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1 Sustainable Livestock Systems Group, Scottish Agricultural College, Bush Estate, Penicuik, Midlothian, EH26 0PH, UK
2 School of Biological Sciences, University of Edinburgh, Ashworth Laboratories, King’s Buildings, Edinburgh, EH9 3JT, UK
Corresponding author: Eileen Wall; e-mail: Eileen.Wall{at}sac.ac.uk.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Key Words: type trait • body condition score • random regression
Abbreviation key: ANG = angularity, BD = body depth, CubS = cubic spline, CW = chest width, LegP = Legendre polynomial, LogL = Log likelihood, RR = random regression, STAT = stature.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Many dairy cattle traits have repeated measurements across time with varying correlations between records for an animal. Examples include milk production, weight information, BCS, and linear type information. Studies have analyzed these data in a number of ways, such as curve fitting (Ali and Schaeffer, 1987; Wilmink, 1987), multivariate analyses (Berry et al., 2003), and random regression (RR) analyses (Olori et al., 1999). Random regression has been used as a method for analyzing repeated data on individuals over time, from lactation records to growth (Schaeffer, 2004). Random regression can be thought of as a covariance function providing multidimensional covariance matrices across a continuous scale (e.g., DIM). It is usual for a low-order polynomial regression curve (e.g., Legendre polynomial, LegP) to be fitted to the data. Traits that have been shown to vary over a lactation, after modeling with RR using polynomial functions, include milk (e.g., Jaffrezic et al., 2002), liveweight (e.g., Meyer, 1998), BCS (e.g., Jones et al., 1999), and type (e.g., Uribe et al., 2000).
Other functions used in RR to model traits over time include spline functions (e.g., cubic splines; CubS) for traits such as lactation yield (White et al., 1999; Druet et al., 2003), weight (Huisman et al., 2002), leptin concentrations (Liefers et al., 2003), and fertility (Roche, 2002). A CubS function fits a smoothing curve across cubic polynomials that have been fitted between adjacent points (knots) such that the smoothing curve and its first and second derivatives are continuous across the range of data (Green and Silverman, 1994).
Previous analyses have shown that single-point linear type measures are correlated to production (Brotherstone et al., 1990; Heuer et al., 1999), health (DeGroot et al., 2002), fertility (Pryce et al., 2001), and longevity (Boettcher et al., 1997; Caraviello et al., 2004). It has also been shown that changes in BCS are antagonistically correlated with fertility, with losses in BCS resulting in increased days open (López-Gatius et al., 2003). Studies have also shown that the magnitude of the correlation between traits and BCS changes across lactation (Berry et al., 2003).
To best understand the relationship of body traits with liveweight, mature body weight, and functional traits, it is important to find the most appropriate model of analysis for each trait, especially if there is a difference between sires and traits in how they change over time. Once modeled, the traits can then be combined or used as indicators for traits that vary with time such as maturity and liveweight. For example, Coffey et al. (2003) developed a phenotypic prediction equation for liveweight from linear type records. In this instance, a fixed formula, based on step-wise regression, was used to predict BW from body depth (BD), chest width (CW), stature (STAT), and angularity (ANG) that did not account for stage of lactation but only the age at inspection due to the block calving pattern present in the prediction data set.
The aim of this study was to investigate change in body traits over the course of the first lactation using RR, fitting LegP and CubS functions. Estimated daily sire solutions from the most appropriate model were plotted for illustrative purposes. The daily sire solutions for each of these traits were then used to predict differences in liveweight of sires’ daughters across first lactation.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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A prior analysis examined the influence of adding additional residual error classes (1 to 15) to account for the variation in the recording of type traits across lactation. The borders for the residual error classes were based on work of Coffey et al. (2002). The optimal number of error classes for this data was 9, based on a log likelihood (LogL) ratio test.
Genetic and environmental variance components were estimated with RR sire models fitted with LegP and CubS functions using ASREML (Gilmour et al., 2002). The order for the fixed LegP for each trait was studied by varying the order of fit of the curve and examining the significance (t-test) of the curve parameter solutions. The order for the random LegP for each trait was tested for significance using LogL ratio testing. The RR model fitted with a LegP was:
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where Yijk = type trait record (BCS, BD, CW, STAT, ANG); hysi = fixed effect of ith herd-by-year-by-season (3 seasons per year) of type classification visit; monthj = fixed effect of the jth month of calving; ß1 and ß2 = linear and quadratic regression coefficients of dependent variable (Y) on age effect; Xage = continuous variable representing age of animal (in months) at calving; dim = DIM at type classification; 
m = fixed regression coefficients; 
km = random regression coefficients for sire k; eijk = residual random error term; m = order of the polynomial; and Pm(dim) = mth LegP evaluated at dim.
Random regression models using CubS functions, as defined by White et al. (1999), were fitted with 9 knot points that coincided with the residual error class boundaries described in Table 1
with the following model:
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where model is previously defined, and b0 and b1 Xdim = overall linear regression fitting a slope and intercept for the overall smoothing spline; bk0 and bk1 Xdim = random deviations from overall regression (slope and intercept) for sire k; and bl zl XDIM and bkl zl XDIM = mean spline deviation and deviation from the mean spline for sire k at knot l (where q is the total number of knots).
Models were compared based on log likelihoods, residual variance estimates, and the difference between actual and predicted values for each of the traits analyzed. The total phenotypic variance of the trait explained by each model, calculated from the square of the correlation between actual and predicted type trait values, was also calculated in an effort to determine the best function to use within a RR model. The Akaike information criterion and Schwarz Bayesian information criterion are also reported although direct comparison between these values for the CubS and LegP function is not valid as the models have different fixed effects.
A subset of data was selected and each record was defined as an early (DIM 10 to 25), mid (DIM 130 to 150), or late (DIM 255 to 290) record based on time of type classification. The 3 time points for each type trait were analyzed using a multivariate linear model. Variance and covariance components between each time point for individual traits were estimated by REML using ASREML (Gilmour et al., 2002).
Individual daily sire solutions for all traits, as estimated by the RR model with the most appropriate function, were calculated. The daily solutions showed how the daughters of a sire deviated from the fixed overall trend curve. Individual daily sire solutions for BCS as estimated from both functions were correlated at specific points across lactation. The formula to predict differences between bulls for daughter liveweight across time was adapted from the liveweight prediction of Coffey et al. (2003), which was derived using data from the Langhill experimental herd. The equation of Coffey et al. (2003) included terms to account for the fixed effect of year of inspection, diet and age of inspection. However, for the purpose of this study, these fixed terms were removed from the equation, as the daily body type trait solutions from the RR models will have adjusted for some of these effects by fitting a herd-year-season effect. We assume that the daughters of a bull were distributed randomly across a range of diets and recorded at a range of ages thus averaging out these effects. The constant term (intercept) from the prediction equation was also removed as this study was interested in examining the differences between sires and traits in how animals changed across lactation rather than predicting solely phenotypic daily liveweight. The individual sire solutions were used to estimate the difference of each sire from the national liveweight curve over time using the following formula (Coffey et al., 2003).
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The validity of assuming a constant liveweight prediction formula across lactation was examined by modeling liveweight as a function of the above type traits, month of lactation, and an interaction between month of lactation and the type traits.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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). A description of the traits studied in the analysis is given in Table 2. Table 1 shows that the records were relatively evenly distributed across the 9 residual classes ranging in size from 1454 records (d 1 to 29) to 4135 records (d 60 to 89). Results are presented from the LegP model with the best order of fit for each type trait. The orders of the fixed and random polynomials in these models are in Table 2.
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). The average correlation between individual sire solutions as estimated from the 2 functions was 0.81, with the correlation being higher in midlactation (results not shown). For example, the correlation between breeding values for bulls with 50 or more daughters as estimated from the 2 functions was 0.84, 0.88, and 0.62 on d 40, 120, and 265, respectively.
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. A higher proportion of the phenotypic variance is explained by the LegP function compared with the CubS function. Values ranged from 30% for ANG to 51% for STAT, which equates to a correlation between actual and predicted values of 0.55 and 0.71, respectively. The combination of the above results suggested that the RR model with the LegP function modeled body traits slightly better than did the CubS function. The results hereafter will describe the estimates obtained from the LegP function unless otherwise stated.
Figure 1 shows that the fixed curve (overall trend) for the traits generally increased across lactation. The fixed trend curve for BCS showed a decrease at the start and end of lactation. Conversely, ANG increased at these times. The fixed overall trend for the other traits was generally linear with STAT increasing at a slower rate than BD and CW. It is important to note that the individual sire solutions (random term in the model) are expressed as deviations from these fixed curves.
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shows that the genetic variance for all traits when modeled using a LegP function changed more dramatically across lactation than when modeled with a CubS function. The genetic variance at the start and end of lactation increased when the LegP function was used. The CubS function produced a "flatter" profile for the estimate of genetic variance across lactation for all traits except BCS. However, the estimate of genetic variance for the middle section of lactation (approximately d 50 to 250) was similar regardless of the function used in the RR model. Figure 2 shows that the genetic variance of BCS was highest at either end of the lactation, a result observed in other studies that modeled BCS with RR models using polynomial functions (Berry et al., 2003; Coffey et al., 2003; Banos et al., 2004).
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) was more consistent across lactation when estimated with the CubS function, ranging from 0.44 in midlactation to 0.66 at the start of lactation, whereas the estimates from the LegP function ranged from 0.19 at the end of lactation to 0.51 in midlactation and 0.37 at the start of lactation. Both the CubS and LegP functions produced moderate heritability estimates for BD (0.26 to 0.55) and CW (0.14 to 0.55) across the majority of lactation. Table 1 shows that both functions produced moderate to high heritabilities for STAT (0.27 to 0.68) and a moderate estimate for the heritability of ANG (0.22 to 0.38) for the majority of lactation. However, the heritabilities estimated with the LegP and the multivariate linear models at the start of lactation were higher than previous estimates. The genetic variances from multivariate sire analyses at 3 times (early, mid, and late lactation) were similar to the results from the LegP function except for STAT. For STAT, the multivariate estimates tracked the genetic variance estimates from the model with the CubS function.
The residual variance across lactation was relatively constant for all traits, with no evidence of higher or lower residual variance at any stage of lactation (Table 1). The residual variance estimated from the RR models was similar for the majority of traits regardless of the function used, although the LegP function tended to give numerically smaller residual variance estimates (not significant when tested with a t-test). However, the estimated residual variance for BCS was smaller when the LegP function was used (P < 0.001), suggesting that the LegP function is a more appropriate function to use in the RR model for BCS.
Daily sire solutions were estimated for BCS, BD, CW, STAT, and ANG from the results of the RR model with the LegP function. Four sires were chosen at random from sires with more than 150 daughters in the data set (Figure 3) to illustrate the differences in sire profiles. Figure 3 shows that there are differences between sires and between traits in the profile of their daughters’ type over lactation. For example, the daughters of some sires grow in stature faster than others, and the daughters of some sires lose more body condition across lactation than others.
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shows that all sires dropped beneath the fixed trend curve for BCS at some stage in lactation. Interestingly, sire B started and finished lactation a BCS unit above the fixed overall trend where sire D appears to differ only slightly from the overall trend. The sire profiles for ANG were less dramatic than BCS but still showed differences in the profiles for the same 4 sires and visually were the mirror images of the BCS sire profiles (e.g., sire B started and finished lactation below the fixed overall trend). Body depth and CW showed linear differences with the daughters of 3 of the sires generally rising faster for the 2 traits than the rest of the population, whereas sire D started above the overall trend curve and finished lactation beneath. This suggested that the daughters of sire D do not change body shape during lactation, which could suggest that they do not put on much weight during lactation.
There was no significant change in the prediction formula for liveweight across the lactation; and therefore, the equation as described by Coffey et al. (2003) was applied to the type trait solutions. Figure 3 shows that some sires grow at a faster rate than the population (sire A), whereas other sires have slower growth (sire D). The daughters of sire A grow consistently faster than the rest of the population indicating that not only do his daughters start their first lactation heavier than their counterparts (+3 kg heavier), but they also finish lactation heavier (+8 kg). However, the daughters of sire B start off lactation heavier (+5 kg) but their growth slows down and at the end of lactation are 2 kg lighter than their counterparts.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The BCS heritability at various points of the lactation were similar to results reported by Berry et al. (2003) who found a early lactation heritability of 0.39 at d 0 (vs. 0.37 at d 19) up to 0.51 at d 151 (vs. 0.51 at d 105 and 0.41 at d 151). The moderate heritability estimates in the majority of the lactation for ANG agreed with the results of the RR analysis of dairy form of Dechow et al. (2004). However, there were discrepancies between the 2 studies for the heritability estimates in early lactation. The moderate heritability estimates for BD and CW and slightly higher estimates for STAT agreed closely with previous multivariate studies (Pryce et al., 2000).
Heritability estimates for the traits tended to be moderate across the lactation but higher at the extreme points of the curve using a LegP function. Previous studies have suggested that there is an increase in the genetic variance at either end of the lactation for traits modeled with polynomial functions if data points are few (Pool et al., 2000; Berry et al., 2003). However, this study truncated early and late lactation records in an effort to improve the modeling of these traits. This study also modeled BCS with a CubS function and saw similar increases at the start and end of lactation, although the increases were not as dramatic as seen in this and other studies that modeled BCS with a LegP function. This suggests that the genetic variance of BCS is truly lower in midlactation. This was further demonstrated by the favorable correlation between the breeding values for BCS estimated from either function across the lactation, although it did drop off slightly at the end of the lactation.
The profiles of variance and heritability for BCS and ANG were similar across the lactation. This is to be expected because BCS and ANG have been shown to be highly correlated (–0.74; Veerkamp and Brotherstone, 1997). The genetic variance at the extremities of the data (early and late lactation) rose when analyzing BCS and ANG with a LegP function. However, when using CubS, the variance of BCS was highest at the start and end of lactation, whereas ANG displayed a relatively flat curve. The data at the early and late stages of lactation are fewer compared with the middle of lactation (1359 and 1123 records in the first and last 30 d of lactation, respectively). There is also a higher variance associated with the BCS records at the start or end of lactation than with ANG. For example, for the first 30 d of lactation, the mean BCS is 4.49 (SD 1.68) whereas ANG has a mean of 5.5 (SD 1.37). The increased phenotypic variance of BCS data in early and later lactation could have a bigger influence on the polynomial function, and thus could "inflate" the genetic variance curve at these points.
The sire deviations from the fixed overall trend curve of the body traits could be used as indicators of body changes in first lactation and therefore related to traits such as maturity and liveweight. Sire B was consistently above the fixed overall trend for BD, CW, and STAT, suggesting that the daughters of this sire are larger than the rest of the population and are still growing throughout their first lactation. This could be indicative that the daughters of this bull are still maturing throughout their first lactation.
These results show that there are differences in the genetic profiles across first lactation for certain type traits, indicating that there are differences between sires in their daughters’ body change in first lactation. It is necessary to account for the differences between sires across time to get the best estimate of a daughter’s performance in these traits at any particular time. An example where the differences between sires should be accounted for is in the prediction of traits such as BW from linear type traits as done by Coffey et al. (2003). These results show that the component traits (BD, CW, STAT, and ANG) in the prediction of liveweight do vary relative to each other across lactation. The 4 chosen sires are good examples of the differences in liveweight that occur during first lactation.
Although the differences in daughter liveweight change for the chosen 4 sires may appear low, some sires with large (>150) progeny group sizes differed from the fixed trend curve by over 15 kg. Sire C, whose daughters began lactation heavier than the population but their growth rate slowed down relative to the fixed trend curve, had the highest PTA for kilograms of milk, fat, and protein for all the sires. Conversely, the daughters of sire A grew faster than the population but sire A had the lowest PTA for the milk production traits. These differences could be indicative of the daughters of sire A partitioning food toward their own growth, whereas the daughters of sire B may partition food toward milk production. Sire B, whose daughters’ growth rate increased relative to the population toward the end of lactation, had the best calving interval PTA of the 4 sires (–0.5 d; Wall et al., 2003), which could indicate that the animal may sacrifice some body weight toward peak lactation production but regain it to maximize reproductive functions.
These results show that there are differences in how cows grow and change shape over their first lactation—some changing very little for these traits and others increasing or decreasing over the duration of the lactation. This is a critical time in the biological development of a cow as it prepares for second calving and successive lactations, essential for its survival in the herd. The linear traits BD and CW have been shown to be moderately correlated to weight and size (Koenen and Groen, 1998). Moreover, animals with deeper bodies have been shown to be more profitable than smaller animals (Pérez-Cabal and Alenda, 2002) even though BD has a negative correlation with herd life indicating that there could be a balance between size, production levels, and longevity (Short and Lawlor, 1992). The results of this study could be used to help identify the optimum profile of body shape change over the first lactation that is most highly correlated to traits such as life span and profitability.
Random regression models allow us to estimate body changes in first lactation in the national population. These methods could be used to highlight bulls that produce lighter or heavier and slower or faster growing daughters; these types of trends could be indicative of later life performance, both for production and nonproduction traits.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Received for publication April 7, 2005. Accepted for publication June 29, 2005.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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This article has been cited by other articles:
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  E. Wall, M. P. Coffey, and P. R. Amer A Theoretical Framework for Deriving Direct Economic Values for Body Tissue Mobilization Traits in Dairy Cattle J Dairy Sci, January 1, 2008; 91(1): 343 - 353. [Abstract] [Full Text] [PDF]
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E. Wall, M. P. Coffey, and S. Brotherstone The Relationship Between Body Energy Traits and Production and Fitness Traits in First-Lactation Dairy Cows J Dairy Sci, March 1, 2007; 90(3): 1527 - 1537. [Abstract] [Full Text] [PDF]
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S. Brotherstone, M. P. Coffey, and G. Banos Genetic Parameters of Growth in Dairy Cattle and Associations Between Growth and Health Traits J Dairy Sci, January 1, 2007; 90(1): 444 - 450. [Abstract] [Full Text] [PDF]
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| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
) across lactation for both functions.
), body depth (•), chest width (
), stature (
), and angularity (
), across DIM 10 to 290.
