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ANIMAL GROWTH, PHYSIOLOGY, AND REPRODUCTION |
SAC, Sustainable Livestock Systems Group, West Mains Road, Edinburgh, EH9 3JG, Scotland, UK
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Abstract |
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 Top Abstract INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Key Words: genetic parameter • growth • growth function • random regression • sheep
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INTRODUCTION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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, in several species; Renne et al., 2003, in mice; Schinckel et al., 2004, in pigs). The fit of a growth function, and hence the variables estimated, will depend on the number and timing of available BW observations. The fastest phase of growth, observed in young animals, is often assumed to be linear, and linear regressions or ratios between BW gain and time are used to model growth. However, growth curves, due to their flexibility, are likely to be more suitable to describe even early growth. The ability to change the shape of the growth curve by breeding may be an attractive prospect for livestock producers (e.g., to increase early growth but restrict mature size, and hence maintenance requirements). To determine the genetic flexibility of the shape of growth curves, genetic parameters must be calculated for the underlying curve variables.
The effect of growth pattern on other economically important traits, such as carcass composition and meat quality, is also important and has been studied in species such as chickens (Aggrey, 2002) and pigs (Schinckel et al., 2003). In sheep, there is little information in the literature on the modeling and genetic control of growth curve variables. Results to date suggest that growth curve variables are heritable in different species and that it may be possible to change the shape of the growth curve through selection on these traits (e.g., Kachman et al., 1988; Lewis and Brotherstone, 2002).
The aims of this study were to compare the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter and to estimate heritabilities for growth curve variables and correlations between these variables.
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MATERIALS AND METHODS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Live BW data were collected on Scottish Blackface (SBF; n = 231) and Texel (n = 240) lambs, born in 2003 and 2004. Female and intact male lambs were recorded. Scottish Blackface lambs were from 11 sires, with between 2 and 49 lambs per sire (average = 21) from an average of 15 dams per sire. Texel lambs were from 10 sires, with between 14 and 37 lambs per sire (average = 24) from an average of 17 dams per sire.
Lambs were grazed on lowland paddocks in mixed-breed groups from birth to slaughter and were weighed at 2-wk intervals during this period. Lambs were finished for slaughter in 5 batches in 2003 and 6 batches in 2004. Selection for each batch depended on BW and BCS. Lambs were finished at a target BCS of 3 (on a subjective scale of 0 to 5; Russel, 1991) and target BW of 35 kg in 2003 and 32 kg in 2004 because of slower growth rates in the second year. A BCS of 3 on this scale is recommended to achieve a target fat class of 3 on the EUROP classification scale on which carcasses are graded in the UK (Quality Meat Scotland, 2004). These guidelines were followed to reflect commercial lamb finishing criteria.
Each finishing batch was of mixed breed and sex. Age at finishing ranged from 91 to 202 d old, with an average of 139 d. One half of the lambs in each finishing batch (balanced for breed and sex) were slaughtered after finishing. The other 50% were slaughtered 30 d later because they formed part of a larger experiment relating x-ray computed tomography scanning (CT) measurements taken at finishing with taste panel analysis and required withdrawal from a CT sedative before slaughter. Lambs in this half of each batch continued to be managed to attempt to achieve positive growth and were weighed regularly during this period until slaughter.
Statistical Analysis
The growth data set contained 7,559 BW records. Each lamb in the data set had between 9 and 27 BW records, with an average of 16 records per lamb. Averages and SD of BW and age at each recording event are shown in Figure 1 for each breed. Results are merged over both years, using day from the designated beginning date of lambing as the independent variable. Not all lambs within year were recorded at each event, especially at the later events, when a decreasing proportion of the lambs remained.
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and are a family of functions that are special cases of a more general model (Turner et al., 1976). The E-M modified model was described by Bünger and Herrendörfer (1994). The forms of the functions used and their characteristics are detailed in Table 1.
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). The nonlinear models were also compared, using these statistics, to polynomial regression models (of order 1 to 6), including a simple linear regression model (first order polynomial), assuming growth during this age range is rapid and almost linear. The nonlinear modified growth models and the simple linear regression model were used to produce for each animal variable estimates with direct biological interpretation and to minimize the least squares deviations directly for those. For further comparison, phenotypic correlations were calculated between estimates of each variable resulting from the different models. For the Gompertz, logistic, and Richards models, the estimated variables and their interpretation were A = estimated final BW, kg; B = maximum ADG, kg/d; C = age at maximum ADG, d; and D = (for Richards only) position of point of inflection in relation to A.
In the Richards model, the extra variable D can be used to calculate BW at the point of inflection of the curve (WPI) and stage of maturity at this point (MPI). For a few animals, the Richards model did not initially converge readily. After setting boundaries: C > 0 and D > –1.0, no problems were encountered when fitting the models for any of the animals.
For the exponential model, the variables can be described as A = estimated final BW, kg (as for the other models); BE = maximum ADG, at birth (d 0), kg/d; CE = initial (birth) BW, kg; and HL = age when 50% of A is reached (half-life), d.
The variables described for the linear model included IC = intercept and RC = slope.
Phenotypic, weighted least squares means were calculated for each breed using REML in GenStat (Lane and Payne, 1996). The approximate SE generated from SAS for each animal were used to calculate approximate variances for each growth curve variable in each model (using n = number of BW records). The reciprocal of the approximate variance was then used as a weighting factor in the least squares analysis to account for the fact that the model-fitting analyses for different animals used differing numbers of records to estimate the growth curve variables, so the variance of these estimates could not be considered uniform across animals. For the traits WPI, MPI, and HL, no SE were available because these variables were derived from the primary variables A, B, C, and D. The reported values for WPI, MPI, and HL are, therefore, unweighted least squares means and given for information only. The maximum model fitted for each trait in the REML analysis was
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where T = growth model variable, µ = mean, B = breed, Y = year, S = sex, R = rearing rank, G = dam age in years, D = birth date (number of days after the designated beginning of the lambing period that an individual lamb was born), S = sire (random), and e = residual error.
All terms in the model were fitted as fixed effects, except sire, which was fitted as a random effect. Rearing rank defined whether a lamb was reared as a single (44% of all lambs), twin (52%), or artificially (4%) to weaning. Artificially reared lambs were only included in the data set if they achieved acceptable growth rates and were at similar BW as the rest of the flock at weaning. If lambs had been fostered on to an ewe other than their natural mother, the age of the ewe that reared the lamb was fitted for dam age.
Additionally, BW as a function of age in days was modeled using random regression methodology in AS-REML, a statistical package that fits linear mixed models using REML techniques and is commonly used for the analysis of animal breeding and genetics data (Gilmour et al., 2001). A breed-specific fixed regression was used to describe the average shape of the BW curve across the growth period, and a random regression was then used to describe the deviations of each individual lamb from the average breed curve (Lewis and Brotherstone, 2002). Polynomials of order 2 to 6 were tested for the fixed (breed) and random (animal) regressions to assess their fit to the data. For each model, the fixed effects and covariates shown in the model above were included, as well as the fixed and random polynomials to describe BW as a function of age. Therefore, the maximum model fitted was
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where T = growth model variable, µ = mean, B = breed, Y = year, S = sex, R = rearing rank, G = dam age in years, D = birth date (number of days after the designated beginning of the lambing period that an individual lamb was born), ß1 to ß12 = regression coefficients, A = lamb age in days, L = animal (random), and e = residual error.
This genetic analysis used data from a pedigree file containing 1,064 records (Texel = 506; SBF = 558), including the sires, dams, and paternal grandparents of all lambs. Information was also included on maternal grandparents for 190 Texel and 83 SBF lambs, paternal great-grandparents for 103 Texel and 53 SBF lambs, and maternal great-grandparents of 66 Texel and 76 SBF lambs.
Log-likelihood values produced by ASREML (and AIC values calculated from these outputs) were used as a guide to compare the fit of each random model, and F- and t-test values to compare the fit of the fixed models. From the best model, animal solutions for each polynomial variable were estimated. Growth rate at a given age can be calculated by taking the first derivative (dy/dx) of the polynomial describing BW as a function of age. Therefore, by calculating the first derivative from the random animal solutions for each animal at a given age, the difference in growth rate of that animal from the breed mean can be calculated. In this way, animal solutions for growth rate (GR) at every 10-d interval from birth to 240 d were calculated (GR10d–GR240d), as well as growth rate at finishing (GRfin) for each animal.
Growth rate for each animal (adjusted for fixed effects and covariates) was then calculated by summing the first derivative from the average breed polynomial and the first derivative from the random animal solutions. Subsequently, t-tests were performed on these data to test for significant differences between breeds for GR60d, GR140d, and GRfin. Day 60 and 140 were chosen as they are close to the ages at which measurements are commonly taken in UK sheep recording schemes (around midlactation and postweaning).
Genetic Analyses.
Genetic analyses of growth model traits were performed in ASREML (Gilmour et al., 2001), using the pedigree file described above. Heritabilities (h2) were estimated, within breed, for the variables from each growth model, as well as for growth rate at commercially relevant ages (GR60d, GR140d, and GRfin), fitting the same fixed model as was used for the weighted, least squares analysis, but fitting animal as a random effect in place of sire. In cases where the full model would not converge in the genetic analysis, some terms were omitted from the model. This is detailed in the Results section. The limited size of the data set and the shallow and incomplete pedigree information available meant that further random effects, such as permanent environmental effects and maternal genetic effects, could not be successfully tested in this analysis. A small number of SBF lambs (3) were artificially reared; therefore, these lambs and this level were removed from rearing rank for the within-breed genetic analyses. This level was retained for the Texel analyses because more lambs of this breed were artificially reared (15 lambs in total, represented in each sex x year combination).
Genetic (rg) and phenotypic (rp) correlations were then estimated separately for each breed, between variables within each nonlinear model and between GR at selected time points (GR60d, GR140d, or GRfin) to evaluate the independence of these variables and their potential for changing the shape of the growth curve.
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RESULTS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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0.979). The Richards model had the greatest average R2 and least log-likelihood value in each breed, suggesting the best fit overall (Table 2). Ranking of the models according their average R2 or log-likelihood value gives the following order: R-M > G-M > L-M > E-M. However, when AIC values were used to compare models, taking account of the number of variables estimated in each function, the Gompertz model had the least value, suggesting that this model is best for predicting growth with the minimum number of parameters. Ranking of the models according their average AIC value gives the following order: G-M > R-M > L-M > E-M. Using each statistical method to compare models, the Richards and Gompertz models produced the best fit and were not significantly different from each other (P > 0.05). The Gompertz model had similar estimates of WPI and MPI to these estimates from the Richards model (Table 3), indicating that greatest BW gains were reached when approximately 0.36 to 0.43 of the estimated mature BW was reached. The fixed value of 0.5 for the logistic model seems less suitable.
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), suggesting an improved fit. The polynomial models of order greater than 1 do not provide biologically meaningful growth variables like the modified nonlinear growth curves. Higher order polynomials may produce problems with multico-linearity and do not give insight into the underlying biological processes involved in growth. However, these models were studied further using the random regression technique described above to produce estimates for growth rate at different ages, the results of which are shown below.
The estimates for A differed depending on the nonlinear modified growth function used, with the logistic model giving the least estimates in each breed and the exponential model the greatest (Table 3). However, the 3 models providing the best fit (logistic, Richards, and Gompertz) provided similar weighted least squares estimates for final BW (A): approximately 40 kg in Texel and 35 kg in SBF. The estimates of B (maximum ADG) also differed little between the logistic, Gompertz, and Richards models. As expected, the logistic model estimated greater values for C (age when maximum ADG achieved) than Gompertz or Richards. These models predicted that both breeds reached their maximum ADG at a similar age of about 4 to 5 wk of age. The linear regression greatly overestimated the observed birth BW (Texel: 4.5 kg, SBF: 3.7 kg), indicating that growth even in this early period was not linear. The average growth rate (=slope of the regression, RC) estimated by the linear model was less than the maximum growth rates (B) estimated from the nonlinear models (L-M, G-M, and R-M), as expected, and much less than the inflated values of BE from the exponential model. However, the exponential model provides an estimate for the age when 50% of the final BW (A) is reached (HL), which was not significantly different between breeds.
For 35 lambs, the Richards model was bound by the limitations set (C > 0 and D > –1.0). Observing the individual growth curve graphs and variables for these lambs (produced by NLIN), the Richards model was estimating the point of inflection to be very close to zero, and the shape of the curve resembled that of the exponential curve. Without the boundaries imposed on C, the position of the point of inflection for these animals was estimated to be before d 0 (i.e., intrauterine). This suggests that the Richards function may be too flexible and may sometimes estimate nonbiological or nonsensical values, which was why the boundaries were imposed. These 35 lambs had an average of 16 BW records each. They did not appear to display atypical growth patterns and had residual variances similar to the others so were not excluded from the analyses. However, SE produced by SAS, when the Richards model was fitted to these lambs that were bound by the limitations on C, were estimated at zero for C and <0.1 for D (less than for all other lambs). Therefore, the weightings used in the least squares analyses for Richards variables C and D were affected for these records, resulting in their exclusion in the analysis of C (weighting unavailable = reciprocal of zero) and unusually large weightings in the analysis of D.
Breed Comparison
Weighted least squares means (generated from the sire model in GenStat) for A (end or mature BW) were greater (P < 0.05) for Texel lambs than SBF lambs using all models in which this variable was estimated (Table 3). Estimates of B (maximum ADG) were also greater in the Texel lambs, but this difference was only significant for the Richards model. Animals reached maximum ADG very early in their life (4 to 5 wk of age), and the raw data show that there was a tendency for Texel lambs to reach this point several days earlier, although breed differences were not significant (P > 0.05). When MPI was fixed (logistic and Gompertz), the BW at which this occurred (WPI) was greater in the Texel lambs. However, when MPI was allowed to vary, in the Richards model, breed differences disappeared. Using the exponential model, the Texel lambs were found to have significantly greater birth BW (CE) than the SBF lambs and greater initial ADG (BE). Using linear regression to model growth, the intercept, which essentially estimates BW at birth, did not differ significantly between Texel and SBF lambs, but the regression slope was greater for the Texel lambs.
In summary, although all nonlinear models fitted the growth of the lambs of both breeds reasonably well, the best fit was reached using the Richards and Gompertz models. However, for a few animals the Richards model predicts values of C and D beyond logical biological limits, requiring boundaries to be imposed. Figure 2 (panels A and B) shows all raw BW for Texel and SBF, respectively, plotted against age. The line on each graph shows values estimated using the average variables resulting from fitting the Richards model with these restrictions on C and D (raw means for variables, as shown in Table 3). Good agreement can be observed between the BW data and the average curve plotted from estimated variables. Figure 2 (panel C) shows the average BW gain in each breed plotted against age, as estimated from the average Richards model variables from the raw data. The breed differences in maximum ADG and age at maximum ADG (although the latter was not significant, P = 0.26), shown in Table 3, can be observed from this figure.
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. The greatest correlations for each variable were between the estimates from the logistic and Gompertz models (>0.97 for each variable). Correlations between estimates from the Richards models and those from the logistic or Gompertz models were less (P < 0.02) for A and B (0.87 to 0.92) and only moderate in size for C and WPI (0.32 to 0.48). Estimates of HL (age when 50% of final BW is reached) from the exponential model were highly correlated with estimates of C from the logistic and Gompertz models (Table 4), although the correlation between this trait and the Richards estimate of C was smaller (0.38).
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shows the estimated BW (panel A) and growth rates (Figure 3, panel B) of the average Texel and SBF lambs, calculated every 5 d from birth to 240 d using the solutions from these random regression analyses. Breed differences were identified between growth rates (predicted using average breed and animal solutions) from random regression (Figure 3, panel B). Least squares means showed that Texel lambs had greater (P < 0.03) growth rates on average than SBF lambs at 60 d (0.27 vs. 0.25 kg/d), 140 d (0.09 vs. 0.07 kg/d), and at finishing (0.12 vs. 0.07 kg/d).
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). A similar shape to the growth curve can be observed from the raw BW data in the scatter plots in Figure 2 (panels A and B). This is likely to reflect the fact that only lambs with poorer growth rates and lower final finishing BW were recorded to these ages (from the later finishing batches). This will affect how the polynomial models are fitted to a greater extent than the other nonlinear growth models, which are constrained to positive growth.
Genetic Analyses
Heritabilities (h2) and genetic (rg) and phenotypic (rp) correlations for the variables estimated within each model are presented in Table 5. For some analyses the full model would not converge. If no convergence occurred, parameter estimates could not be obtained. In some other cases, convergence could only be achieved with a reduced model.
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In Texel lambs, estimates of heritabilities for variables A, B, and C using the Richards model were again moderate to high. However, for SBF lambs, heritabilities were smaller than those predicted from the logistic or Gompertz models and genetic parameters for C could not be obtained. The variable D was moderately heritable in Texel but showed little heritability in SBF. Genetic correlations between A and B and between B and C (available for Texel only) showed similar trends as in the logistic and Gompertz models. However, rg between A and C could not be obtained for SBF and for Texel was positive and moderate in size, with a negative rp, as opposed to the negative estimates of rg found between these traits using the other models. This fact, along with the large SE for the estimate of rg, questions the reliability of this correlation. The variable D showed a strong negative rg with B in Texel (with a very small rp) but a strong positive rg with B in SBF (with a large SE and a moderate positive rp). Correlations of D with other variables could not be obtained for SBF. In Texel, there was little genetic association between A and D, despite a moderate negative rp, and correlations of C with D were high and positive.
Using the exponential model, similar heritability estimates were achieved for A as with the Richards model. The variable BE showed little heritability in SBF but moderate levels in Texel, as did HL. The variable CE showed a moderate to high heritability in SBF lambs but little heritability in Texel when a sire model was used. A negative rg was found between A and BE for Texel, but this value was very high and positive for SBF, despite a negative rp. Similarly, a high negative rg was found between HL and BE for Texel, and a positive rg for SBF. However, the extremely large SE for rg makes the SBF estimate unreliable, as is the estimate for rg between A and CE.
From the linear regression modeling, the only variable to show a significant heritability was IC in Texel lambs (0.807, SE = 0.227). The variable IC in SBF lambs had a heritability estimate of 0.08 with a SE of 0.14. Heritability estimates for RC were 0.17 and 0.18 in Texels and SBF respectively, with SE of 0.15 and 0.19, making these estimates not significantly different from 0. Correlations would not converge between intercept and slope in either breed.
The estimates of heritability for the growth rate calculations resulting from the random regression model (Table 6) differed considerably between breeds. The variable GR60d showed a low heritability in Texel, with moderate to high estimates for GR140d and GRfin. However, a moderate heritability was estimated for GR60d in SBF but very low heritabilities for GR140d and GRfin. Correlations (rp and especially rg) were very high and positive between GR140d and GRfin. Genetic correlations between GR60d and GRfin were negative in each breed (with large SE). This trend was also seen between GR60d and GR140d in SBF. In Texel the genetic correlation between these traits was estimated as unity; however, the large SE suggests that this estimate is unreliable.
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DISCUSSION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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; McManus et al., 2003; Schinckel et al., 2004). In general, the goodness-of-fit of these models for growth data for various species tended to be similar to, or poorer than, that of the Richards or Gompertz models, and correlations between variables estimated by the different models were high.
In the current study, the NLIN procedure was used in SAS to fit each nonlinear growth function to the data from each lamb independently, as has been used in past growth studies (e.g., Renne et al., 2003). The resulting variables were then adjusted for fixed effects and the random effect of sire using REML in GenStat to produce least squares means. This method allowed plots for individual lambs to be observed to check for unusual growth patterns or incorrect fitting of the models. In recent years an alternative method, using mixed model nonlinear analysis (such as the NLMIXED procedure in SAS), has been proposed for modeling serial BW data, which may be less labor-intensive and may better model the variance-covariance structure of growth data and reduce the residual variance compared with traditional methods such as NLIN (Schinckel et al., 2004; Wang and Zuidhof, 2004). This method has been used in several growth studies published in recent years (e.g., Schinckel et al., 2003, 2004; Wang and Zuidhof, 2004) and should be considered for future analyses to estimate growth variables for sheep populations, given the fact that the current results suggest that selection on growth variables may be possible.
All models tested in the current study fitted the growth data for the Texel and SBF lambs well, according to the R2 obtained. However, all models appeared to underestimate mature size, with the least estimates resulting from the logistic model (as was found by Renne et al., 2003, in mice, and by McManus et al., 2003, in Brazilian sheep). In a previous study using data from our SAC flocks from 2003, the mature BW for Texel and SBF (averaging male and female estimates) were 83.1 and 71.5 kg, respectively (N. R. Lambe, E. A. Navajas, K. A. McLean, G. Simm, and L. Bünger, SAC, Edinburgh, UK, unpublished data). The underestimations observed here may result from the fact that only one part of the growth curve is being observed and there are no measurements in the data set reflecting growth after 8 mo of age. An earlier study on female mice, with BW up to full maturity and throughout their lifetime, showed clearly that if growth curves were based on data from early growth periods they underestimated considerably the mature BW (Bünger and Schönfelder, 1984). This may also reflect the fit of the model to the data. Alternative growth functions, which were not tested here, such as the generalized Michaelis-Menten equation (López et al., 2000) that allows for asymmetric growth rate on either side of the point of infection, may have produced more realistic estimates of mature BW. However, in the study by López et al. (2000), the rankings of animals in terms of growth variables computed using the generalized Michealis-Menten and the Richards and Gompertz functions, were similar, as were the goodness-of-fit estimates of these models. Therefore, if the aim is to select animals within a population, final BW estimates from any of these models would be of value. The estimated A values in this study should not be considered, therefore, as predictors for true mature BW but as a final BW value for slaughter lambs.
The logistic model estimated greater values for C and for WPI than the Gompertz or Richards models. These differences are largely due to the fact that the logistic model fixes MPI at 0.5, whereas the Gompertz model fixes this value at 0.37 and the Richards model allows this value to vary (Renne et al., 2003). The average MPI values estimated for the Richards model were closer to the Gompertz value of 0.37. This also explains the lower correlations of C estimated by the Richards model and those estimated by the other models.
The Richards and Gompertz models fitted the data best in each breed. However, only one population of sheep of each breed has been modeled here, and all of these animals (of both breeds) were managed as one flock. Therefore, it cannot be assumed that these models would produce the best fit in other sheep populations. In a study of Bergamasca sheep in Brazil (McManus et al., 2003), growth was modeled using the Brody, Richards, and logistic functions and the logistic function was considered as the best fit, although coefficients of determination were not significantly different. The Richards model is more flexible than some alternative models due to the fact that the position of the point of inflection is allowed to vary relative to A (determined by D). Therefore, a larger number of biologically relevant variables can be estimated to describe the shape of the growth curve. However, the lower AIC values estimated for the Gompertz model suggest that the extra variable estimated in the Richards model is not effectively improving the fit to the data over the Gompertz function. The problems encountered for a subsection of the lambs, in which estimates of C and D in the Richards were constrained by set boundaries to allow biologically relevant values, indicate that the increased flexibility of the Richards model may occasionally produce illogical variable estimates. These factors suggest that of the nonlinear growth models considered here, the Gompertz model provides the best fit for describing BW data during the growth of Texel and SBF lambs from birth to slaughter. This would imply that this model would be best for future analyses of growth curve variables in the populations studied here.
By fitting a random regression polynomial model, the opportunity existed to estimate growth rate at many points along the growth curve and to choose the most commercially relevant time points to study further. This polynomial model also allowed more flexibility in the shape of the growth curves of individual animals than some of the other nonlinear models because no assumptions are made about the shape of the curve relative to time (Lewis and Brotherstone, 2002). The average growth curve for each breed obtained from the solutions of this analysis does not reflect the sigmoid-shaped growth curve expected from early animal growth. The accelerating phase will largely occur during gestation, so it is not expected to be observed clearly in postnatal growth. However, the downturn observed in the BW graphs after approximately d 180, following the deceleration phase of the growth curve, and the negative growth rate shown are not expected and are likely to reflect the fact that only lambs with poorer growth rates and lower final finishing BW were recorded to these ages (from the later finishing batches). Ideally, all lambs in the data set would have been recorded to the same age, with the same number of records and frequency of weighing, but this was constrained by the objectives of the larger study. The results here may be affected by the fact that the faster-growing animals (or those which fattened to target BCS more quickly) had fewer BW measurements with which to estimate growth curve variables. Lambs with more BW measurements had reduced average R2 values for all models studied. This could be influenced by the fact that slower-growing animals are more likely to be exposed to deteriorating pasture quality and climatic conditions later in the season, which will affect growth rate and may cause periods of reduced or even negative growth. These factors may affect the accuracy of estimated growth curve variables, which was accounted for using the weighted least squares analysis but may also be influencing other results, such as the estimated correlations. Measurement taken on the second half of each finishing batch, whilst being retained for 30 d following finishing, may also have altered the shape of the average estimated growth curves. At finishing all lambs were CT scanned, which involves a period of several hours of food withdrawal, sedation, and a large amount of handling. This is likely to have a negative impact on subsequent growth rate, at least in the immediate aftermath. Although all attempts were made to maintain good rates of positive growth throughout the trial, we cannot assume that growth was not limited by environmental factors, such as the stress of handling, climatic conditions, and nutrition. These considerations may further support modeling data sets such as this using nonlinear models like those tested, which are constrained to positive growth.
The large SE associated with many of the estimated genetic parameters imply that these results should be used with caution and should be confirmed using larger data sets when possible. However, some interesting trends have emerged from these initial analyses. Many of the heritabilities estimated here for modified growth curve variables A, B, and C are of comparable magnitude (moderate to high) as similar parameters estimated in previous studies in other sheep breeds (Lewis et al., 2002) and other species (e.g., mice: Kachman et al., 1988; chickens: Grossman and Bohren, 1985). Although SE were fairly large (mainly due to the relatively small data set and shallow pedigree structure), the moderate to large heritability estimates for growth curve variables A, B, and C in Texel lambs suggest that it would be possible to select for these traits estimated using any of the relevant growth curve models. The moderate heritability for D in the Richards model and BE and HL in the exponential model for Texel also indicates that selection on these variables would be possible. However, in SBF lambs, only variables estimated using the logistic or Gompertz models have heritabilities high enough to suggest that selection on model variables would be successful. The lower heritabilities for growth curve variables estimated for SBF compared with Texel lambs could be due to biological or genetic differences between the breeds, but may also be caused by the less complete pedigree structure available for SBF lambs in the current data set. In Texel lambs, the genetic correlations between the growth curve variables within model, although large in most cases, were not greater than 0.9 or less than –0.8, which suggests that it would be possible to decouple these relationships and select for a change in 1 variable and also keep another stable or select in the opposite direction, so changing the shape of the growth curve. The greater genetic correlations in the SBF lambs (>0.9 or <–0.9 in many cases) imply that selecting for growth curve variables independently may be more difficult in this breed.
Due to the limited size of the data set and pedigree file, a simple animal random regression model was run using ASREML. In the random regression model used by Lewis and Brotherstone (2002) to model Suffolk lamb growth from a larger data set, a permanent environmental effect (between repeat measurements of an individual), and a dam effect (to account for prenatal environment) were also fitted. The fact that these effects were not accounted for in the current study may be inflating the additive genetic variance and so the heritability estimates obtained. Nonetheless, some clear effects can be observed from the random regression results.
In Texel lambs, growth rate (estimated by random regression models) at 20 wk of age and at finishing had moderate to high heritabilities and appeared to be under the same genetic control (rg = 1). This implies that lambs could be selected for high or low growth rate after weaning, and this will result in lambs that are genetically faster or slower growing, respectively, when they reach finishing (target BW and condition). Scottish Blackface lambs also showed high correlations between these traits but low heritabilities. Growth rate measured at midlactation (GR60d) differed in heritability to growth rate measured at finishing and showed only moderate genetic correlations with this trait, suggesting that early growth rate is a different genetic trait to later growth rate. Lewis and Brotherstone (2002) found that the same was true for BW in early and later growth of Suffolk lambs. Although large SE limit the accuracy of the genetic correlation estimates between growth rate at 60 d of age and finishing, the results suggest a negative relationship between lamb growth rates midway through rearing and at finishing. This implies that lambs with a genetically greater growth rate midrearing have a steeper slope to their growth rate graph, so growth rate declines more quickly, causing a lower genetic growth rate at finishing. The negative genetic correlation estimates were moderate, which would allow scope to change these relationships, so the shape of the growth curve, through selective breeding.
Having estimated initial genetic parameters for the most informative growth curve variables and for growth rate at commercially important stages of development in 2 economically important UK breeds, genetic relationships can now be examined between these traits and other important production traits, such as carcass composition and meat quality. In this way, optimum growth rates and growth curve shapes can be investigated in future analyses.
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2 Corresponding author: Nicola.Lambe{at}sac.ac.uk
Received for publication January 23, 2006. Accepted for publication May 26, 2006.
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