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Animal Sciences Group, Division Animal Resources DevelopmentP.O. Box 65, 8200 AB Lelystad, The Netherlands
Corresponding author: M. P. L. Calus; e-mail: mario.calus{at}wur.nl.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Key Words: environmental sensitivity • environmental parameter • genotype x environment interaction • random regression model
Abbreviation key: EP = environmental parameter, ES = environmental sensitivity, GxE = genotype x environment interaction, HYS = herd-year-season
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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An environmental parameter (EP) reflects the environment encountered by the animals. An EP can reflect production level of a herd (Veerkamp and Goddard, 1998; Calus et al., 2002; Kolmodin et al., 2002), or other characteristics of the herd, such as average calving interval or average age at calving (Fikse et al., 2003). Describing GxE for dairy cattle with a covariance function of an EP is recently described for a limited number of EP (Veerkamp and Goddard, 1998; Calus et al., 2002; Kolmodin et al., 2002; Fikse et al., 2003). The use of an EP in a covariance function has the advantage that environments are treated as a continuum, rather than a set of arbitrarily defined groups of the data. The EBV of an animal, which is divided into an environment independent and an environment dependent part, is also called reaction norm (Falconer and Mackay, 1996). The simplest form of a covariance function describes the ES of the genotype as a linear function of the EP, but higher order functions are possible. Covariance functions can be estimated by a two-step procedure or by random regression models (Van der Werf et al., 1998).
The objective of this paper is to estimate ES for milk production traits for a range of EP in order to identify those EP that gave most ES and to investigate the effects of ES on reranking in the Dutch economic index (INET) combining milk, fat, and protein yields.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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In the pedigree file, a maximum of five generations of sires were included, together with the pedigrees of dams of first and second generations of sires and the sires’ maternal grandsires. A total of 4769 sires with daughters in the data were identified. Sires had on average 32 daughters. The relationship matrix contained 14,382 animals.
Traits
Five traits were evaluated: average daily milk yield, fat yield, protein yield, fat percentage, and protein percentage. Milk, fat, and protein yield were calculated as the average of the test-day yields between 5 and 305 DIM. Fat and protein percentage were calculated as the average yield of fat and protein divided by the average milk yield.
Environmental Parameters
Environmental parameters were calculated for each herd-year level, based on calving date. Potentially a large number of EP could be defined, but parameters used here were chosen because they: 1) reflect management and environment, 2) are obtainable from the available data, 3) are continuous rather than categorical, i.e., the parameter is expressed on a scale rather than defined in several classes, and 4) are not too strongly correlated with each other. Each parameter was averaged over all heifers calving in the relevant herd-year. For parameters that reflected traits with more records per lactation, first an average was calculated for each selected animal.
Test-day record parameters.
Average protein and SCC were calculated from test-day records in 1998 and 1999. Each SCC test-day record was transformed to a SCS, by SCS = log10(SCC). Persistency was calculated in two different ways. First, persistency was calculated for each animal from the ratio of milk production on the test-day closest to 60 DIM to milk production on the test-day closest to 240 DIM (Zwald et al., 2001), both in a range of 42 d around those. Second, persistency was taken as the highest test-day milk production of a heifer divided by its average test-day milk production. This last parameter is called relative peak milk yield.
Age at calving and herd size parameters.
Average age at calving and number of freshened heifers were calculated over all heifers that calved during the year, regardless how many days they produced. In both years, the change in number of freshened heifers was set to the difference between 1998 and 1999.
Energy balance parameters.
Energy balance reflects the ability of management to tune the feed intake to the energy requirements and therefore indicates whether tissue reserves are mobilized or deposited in the cow. Body condition score reflects cumulated energy balance (Chilliard et al., 1991). Body condition score was measured during classification and only once during the first lactation. Average BCS was calculated from all classified heifers in a herd that calved in the same year. Other traits that reflect energy balance are change in fat percentage and fat over protein ratio (De Vries and Veerkamp, 2000). Change in fat percentage was calculated as the difference in fat percentage on the test-day closest to 77 DIM and the test-day closest to 14 DIM (De Vries and Veerkamp, 2000), both in the range from 10 to 100 DIM. Fat over protein ratio was calculated by test day and then averaged across test days.
Calving and insemination parameters.
Calving interval is the period between first and second calving. The number of inseminations required for a successful second calving was estimated during first lactation. The herd calving pattern was represented by peak date of calving and distribution of calving dates over the year. The peak date of calving shows the date around which the heifers are calving and the distribution of the calving dates shows whether the heifers are calving near that date or throughout the whole year. Average day of calving can be calculated by numbering each day of the year from 1 to 365 and obtaining the average of the renumbered calving dates (Zwald et al., 2001). A disadvantage of this method is that a nonequal distribution of calving during a year, e.g., if the peak date of calving does not fall on July 1st, leads to an underestimation or an overestimation of the peak date of calving. Here, a slightly different procedure is used. The peak date of calving is calculated by iteratively repeating the following procedure: 1) calculate the average of calving dates (Zwald et al., 2001) and 2) define a maximal time period in the same calendar year with the average of step 1 as central point. For instance, with an average calving date of d 140, the new period ranges from d 0 to 280. If the period became shorter than 182 d, it was expanded over the borders of the calendar year. Insemination data from 1997 and 2000 were available to make this expansion feasible. The time period in step 1 is in the first iteration the calendar year and in later iterations the period defined in step 2 in the previous iteration. Steps 1 and 2 are repeated until the average day of calving no longer changes. The converged average day of calving is considered to be the peak date of calving. For a few herds, two peaks of calving in a year made convergence impossible. If convergence had not occurred after 1000 iterations, the average day of calving of all 1000 iterations was taken. Values for 1999 were adjusted by substracting 365 d to come to the same standard as in 1998. The distribution of calving dates during the year was calculated by the use of an interval of 182 d and one of 365 d, both centered on the peak date of calving. The distribution of calving dates was calculated as the ratio of the number of calving dates in the short interval to the number of calving dates in the long interval.
Estimating Variance Components and Environmental Sensitivity
Variance components were estimated by using a sire model. Environmental sensitivity was modeled by applying a random regression for each sire, representing its EBV, on values of an EP for the herds in which his daughters were producing. A fixed linear and quadratic regression for age at calving was included, as was a fixed effect to account for herd-year-season (HYS) groups. Furthermore, a fixed polynomial was also applied to the EP, to account for the average effect in each environment. An HYS effect was not fully covered by the herd-year effect. In each situation, only one EP was used for both the random regression for sires and the fixed regression for herd-year. The residual variance was calculated for 10 equally sized groups, based on increasing EP, to include heterogeneous residual variances in the model.
The HYS groups were defined by a method that optimizes the composition of HYS groups based on the calving dates and intervals between consecutive calving dates in a herd (Crump et al., 1997). Initially, the criteria of a maximum period of 91 d and a minimum of five animals per HYS group were applied. If some animals were not assigned to an HYS group based on these criteria, they were forced to join one by relaxing the criterion for the maximum period. The same was applied to animals from groups that had fewer than five animals, to force them to join another HYS group.
The applied model was:
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where:
Yijklmnoq is the performance of heifer q,
µ is the average performance over all animals,
HYSi is the effect of herd-year-season group i,
0 and 1 are coefficients of linear and quadratic fixed regression on age at calving j in days, respectively,
AGEj is age at calving in days of heifer q,
ßk is coefficient k of a fixed regression on element k of the orthogonal polynomials of all environments,
Pkm is element k of the orthogonal polynomial resembling an environmental parameter of environment m,
ln is coefficient l of the random regression on the orthogonal polynomials of all environments of the daughters for sire n,
Plm is element l of the orthogonal polynomial resembling an environmental parameter of environment m,
s is the largest significant coefficient l of the random regression, and
Eijklmnoq is the residual effect of heifer q in environment m within group of environments o (o = 1, 2, ..., 10).
The order of the polynomials for the fixed regression on an EP was arbitrarily set to 10 in each situation. For the random regression, the order of the polynomial was increased per combination of trait and EP until the extra added components of the next order did not significantly improve the fit of the model or the variance of the extra component was zero. The log likelihood ratio test (Kirkpatrick et al., 1990) was used to compare the fit of two models with consecutive orders of polynomials.
The sire variances for values of an EP are calculated as 
S’, where is a matrix with polynomial coefficients for a value of the EP on each row and S is an n x n matrix, where n is the highest order of the polynomial + 1, with variances of each random regression coefficient on the diagonal and covariances between the random regression coefficients on the off-diagonals. The residual variance was calculated for 10 different groups. Residual covariances between groups were assumed to be zero. Covariances between sire and residual effects were assumed to be zero and not taken into account.
Several criteria can be defined to rank EP based on the given amount of GxE. In this study, we used the absolute change in sire variances between 25 and 75% of the environmental scale as an indicator of change in sire variance across environments and therefore of the given amount of GxE. To check the results of the random regression model, a multitrait model was applied for selected combinations of traits and EP. The program ASREML (Gilmour et al., 2002) was used for all analyses.
Economic Index
The Dutch INET is an economic index that includes milk, fat, and protein yield and is calculated as INET = -0.08 x EBV(milk yield) + 1 x EBV(fat yield) + 6 x EBV(protein yield). The INET was used to investigate the effects of ES on the combination of milk, fat, and protein yields. First, the INET was calculated based on the results of the described model. No base adjustments in the index were made, i.e., average breeding values were not adjusted based on the average of the whole current population. Secondly, the economic weight was readjusted to real economic weights in a few environments. The correlated response of selection in a different environment is:
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where CR is the correlated response in environment Y, rXY is the genetic correlation between environment X and Y, 
X and Y are genetic standard deviations in environments X and Y, and RX is the response of selection in environment X. The adjustment factor of the weights of the INET is then equal to rXY x (Y/X). If no reranking occurs or adjustment is for scaling effects only, i.e., rXY = 1, this reduces to (Y/X).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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based on 151,696 heifers in 6780 herds. Herds differed considerably for the EP, for example, average protein ranged from 0.46 kg of protein per day to 1.21 kg of protein per day, average age at calving from 672 to 1028 d and herd size from 5 to 270 numbers of heifers calving. Correlations among all EP ranged from -0.43 to 0.45 but were generally weak. Strongest correlations were found for pairs of EP that were calculated from the same traits, such as EP defined on production traits and defined on the number of freshened heifers in a herd. As peak date of calving is one of the newly defined EP and had a considerable effect, the number of animals with peak date of calving in a certain month is shown for both years (Figure 1). This illustrates that most herds have their heifers calving in the autumn, although this is less clear for 1999 than for 1998.
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. Milk, fat, and protein yield each had significant reaction norms in combination with 12 EP. These three traits generally showed the same order of significant polynomials for a given EP. Fat and protein percentage had significant reaction norms in combination with 6 and 8 EP.
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. The heritabilities were comparable across environments for all combinations of traits and EP.
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). For the trait protein yield, average protein, BCS, calving interval, age at calving and persistency were the most important EP (Figure 2). Age at calving and calving interval showed the same pattern of sire variance, which decreased by a third across the environmental scale. The sire variance showed the most curvilinear relationship with average protein. For average protein and BCS, the sire variances doubled across the environmental scale. For the EP average BCS, the sire variances for milk, fat, and protein yield are shown in Figure 3. The environmental scale in Figure 3 resembles the interval of the mean EP ± two standard deviations. The sire variances are following a similar pattern across the environmental scale.
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Economic Index
The overall economic value for milk, fat, and protein yield, called INET, was calculated on the scale of the EP average BCS for the 10 sires with the highest number of daughters in the data (Figure 4). These bulls are not representative for all bulls in the population, but they represent the breeding bulls that are widely used by dairy farmers. The INET increases with increasing average BCS, and little reranking happened. The sire with the highest change of INET shows an INET of 65 Euros for herds, with an average BCS of 3.5 and an INET of 120 Euros for herds with an average BCS of 6.0.
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. The change of the economic weights with the change of the EP clearly illustrates the effect of scaling.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Twelve EP gave significant reaction norms for milk, fat, and protein yield. Results for six of these parameters for milk yield were reported in literature. Significant ES for the EP herd size, relative peak milk yield, persistency, and age at first calving were found (Fikse et al., 2003), but no significant reaction norms for the EP fat over protein ratio and calving interval were found in that study. Average protein and BCS showed the highest ES based on our definition. Average protein is proven to be a useful EP before (Calus et al., 2002; Kolmodin et al., 2002). These results indicate that adjusting for heterogeneous variances in the genetic evaluation model might be possible by using EP.
The situation in which the EP is calculated based on the evaluated trait needs some attention. The fact that EP are calculated as phenotypic averages within a herd implies that the breeding values are partly based on the breeding values of sires of the cows producing in a herd. Kolmodin et al. (2002) suggested that this may not be a problem, but no extensive evidence was given. In the case of random use of sires across environments, this will probably not be a problem, as the average breeding value will be zero, but the precise implication of including the evaluated trait in the calculation of the EP is not clear yet.
It is tempting to suggest that significant scaling effects shown for some of the EP, might be a result of the association with yield, because generally an increasing level of production also leads to increasing variance. In this study, both BCS and calving interval showed changing sire variances with increasing values of the EP (Table 3
), and BCS and calving interval had correlations of 0.19 and -0.01 with average protein. However, herds with an average BCS of four and herds with an average BCS of six, both had an average 305-d protein production of 250 kg, indicating that only limited effect can be expected from the low correlation between protein yield and BCS. Still, it illustrates the problem of interpreting EP, and the need to consider multiple EP simultaneously.
Body condition score gave considerable scaling effects. Body condition score reflects cumulated energy balance (Chilliard et al., 1991). It was reported (Cromie, 1999) that defining environments based on the amount of concentrate fed causes scaling effects that are comparable to scaling effects if environments are defined on average protein. These results support the suggestion of others (Calus et al., 2002; Kolmodin et al., 2002) that feed intake and feed supply are important parameters in relation to environmental sensitivity of genetic merit for milk yield.
Environmental Sensitivity
Environmental sensitivity was defined by Falconer (1990) as the difference between phenotypic values of a genotype or a population in two environments, divided by the difference of the means of all individuals in both environments. In our study, ES is defined at a population level as the variance in reaction norms of genotypes.
Genetic correlations of a trait across environments were high, indicating that reranking hardly occurred across environments, as was expected from literature (Calus et al., 2002; Kolmodin et al., 2002; Fikse et al., 2003). However, sire variances showed considerable scaling effects for a number of the EP. At the same time, heritabilities were comparable across environments, indicating that scaling effects for environmental and sire variances were comparable. Heterogeneous heritabilities for comparable models were reported, but in these studies the heterogeneity of residual variances was not taken into account (Calus et al., 2002; Kolmodin et al., 2002). If heterogeneity of sire variances is accommodated in the model, but heterogeneity of residual variance is not, the presence of scaling effects is likely to cause heterogeneity of heritabilities.
Herds with high protein, high persistency, young age at calving, high BCS, short calving intervals, and calving peak in the fall or winter appeared to have the highest genetic variance for milk, fat, and protein yield. This means that herds that have one or more of these characteristics are more likely to benefit more from the use of bulls with high genetic merit and the use of expensive high genetic merit bulls is more easily justified in those herds. At the same time, selection of animals on those herds will be more effective when there is an insufficient correction for heterogeneous variances in the breeding value estimation.
Economic Index
The economic value of a trait was affected if the trait showed large scaling effects. If scaling effects are different among traits, the relative importance of these traits in an economic index can change (Namkoong, 1985). The economic index might give different selection responses depending on herd environment, and therefore reranking across environments might occur. This might reduce the total benefit of selection based on this economic index. In this study, the economic values of the traits in the index were only adjusted for scaling effects. Genetic correlations among environments of the adjusted economic values (Table 5) ranged from 0.93 to 0.99. Taking these into account would cause greater differences across environments. As shown here, reranking based on INET will be small, for a number of reasons. First, the scaling effects of milk, fat, and protein yield are comparable across environments. Second, the genetic correlations among these three traits are high and therefore the economic index is relatively insensitive for changes in economic values (Veerkamp et al., 1995a). However, if other traits are included in the economic index, with scaling effects that are independent from those of production traits, the scaling effects could cause considerable reranking based on the economic index (Namkoong, 1985). This clearly indicates that scaling effects might be of importance in animal breeding programs.
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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 January 19, 2003. Accepted for publication June 13, 2003.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
) and 1999 (
).
), age at calving (
) given the deviation of the mean environmental parameter in standard deviations.
