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Within-Herd Heritability Estimated with Daughter–Parent Regression for Yield and Somatic Cell Score

C. D. Dechow^*,1 and H. D. Norman

^* Department of Dairy and Animal Science, The Pennsylvania State University, University Park 16802
Animal Improvement Programs Laboratory, ARS, USDA, Beltsville, MD 20705-2350

¹ Corresponding author: cdechow{at}psu.edu

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Estimates of heritability within herd (h_WH² ) that were generated with daughter–dam regression, daughter–sire regression, and REML were compared, and effects of adjusting lactation records for within-herd heritability on genetic evaluations were evaluated. Holstein records for milk, fat, and protein yields and somatic cell score (SCS) from the USDA national database represented herds in the US Northeast, Southeast, Midwest, and West. Four data subsets (457 to 499 herds) were randomly selected, and a large-herd subset included the 15 largest herds from the West and 10 largest herds from other regions. Subset heritabilities for yield and SCS were estimated assuming a regression model that included fixed covariates for effects of dam yield or SCS, sire predicted transmitting ability (PTA) for yield or SCS, herd-year-season of calving, and age within parity. Dam records and sire PTA were nested within herd as random covariates to generate within-herd heritability estimates that were regressed toward mean h_WH² for the random subset. Heritabilities were estimated with REML using sire models (REML_SIRE), sire–maternal grandsire models (REML_MGS), and animal models (REML_ANIM) for each herd individually in the large-herd subset. Phenotypic variance for each herd was estimated from herd residual variance after adjusting for effects of year-season and age within parity. Deviations from herd-year-season mean were standardized to constant genetic variance across herds, and records were weighted according to estimated error variance to accommodate h_WH² when estimating breeding values. Mean h_WH² tended to be higher with daughter–dam regression (0.35 for milk yield) than with daughter–sire regression (0.24 for milk yield). Heritability estimates varied widely across herds (0.04 to 0.67 for milk yield estimated with daughter–dam regression), and h_WH² deviated from subset means more for large herds than for small herds. Correlation with REML_ANIM h_WH² was 0.68 for daughter–dam and was 0.45 for daughter–sire h_WH² for milk yield. The correlation between daughter–sire h_WH² and REML_MGS was greater than the correlation between daughter–dam h_WH² and REML_MGS. Data adjustments had a minimal impact on breeding value bias. Within-herd heritability can be estimated rapidly using regression techniques with moderate accuracy, but adjusting lactation records for h_WH² resulted in only a small improvement in the accuracy of genetic evaluations.

Key Words: heritability • daughter–dam regression • daughter–sire regression

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Genetic evaluations for most traits assume that heritability is constant across herds within a breed. However, management and environmental factors that vary across herds could result in different heritabilities. In addition, the accuracy of records that contribute to genetic evaluations varies across herds. Inaccurate parent identification reduces heritability estimates and PTA accuracy (Gelderman et al., 1986; Banos et al., 2001). Herd characteristics that may not directly influence data accuracy, such as larger herd size or higher maximum monthly temperature, also were associated with lower heritability estimates in an across-country study (Zwald et al., 2003). The herd characteristics that have received the most attention for their relationship to heritability are mean yield and yield variance. Heritability estimates typically increase as mean herd yield and herd phenotypic variance increase (Lofgren et al., 1985; Vinson, 1987; Van Tassell et al., 1999).

Herd-year heritability for yield is assumed to increase when the standard deviation (SD) for phenotype increases (Wiggans and VanRaden, 1991) and is constrained to range from 0.25 to 0.35 in the US genetic evaluation of Holsteins (Van Tassell et al., 1999). Within-herd heritability is accounted for by standardizing yield to a constant genetic SD prior to generating EBV and weighted by the ratio of base error variance to herd error variance while generating EBV (Wiggans and VanRaden, 1991). Final type scores are standardized to a constant phenotypic variance to account for reduced variance as the herd mean type score increases, but herd heritability is not assumed to vary (Weigel and Lawlor, 1994).

Efforts to standardize records to constant genetic or phenotypic variance have resulted in improvements in the accuracy of sire PTA (Wiggans and VanRaden, 1991; Powell et al., 1994; van der Werf et al., 1994; Weigel and Lawlor, 1994). The use of direct estimates of within-herd heritability (h_WH²) may be more precise than heritability inferred from herd variance. Estimating a separate heritability for a large number of herds on a routine basis using REML is not feasible, and heritability estimates are not accurate for small data sets (Falconer and Mackay, 1996). Alternatively, regression techniques could be used that are computationally feasible. Within-herd heritability could be regressed toward the mean for small herds that lack sufficient data to estimate h_WH² accurately. Daughter–dam regression and paternal half-sibling correlations can be used to derive heritability (Falconer and Mackay, 1996), and both are based on sources of pedigree information that are recorded to some extent in nearly all herds.

Most herds have too few paternal half-siblings to estimate heritability directly from half-sibling correlations. Regressions on sire PTA, which are generated primarily with half-sibling records, give some indication of genetic variation and could be used to infer herd heritability. In a comparison of grazing and confinement herds in the United States, genetic variance in the grazing herds was estimated to be 62 to 87% lower than in confinement herds (Kearney et al., 2004). Regression of mature-equivalent (ME) milk on sire PTA for milk was correspondingly lower in grazing herds (0.78) than in the confinement herds (0.99).

The objectives of this study were 1) to estimate h_WH² rapidly and accurately using regression techniques, 2) to evaluate h_WH² differences and factors that contribute to those differences, and 3) to evaluate the effect on genetic evaluation accuracy when using h_WH² to standardize records across herds to constant genetic variance and to weight records according to estimated error variance.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Data
Mature-equivalent milk, fat, and protein yields and mean SCS records from first- through fifth-parity Holstein cows that had calved between January 1997 and June 2004 were obtained from the USDA national lactation database for selected states that represented 4 regions: West (California), Midwest (Wisconsin), Northeast (New York and Pennsylvania), and Southeast (Alabama, Arkansas, Florida, Georgia, Louisiana, Mississippi, North Carolina, Oklahoma, South Carolina, Tennessee, and Texas). Four data subsets were created to provide replication across multiple samples and to analyze a large number of herds within computational limits. The 4 subsets were created by randomly selecting herds across regions. A fifth subset was created by selecting the largest herds from the 4 original subsets: the 10 largest herds from the Northeast, Southeast, and Midwest regions and the 15 largest herds from the West. Herd size in the large-herd subset ranged from 1,076 lactation records from 671 cows to 19,856 lactation records from 9,497 cows.

All cows were required to have either a dam from the same herd or a sire with an official genetic evaluation. Dams were required to be from the same herd because heritability estimates were intended to reflect h_WH² and not the general population heritability. A minimum of 4,500 kg of ME milk was required, and records from second and later parities were retained only if a first-parity record was available. Contemporary groups were similar to those used in national genetic evaluations. Herd-year-seasons of calving were 6 bimonthly calving seasons. For herd-year-seasons with <5 cows, seasons were expanded to 4-mo intervals. Herd-year was substituted for herd-year-season if <5 cows were in the herd-year-season after expanding the season length; herd-years with <5 cows were excluded. Of the original records across subsets, 24% were removed because of additional data edits.

The numbers of records, cows, daughter–dam pairs, sires, and herds for each data subset are shown in Table 1. Data subsets ranged from 206,766 to 290,544 records. Percentages of cows with a dam record from the same herd ranged from 55 to 59% (large-herd subset). The mean number of records by region ranged from 51,469 (Midwest) to 72,306 (West).

[1]

where y is a vector of ME milk, fat, or protein yields or SCS, X is the incidence matrix for fixed effects, B is a vector of fixed effects (age within parity and year-season of calving), Z is the incidence matrix for additive pedigree (animal, sire, or sire + MGS), u is a vector of random pedigree effects, W is the incidence matrix for permanent environmental effects, p is a vector of random permanent environmental effects, and e is a vector of random residuals.

Daughter–Dam and Daughter–Sire Estimates for h_WH²
The h_WH² for milk, fat, and protein yields and SCS were estimated with daughter–dam and daughter–sire regressions. Dam records were the residuals from the following model:

[2]

where y is ME milk, fat, or protein yield or SCS for parity i of cow in year-season j; b_i is the coefficient for fixed regression on age nested within parity (A), H is a fixed effect of year-season, and e is the effect of the random residual. The analysis was applied to each herd individually, which was computationally feasible and easily accommodated with the MIXED procedure of SAS (SAS Institute, 2000). Daughter ME milk, fat, and protein yields and SCS were then regressed on the corresponding dam record. Daughter–dam and daughter–sire regressions were conducted simultaneously. This procedure required no missing values to make use of all available dam records when sire PTA was missing, or to make use of sire PTA when dam records were missing. Sire PTA and dam records were averaged for each herd-year-season and included for cows with missing values.

Regression models to estimate h_WH² included fixed regression coefficients to estimate mean heritability for each data subset. An additional random coefficient nested within herd allowed the calculation of h_WH² estimates that were regressed toward the subset mean. The model for estimating heritabilities in AS-REML (Gilmour et al., 2002) was

[3]

where y is ME milk, fat, or protein yield or SCS for parity i of cow in herd l, herd-year k, and herd-year-season j; b_i is a coefficient for fixed regression on age (A) nested within parity i; H is a fixed effect of herd-year-season; b₂ is a coefficient for fixed regression on dam record (D); b₃ is a coefficient for fixed regression on sire PTA (S); b₄ is a coefficient for fixed regression on the interaction between sire PTA and herd-year SD for yield or SCS; b_1l is a coefficient for random regression on dam record nested within herd (F); b_2l is a coefficient for random regression on sire PTA nested within herd (G); and e is an effect of the random residual. An analysis of milk yield without regression on fixed effects [b₂D, b₃S, and b₄(S x SD_k)] was also performed to determine the effect of deviating from an overall fixed regression coefficient.

Herd phenotypic variance estimates (and herd-year SD) were derived using residual variance for each herd from model [2]. Residual variances from current, previous, and subsequent herd-years and mean residual variance for the data subset were weighted according to the procedures of Wiggans and VanRaden (1991) to estimate herd-year phenotypic variance that was regressed toward the subset mean with the following formula:

where _HY² is the phenotypic variance estimate for the current herd-year, ²_S is the average residual variance (e_ij) from model [2] for j herd-year seasons in the current year, ²_HY is e_ij in the current year, ²_HY–1 is e_ij for the previous year, ²_HY+1 is e_ij in the subsequent year, N_HY are the degrees of freedom for the current year, N_HY–1 are the degrees of freedom for the previous year, and N_HY+1 are the degrees of freedom for the subsequent year. The degrees of freedom were assumed to be the number of records minus 1. Weights derived from the inverse of standard errors could replace degrees of freedom, but that approach was not examined in this study.

The h_WH² from the daughter–dam regression was 2(b₂ + b_ll). To estimate h_WH² from the daughter–sire regression, the additive genetic SD for the herd was first assumed to be

where SD_US is the genetic SD assumed for USDA-DHIA Holstein genetic evaluations (755 kg for ME milk). Thus, a herd with

was assumed to have twice the genetic SD of the general population. The h_WH² from daughter–sire regression was herd additive genetic variance divided by _HY². Because _HY² was used in the analysis of daughter–sire regressions, h_WH² heritability could vary each year for daughter–sire regression. Midparent h_WH² was the mean of h_WH² from daughter–dam and daughter–sire regressions.

The relationship between h_WH² and herd parameters that could be indicators of h_WH² was assessed with a multiple regression model in the GLM procedure of SAS (SAS Institute, 2000) with h_WH² as the dependent variable. Independent variables included region (California, Northeast, Southeast, Wisconsin), average number of first-lactation animals calving per year within region, percentage of cows identified by a registration number, average age at first calving, herd average yield or SCS, and herd phenotypic SD of yield or SCS.

Data Adjustment
Animal-model EBV were generated with BLUPF90 (Misztal, 2004) with and without adjustment for h_WH² with methods similar to those of Wiggans and VanRaden (1991). The model to estimate breeding values was similar to model [1]. The only difference was that EBV were generated with records from all herds in a subset, so year-season was replaced with herd-year-season and only animal was considered as a pedigree effect.

Records were standardized to constant genetic variance prior to estimation of breeding values, whereas error variance differences among herds were accommodated by weighting records simultaneously with estimation of breeding values. Genetic and permanent environmental variances were identical to those used in national genetic evaluations, which are based on assumed heritabilities of 0.30 and repeatabilities 0.55 for yield traits (Van Tassell et al., 1999) and 0.10 and 0.35, respectively, for SCS (Schutz, 1994). Estimates of h_WH² for yield were constrained to a range between 0.10 and 0.50 before adjusting for h_WH². Heritability constraints were made to prevent overextrapolation and because negative weights would have been obtained if herd heritability had been allowed to be greater than the assumed repeatability.

Daughter milk, fat, and protein yields and SCS were deviated from herd-year-season means for those traits. Resulting deviations were multiplied by the ratio of SD_US to herd additive genetic SD. Changes in error variance were accommodated by weighting records with the ratio of error variance for national genetic evaluations to estimated error variance after adjusting for herd additive genetic SD (Wiggans and VanRaden, 1991).

Tests of Data Adjustments
Methods derived by van der Werf et al. (1994) and Reverter et al. (1994) to detect bias in genetic parameter estimates were adapted to determine the effect of data adjustments. The methods rely on comparisons of EBV in subsequent genetic evaluations. For each data subset, EBV were first generated only with records from cows calving in 2000 and earlier (EBV2000) and second with the complete data subset (EBV2004). Data adjustments for EBV2000 were based on h_WH² generated with records from calvings in 2000 and earlier. The EBV from sires that entered a young sire program between July 1995 and July 1997 were selected to evaluate the effects of data adjustments. Sires were required to have 1) daughters that calved in multiple herds by 2000 or earlier, 2) daughters in at least one additional herd after 2000, 3) a reliability for EBV2000 of at least 50% for yield or 35% for SCS, and 4) a reliability for EBV2004 of at least 80% for yield or 60% for SCS. The EBV2000 for sires that entered AI in this time period would be derived from first-crop daughters, whereas EBV2004 would include second-crop daughters. The effect of data adjustments on bias attributable to factors such as preferential treatment of daughters sired by elite proven bulls can then be detected.

The EBV2004 were regressed on EBV2000, and fluctuations in EBV were compared across subsequent genetic evaluations to determine the effects of data adjustments. van der Werf et al. (1994) obtained an observed genetic variance based on EBV fluctuation with the following formula:

where _a² is observed genetic variance based on fluctuations in genetic evaluations, EBV_2004i is EBV2004 for sire i, EBV_2000i is EBV2000 for sire i, r_i ² is the change in reliability from EBV2000 to EBV2004 for sire i, and n is the number of sires. The ratio of _a² to the genetic variance used to derive EBV indicates whether fluctuations were larger than expected relative to the amount of information gained in subsequent evaluations, whereas regression of EBV2004 on EBV2000 would be expected to be 1 in the absence of any bias (Reverter et al., 1994). The significance of differences in fluctuations was determined by comparing _a² before and after data adjustments with a 2-tailed paired t-test.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Large Herd h_WH²
Means and correlations among daughter–dam h_WH², daughter–sire h_WH², midparent h_WH², REML_SIRE h_WH², REML_MGS h_WH², and REML_ANIM h_WH² for milk yield are shown in Table 2 for the large-herd subset. Mean h_WH² was highest when estimated with daughter–dam regression (0.32) and lowest when estimated with REML_SIRE (0.19). Heritability estimates ranged from 0.04 to 0.45 for daughter–dam h_WH², 0.01 to 0.64 for daughter–sire h_WH², and 0.04 to 0.36 for REML_ANIM h_WH². The h_WH² estimated with REML_ANIM had standard errors ranging from 0.02 to 0.08. Daughter–sire h_WH² could change by year within herd because the estimation of daughter–sire h_WH² was dependent on herd-year SD. The intraclass correlation for daughter–sire h_WH² ranged from 0.91 (fat yield) and 0.95 (milk yield), indicating that daughter–sire h_WH² varied little across years within the same herd. Thus, daughter–sire h_WH² were averaged across years for each herd when generating the correlations shown in Table 2 and in subsequent tables. Correlations among heritability estimates ranged from 0.31 between daughter–dam and REML_SIRE h_WH² to 0.94 between REML_SIRE and REML_MGS h_WH².

View larger version (13K): [in this window] [in a new window]   Figure 1. Box plot of daughter–dam h2 estimates for milk yield by the total number of lactation records per herd (herd size) used to estimate hWH2. Median values are represented by the horizontal center line, the top and bottom of the shaded boxes represent the interquartile range, the vertical bars represent extreme values that are within 1.5 times the interquartile range, and the asterisks represent extreme values outside that range.

View larger version (14K): [in this window] [in a new window]   Figure 2. Box plot of daughter–dam h2 estimates with no fixed regression coefficient for milk yield by the total number of lactation records per herd (herd size) used to estimate hWH2. Median values are represented by the horizontal center line, the top and bottom of the shaded boxes represent the interquartile range, the vertical bars represent extreme values that are within 1.5 times the interquartile range, and the asterisks represent extreme values outside that range.

View this table: [in this window] [in a new window]   Table 8. Ratio of genetic variance estimated from fluctuations in subsequent genetic evaluations to assumed true genetic variance (2a/2a) and the regression (b) of subsequent breeding values on previous breeding values before and after adjustment for within-herd h2 from daughter–dam and daughter–sire regressions, and midparent1

The relationships between herd factors and midparent h_WH² are shown in Table 9. All factors were significant (P < 0.05) and are arranged in order of the factor associated the largest proportion of variance based on type III mean square estimates (SD of milk yield) to lowest variance (region). The variance for percentage of cows identified with a registration number is based on linear + quadratic regression coefficients. Regression coefficients indicate that greater herd phenotypic SD, higher average milk yields, a higher percentage of registered cows, and an earlier age at first calving are associated with higher h_WH² . Midparent and daughter–sire h_WH² were lower from herds in California, and larger herd size (represented by more first-lactation cows) was associated with lower h_WH² in California. Daughter–dam h_WH² tended to be less strongly related to herd SD and herd average, and more strongly related to the percentage of registered cows than were midparent or daughter–sire h_WH². Trends for fat yield, protein yield, and SCS were similar, except that herd average SCS was not significantly associated with h_WH ².

View this table: [in this window] [in a new window]   Table 9. Type III mean square estimates (2), values for herds in the 10th and 90th percentiles, and predicted change in within-herd heritability ( hWH2) from the 10th to 90th percentile for the following independent variables: herd-standard deviation of mature-equivalent milk yield (milk SD), region (California, Northeast, Southeast, Wisconsin), average number of first-lactation animals calving per year (heifers, n) nested within region, herd average mature-equivalent milk yield (milk average), percentage of cows identified by a registration number (PCTHOL), and average age at first calving

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

Within-herd h² could be regressed toward herd parameters that influence h_WH² . Herd average and SD, region of the country or state, percentage of registered cows, herd size, and average age at first calving were all significantly associated with h_WH² . Herds with greater phenotypic variance had higher heritability, which is consistent with other studies (Van Tassell et al., 1999). The heritability of yield has previously been estimated to be lower in California than in New York or Wisconsin, and heritability estimates are higher when estimated with registered daughters (Carabaño et al., 1990; Dimov et al., 1995). Larger herd size was associated with reduced heritability in some regions, which is consistent with results from Zwald et al. (2003). Although these herd parameters give some indication of h_WH² , the total variance explained by the multiple regression model was 31% (R² = 0.31), indicating that the majority of variance in h_WH² was not accounted for by the factors analyzed.

Daughter–dam h_WH² generally were higher than daughter–sire h_WH². For SCS, daughter–dam h_WH² were approximately twice as high (0.24) as the parameters used for national genetic evaluations (Schutz, 1994) and 4 times greater than daughter–sire h_WH² . Daughter–dam h_WH² for milk yield were higher than previously reported heritability estimates from paternal half-sibling correlations (Van Vleck and Bradford, 1965; Van Vleck and Bradford, 1966). Environmental effects common to daughters and dams likely inflate daughter–dam h_WH² , as would any maternal or cytoplasmic effects (Van Vleck and Bradford, 1965). The relative ranking among herds for daughter–dam h_WH² would be accurate if common environmental and maternal effects were similar across herds.

Lower daughter–sire h_WH² could also indicate that sire misidentification is more common than dam misidentification. Sire misidentification would have a minimal impact on daughter–dam h_WH² , and presumably influence h_WH² from REML_SIRE and REML_MGS more severely than REML_ANIM. Daughter–dam h_WH² was not as strongly correlated with h_WH ² generated from REML_SIRE and REML_MGS. Conversely, daughter–sire h_WH² was more strongly correlated with h_WH ² generated by REML_MGS than h_WH² generated with REML_ANIM.

Because of an interaction between genotype and environment, daughter–sire h_WH ² would be biased downward more severely than would daughter–dam h_WH ² . Both dam and daughter were required to be from the same herd, which would limit the effect of a genotype–environment interaction on h_WH ² estimates. Sire PTA are generated across herds, and regression on sire PTA would be depressed if a genotype–environment interaction existed. Variance of the sire–herd interaction can be combined with additive genetic variance to estimate mean h_WH ² across herds (Notter et al., 1992). The herd–sire interaction was estimated to be approximately 2% of phenotypic variance for milk yield in Holsteins (Dimov et al., 1995), which indicates that daughter–sire h_WH ² could be appreciably depressed by the presence of a genotype–environment interaction.

The effect of data adjustment on EBV fluctuations was inconsistent and only daughter–sire h_WH ² adjustments increased regression coefficients of EBV2004 on EBV2000. Some possible negative impacts of adjusting for h_WH ² should be considered. Daughter–dam regression could expand the influence of preferential treatment. Preferential treatment within certain cow families is likely to increase daughter–dam h_WH ² , and genetic evaluations that adjust for daughter–dam h_WH ² would weight those records even more heavily. In addition, the method used to generate daughter–sire h_WH ² has part–whole influences. Records are weighted more heavily in herds in which daughter yield is highly correlated with past sire evaluations, which could create a stronger relationship between daughter performance and sire evaluations in future evaluations and inflate future daughter–sire h_WH². Alternative uses for h_WH² might avoid such issues and should be investigated. Reliability could be adjusted to reflect the impact of h_WH². Progeny-test herds with low h_WH may be candidates for DNA parentage verification or removal from progeny-test programs.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Estimates for h_WH ² can be generated using the regression of daughter records on dam records and the regression of daughter records on sire PTA with moderate accuracy. Daughter–dam h_WH ² were a stronger indicator of heritability estimated with an animal model, whereas daughter–sire h_WH ² were stronger indicators of heritability estimated with sire and sire–MGS models. Both daughter–dam and daughter–sire methods demonstrate that significant differences exist among herds for heritability. Those differences could result from variability in recordkeeping (especially more accurate pedigrees), genotype–environment interaction, or other identifiable herd factors, including the percentage of registered cows, herd size, herd average yield or SCS, herd standard deviations for yield and SCS, average age at first calving, and region of the country. Heritability differences among herds could substantially alter the accuracy of EBV depending on the average h_WH ² of the herds in which a bull’s daughters are located.

Data adjustments generally did not reduce fluctuations in subsequent genetic evaluations and only daughter–sire h_WH ² improved regressions of subsequent EBV. For the methods that were investigated, the effect of preferential treatment on h_WH ² is not clear, or whether part–whole influences from past genetic evaluations would artificially inflate h_WH ² for some herds. Other methods of incorporating h_WH ² into genetic evaluations, such as adjusting reliability estimates based on h_WH ² , that would avoid effects of preferential treatment and part–whole relationships should be investigated.

	ACKNOWLEDGEMENTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
The authors appreciate funding from the Agricultural Research Service, USDA. The cooperation of AgriTech Analytics (Visalia, CA), AgSource Cooperative Services (Verona, WI), Dairy Records Management Systems (Raleigh, NC), DHI Computing Services (Provo, UT), and Texas DHIA (College Station, TX) in supplying yield data through the National Genetic Improvement Program was invaluable. The assistance of S. M. Hubbard, Animal Improvement Programs Laboratory (Beltsville, MD), and 2 anonymous reviewers in manuscript preparation is appreciated.

Received for publication December 30, 2005. Accepted for publication August 9, 2006.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 


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