| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
ANIMAL GENETICS |
Department of Animal Sciences, Colorado State University, Fort Collins 80523
 |
Abstract |
|---|
 Top Abstract INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
|---|
Key Words: BLUP • feed intake • pen • genetic evaluation • pooled observation
|
INTRODUCTION |
|---|
|
TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
|---|
The logical development of an improvement program begins with definition of a goal. Next, the list of traits that influence the goal can be identified, along with their relative importance. This collectively defines the breeding objective. Given a breeding objective, a possible list of characteristics to measure can be identified, and these are known as selection criteria. A businesslike approach to the design of an improvement scheme involves assessment of economic consequences of alternative selection strategies that, among other factors, vary the nature and extent of the selection criteria.
It has often been more cost-effective to exclude characteristics that were expensive to measure (e.g., feed intake), or could only be measured late in life (e.g., longevity) or after slaughter (e.g., carcass attributes). Traits in the breeding objective that relied on such characteristics were either not subject to selection or were assessed from weakly correlated selection criteria.
Collective or pooled observations provide an option between extremes of making no measurement or measuring many individuals. Pooled observations are composed of a measurement that cannot be attributed to a particular individual (e.g., measurement of feed intake on a pen of 2 or more animals, or assessment of a milk characteristic on a pooled herd test sample from 2 or more cows). The analytical approach to such pooled data and the impact of pooling on ruû has received no attention to our knowledge. This paper presents exact and approximate analytical approaches and assesses both techniques in comparison to using individual measurements.
|
MATERIALS AND METHODS |
|---|
|
TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
|---|
 |
in which y represents observations on individual animals, b is a vector of unknown fixed effects, X is an incidence matrix whose rows relate each individual observation to their fixed effects in b, u is a vector of random additive effects, Z is an incidence matrix relating each observation to its corresponding genetic effect, and e is a vector of random residual effects. Given E[u] = 0 and E[e] = 0, then as a consequence E[y] = Xb. Assuming var[u] = G, var[e] = R, cov[u,eT] = 0, then var[y] = ZGZT + R and BLUP of u (i.e., û) can be obtained by solving the usual mixed model equations (Henderson, 1975
, 1984):
 | [1] |
Define the partitions in the left hand side of [1] as 
and elements of its inverse as 
. The accuracy of prediction of particular elements of u (referred to as ruû), the correlation between true and estimated merit, can be calculated from the square root of the ratio of the relevant diagonal element of G – C22 over the corresponding diagonal element of G. We refer to the correlations so obtained as measures of theoretical accuracy.
Suppose we measured individual records on a number of animals including one observed in herd 1 and 3 observed in herd 2 with phenotypic observations of 4.90, 7.30, 6.48, and 5.99 kg of feed intake, respectively. In this example,
 | [2] |
with var[u] = G = A
2u and var[e] = R = Ie2, in which A is the numerator relationship matrix among animals in u, I is an identity matrix of order equal to the number of observations, and 2u and e2 are genetic and residual variances, respectively.
Suppose the 4 animals were not individually observed, but animals 1 and 2 were in a pen together, as were animals 3 and 4. The observations are now pen sums, and each row of X and Z must reflect the incidence of all individuals in that pen. Vectors y and e and matrices X and Z from [2] can be modified (denoted with subscript p) to reflect pooling by summing together the corresponding rows for the animals making up the pool. Accordingly,
 |
with u (and therefore G) and b as defined previously. Due to the change in nature of eP, var[ep] no longer has elements 2e but is a diagonal matrix (RP) with elements nje2 where nj represents the number of individual animals that contributed to pooled observation j. Substituting yP, XP, ZP, and RP in [1] in place of y, X, Z, and R and solving the resultant equations will provide BLUP estimates of [u], but these will now have reduced accuracy and increased prediction error covariances in comparison with the situation in which animals were individually observed.
A natural approximation for the analysis of pooled data involves the apportioning of the pen sums equally among each of the individuals constituting the pool and assuming these average observations (denoted by subscript A) were observed. In that case,
 |
with remaining terms as in [2]. The above 3 (individual control, pooled exact, and pooled approximate) methods were compared in the analysis of simulated data.
Simulated Data
A data set of individual animal records for feed intake was simulated for grand progeny of a foundation population of 200 sires and 1,000 dams. The heritability for simulated feed intake was 0.34, the mean 6.48 kg, and phenotypic SD 0.62 kg (Koots et al., 1994a,b). The breeding values for the foundation sire i (us(i)) and foundation dam (ud(i)) were drawn independently from N(0,2u). Sires and dams were mated, and the resulting 1 offspring breeding values were created as 
in which 
i was independently drawn from 
. A residual effect (ei) for each animal with a record (second generation only) was independently drawn from N(0,2e).
Resulting first-generation offspring were mated together to produce a second-generation data set that was used for the analysis containing 200 maternal grandsires (MGS), 49 sires, and 1,000 offspring. The average sire had 20 offspring. The numbers of sires and MGS and their distribution across herds was simulated to reflect a real life bull test (L. L. Leachman, Wellington, CO, personal communication). Second generation offspring represented 18 contemporary groups reflecting different herd origins of the test animals. Herd-origin effects were included as fixed effects in [2] but did not need to be simulated because of the translation invariance of BLUP (Henderson, 1984).
Animals with individual records were pooled in pairs and in groups of 4 or 12 animals. The pooled pen observations were obtained by adding the individual records from each animal in the pool. Average pen observations were obtained by dividing the pool sum by the number of animals in the pool.
Pooling was undertaken in 3 ways, at random, by MGS, and by sire. When offspring were pooled by MGS or by sire, some mixed pools had to be created when the number of offspring per MGS or sire was not divisible by the pen size. Pooling by sire is appealing to livestock managers because the pooled observations can be readily attributed to the sire. However, any fixed effects that are confounded with the pen effects would bias the sire effects. In practice, there can be spatial performance trends due to subtle environmental differences between pens. Accordingly, a second simulation was undertaken whereby fixed pen effects were added to pooled records. Pen effects were drawn from a normal distribution with variance representing 10% of the phenotypic variance.
Strictly speaking, the accuracy assessed from the mixed model equations is an apparent or theoretical accuracy. It will only reflect the actual accuracy if the assumed model is correct or very close to the true underlying model. In practice, the model equation is at best a reasonable approximation of the state of nature. Furthermore, the variance components represented in G and R are usually only estimates of true values. Using simulated data, an actual measure of accuracy can be obtained by comparing the true breeding values to the model-dependent estimates of the breeding values. We refer to the product-moment correlation between true simulated and estimated breeding values as the empirical accuracy.
|
RESULTS AND DISCUSSION |
|---|
|
TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
|---|
In the control analysis with individual observations, the sires of the animals with observations will be more reliably assessed than the offspring themselves. The empirical and theoretical accuracies for estimated breeding values of sires were 0.77 and 0.75. Ignoring fixed effects and relationships, the expected accuracy from a progeny test involving unrelated dams producing n = 20 offspring is 
, in close agreement with observed values.
Pooling animals in pens reduced the amount of information that could be obtained from each individual observation. Pens of size 2 halve the number of observations. Larger pens further reduce the amount of information. Decreasing the amount of information available as selection criteria reduces the accuracy of evaluation. Accordingly, empirical accuracies for animals with records (Table 1) and for sires (Table 2) eroded when they were sorted into pens, regardless of the method of pooled analysis. For example, with random allocation of animals to pens, the empirical accuracy for individuals reduced to 0.50 for pens of 2 and 0.41 for pens of 4. Corresponding values were 0.48 and 0.38 for the approximate method. There was little or no practical difference between the empirical accuracies based on exact methodology and the approximate method, although the exact method was fractionally superior.
|
|
) were in close agreement with the empirical accuracies for the exact method, eroding with pooling. The theoretical accuracies are identical regardless of pen size when the approximate method was used, as the pooling strategy is not reflected in the coefficient matrix. The approximate method produces theoretical accuracies equal to the values that would pertain if every animal had an actual (not pooled) observation. Accordingly, the theoretical accuracies overstate the realized accuracy of the estimated merit, more so when larger pens are used.
|
Pen effects can be included as fixed effects in the analysis when individual observations are collected for each animal in the pen. However, when all offspring in a pen are from the same sire, their records cannot contribute directly to the evaluation of the sire if pen is fitted as a contemporary group. In contrast, when a pen is composed of offspring of more than one sire, and the distributions of offspring are different from pen to pen, pooled records can contribute to the evaluation of sires, even if pen effects are fitted.
The addition of pen effects contributing to variation in observations (at 10% phenotypic variance) had remarkably little influence on empirical accuracies. However, it should be noted that even with pens of 12 animals, the typical sire had offspring in at least 2 pens. Evaluations based on the exact or approximate methods were almost identical, and both provided useful information as to the merit of individuals and their sires when pen effects existed but were ignored in the evaluation.
The methodology presented here applies to multigenerational data with no modification, at least for the usual circumstances with zero residual covariances between animals of different generations. It can be extended to a multivariate setting composed of individual observations for one (or more) trait(s) and a pooled observation for another. However, in that case, R will typically include nonzero residual covariances between the observation on the pooled trait and all the individual observations on the correlated trait(s). Such residual covariance structures can be readily taken into account using the brute force approach of the animal breeder’s toolkit (Golden et al., 1992) but may be problematic in other widely used mixed model software.
|
IMPLICATIONS |
|---|
|
TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
|---|
1 Corresponding author: Dorian.Garrick{at}ColoState.edu
Received for publication May 26, 2005. Accepted for publication September 6, 2005.
|
LITERATURE CITED |
|---|
|
TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONIMPLICATIONSLITERATURE CITED |
|---|
This article has been cited by other articles:
|
|
 |
|
  S. L. Gruber, J. D. Tatum, T. E. Engle, M. A. Mitchell, S. B. Laudert, A. L. Schroeder, and W. J. Platter Effects of ractopamine supplementation on growth performance and carcass characteristics of feedlot steers differing in biological type J Anim Sci, July 1, 2007; 85(7): 1809 - 1815. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
