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Poult Sci 2007. 86:30-36
© 2007 Poultry Science Association
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GENETICS

Estimation of Genetic Parameters for Cumulative Egg Numbers in a Broiler Dam Line by Using a Random Regression Model

P. T. Luo*,{dagger}, R. Q. Yang{ddagger},1 and N. Yang*,1

* Department of Animal Genetics and Breeding, College of Animal Science and Technology, China Agricultural University, Beijing 100094, China; {dagger} Beijing Poultry Breeding Company Ltd., Beijing 101301, China; and {ddagger} School of Agriculture and Biology, Shanghai Jiaotong University, Shanghai 201101, China

1 Corresponding author: nyang{at}cau.edu.cn and runqinyang{at}sjtu.edu.cn


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The random regression model (RRM) methodology was applied to the estimation of genetic parameters for cumulative egg numbers and monthly egg production in a broiler dam line. The data were extracted from records of a commercial dam line in 2001 to 2003. A total of 99,193 records from 6,475 hens and 9,111 pedigreed animals were used in the current study. The variance components were estimated using Gibbs sampling procedure. According to the Bayesian information criterion and Bayes factor, an RRM with Legendre polynomial of 2 orders for hatching groups and additive genetic effects and of 4 orders for permanent environmental effects was chosen as the optimal model for cumulative egg numbers in the broiler dam line. The heritability estimates of the cumulative egg numbers between wk 1 and 40 of production ranged from 0.16 to 0.54, whereas heritability estimates from wk 12 to 20 of production were moderate. The ratios of permanent environmental variance to phenotypic variance were large, indicating that the RRM could produce better estimates of additive genetic effects. The genetic and phenotypic correlations between cumulative egg numbers at different production weeks estimated with the optimal RRM were generally higher when the overlapping weeks were greater. In addition, genetic parameters for monthly egg production could also be obtained by the optimal RRM, and the heritability estimates ranged from 0.03 to 0.18. It was suggested that early selection based on cumulative egg numbers in the first 19 wk of production could effectively improve annual egg production in the broiler dam line.

Key Words: genetic parameter • broiler dam line • egg production • random regression model • heritability


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In broiler production, egg production is an important economic trait for broiler breeders. Selection for early period part-records, generally up to 40 wk of age, is the usual approach for improving egg production in egg-type and meat-type chickens, which has been shown to make substantial genetic improvement (Fairfull and Gowe, 1990). However, selection based on part-records has significant unfavorable effects on some important traits, including earlier age at first egg, poorer laying persistency after peak (Yang, 1994), and poor selection accuracy. A comprehensive estimation of heritabilities and genetic correlations among different part-records and complete egg production is needed for designing a sustainable selection program in broiler dam lines. At present, few estimates of egg production have been reported in broiler breeders.

The cumulative egg number is a longitudinal trait that depends on weeks or months of production. The random regression model (RRM) methodology (Henderson, 1982; Schaeffer and Dekkers, 1994) has been increasingly used to analyze these kinds of traits because it has the flexibility and ability to describe individual gene expression at different points of time (Swalve, 2000; Jensen, 2001). On the application of RRM to chickens, the earliest report was Anang et al. (2000). Anang et al. (2002) and Mielenz et al. (2002) investigated the use of monthly production records for genetic evaluation of laying hens. Their analysis methodology derived from a test day model with random regression in dairy cattle and compared it with other models, including random regression with covariates derived from the regression of Ali and Schaeffer (1987), random regression with covariates derived from quadratic polynomial, and fixed regression with covariates derived from Ali and Schaeffer (1987), Ptak and Schaeffer (1993), and Anang et al. 2001). A multivariate longitudinal mixed model was developed and implemented for the genetic evaluation of male and female fertility and hatch-ability in chickens (Sapp et al., 2004). Sapp et al. (2005) recommended that the longitudinal multiple-trait best linear unbiased prediction method be used for genetic evaluation of hens and roosters for setting eggs, percentage fertility, and percentage hatch of fertile eggs, comparing them with cumulative single-trait by the simulations. The objective of the present study was to apply the random regression model to estimate the genetic parameters for cumulative egg numbers with actual data from a broiler dam line.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Data
Records for egg number and pedigree information were from 3 generations of a broiler dam line (L4) in Beijing Poultry Breeding Company Ltd (West Zhaoquanying Town, Shunyi District, Beijing, China) during 2001 to 2003. The L4 line had been selected for increased egg production, increased growth rate, and other traits since 1987, with 100 pedigree pens per generation, each pen with 12 females and 1 male. Each full-sib family produced 3 females. Each half-sib family had 30 to 36 females for the trap nesting egg performance test. Chicks participating in egg testing were raised on the same conditions as the broiler breeders and experienced feed restriction during the rearing period. The trap nesting egg test started at 26 wk and ended at 65 wk, collecting eggs 5 d/wk. The raw data of about 250,000 records for weekly egg number were obtained. Cumulative egg numbers were generated by summing the egg numbers for each week. The age at first egg (AFE) was defined as the first week of production. In the editing process, individuals were omitted if AFE were less than 24 or greater than 30 wk, or the laying period exceeded 40 wk of production or total cumulative egg numbers were less than 60, or errors were detected in hatching records. To maintain a balanced structure of data, individuals of less than 35 wk of production and hatches with less than 300 records were deleted. Pedigrees were traced back 3 generations or to unknown parents. Due to the limitation of computer memory and computing time, only cumulative egg numbers of odd weeks of production were used. After editing, a total of 99,198 records on 6,475 hens and 9,111 pedigreed animals from 329 sires and 2,425 dams were used to estimate the genetic parameters for cumulative egg numbers. In addition, monthly egg production was calculated by summing egg numbers in 4 consecutive wk from 26 wk of age for each individual.

Model
According to the structure of the analyzed data and the Legendre polynomials of different orders used to describe the changes of fixed and random effects with week of production, a single-trait RRM for cumulative egg numbers was formulated as


Formula

where yijkt was the accumulative egg at t weeks of production on kth individual belonging to the ith AFE and the jth hatch group; AFEi was an effect of ith AFE; ßjm was the fixed regression coefficients for the jth hatch group; akm was the additive genetic random regression coefficient that was specific to each individual in the pedigree; pkm was the random regression coefficient that was specific to each individual; eijkt was the residual effect for each observation, and q1, q2, and q3 were the orders of the Legendre polynomials for the fixed, additive genetic, and permanent environmental effects, respectively. In general, the covariate of the Legendre polynomial is


Formula

The first 5 Legendre polynomials are then derived as


Formula

In matrix notation the RRM for cumulative egg numbers can be written as


Formula

where b denotes the vector of all fixed effects, a was the q2 x 1 vector of random regression coefficients for each individual in the pedigree, and p was the q3 x 1 vector of permanent environment effects for individuals with records. The e was the vector of residual effects and X, Z, and Q were corresponding incidence and covariate matrices. Assume that


Formula

and


Formula

with


Formula

where G was the q order covariance matrix of random genetic regression coefficients, assigned the same for all individuals; A was the additive genetic relationship matrix among the individuals in the pedigree; I was an identity matrix; P was the q order covariance matrix of the random permanent environment coefficients; and R was the diagonal matrix with different residual variances allowed for different time intervals for the period measured and R = diag({sigma}2e1,2{sigma}2e3,4···{sigma}2e35,40). Residual effects on different weeks of production were uncorrelated within and between individuals.

Methods
Covariance matrixes of additive genetic random regression coefficients, permanent environment random regression coefficients, and residual variances of RRM for the cumulative egg numbers were estimated using GIBBS via DMU package (Madsen and Jensen, 2000). A total of 50,000 and 10,000 rounds, respectively, for total iteration and burn-in period were given in editing the DRIVE FILE of DMU, i.e., a single chain length of 50,000 was generated where the first 10,000 iterations of the chain were discarded as the burn-in period and remaining 40,000 iterations were used for the estimation of means of the marginal distribution of the variance and covariance components. Covariance functions for genetic and permanent environment effects, heritabilities, and ratios of permanent environmental to phenotypic variances were calculated as described by Kirkpatrick et al. (1990) and Jamrozik and Schaeffer (1997).

Based on the optimal RRM, heritability (hi2) at ith month, and genetic and phenotypic correlation (ra(i,40) and rP(i,40)) between egg number at ith month and total cumulative egg numbers can be estimated by the following formulas:


Formula


Formula

and


Formula

for i = 1st, 2nd, ···, 10th month corresponding to t = 1st, 5th, ..., 37th wk, where Cova and Covp were genetic and phenotypic covariance for cumulative egg numbers.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Optimal RRM
On the basis of a visual inspection of the phenotypic means of cumulative egg numbers plotted against weeks of production, it was determined that the Legendre polynomial of order 2 (q1 = 2) as the submodel accounts for the phenotypic trajectory of the average observations across all animals belonging to the jth hatch group. The 2 random regression effects, additive genetic and permanent environmental effects, were characterized by using the Legendre polynomials of different orders. The range of orders varied from 2 to 4. The models were designated as LPq2q3; for example, LP23 is a model with Legendre polynomial of order 2 for the additive genetic effects and of order 3 for the permanent environmental effects. A total of 9 RRM were compared. The choice of the optimal RRM was based on the Bayesian information criterion (Schwarz, 1998) and the Bayes factor (BF, Kass and Raftery, 1995):


Formula

where log(MLk) was the log of maximum likelihood value of model k; pk was the number of free parameters in model k; and n was the number of observations that contribute to the likelihood, and


Formula

This was a contrast of model M0 against model M1, where p(y | M = Mk) was an integrated (marginal) likelihood. According to Kass and Raftery (1995), a log of BF [log(BF)] value greater than 5 indicates a very strong evidence in favor of model M0. Generally small values are favorable for Bayesian information criterion, but large values are favored for BF. For BF the model LP65 was used for M1.

The results of the 2 statistical criteria from 9 competing RRM were listed in Table 1Go. The model LP24 with minimum marginal likelihood was used for M1 in log(BF). The LP24 model, the RRM with the Legendre polynomial of 2 orders for fixed and additive genetic effects and of 4 orders for permanent environmental effects, was shown the best on both criteria and therefore chosen as an optimal model for genetic parameter estimation of cumulative egg numbers in a broiler dam line.


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  		Table 1. Statistical criteria of different random regression model1
 
Parameter Estimation
By calculating the means and the standard deviations of the Gibbs samples from posterior distributions of estimated parameters, estimates of parameters and their standard errors were obtained from the optimal RRM for cumulative egg numbers. Estimates of (co)variances (and their standard errors) for additive genetic and permanent environment random regression coefficients are given in matrixes A and Pe below, respectively. All covariances of random-regression coefficients were significantly different from zero. All correlations between additive genetic random regression coefficients were positive. Most of the correlations between random-regression coefficients were also positive for permanent environment effects.


Formula


Formula

Estimates and their standard errors for residual variances were listed in Table 2Go. Estimated residual variances were greater at the beginning and the end of laying period. The maximum value in first time interval was about 3 times greater than the minimum in fifth time interval.


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  		Table 2. The sample size and estimates of residual errors variances within production week interval
 
The estimates of genetic, permanent environmental, and residual variances for cumulative egg numbers over the weeks of production were shown in Table 3Go. The genetic variances were basically the same from production wk 1 to 10. Thereafter, the genetic variances gradually increased along with the production weeks. The permanent environment variances were relatively high for the first few production weeks as influenced by variation in sexual maturity, remained steadily low during peak production, and then increased as hens aged.


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  		Table 3. Estimates of genetic (Va), permanent environmental (Vpe), residual (Ve), and phenotypic (P) variances, heritibilities (h2), and ratio of permanent environment to phenotypic variance (PE) for accumulated eggs at selected weeks of production
 
The heritabilities of the cumulative egg numbers from production wk 1 to 40 varied between 0.16 and 0.54 (Table 3Go). The heritabilities increased in the first 3 production weeks and slowly decreased from production wk 4 to 6 but rose again from production wk 7. The maximum value was reached at production wk 35 and then dropped significantly after that. The ratios in variance of permanent environment effects to phenotypic variance showed an opposite trend to the heritabilities. The ratios in variance of the permanent environment effects to phenotypic variance before production wk 18 were greater than the corresponding heritabilities but were lower after production wk 19 excluding wk 40.

The estimates of the phenotypic and genetic correlations among weeks of production for the cumulative egg numbers were given in Table 4Go. All the phenotypic correlations were greater than the corresponding genetic correlations except for the first 3 wk of production, and phenotypic and genetic correlations were positive. The initial weeks of production showed less correlation with later stages of production. The correlations between the cumulative egg numbers at different weeks of production were generally higher when the overlapping weeks were greater. The 3-dimensional graphs for the estimated genetic correlations between weeks of production were illustrated in Figure 1Go.


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  		Table 4. Estimates of genetic (upper triangle) and phenotypic (lower triangle) correlations between accumulated eggs at selected weeks of production with covariance functions
 

Figure 1
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  		Figure 1. Estimated genetic correlations (ra) between accumulated eggs at different weeks of production.

 
A total of 10 estimates of heritabilities for the monthly records and genetic and phenotypic correlations between the monthly records and the total cumulative egg numbers from production wk 1 to 40 were listed in Table 5Go. The values of the heritability estimates ranged from 0.03 to 0.18, much lower than those for the cumulative eggs. The genetic correlations between monthly and total egg production were very high except for the first month when sex maturity and laying peak may play more important roles.


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  		Table 5. Estimates of heritability for monthly records, genetic and phenotypic correlations between monthly records and total cumulative egg numbers
 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The current study is the first attempt to estimate the genetic parameters of cumulative eggs in broiler breeders with the random regression model. Estimates of genetic parameters for egg production traits have been extensively reported in egg-type chickens, but few can be found in broiler breeders. The reported estimates of heritability for egg number varied from 0.11 to 0.53 (Francesh et al., 1997; Nurgiartiningsih et al., 2002, 2004; Szwaczkowski, 2003). The heritability estimates of cumulative egg numbers (0.16 to 0.54) in the present study were generally in agreement with previous studies, indicating a moderate to low additive genetic variance for egg production in broiler breeders. The estimates of heritabilities were relatively low at the beginning of the laying period, which could be attributed to the significant physiological changes for hens commencing egg production. In the current study, the accuracy of estimation would have been improved by properly accounting for AFE and the heterogeneity in the residual variance among the week intervals in the current RRM. As the test period went on, the physiological changes of hens were relatively stable, the more information was fitted in the analyses of cumulative egg production. As a result, the permanent environment variances were gradually increased, and the estimates of heritability increased.

As hens aged in the latter part of laying period, they were vulnerable to diseases and environmental stress. At the same time, management efficiency might be poorer in the latter part of laying period, which would lead to more errors in laying records and other data collection. As a result, the permanent environmental variances increased. With other routine methods that could not properly account for the effects of permanent environmental variances, the heritability estimates were generally lower for these periods. In addition, the environment during trap nesting egg test changes constantly with generation, season, diet, and vaccination programs, which result in greater permanent environmental variances. The ratios of permanent environmental variance over total variance were from 0.44 to 0.77 for different cumulative weeks. Application of RRM can effectively separate the permanent environmental variances and thus provides more accurate estimates of genetic parameters for cumulative egg numbers. These genetic parameters should be useful in designing a proper selection scheme for broiler breeding program along with estimates of genetic parameters for growth rate, feed efficiency, and other important traits.

The choice of the random regression model in dealing with cumulative egg numbers had obvious advantages. Phenotypic changes of the cumulative egg numbers with weeks or months of production had such evident growth pattern (beeline or parabola) that can be more accurately fitted with simple regression models, whereas the weekly or monthly egg numbers would be more difficult to fit with the same type of models. For the current data, the phenotypic trajectory of the monthly egg numbers needed to be modeled with the Legendre polynomial of 4 orders, and it also followed the AS lactation curve as reported by Anang et al. (2002) and Mielenz et al. (2002). But the pattern of the weekly egg numbers was too complex to be fitted. The number of parameters to be estimated in the RRM for accumulate eggs was less than that for the weekly or monthly egg numbers, which significantly reduced the cost of computing. Not only the heritability of the egg number at wk 1 or mo 1 (the first 4 wk of production) and the genetic correlation of the egg numbers between wk 1 or mo 1 and the total cumulative egg numbers, all results from monthly egg numbers may be estimated by RRM established for cumulative egg numbers. In this regard, the current results were in general agreement with those published by Anang et al. (2002) and Mielenz et al. (2002). In general, heritabilities estimates from the cumulative egg production were higher than those from monthly production, possibly due to the limited number of records used in the monthly egg number estimations.

Genetic correlation between different part records of egg production is an important parameter for describing the dynamics of egg production and designing an early selection program. The genetic correlations between cumulative eggs of different production weeks with total cumulative eggs increased with production weeks. For different laying periods, mo 5, 6, and 7 showed the highest genetic correlations (>0.95) with the total cumulative eggs. Besbes et al. (1992) reported that the genetic correlation between egg production for 26 to 38 wk and 26 to 54 wk was 0.66. In the current study, the genetic correlations between the cumulative eggs for production wk 19 and the total cumulative eggs till wk 40 were as high as 0.81, and the genetic correlation between the fifth monthly records (egg production from production wk 16 to 20) and the total cumulative egg numbers was 0.95. In a balanced consideration of selection response and generation interval, early selection based on the first 19 wk of cumulative egg numbers could effectively improve annual egg production in the broiler dam line.


   ACKNOWLEDGMENTS
 
The current research was supported in part by grants from the National Outstanding Youth Science Foundation of China (no. 30225032) and the State Major Basic Research Development Program of China (no. 2006CB102102).

Received for publication March 18, 2006. Accepted for publication September 16, 2006.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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Anang, A., N. Mielenz, and L. Schuler. 2002. Monthly model for genetic evaluation of laying hens. II. Random regression. Br. Poult. Sci. 3:384–390.

Besbes, B., V. Ducrocq, J. L. Foulley, M. Protais, A. Tavernier, M. Tixier-Boichard, and C. Beaumont. 1992. Estimation of genetic parameters of egg production traits of laying hens by restricted maximum likelihood applied to a multiple-trait reduced animal model. Genet. Sel. Evol. 24:539–552.

Fairfull, R. W., and R. S. Gowe. 1990. Genetics of egg production. Pages 705–759 in Poultry Breeding and Genetics. R. D. Crawford, ed. Elsevier, Amsterdam, the Netherlands.

Francesh, A., J. Estany, L. Alfonso, and M. Iglesias. 1997. Genetic parameter for egg number, egg weight and egg shell colour in three Catalan breed. Poult. Sci. 76:1627–1631.[Abstract/Free Full Text]

Henderson, C. R., Jr. 1982. Analysis of covariance in the mixed model: Higher level, no homogenous, and random regressions. Biometrics 38:623–640.[ISI][Medline]

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Kass, R. E., and A. E. Raftery. 1995. Bayes factors. J. Am. Stat. Assoc. 90:773–795.[ISI]

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Madsen, P., and J. Jensen. 2000. A user’s guide to DMU. Danish Inst. Agric. Sci., Res. Centre, Foulum, Denmark.

Mielenz, N., A. Anang, R. Preisinger, M. Schmutz, and L. Schueler. 2002. Genetic evaluation of laying performance data—Comparison of models based on monthly records. Pages 19–23 in Proc. 7th World Congr. Genet. Appl. Livest. Prod., Session 20. Montpellier, France.

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