growth models (Brody, Richards, and Logistic), the Logistic model showed the goodness of fit. Lambe et al (2006) selected the Richards and Gompertz models for their accuracy of fit among four competing models (Gompertz, logistic, Richards and the exponential model). The Gompertz and Von Bertalanffy models showed the best fit in Morkaraman and Awassi lambs (Topal et al, 2004); Gompertz model in Suffolk sheep .…”

“…However, the advantage of growth models such as Logistic and Gompertz (Renne et al, 2003;Lambe et al, 2006), Von Bertalanffy (Topal et al, 2004) and Brody model (Bathaei and Leroy, 1998), which give an explanation of what is biologically occurring during the growth phase of an animal, and their importance on breeding program (Varona et al, 1997;Lewis and Brotherstone, 2002) were unknown in WAD sheep. Therefore, model selection to predict typical growth in livestock industry, became a daunting task, given the broad range of criteria for goodness of fit, as the Akaike's Information Criteria (AIC) (Akaike, 1974), the coefficient of determination (R 2 ), the mean squares errors (MSE), the loglikelihood (lnL) values, and the least average prediction error (APE) (Brown et al, 1976;Goonewardene et al, 1981;Beltran et al, 1992;Lambe et al, 2006).…”