J. Anim. Sci. 2006. 84:25-31
© 2006 American Society of Animal Science
Age of dam and sex of calf adjustments and genetic parameters for gestation length in Charolais cattle1
D. H. Crews, Jr.2
Agriculture and Agri-Food Canada Research Centre, Lethbridge, Alberta T1J 4B1 Canada
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Abstract
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To estimate adjustment factors and genetic parameters for gestation length (GES), AI and calving date records (n = 40,356) were extracted from the Canadian Charolais Association field database. The average time from AI to calving date was 285.2 d (SD = 4.49 d) and ranged from 274 to 296 d. Fixed effects were sex of calf, age of dam (2, 3, 4, 5 to 10,
11 yr), and gestation contemporary group (year of birth x herd of origin). Variance components were estimated using REML and 4 animal models (n = 84,332) containing from 0 to 3 random maternal effects. Model 1 (M1) contained only direct genetic effects. Model 2 (M2) was G1 plus maternal genetic effects with the direct x maternal genetic covariance constrained to zero, and model 3 (M3) was G2 without the covariance constraint. Model 4 (M4) extended G3 to include a random maternal permanent environmental effect. Direct heritability estimates were high and similar among all models (0.61 to 0.64), and maternal heritability estimates were low, ranging from 0.01 (M2) to 0.09 (M3). Likelihood ratio tests and parameter estimates suggested that M4 was the most appropriate (P < 0.05) model. With M4, phenotypic variance (18.35 d2) was partitioned into direct and maternal genetic, and maternal permanent environmental components (
= 0.64 ± 0.04,
= 0.07 ± 0.01, rd,m = 0.37 ± 0.06, and c2 = 0.03 ± 0.01, respectively). Linear contrasts were used to estimate that bull calves gestated 1.26 d longer (P < 0.02) than heifers, and adjustments to a mature equivalent (5 to 10 yr old) age of dam were 1.49 (P < 0.01), 0.56 (P < 0.01), 0.33 (P < 0.01), and 0.24 (P < 0.14) d for GES records of calves born to 2-, 3-, 4-, and
11-yr-old cows, respectively. Bivariate animal models were used to estimate genetic parameters for GES with birth and adjusted 205-d weaning weights, and postweaning gain. Direct GES was positively correlated with direct birth weight (BWT; 0.34 ± 0.04) but negatively correlated with maternal BWT (0.20 ± 0.07). Maternal GES had a low, negative genetic correlation with direct BWT (0.15 ± 0.05) but a high and positive genetic correlation with maternal BWT (0.62 ± 0.07). Generally, GES had near-zero genetic correlations with direct and maternal weaning weights. Results suggest that important genetic associations exist for GES with BWT, but genetic correlations with weaning weight and postweaning gain were less important.
Key Words: beef cattle Charolais genetic parameter gestation length
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INTRODUCTION
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Phenotypes measured in young animals, which are indicators of more valuable traits measured later in life, are useful in the design of selection programs. These indicators have further value to genetic evaluation if they have substantial genetic correlations with several economically important traits and if they are easily measured. Genetic and phenotypic variation in most growth traits measured up to 1 yr of age have been well documented (Koots et al., 1994a
); however, in some cases genetic correlations among growth traits and indicators measured at birth are not well known (Koots et al., 1994b
).
In 2004, the Canadian Charolais Association (CCA, Calgary, Canada) initiated a national cattle evaluation including gestation length (GES). Numerous studies (e.g., Cundiff et al., 1998
; MacNeil et al., 1999
; Bennett and Gregory, 2001
) have characterized breed, selection line, sex of calf, heterosis level, and age of dam effects and genetic parameters for GES in experimental, crossbred populations. These and other studies have also shown significant genetic correlations between GES and other traits. However, studies of GES in field populations are less common. Estimation of relevant adjustment factors and genetic parameters for GES in purebred field populations would also be useful. Therefore, the objectives of this study were to estimate 1) sex of calf and age of dam adjustment factors, 2) genetic parameters, including estimation of maternal effects, 3) genetic and residual correlations with growth traits, and 4) genetic trend for GES in Canadian Charolais.
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MATERIALS AND METHODS
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Data
Artificial insemination and calving date records (n = 40,356) were available from the CCA performance database to compute GES for purebred animals born between 1961 and 2004. An animal model pedigree (n = 84,332) that included a minimum of 3 ancestral generations beginning with animals with GES records was constructed from the CCA pedigree database. Using this pedigree, valid birth, weaning, and yearling weight records were then extracted. Birth weight (BWT) records were adjusted for age of dam and sex of calf prior to analysis. Similarly, weaning weight (WWT) was adjusted for age of dam, sex of calf, and to 205 d of age. Yearling weights were adjusted to 365 d of age, and 160-d postweaning gain (PWG) was defined as the nonnegative difference between 365-d yearling and 205-d WWT. Adjustment procedures for growth traits (BWT, WWT, and PWG) were according to Beef Improvement Federation guidelines (BIF, 2002
). Due to very low incidence and potential confounding, records on twins were excluded.
With respect to growth traits, valid records were retained for the adjusted phenotypes BWT (n = 43,772), WWT (n = 19,692), and PWG (n = 14,350). Because one of the objectives was to estimate the importance of maternal effects on GES, animals with records were required to have their maternal parent identified. Of the animals with GES, 29,345 had at least 1 growth trait recorded as well; however, only 9,052 animals had valid records for all 4 traits. The final data set contained 5,931 sires and 38,254 dams. Dams had from 1 to 9 progeny with GES records (average = 1.72 progeny with GES records per dam), and approximately 40% of dams had > 1 progeny with GES records.
Univariate Models for Gestation Length
The development of an initial univariate genetic model for GES involved comparison of 4 animal models that contained from 0 to 3 random maternal (co)variance components. Model 1 (M1) contained direct genetic effects only. Another model, which was M1 plus an uncorrelated random dam effect, which included both maternal genetic and permanent environmental effects, provided a significantly (P < 0.05) better fit than M1 and led to the investigation of alternative models for maternal effects (data not presented). Model 2 (M2) was also similar to M1 but additionally contained a maternal genetic component with the direct x maternal genetic covariance constrained to zero. Model 3 (M3) was equivalent to M2 without the covariance constraint. Finally, model 4 (M4) was M3 with the addition of a maternal permanent environmental effect. Components of (co)variance, genetic parameters, and their SE were estimated using the ASREML software package (Version 1.10; VSN International Ltd., Hemel Hempstead, UK), which employs an average information REML algorithm.
The 4 univariate GES models were compared on the basis of parameter SE and model log likelihood, which allowed for likelihood ratio tests. The likelihood ratio test statistic, defined as the difference between 2 times the log likelihood of a model with more parameters and that of a model with fewer parameters, was assumed distributed as
2 with df equal to the difference in numbers of parameters between the 2 models. Specific comparisons were made between M3 and M2 to test for significance of the direct x maternal covariance and between M4 and M3 to test for significance of the maternal permanent environmental effect. The complete representation of M4 in matrix notation is y = Xb + Zdud + Zmum + Zpeupe + e, with first and second moments assumed to be
with
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in which the known design matrices for fixed (X), direct (Zd) and maternal (Zm) genetic effects, and maternal permanent environmental effects (Zpe) relate observations in the vector y to unknown fixed (b) effects, direct (ud) and maternal (um) breeding values, and maternal permanent environmental deviations (upe), respectively. The vector e contains random residuals specific to animals. The matrix A consists of numerator relationships among all animals (n = 84,332), Iq is an identity matrix of order equal to the number of dams with progeny with GES records (n = 23,467), and In is an identity matrix of order equal to the number of animals with GES observations (n = 40,356). Direct genetic, maternal genetic, maternal permanent environmental, and residual variances are represented by
,
,
pe2, and
, respectively. Direct and maternal genetic, and maternal permanent environmental variances led (as proportions of phenotypic variance) to estimates of direct (
) and maternal (
) heritability, and the proportion of phenotypic variance attributed to maternal permanent environmental effects (c2), respectively. The covariance between direct and maternal genetic effects (
d,m) was used to obtain the direct x maternal genetic correlation. Reduction of the matrix representation of the full M4 to the more reduced M1, M2, and M3 models is straightforward.
The fixed effects portion of univariate GES models included gestation contemporary group (year of birth x herd of origin subclasses, n = 1,673), sex of calf, and age of dam (2, 3, 4, 510,
11 yr, rounded to the nearest year). Analyses of variance indicated that age of dam x sex of calf interactions for GES were relatively unimportant (P > 0.05). Linear contrasts were used to estimate factors required to adjust GES records to a mature age of dam and male equivalent. Both direct and maternal breeding values from the solution to the model for GES were regressed on year of birth to estimate genetic trend.
Bivariate Models for Gestation Length with Growth Traits
As described later, model M4 for GES was the basis for 3 bivariate models used to estimate genetic and residual correlations of GES with BWT, WWT, and PWG. Due to the size of the final data set and computing limitations, some model (co)variance components were held constant in order to obtain converged solutions. Specifically, single trait components for BWT, WWT, and PWG were held constant to values reported by Crews et al. (2004)
, as discussed later. Further, univariate (co)variance components were held constant to values from M4 for GES. Therefore, the bivariate models were used only to estimate genetic and residual covariances and correlations of GES with growth traits.
Because BWT, WWT, and PWG phenotypes were pre-adjusted, the fixed effects portions of models for those traits included only contemporary group, defined as year of birth x herd of origin (n = 1,964) for BWT, year of birth x herd of origin x weaning management group (n = 1,107) for WWT, and year of birth x herd of origin x yearling management group (n = 745) for PWG. The random portion of the models for BWT, WWT, and PWG were equivalent to M3, M4, and M1 as described previously for GES, respectively. As with the univariate models for GES, variance components, correlations, and associated SE for the 3 bivariate models were estimated using ASREML. Multivariate genetic and residual covariance matrices including estimates from the bivariate models were inverted and eigenvalues computed using OCTAVE, an interpreted matrix language component of the Linux (Red Hat Version 8.0, Research Triangle Park, NC) operating system.
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RESULTS AND DISCUSSION
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Table 1
reports summary statistics for GES and growth traits in this sample. It is noteworthy that once GES records were extracted and BWT added, progressively fewer animals had records for WWT and PWG. Even though CCA has adopted whole-herd reporting rules, the data for this study included animals born between 1960 and 2004, which is a much longer time period than that wherein Charolais producers were required to report growth performance on all animals. The average GES in these data (285.2 d) supports numerous previous studies and was less than 1 d different from the mean for Charolaissired calves reported by Cundiff et al. (1998)
and by Baker and Lunt (1990)
.
Univariate Genetic Models for Gestation Length
Review of the literature reveals little consistency among the genetic models used to analyze GES in beef cattle. For example, Gregory et al. (1995)
analyzed purebred and composite data using a model with direct effects only, similar to M1 as described above. A similar model was used by MacNeil et al. (1999)
. Then, MacNeil et al. (2001)
fit a model for GES including direct genetic effects and an uncorrelated random effect associated with dams that included both maternal genetic and maternal permanent environmental effects. Further, Bennett and Gregory (2001)
fit a model to GES that included both direct and maternal genetic effects with a direct x maternal covariance. The random model employed by Bennett and Gregory (2001)
was equivalent to M3 described herein.
Comparison of alternative models for GES (Table 2
) therefore focused on partitioning of direct and maternal effects. As expected, phenotypic variance for GES (18.31 to 18.37 d2) was similar across the 4 models considered in this study. Direct genetic variance (11.23 to 11.81 d2) and therefore direct heritability estimates (0.61 ± 0.02 to 0.64 ± 0.04) were also similar across all models. The present direct heritability estimates were most similar to those (0.64) of Cundiff et al. (1986)
and also those (0.59) reported by Bennett and Gregory (2001)
, but other studies have reported lower estimates (0.37 to 0.46; Gregory et al., 1995
; MacNeil et al., 2001
). Model comparisons on the basis of likelihood and SE associated with direct and maternal genetic parameters clearly suggest a significant maternal effect on GES. The models including maternal genetic effects both with a constraint on the direct x maternal covariance (M2) and without a covariance constraint (M3) provided progressively better fit (i.e., higher likelihood) to the data than the model containing only direct genetic effects (M1). It appeared, however, that M2 provided a somewhat inadequate model for maternal effects, possibly because the constraint forced direct and maternal effects to be uncorrelated. The maternal heritability estimate from M3 (0.09 ± 0.01) was similar to that reported by Bennett and Gregory (2001)
, who used a similar model to M3 for GES. The direct x maternal genetic correlation in M3, however, was larger (0.29) than the estimate of 0.18 reported by Bennett and Gregory (2001)
. The difference in likelihood between M3 and M2 (87.8), along with the direct x maternal correlation estimate and SE, supports the hypothesis that the direct x maternal correlation was different from zero (P < 0.001) and therefore M3 might be preferable to M2. A likelihood ratio test comparing M4 with M3 is equivalent to a test of fit for the maternal permanent environmental effect. The difference in likelihood (8.1) gives evidence that the maternal permanent environmental effect on GES is significantly (P < 0.01) different from zero; however, the proportion of phenotypic variance attributable to these effects seemed small (c2 = 0.03 ± 0.01). With M4, maternal heritability (0.07 ± 0.01) was similar to the estimate of 0.09 obtained with M3, but with M4 the direct x maternal genetic correlation increased in magnitude to 0.37 ± 0.06 compared with the estimate of 0.29 ± 0.06 obtained with M3. The negative direct x maternal genetic correlation of 0.18 reported by Bennett and Gregory (2001)
is supported by the present estimate from M4, which also supports the general trend of negative direct x maternal genetic correlations for traits measured prior to weaning such as BWT and WWT (Koots et al., 1994b
).
Further comparison of solutions from M1, M2, M3, and M4 revealed a high degree of similarity between direct EPD (i.e., ¹/3 breeding value = 0.5ud) obtained from the 4 models (data not presented in tabular form). For example, direct GES EPD from M4 had correlations from 0.987 (with M1 and M2) to 0.999 (with M3) with corresponding solutions from simpler models. Maternal GES EPD were also similar between M3 and M4 (r = 0.976) but were less similar between M4 and M2 (r = 0.688), which further suggests that M2 was suboptimal for these data. At least part of the discrepancy between maternal GES EPD from M2 vs. M4 is due to the low maternal heritability obtained with M2, resulting in a very small range (0.04 to 0.06 d) in maternal GES EPD compared with those from M4, which ranged from 0.90 to 1.21 d. Based on these results, M4 and M3 seem to produce nearly equal genetic evaluation results. The decision on implementation of M3 vs. M4 would therefore depend on adequate data structure for separation of maternal genetic and maternal permanent environmental effects.
Breeding values from M4 were used to investigate direct and maternal genetic trend in GES. Over the period including birth years from 1960 to 2004, regression of direct and maternal GES EPD on sequential year of birth yielded estimated coefficients of 0.035 for direct EPD and 0.002 for maternal EPD. It appears from these results that there has been essentially no significant genetic trend for direct or maternal GES in Canadian Charolais.
Sex of Calf and Age of Dam Adjustments for Gestation Length
The linear contrasts leading to adjustments for age of dam and sex of calf effects on GES are summarized in Table 3
. The objective with this approach was to estimate those adjustments required to express GES phenotypes on a mature (5 to 10 yr old) age of dam and male equivalent. Preadjustment of phenotypes for systematic fixed effects is desirable in large-scale genetic prediction because it minimally reduces the numbers of equations to be solved, and preadjustment has become common practice, at least for age of dam and sex of calf, in national beef cattle evaluation (BIF, 2002
).
In the final data set, GES records were available on 20,271 bull calves and 20,085 heifer calves. Results showed that bull calves gestated 1.26 ± 0.38 d longer than heifers, which supports several previous studies of GES. Among the more recent of these, bull calves were born from 1.58 to 2.00 d later than heifer calves in crossbred populations (Newman et al., 1993
; MacNeil and Newman, 1994
; Cundiff et al., 1998
), but these reports allude to numerous studies also showing longer GES for bulls vs. heifers. The estimate in the current study is slightly less than the range reported in the literature, which may partially be due to differences in purebred and crossbred populations. Tubman et al. (2004)
, for example, reported GES of 278.4 and 279.6 d for heifers and bulls, respectively, which is a difference (1.20 d) similar to that found in the current study. From these results, it is recommended that GES records of Charolais heifer calves be adjusted by +1.26 d to a bull calf equivalent. As is commonly known, bull calves were heavier at birth than heifers (by approximately 2.35 kg). The regression of BWT on GES suggested that BWT increased by 0.28 kg/d of gestation. The difference in GES between bull and heifer calves, therefore, seems to be insufficient to completely explain sex of calf differences in BWT.
Reports on the effects of age of dam on GES have been somewhat conflicting. Newman et al. (1993)
, for example, estimated positive coefficients for both linear and quadratic age of dam regressions on GES. Similarly, Cundiff et al. (1998)
reported that GES were shorter for calves born to cows calving at 3 yr of age, and for calves born to calves of cows
12 yr of age, compared with those from cows aged 5 to 9 yr. However, both linear and quadratic age of dam regressions on GES were not significantly different from zero in a study by Reynolds et al. (1990)
, although in their study the average cow age was 4.9 yr and most cows were
3 yr of age. Also, MacNeil and Newman (1994)
reported that the difference in calving date among specific age classes of cows (2, 3, 4, and 10+ yr) with cows aged 5 to 10 yr were not significant.
In the current study, GES records were available on calves from cows that were 2 (n = 14,106), 3 (n = 5,308), 4 (n = 4,971), 5 to 10 (n = 14,920), and
11 (n = 1,051) yr of age at calving. Results (Table 3
) suggested a somewhat linear effect of age of dam on GES, in which increasing age of dam was associated with longer GES except for calves from dams
11 yr old. Age of dam classes were specifically compared with the 5 to 10 yr old mature equivalent such that the solutions would lead directly to adjustment factors for a mature age of dam equivalent, similar to the procedure for WWT (BIF, 2002
). The largest difference (1.49 ± 0.06 d, P < 0.01) from the mature age of dam class was for GES of calves born to 2-yr-old cows. The difference in GES for calves from 3- (0.56 ± 0.07 d, P < 0.01) and 4-yr-old (0.33 ± 0.06, P < 0.01) dams (i.e., vs. those from 5- to 10-yr-old dams) were progressively smaller than the difference for calves out of 2-yr-old dams. The adjustment for GES of calves from dams
11 yr old (0.24 ± 0.13) reflected only a tendency (P < 0.14) for GES to differ between that of mature cows. The fact that this difference does not differ from zero may be partially due to the fact that far fewer GES records were available on calves from cows
11 yr of age compared with the other classes. The results of this study are in agreement with previous work wherein age of dam ranged widely from immature to aged, and older cows tended to produce calves having a longer GES.
Genetic and Residual Correlations of Gestation Length with Growth
Genetic and residual correlations of GES with BWT, WWT, and PWG were of interest, but considering the size of the system of equations to be solved, computational limitations required that estimates be derived from 3 bivariate models and that certain components of each model be constrained to constant values. Crews et al. (2004)
, using a related data set, reported genetic parameters for BWT, WWT, and PWG that were values assumed constant for the current study, which are summarized in Table 4
. Further, genetic (co)variances and residual variance estimates from M4 as previously discussed were assumed constant for GES. Therefore, only genetic and residual covariances between GES and individual growth traits will be discussed here (Table 5
).
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Table 4. Summary of variance components and genetic parameters for birth weight, adjusted 205-d weaning weight, and postweaning gain used in bivariate analyses with gestation length
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Table 5. Genetic covariances and correlations (± SE) of direct (GESd) and maternal (GESm) components of gestation length with growth traits
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The estimated genetic correlation between direct GES and direct BWT was moderately positive (0.34 ± 0.04). Gregory et al. (1995)
reported a direct genetic correlation of 0.21 ± 0.11 between BWT and GES. Bennett and Gregory (2001)
reported a direct genetic correlation of 0.36 between BWT and GES. The estimate in the current study was intermediate and comparable to these previous reports, as well as the estimate of 0.45 ± 0.08 reported by Cundiff et al. (1986)
. Direct genetic correlations of GES with WWT (0.11 ± 0.08) and PWG (0.01 ± 0.07) were lower than the correlations estimated for GES with direct BWT. Bennett and Gregory (2001)
reported direct genetic correlations of 0.16 and 0.09 for GES with 200-d weight and 168-d gain, respectively, which were also lower than the direct genetic correlation of GES with BWT in that study. Gregory et al. (1995)
also reported a near-zero direct genetic correlation between GES and 200-d weight (0.08 ± 0.13), but in that study direct GES had a genetic correlation of 0.16 ± 0.12 with postweaning ADG. Direct GES had a relatively low and negative genetic correlation with maternal BWT (0.15 ± 0.05), and the genetic correlation of direct GES with maternal WWT (0.14 ± 0.09) was similarly low and negative. From these results, it is apparent that direct GES is moderately correlated with direct and maternal BWT; however, associations of direct GES with postnatal weight and gain were less.
Genetic covariances and correlations of maternal GES with growth are also reported in Table 5
. The genetic correlation between maternal GES and direct BWT (0.20 ± 0.07) contrasted with the genetic correlation of direct GES with direct BWT. The genetic correlation between maternal GES and maternal BWT (0.62 ± 0.07) was high and positive. Bennett and Gregory (2001)
also reported a high and positive estimate of 0.41 for this parameter. Maternal GES had near-zero correlations of 0.06 ± 0.11 and 0.14 ± 0.13 with direct and maternal WWT, respectively. Similarly, the maternal genetic correlation of GES with 200-d weight in the study by Bennett and Gregory (2001)
was low (0.10). The moderate genetic correlation of 0.32 ± 0.11 estimated between maternal GES and PWG did not conform to the trend in these data for direct x maternal correlations to be negative, and no definitive explanation for this association can be given. Similar to the results noted for direct GES, maternal GES generally had stronger associations with direct and maternal BWT than with either WWT or PWG. Table 6
contains estimated residual covariances and correlations, and like the genetic correlation results, GES had a positive residual correlation with BWT, but residual associations of GES with WWT and PWG were near zero. Bennett and Gregory (2001)
also noted that GES had a higher residual correlation with BWT than with either 200-d weight or 168-d gain.
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Table 6. Residual covariances and correlations (± SE) of gestation length with birth and weaning weights, and postweaning gain
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From the (co)variances listed in Tables 4
, 5
, and 6
, the 7 x 7 genetic and 4 x 4 residual covariance matrices required for multivariate genetic evaluation can be assembled. However, because these matrices result from combining results across the 3 bivariate models, the issue of conformability was of interest. To solve the mixed model equations common to genetic evaluation, both genetic and residual covariance matrices must be positive definite. In these data, the 7 eigenvalues of the genetic and 4 eigenvalues of the residual covariance matrices, respectively, were greater than zero, indicating their suitability for use in solving the multivariate system of equations among GES, BWT, WWT, and PWG as described here.
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IMPLICATIONS
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Within the population of Canadian Charolais, maternal effects on gestation length are important but account for a lower proportion of phenotypic variance than do direct genetic effects. The complete maternal animal model provided a better fit than reduced models with fewer maternal effects, although the maternal permanent environmental effect was small. Gestation length had genetic and residual correlations of moderate to high magnitude with birth weight, but associations of both direct and maternal components of gestation length with weaning weight and postweaning gain were generally less important. Genetic and residual (co)variance estimates can be used to develop multivariate genetic evaluation programs including gestation length, birth weight, weaning weight, and postweaning gain, although the choice of model for gestation length will depend on implementation of full maternal versus more reduced models.
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Footnotes
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1 AAFC-LRC manuscript number 38705042. Funding support from the Canadian Charolais Association and the AAFC Matching Investment Initiative is gratefully acknowledged. Data extraction and editing by M. Brooks and R. E. Crews is also appreciated. 
2 Corresponding author: dcrews{at}agr.gc.ca
Received for publication July 25, 2005.
Accepted for publication September 6, 2005.
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