Calculation of a cow culling merit index including specific heterosis in a multibreed dairy population

The objective of this study was to compare two models for the estimation of producing values (EPV) for lactation yields of milk, fat and protein, and calving interval (CI), which were combined in an index called the Cow Culling Merit Index (CMI), in Irish dairy cattle. Data comprised 188 927 records for production and 157 117 records for CI, collected on North American Holstein Friesian (HO), Friesian (FR), Jersey (JE), and Montbéliarde (MO) pure breeds, and some of their crosses. Cows calved from 2002 to 2006 and were from parities 1 to 5. Coefficients of specific heterosis for HO×FR, HO×JE, and HO×MO were calculated for each cow from parental breed information. The coefficient of general heterosis (GH) for each cow was obtained as the sum of the specific coefficients previously estimated. Model 1 included fixed effects of contemporary group, age at calving within parity, linear regression on gene proportions for FR, JE, and MO, and linear regression on the coefficient of expected GH. Additive genetic, permanent environmental, and error were random effects. Model 2 was based on Model 1 but GH was replaced by linear regressions on coefficients of expected specific heterosis for HO×FR, HO×JE, and HO×MO. Estimated producing values were calculated as the sum of estimated breeding value, permanent environmental and heterosis effects. The inclusion of coefficients of specific heterosis in the model did not produce re-ranking of animals but important differences in EPVs were observed in crossbred cows. These changes are important if EPVs are used to develop a culling merit index.


Introduction
Commercial dairy cattle production in Ireland relies on several breeds, and the most important are North American Holstein Friesian (HO), Friesian (FR), Jersey (JE), and Montbéliarde (MO).Genetic evaluations across breeds are routinely computed by the Irish Cattle Breeding Federation (ICBF).The ICBF, in conjunction with Teagasc (the Irish farm research and advisory body), the Irish Department of Agriculture and other international collaborators, has developed a number of economic selection indexes suitable for Irish conditions and an overall index called the Economic Breeding Index (EBI).The aim of the EBI is to aid dairy farmers in identifying the most profitable bulls and cows for breeding dairy herd replacements.Milk production and fertility are the main contributors to farm profit and the economic weights in the selection index reflect their importance.
The across breed evaluation facilitates the comparison of estimated breeding values (EBV) on cows with differing breed contributions.Also, adjusting for heterosis allows more accurate selection of sires based on EBI through better estimation of the additive genetic effects.Farmers use the EBI to choose the best sires for the herd, to select cows to breed replacement heifers and as a tool for culling decisions.Estimated producing value (EPV) for traits of interest can be calculated for cows as the sum of their EBV plus permanent environment and heterosis effects, and can be adopted to estimate the future performance of the animal in the same herd, which would be useful for the purpose of culling (HENDERSON 1975).
The current model of genetic evaluation adjusts for a coefficient of general heterosis, calculated for each animal on the basis of its total heterozygosity, without investigating the effect of specific breeds.This assumes that cows from different breed combinations (e.g. a first-generation HO×FR cow and a first-generation HO×JE cow) will express the same level of heterosis.Recently, PENASA et al. (2009) found that significantly different specific heterosis effects exist in the Irish dairy population.
The aim of this study was to investigate the effect of including coefficients of general and specific heterosis in the calculation of EPVs for lactation yields of milk, fat, and protein and calving interval (CI), which were then combined with economic values to calculate an index called the Cow Culling Merit Index (CMI).

Data
A total of 188 927 records of 305-d milk, fat, and protein yield, and 157 117 records of CI were used in the analysis.Production data were from 104 160 cows while CI information was available for 88 094 cows.Full details on datasets and breed structure of contemporary groups are reported in PENASA et al. (2009).Briefly, lactation yields adjusted to 305 days using the standard lactation curve method (OLORI and GALESLOOT 1999) were obtained from ICBF.Records on cows from parities 1 to 5 calving in the spring (January to June) from 2002 to 2006 were extracted.Four dairy breeds (HO, FR, JE, and MO) were identified as having enough records to estimate breed effects for the traits.The proportion of genes was calculated for each cow as: where α i p is the proportion of genes from breed i in the progeny, α i s is the proportion of breed i in the sire, and α i d is the proportion of breed i in the dam.Coefficients of specific heterosis were calculated between any pair of the four dairy breeds using the following identity (DICKERSON 1973): where δ ij p is the coefficient of expected heterosis between fractions of breeds i and j in the progeny, α i s and α j s are proportions of breeds i and j in the sire, and α i d and α j d are proportions of breed i and j in the dam.Three types of crosses (HO×FR, HO×JE, and HO×MO) were chosen to estimate specific heterosis effects because the distribution of cows across classes of coefficients of expected heterosis was suitable for this purpose (PENASA et al. 2009).The coefficient of general heterosis for each cow was obtained by summing coefficients of specific heterosis previously calculated.

Models
Tests for normality were used to assess the deviation of the data from the normal distribution.Because of the large number of records available, the deviation of all traits was statistically significant.Nevertheless, the values of skewness and kurtosis were relatively low, with the highest absolute values for CI (0.75 and 0.55, respectively), so that the application of linear models will be justified.
Breed and heterosis effects for lactation yields of milk, fat and protein, and CI were obtained in ASReml (GILMOUR et al. 2002) under the following univariate repeatability animal models: where y is the vector of observations for lactation yields of milk, fat or protein, or CI, b1 is the vector of fixed effects of overall mean, contemporary group, and age at calving within parity, b2 is the vector of fixed regression coefficients of breed additive effects for FR, JE and MO (HO breed set to zero for comparison), b3 is a scalar of regression coefficient for GH, b4 is the vector of fixed regression coefficients for specific heterosis (HO×FR, HO×JE, and HO×MO), a is the vector of random additive genetic effects, c is the vector of random permanent environmental effects, e is the vector of residuals, and where X1, X2, X3, X4, Z, and W are the incidence matrices relating fixed effects, fixed additive breed effects, fixed GH effects, fixed specific heterosis effects, random additive genetic effects, and random permanent environmental effects, respectively.Variances of the random effects were considered as follows: where σ 2 a , σ 2 c , and σ 2 e are the variances of animal, permanent environmental, and residuals effects, respectively, A is the numerator relationship matrix, Ic is an identity matrix of size c (the number of animals with records) and Ie is an identity matrix of size equal to the number of records for either production or CI traits.Heritabilities and repeatabilities for production were assumed in 0.35 and 0.55, respectively, which are those currently used for routine genetic evaluation of 305-d milk yield traits in Ireland (INTERBULL 2009).Heritability for CI was assumed in 0.04, again according to INTERBULL (2009), and repeatability in 0.08, according to the study of KEARNEY et al. (2004).Heritability for CI was comparable with estimates reported by DAL ZOTTO et al. (2007) in different environmental conditions.
A t-test was used to assess if effects for FR, JE, and MO were significantly different from HO as well as if heterosis effects were significantly different from zero.
Estimated breeding value (EBV) for animal k and for each trait was obtained as: where αFR, αJE, and αMO are proportions of FR, JE, and MO genes in animal k, respectively, ĝFR, ĝJE, and ĝMO are the estimated effects of FR, JE, and MO breeds, respectively, and âk are the estimated random additive genetic effect for animal k.Estimated producing value (EPV) of cow k with records was obtained according to the two models as:

Results and discussion
Descriptive statistics for lactation yields and CI are shown in Table 1, along with estimates of crossbreeding effects obtained under the two models.Means and standard deviations were similar to those reported by EVANS et al. (2006) for commercial Holstein-Friesian cows.Breed effects obtained using the two models were similar.Estimates for milk and protein yield were always in favour of HO, the breed set as the reference in our study.Only fat production from Model 1 was significantly (P<0.05)higher for JE than HO cows, but the latter breed produced 1 680 kg more milk and 27.7 kg more protein than the former.These differences were larger compared to those reported by BUCKLEY et al. (2008) from an experimental trial comparing Holstein-Friesian, JE and their crosses under Irish grazing conditions.In that experiment, the JE produced 1 283 kg less milk and 19 kg less protein compared to Holstein-Friesian.However, fat yield from JE was 13.1 kg higher in BUCKLEY et al. (2008) than in our study.In New Zealand dairy cattle, the JE produced 904 kg less milk and 9.6 kg less fat compared to Holstein-Friesian cows (AHLBORN-BREIER and HOHENBOKEN 1991).In a study involving dairy herds in the United States, additive breed effects for JE were −2 962 kg for milk yield, −34 kg for fat yield and −47 kg for protein yield compared to Holstein-Friesian (VANRADEN et al. 2007).Friesian and MO were similar for lactation yields (Table 1) and inferior than HO.Breed effects for MO cows agree with results reported by DILLON et al. (2003) in which the MO produced 875 kg less milk, 38 kg less fat, and 24 kg less protein than Holstein-Friesian cows.Breed effects for CI showed that FR and JE had significantly shorter CI compared to HO cows, regardless of the model used, while MO had shorter CI than HO only with Model 1.
General and specific heterosis effects for production traits were all positive and significantly different from zero (P<0.001).Heterosis effects for CI were negative but significantly different from zero only for HO×MO (P<0.05)indicating that HO×MO cows had shorter CI than the average of the parental purebreds.Heterosis estimates expressed as percentage of the overall mean were slightly lower than those reported in New Zealand (HARRIS 2005) and the United States (VANRADEN and SANDERS 2003) but similar to experimental results from BUCKLEY et al. (2008) andPENASA et al. (2007).In general, crossbreeding effects from this study slightly differed from results reported by PENASA et al. (2009) using the same datasets.The differences are probably attributable to the shorter pedigree considered in our study (only cow, sire, dam and grandparents) and to the use of different softwares to obtain the estimates.
3) −12.4 (15.0) −28.9 (13.0) −15.1 (15.0) 3.1 (16.5) 10.2 (13.5animal model with coefficient of general heterosis, Model 2 repeatability animal model with coefficients of specific heterosis, 1 HO North American Holstein Friesian, FR Friesian, JE Jersey, MO Montbéliarde, HO×FR North American Holstein Friesian × Friesian, HO×JE North American Holstein Friesian × Jersey, HO×MO North American Holstein Friesian × Montbéliarde, *means significantly different from zero at P<0.05 δGH is the total heterozygosity of cow k, δHO,FR, δHO,JE, and δHO,MO are specific heterozygosities between HO×FR, HO×JE, and HO×MO of cow k, respectively, ĥGH is the estimate of general heterosis effects, ĥHO×FR, ĥHO×JE, and ĥHO×MO are estimates of specific heterosis effects, and ĉ k is the solution for the permanent environmental effect of cow k.Estimated producing values for lactation yields of milk, fat and protein, and CI were combined into an economic index useful for cow culling decisions.This index can be termed Cow Culling Merit Index (CMI) and was calculated for each cow as: where Economic values (EV) may be estimated as suggested byPIETERS et al. (1997), and for the CMI were equal to −0.09 €/kg milk, 1.26 €/kg fat, 6.91 €/kg protein, and −11.97 €/day of CI (ICBF website, http://www.icbf.com)which are the current economic values included in the calculation of the EBI and used by farmers for the identification of the most profitable bulls and cows for breeding dairy herd replacements.The set of EVs used for the two indexes (CMI and EBI), should be different because the time horizon of each index is different.In particular, EVs for the CMI should aim to measure the future economic circumstances of the cow during her productive life while the EVs for the EBI should aim to measure the economic circumstances of the future progeny of the cow.

Table 2
Means and standard deviations (within brackets) of estimated producing values for milk yield traits and calving interval obtained under two linear models for different breed groupsMittelwerte und Standardabweichungen (innerhalb der Klammern) für geschätzte Produktionswerte für Milchleistungsmerkmale und das Kalbeintervall für verschiedene Rassengruppen bei Anwendung von zwei verschiedenen Modellen