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,1
* National Fund for Scientific Research, B-1000 Brussels, Belgium
Animal Science Unit, Gembloux Agricultural University, B-5030 Gembloux, Belgium
1 Corresponding author: gengler.n{at}fsagx.ac.be
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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of lifetime profit per 1% increase in inbreeding for the Holstein animals in the Walloon region of Belgium.
Key Words: incomplete pedigree • inbreeding • global economic index • genetic evaluation
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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One of the main economic consequences of inbreeding is inbreeding depression, the reduction of the mean phenotypic value for economically important quantitative traits. The effect of inbreeding on mean phenotypic performance can be studied and accounted for by introduction of a linear regression term of phenotypic performances on inbreeding coefficient in the genetic evaluation model. Nonlinear effects may exist but were not the topic of this study.
The losses due to inbreeding reported in the literature differ in scale but mostly have the same direction. For production traits, they range from –9.84 kg of milk to –29.6 kg of milk, from –0.55 kg of fat to –1.08 kg of fat, and from –0.80 kg of protein to –0.97 kg of protein (Casanova et al., 1992; Miglior et al., 1992, 1995; Wiggans et al., 1995; Smith et al., 1998) per 1% increase in inbreeding and for a lactation. Inbreeding may increase SCC (Miglior et al., 1995; Smith et al., 1998; Mrode et al., 2004); however, only a few studies tried to assess this. Miglior et al. (1995) showed that inbred animals could be inclined to develop mastitis. The effects of inbreeding on type traits were seldom reported and generally considered weak (Misztal et al., 1997; Smith et al., 1998). Traits most affected by inbreeding are often connected with reproductive performance (Miglior, 1994; Smith et al., 1998; Cassell et al., 2003). Impact of inbreeding on economic indexes has not been reported frequently. Smith et al. (1998) showed a loss of $22 to $24 lifetime net income (a parameter that estimates the economic impact of inbreeding) per 1% increase in inbreeding.
The aims of this study were to estimate the effect of inbreeding on production traits, type traits, and SCS, traits that were included in the calculation of breeding values for Walloon dairy cattle, and to combine these separate effects to estimate the effect of inbreeding on the current global economic index (VG). Because the current index does not yet contain traits that are traditionally linked to high inbreeding depression (fertility and longevity), the results are only a lower bound of the total economic losses. Therefore, even if the results for those traits need to be added later, this study provides a framework to quantify the impact for further uses, such as in mating programs.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The countries of origin of the Holstein animals in the pedigree file are presented in Table 1
. A relatively large proportion of the Holstein animals in the pedigree come from outside Belgium, mostly from the larger neighboring countries and from Canada and the United States. In recent years the proportion of animals with unknown ancestors has decreased sharply because of efforts to encourage calf registration. Table 2 shows the pedigree depth in Holstein cows with production records and their sires and maternal grand sires. Pedigree depth was expressed as equivalent complete generations of ancestors. Equivalent complete generations represent the logarithm in base 2 of the sum of the number of base ancestors (ancestors without known parents) over the whole pedigree of a given animal. This allowed us to access the average number of complete generations for all animals. The average number of known generations for cows with records born in 2000 reached 8.50 generations; for more recent birth years of sires (e.g., 1995) and maternal grand sires (e.g., 1992), the average numbers of known generations were equal to 10.06 and 9.35, respectively.
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Data for Production Traits and SCS
For production traits and SCS, data were limited to first, second, and third parities. Data for yield traits consisted of 12,742,020 test-day records from 731,442 cows. The SCS were computed from SCC using the formula by Ali and Shook (1980): SCS = [log2(SCC/ 100,000)] + 3. Table 3 gives additional details of the production and SCS data for Holstein cows used in the routine run of February 2004.
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gives more details for type traits used in the routine run of February 2004. Currently, a majority of first-calving cows and an increasing number of later calving cows are scored because the linear scores are used in a computerized mating program. Therefore, the subset of classified animals represents a relatively large proportion of the animals with production records.
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Current Genetic Model for Production Traits.
A multilactation, multitrait random regression test-day model (RRTDM) is used in the Walloon region of Belgium. The model used currently can be written as
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where y is a vector of precorrected milk, fat, and protein test-day records; b is a vector of fixed effects (herd x test date, stage of lactation, stage of lactation x age at calving x season of calving, gestation stage); h is a vector of herd x period of calving random regression coefficients; a is a vector of additive genetic random regression coefficients; p is a vector of permanent environmental random regression coefficients; e is a vector of random residuals; X, W, and Z are incidence matrices; and Q is the covariate matrix for second-order Legendre polynomials. The precorrection is applied to account for environmental effects of age within lactation x stage x breed classes. This process allowed correction for maturity differences within lactation according to breed composition; more details are provided in Auvray and Gengler (2002).
Current Genetic Model for SCS.
The genetic evaluation model is a multilactation RRTDM similar to the one used for milk, fat, and protein. There are only 2 major modifications. First, no common herd environment effect is defined because previous research showed that this effect is very small for SCS and the model is only multilactation, not multitrait. Second, an iterative weighting of SCS records by a function expressing the probability of a mastitis event was introduced in the genetic evaluation model (Gengler and Mayeres, 2003). This modification is significant because it allows the transition from a purely descriptive evaluation of SCS to an evaluation that allows a better expression of the relationship between mastitis incidence and given test-day.
The RRTDM for SCS is written as
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where y is the vector of daily SCS, b is a vector of fixed effects (the same as for the production model), p is a vector of permanent environmental random regression coefficients, a is a vector of additive genetic random regression coefficients, and e is a vector of random residuals.
Current Genetic Model for Type Traits.
The genetic evaluation model used for type traits is based on the one used for the genetic evaluation of non-Holstein breeds in the United States (Gengler et al., 1999, 2001a,Gengler et al., b). This genetic evaluation method consists of 3 interdependent iterative systems that solve regular mixed model equations on a canonical scale, allowing the update of canonical traits to account for missing original traits. Integrated into this system is an adjustment for heterogeneous variance. The general model on a canonical scale can be written as
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where for a particular type trait, yQ is the vector of canonical type trait records adjusted for heterogeneity; h is the vector of fixed effects of herd, date scored, and parity (first or later) group (contemporary group); s is the vector of system specific fixed effects for age and lactation stage within parity group (first or later); c is the vector of classifier specific fixed effects for age and lactation stage; p is the vector of random effects of permanent environment; a is the vector of random additive genetic effects of animals and genetic groups; X, S, C, and Z are the common incidence matrices for all traits that associate h, s, c, p, and a, respectively, with y; and e is the vector of random residual effects. Computation of canonical type-trait records adjusted for heterogeneity during iterations can be written as
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where 
is the multiplicative scaling matrix, its inverse being the adjustment matrix; 
is a vector containing the means of the traits; Q1 and Q2 are the transformation matrices defined as in Ducrocq and Besbes (1993) and obtained from the transformation matrix Q; and 
Q are the current solutions on a canonical scale. More details can be found in Gengler et al. (2001c).
Partial and Global Economic Indexes.
Theses indexes are called VG for the global economic index, partial economic index milk (VL) for the milk production traits, partial economic index type (VT) for the morphology traits, and partial economic index functionality (VF) for the functional traits index, where VG is the sum of VL, VT, and VF. Currently, the VL contains milk, fat, and protein yields; the VT contains 15 type traits; and the VF contains only SCS. The partial index VT is itself subdivided into 3 second-order indexes: partial economic index udder (VP) for the udder traits, partial economic index body (VC) for the development and frame traits, and partial economic index feet and legs (VM) for the feet and legs traits. All of these partial economic indexes can be considered as the economic value of one standardized unit of the underlying linear combination of traits (for milk, type, and functional traits) multiplied by the number of standardized units. The derivation and computations were done following the example given by VanRaden (2000). The only major change, beyond the adaptation of the profit function to our situation, was that the economic values of one standardized unit of the underlying linear combination of traits were obtained by multiple regression instead of taking partial derivatives. Normally, in deriving economic values often called "a" values, correlations among the evaluated traits should not matter, because these correlations should be used instead to solve for multitrait additive genetic values. Thus, the economic values should be partial derivatives of true profit with respect to the evaluated traits, and true profit included correlated, nonmeasured traits such as feed consumption (VanRaden, 2000). However, our objective was to obtain approximate "b" values because our additive genetic values were not multitrait and several traits in the selection objective (e.g., longevity) were not yet evaluated. These approximate "b" values allow us to consider the linear combination of genetic values for the available traits as the best linear predictor of true profit.
These indexes provide a simple tool for the Walloon breeders to choose parents despite the presence of over 30 different evaluated traits. They embody their economic selection goal of overall profitability over the productive life, as well as its components. Table 5 gives the relative importance of these traits in the partial and the global economic indexes.
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Estimation of Inbreeding Depression
A linear regression of phenotypic performance on inbreeding coefficient was added to the genetic evaluation models to estimate inbreeding depression for production traits, type traits, and SCS. Solutions were given per 1% increase of inbreeding.
Calculation of Impact of Inbreeding on Walloon Genetic Evaluations
The combination of the effects of inbreeding on separate traits in the Walloon genetic evaluations and use of weighting presented in Table 5
allowed estimation of effects of inbreeding on different partial indexes and the global economic index per 1% increase in inbreeding.
Estimation of Standard Errors
In many analyses using linear mixed models, no standard errors of solutions are obtained, because they are of secondary importance to obtaining predicted breeding values or estimating variance components. Knowing these standard errors is useful, however, as it allows the application of hypothesis tests. Even if exact knowledge of standard errors is impossible in large mixed models, there are methods to approximate them. The method used in this study was presented by Gengler and Croquet (2005) and based on a suggestion by Van-Vleck (1992). Harville (1979) presented a method called the mixed model conjugate normal equations based on a suggestion by Henderson (1974). The mixed model equations are usually expressed as
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where y is the vector of observations, ß is the vector of fixed effects, u is the vector of random effect, X and Z are the incidence matrices linking y with ß and u, e is the vector of residuals, R = V(e) and G = V(u). The mixed model equations can be simplified as C
= r, with = C–1r, where C is the coefficient matrix, s is the solution vector (containing both ß and u), and r is the vector of right-hand-side (RHS). To test the significance of an estimable function of the elements of 
, the error variances and the covariances of the different concerned fixed effects are needed. From the mixed model theory and under the hypothesis that R and G are known exactly
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A basic property of mixed models is that V() = Cßßso that V(k') = k'V()k = k'C–1k. However, C–1 is usually impossible to compute. The alternative method used replaced the RHS by a contrast vector k (contained only values 0 and one single 1 related to the fixed effect to test) and the vector s by the vector 
so that: = C–1k. Then, after premultiplying by k' we obtain k' = k'C–1k, which is what is needed. The square root of k'C–1k gives the standard error associated with the determined fixed effect.
In our situation, a block Csßß of Cßß was needed. Its elements were obtained by computing linear functions of element of Cßß and by backsolving to obtain the needed elements of the block. In matrix notation, let K be the coefficients of the linear functions and D a matrix containing the results of the linear functions obtained by computing K'C–1K. The elements of the block were then obtained as Csßß = (KsKs')–1KsDKs'(KsKs')–1 where Ks is the part of K associated with the block Csßß
Standard error for the average inbreeding depression estimated for a trait (milk, fat, protein, and SCS) on 3 lactations was obtained using a submatrix containing the error (co)variance for the estimated inbreeding depression on the trait for each of the 3 lactations. The computations for milk, fat, and protein were treated simultaneously. Standard errors associated with the inbreeding effect on partial and second-order economic indexes were estimated using error (co)variance submatrices for the inbreeding depression estimated for each trait used in the definition of each of these indexes. The standard error of the inbreeding effect on the global economic index (VG) was estimated using selection index theory, because no error (co)variance matrix exists between the partial indexes (VL, VT, and VF).
A t-test was used in all cases to determine the significance of the different inbreeding effects:
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The number of degrees of freedom of the t variable can be approximated by N-rank(X) under the hypothesis that R and G are known exactly (L. D. Van Vleck, Univ. Nebraska, Lincoln, personal communication).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Level of Inbreeding
The mean inbreeding coefficient of Belgian Holstein females was 3.7% in 2003. Trends in mean inbreeding for Belgian Holstein males and females over the past 40 yr are shown in Figure 1. Inbreeding of the Belgian Holstein cattle population has increased since 1965, but the increase was nonlinear over time and 2 periods for both females and males can be distinguished. Until the beginning of the 1980s, the mean level of inbreeding was small, with the annual average increase in mean inbreeding coefficient below 0.02%. By the end of the 1990s, the mean inbreeding had become much larger, with annual average increases of 0.14% for females. The trend for males was similar, but less stable because of the relatively low number of animals.
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Inbreeding Depression
Tables 6, 7, and 8 present effects of a 1% increase in inbreeding on the different traits evaluated in the Walloon region of Belgium. Each of these effects is presented with its standard error and its significance.
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presents estimates of 305-d lactation losses for yield traits per cow and per 1% increase in inbreeding. All of the inbreeding effects shown in Table 6 are highly significant. However, the losses per lactation for milk yields caused by inbreeding estimated in this study were lower than values cited in the North American literature (Miglior et al., 1995; Wiggans et al., 1995; Smith et al., 1998). An explanation could be that the scale of inbreeding depression is not a constant value, but is relative to the mean production. In consequence, in less productive populations such as the Walloon Holstein cattle (Table 3) compared with North American Holsteins, one would also expect less inbreeding depression.
Effects of 1% increase in inbreeding on SCS are showed in Table 7. The inbreeding depression on SCS presented in Table 7 was relatively low, but, as for production traits, the estimated inbreeding depression was very highly significant for each of the 3 first lactations. This result was in accordance with literature (e.g., Miglior et al., 1995; Smith et al., 1998; Thompson et al., 2000). On average, inbred animals tended to have higher SCS than non-inbred animals; therefore, because SCS is a parameter related to mastitis events (Coffey et al., 1986; Emmanuelson et al., 1988; Lund et al., 1994), this may mean that inbred animals tend to be more sensitive to mastitis perhaps because of a weakening of the immune system due to inbreeding (Miglior et al., 1995). For Miglior et al. (1995), a reason that could explain the small magnitude of inbreeding depression for SCS is the small dominance variance for SCS. Another explanation is that inbreeding affects production negatively, but production and SCS are negatively correlated phenotypically, leading to a partial cancellation of potential negative direct effects of inbreeding on SCS.
Table 8 presents estimates of inbreeding depression on type traits per 1% increase in inbreeding expressed in standardized and nonstandardized units, the first being easier to interpret because they remain on the original scoring scale. The standardized units, however, are used in the computations of the indexes. Table 8 shows that estimates of inbreeding depression for type traits tended to be small for all evaluated traits and nonsignificant for some. In particular, in this study, inbreeding was found to have negligible effects on loin strength, rump angle, rear leg set, udder balance, udder texture, fore udder, rear udder height, rear teat placement, angularity, overall rump, overall fore udder, and the overall dairy trait. However, we see the expected, very highly significant, inbreeding effects on stature and other traits related to the general development and appearance of the animals. Therefore, inbred cows tend to be smaller than non-inbred cows. In general, the type traits most affected by inbreeding, on the nonstandardized scale, were overall development, overall conformation score, overall feet and leg score, overall rear udder, stature and body depth; the inbreeding effect for all of these traits being at least highly significant. For Misztal et al. (1997), the type traits most affected by inbreeding, also on a nonstandardized scale, were body depth, chest width, and stature. As for Misztal et al. (1997), the estimates were positive for several type traits, the largest being for udder depth. For SCS, small or favorable inbreeding effects on type traits could be associated with small dominance variances (Misztal et al., 1997) or with competing partial relationships with inbreeding effects on production. Also, morphologically superior animals that are related could be used preferentially in matings to improve the type of animals. A recent example is the bull Hanoverhill Starbuck in Canada who is voluntarily accumulated in the pedigrees of Canadian Holsteins (Van Doormaal et al., 2005). This practice is called linebreeding. Because of the best linear unbiased estimator (BLUE) property of our inbreeding depression estimates, no confounding should happen; however, as we regress on estimated inbreeding, the conditions for BLUE are not totally fulfilled, and we can, therefore, not totally exclude this hypothesis. Under the assumption that the estimates are not totally BLUE, we might underestimate the effect of inbreeding and in extreme situations, even estimate positive inbreeding depressions due to confusion of positive additive genetic effects and negative effects of inbreeding. This hypothesis may also explain positive values for effects of inbreeding on VP shown in Table 9. This last result could also be an artifact of less milk production of inbred animals, which therefore have smaller, better looking udders. For the VC and the VM, however, inbreeding depressions remained negative, as expected.
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presents effects of inbreeding on the VG and the different partial indexes used in the Walloon region of Belgium; results are presented with their standard errors and their significance. Table 9 shows that the inbreeding effect was at least highly significant for all of these indexes. The influence of inbreeding on VL was –4.77 , the largest of all the indexes. The inbreeding depression for VF was rather low, as expected given the limited influence of inbreeding on SCS. The inbreeding depression for VT was negative, despite a positive value for VP.
In total, the loss resulting in a 1% increase in inbreeding on the VG summed to –6.13 . Obviously, this result is an underestimation of the real economic impact because traits such as fertility, longevity, and health that are linked with high inbreeding depression are not yet accounted for in the VG. However, this result also means that, given the current selection indices, if we choose between 2 bulls for a mate, every 1% difference in inbreeding in their offspring has to be compensated by 12.26 VG points. For example, if one bull creates 6% inbreeding, and the other 1%, the difference the first one has to compensate is more than 61 VG points. This small example also shows the important ranking differences that may occur when breeding values are adjusted for inbreeding. Given these facts and the unfavorable trend of inbreeding in the Holstein population, the United States recently decided to consider inbreeding both in the genetic evaluations and in the expression of breeding values or PTA (VanRaden and Tooker, 2004) using the methods developed by Van-Raden and Smith (1999). This approach is necessary, because simply preventing inbred matings is only effective to decrease inbreeding coefficients in the short term; it hardly has an effect on effective population size and future genetic diversity.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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The effect of inbreeding was significantly different from zero for the vast majority of traits currently evaluated genetically, with the exception of some type traits, and for all of the indexes used in the Walloon region of Belgium. Inbreeding was found to have a deleterious effect on most of these traits.
The global economic index, which measures the expected lifetime economic profitability, showed that inbred animals have a lower value than the average of their parents. With a loss of 4.77 per 1% increase in inbreeding, the VL is the component of the global economic index most strongly affected by inbreeding. Results for type traits were less clear cut than for production, but still showed a loss of 1.23 per 1% increase in inbreeding in VT. Inbreeding depression was rather low for VF, which is for the moment only based on SCS. Inbreeding depression on the global economic index was approximately –6.13 and thus appears relatively low but may still induce rerankings if considered in mating decisions.
In the future, this index will contain parameters as fertility, longevity, and health that are likely to be more sensitive to inbreeding, and a revised VG should thus be more profoundly affected by inbreeding. The recognition of the potential related animals before a mating decision can minimize inbreeding and the associated losses.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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Received for publication December 23, 2004. Accepted for publication December 20, 2005.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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