Estimation of genetic parameters for monthly egg production in laying hens based on random regression models

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1 J Appl Genet 50(1), 2009, pp Original article Estimation of genetic parameters for monthly egg production in laying hens based on random regression models A. Wolc, T. Szwaczkowski Department of Genetics and Animal Breeding, Poznan University of Life Sciences, Poznañ, Poland Abstract. Heritability and genetic correlations of monthly egg production under random regression models were estimated. Three layer lines (A22, A88, K66) in six consecutive generations were analysed. A22 (13,770 recorded hens) and A88 (13,950 recorded hens) are maternal lines of Rhode Island White birds selected on egg production and shell colour; K66 (9,351 recorded birds) is a paternal line of Rhode Island Red birds selected on egg weight. Eight models with different orders of Legendre polynomials were applied. Adequacy of the models was checked by the Akaike Information Criterion. According to the most adequate model including second order Legendre polynomials for fixed effects and third order for additive genetic and permanent environmental effects, relatively high heritabilities were estimated in the first (h 2 =0.3) and final (h 2 above 0.3) periods of production with a substantial decrease in heritability during the egg production peak. Methodology based on random regression animal models can be recommended for genetic evaluation of laying hens. Keywords: egg production, heritability, laying hens, Legendre polynomials, random regression models. Introduction In the last decades traits expressed over a trajectory of time were analysed either as cumulative records or measured at given time intervals in hens mostly in monthly periods. Monthly records were treated as repeated records of one trait, assuming genetic correlation equal to one. In other approaches, multitrait analysis (each record treated as a separate trait, correlated to other records), fixed regression (with average production curve included as a fixed effect) and random regression models were suggested for analysis of longitudinal data (Anang et al. 2001, 2002; Kranis et al. 2007). In random regression models, breeding value of each animal is described by a set of random polynomial coefficients (Meyer and Hill 1997). Random regression models were implemented for routine breeding value prediction in dairy cattle (Schaeffer et al. 2000). Subsequently they have been applied to other traits, like body weight (Legarra et al. 2004), and functional traits (Karacaören et al. 2006). In the studies of Anang et al. (2002), Kranis et al. (2007), Luo et al. (2007) egg production was analysed under random regression models. Regression models enable a higher accuracy of selection, as they make use of information on the course of traits, and make it possible to change the course of a trait through selection (Huisman et al. 2002b). They take into account individual and average production curves and do not need standardisation on specific age of animals (Huisman et al. 2002a). The objective of this study was to compare random regression models with different orders of Legendre polynomials and estimate heritability and genetic correlations of monthly egg production in laying hens. Materials and methods Six consecutive generations of three layer lines were analysed. The lines were created in the 1980s Received: July 7, Revised: October 1, Accepted: December 16, Correspondence: T. Szwaczkowski, Department of Genetics and Animal Breeding, Poznan University of Life Sciences, Wolynska 33, Poznan, Poland; tomasz@jay.au.poznan.pl

2 42 A. Wolc, T. Szwaczkowski in the Poultry Research Branch of the National Research Institute of Animal Production, in Zakrzewo, Poland. A22 (13,770 recorded hens) and A88 (13,950 recorded hens) are maternal lines of Rhode Island White birds selected on egg production and shell colour; K66 (9,351 recorded birds) is a paternal line of Rhode Island Red birds selected on egg weight. The data were collected on one pedigree farm. Base population consisted of 1,226; 688; 551 birds for A22, A88 and K66 line, respectively. Numbers of sires and dams per generation are given in Table 1. Hens were naturally mated and kept in single cages (750cm 2 per hen), with environmental conditions automatically controlled according to standard schedules. Birds were fed ad libitum with a standard diet (16 17% protein, kcal kg 1, 3.5 4% Ca). Egg production was registered over a period of 9 months using a scanner. Descriptive statistics of the populations are given in Figure 1. The analysis of monthly records was based on the following random regression model: n1 y = HY + b z + a z + p z ikl i m klm km klm km klm m= 0 m= 0 m= 0 n2 n3 +e ikl where: y ikl is a record of k-th hen in l-th month, HY i is a fixed effect of i-th hatch-year, b m is m-th fixed regression coefficient, a km is m-th random regression coefficient for additive genetic effect, p km is m-th random regression coefficient for permanent environmental effect, z klm is covariate a value of Legendre polynomial on month, e ikl is random residual effect, n 1, n 2, n 3 are numbers of covariates, dependent on the order of Legendre polynomials. Table 1. Number of sires and dams per generation in the studied layer lines Generation A22 A88 K66 sires dams sires dams sires dams I II III IV V VI The following structure of (co)variance matrices for random effects was assumed: a G A 0 0 Var p = 0 P I 0 e 0 0 R where: G and P are covariance matrices of the random regression coefficients for animal and permanent environmental effects, R is the diagonal matrix of the form I σ 2 e and σ 2 e is residual variance, A is an additive geneticrelationship matrix, I is the identity matrix, is the Kronecker product. According to the suggestion of Strabel et al. (2005), regression coefficients were derived from Legendre polynomials. The use of Legendre polynomials for both fixed and random regression models was also recommended by other authors (Pool and Meuwissen 1999; Jamrozik and Schaeffer 2002; Szyda et al. 2008). The advantages of such an approach are: orthogonality of the functions, which is useful for analyzing patterns of genetic variation, accurate prediction of missing values and relatively good convergence (Pool et al. 2000). The orders of polynomials are given in Table 2. Following the suggestion of Legarra et al. (2004) orders of polynomials higher than four were not used. Figure 1. Average egg production in the studied layer lines

3 Random regresion models for egg production 43 Table 2. The orders of Legendre polynomials used to model fixed and random effects Model Fixed effect Genetic effect Permanent environmental effect I II III IV V VI VII VIII Table 3. Values of the Akaike Information Criterion for the studied models, expressed as a deviation from the simplest model Model A22 line A88 line K66 line I II III IV V VI VII VIII AI-REML approach (Johnson and Thompson 1995) was applied to estimate variance components. Cholesky decomposition with logarithm transformation of diagonal elements was used for maximization. Different starting values were used to obtain convergence in the A22 line. Variance components estimated for this line were then used as starting values in other lines. The calculations were done using DXMRR program form the DFREML package (Meyer 2001). Standard errors of the heritability estimates were approximated using the formula of Robertson (1959). This formula was used for estimation of approximate standard errors in test day models by Strabel (1998). Akaike Information Criterion (Akaike 1974) was used to evaluate adequacy of the models: AIC = 2log(likelihood) +2*(number of independently adjusted parameters) The model with the minimum AIC is regarded as the best model (Wada and Kashiwagi 1990). The criterion balances adequacy and complexity of the models by the penalty on the number of estimated parameters, and it applies to nested and non-nested models (Forster 2000). Results and discussion Values of AIC for the examined models are listed in Table 3. These criteria indicate that model VII, including second order polynomial in the fixed part and third order polynomial for additive genetic and permanent environmental effects, is the best model for the A22 and K66 lines. In the A88 line two models had lower AIC values than model VII. A similar model (to presented above) appeared to be second best also for cumulative egg production in broilers (Luo et al. 2007). Norberg et al. (2004) suggested that the order of the polynomial modelling additive genetic effect should not exceed the order of the polynomial for permanent environmental effect. However, it was not confirmed in the A22 line, as models II and III led to similar pattern of changes in heritability estimates (Figure 2). For other lines, in models V and VI, an additional increase of heritability about the 5th month appeared (Figures 3 and 4). The results correspond to investigations carried out by Pool and Meuwissen (1999), who reported that model adequacy was better for models with higher order polynomials. The tendency of increasing adequacy with the order of polynomial can be observed comparing models I, IV and VIII models with increasing (but the same for all model components) polynomial orders. Application of first order polynomials led to an unsatisfactory description of the average egg production. Problems with convergence appeared when the order of the polynomial modelling additive genetic effect differed from the order of the polynomial for permanent environmental effect. Similar difficulties were reported by Norberg et al. (2004). It should be stressed that the results presented in this study have been obtained under an assumption of homogeneity of residual variances. However, some authors have modelled residual variance as a function of time (Jaffrezic et al. 2000) or time interval (Ibáñez et al. 1996). Inclusion of heterogeneous residual variances had little influence on the values of genetic parameter estimates. On the other hand it led to an increase of computing time per iteration and to slower convergence. Random regression models enabled a description of changes in additive genetic variance during 9 months of production. Heritability under random regression models is shown in Figures 2 to 4. Standard errors of heritability estimates ranged from to According to the most adequate model (model VII) relatively high heritabilities were estimated in the first (h 2 close to 0.3) and final periods (h 2 above 0.3 in A22 and A88 lines) of

4 44 Figure 2. Heritability estimates of egg production in A22 line Figure 3. Heritability estimates of egg production in A88 line Figure 4. Heritability estimates of egg production in K66 line

5 Random regresion models for egg production 45 Table 4. Matrix of genetic (above the diagonal) and permanent environmental (below the diagonal) correlations of monthly egg production in the A22 line under a random regression model (model VII) Month production, with a substantial decrease during the egg production peak. In K66 an increase in the final period was smaller. This result confirms the tendencies observed under multitrait model (Wolc et al. 2007), but the random regression model led to higher estimates, especially in the post-peak phase. A comparable tendency was also reported by Anang et al. (2002) for White Leghorn hens (h 2 equal to 0.57 in the first month and 0.14 in the fourth month), and Kranis et al. (2007) in turkeys (h 2 equal to 0.13 in the first month and 0.05 in the fourth month). Similar patterns of heritability changes were also obtained by some authors studying milk production (Kettunen et al. 2000; Cobuci et al. 2005) or electrical conductivity of milk (Norberg et al. 2004). Changes of heritability over time may result from activation of different genes during the production cycle. Early stages of production are under the influence of sexual maturity whereas after the 7th month of production, genes related to persistency of egg production could be more influential. For the most adequate model VII genetic correlations ranged from 0.78 to 0.94 (A22 line), 0.53 to 0.91 (A88 line), 0.54 to 0.94 (K66 line). A typical correlation pattern is given in Table 4. Correlation coefficients in this study were lower than under the multitrait model and were more often negative. Kranis et al. (2007) estimated genetic correlations between 0.09 and 0.95 under a random regression model and between 0.05 and 0.88 under a multitrait model. Correlations were higher for the consecutive periods, whereas negative estimates were mostly obtained for the first two months with other periods. Low correlations between the first and later periods were confirmed on the phenotypic level. This may suggest a different genetic background of initial egg production. A similar tendency was found in the literature under multitrait models (Preisinger and Savaº 1997; Savaº et al. 1998; Anang et al. 2000, Wolc et al. 2007) which can be treated as reference (unconstrained) model. Conclusions The methodology based on random regression animal models appears promising and could be recommended for estimation of genetic parameters in laying hens. The use of different orders of Legendre polynomials confirmed their usefulness in modelling of fixed and random effects. The model including second order polynomial in the fixed part and third order polynomial for additive genetic and permanent environmental effects was most suitable for estimation of variance components in the studied populations. Acknowledgements. Karin Meyer is kindly acknowledged for providing the DFREML package program. Anna Wolc acknowledges a scholarship from the Foundation for Polish Science (contract 113/2007). Thanks go to the anonymous reviewers for their very useful comments on the paper. The authors would like to thank Mr Ian White for suggestions and comments on a draft copy of this paper. REFERENCES Akaike H, A new look at the statistical model identification. IEEE Trans Automat Control 19: Anang A, Mielenz N, Schüler L, Genetic and phenotypic parameters for monthly egg production in White Leghorn hens. J Anim Breed Genet 117: Anang A, Mielenz N, Schüler L, Monthly model for genetic evaluation of laying hens. I. Fixed regression. Br Poult Sci 42: Anang A, Mielenz N, Schüler L, Monthly model for genetic evaluation of laying hens. II Random regression. Br Poult Sci 43:

6 46 A. Wolc, T. Szwaczkowski Cobuci JA, Euclydes RF, Lopes PS, Costa CN, Torres R, Pereira PS, Estimation of genetic parameters for test-day milk yield in Holstein cows using a random regression model. Genet Mol Biol 28: Forster MR, Key concepts in model selection: performance and generalizability. J Math Psych 44: Huisman AE, Kanis E, Van Arendonk JAM, 2002a. Application of random regression models in pig breeding to select on growth and feed intake patterns. Proc 53 EAAP: 1 8. Huisman AE, Veerkamp RF, and Van Arendonk JAM, 2002b. Genetic parameters for various random regression models to describe the weight data of pigs. J Anim Sci 80: Ibáñez MA, Carabaño MJ, Foulley JL, and Alenda R, Heterogeneity of herd-period phenotypic variances in the Spanish Holstein-Friesian cattle: Sources of heterogeneity and genetic evaluation. Livest Prod Sci 45: Jaffrezic F, White IMS, Thompson R, Hill WG, A link function approach to model heterogeneity of residual variances over time in lactation curve analyses. J Dairy Sci 83: Jamrozik J, Schaeffer LR, 2002 Bayesian comparison of random regression models for test-day yields in dairy cattle. Proc. 7th World Congr Genet Appl Livest Prod, Montpelier, August 19 23, 2002, Abs Johnson DL, Thompson R, Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. J Dairy Sci 78: Karacaören B, Jaffrézic F, Kadarmideen HN, Genetic Parameters for Functional Traits in Dairy Cattle from Daily Random Regression Models. J Dairy Sci 89: Kettunen A, Mäntysaari EA, and Pösö J, Estimation of genetic parameters for daily milk yield of primiparous Ayrshire cows by random regression test-day models. Livest Prod Sci 66: Kranis A, Su G, Sorensen D, Woolliams JA, The application of random regression models in the genetic analysis of monthly egg production in turkeys and a comparison with alternative longitudinal models. Poult Sci 86: Legarra A, Misztal I, Bertrand JK, Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle. J Anim Sci 82: Luo PT, Yang RQ, Yang N, Estimation of genetic parameters for cumulative egg numbers in broiler dam line by using a random regression model. Poult Sci 86: Meyer K, Hill WG, Estimation of genetic and phenotypic covariance functions for longitudal or repeated records by restricted maximum likelihood. Livest Prod Sci 47: Meyer K, DFREML ver University of New England. Australia. Norberg E, Rogers GW, Goodling RC, Cooper JB, Madsen P, Genetic parameters for test-day electrical conductivity of milk for first-lactation cows from random regression models. J Dairy Sci 87: Pool MH, Janss LLG, Meuwissen THE, Genetic parameters of Legendre polynomials for first parity lactation curves. J Dairy Sci 83: Pool MH, Meuwissen THE, Prediction of daily milk yields from a limited number of test days using test day models. J Dairy Sci 82: Preisinger R, Savas T, Vergleich zweier Methoden zur Schätzung der Varianzkomponenten für Leistungmerkmale bei Legehennen. Züchtungskunde 69: Robertson A, Experimental design in the evaluation of genetic parameters. Biometrics 15: Savaº T, Preisinger R, Röhe R, Kalm E, Genetische Parameter und optimale Prüfdauer für Legeleistung anhand von Teillegeleistungen bei Legehennen. Arch Tierzucht 41: Schaeffer LR, Jamrozik J, Kistemaker GJ, Van Doormaal BJ, Experience with a Test-Day Model. J Dairy Sci 83: Strabel T, Wykorzystanie próbnych udojów do oceny wartoœci hodowlanej byd³a mlecznego. Ph.D. Thesis, Univ Life Sci Poznan, Poland (in Polish) Strabel T, Szyda J, Ptak E, Jamrozik J, Comparison of random regression test-day models for Polish Black and White cattle. J Dairy Sci 88: Szyda J, Ptak E, Komisarek J, arnecki A, Practical application of daughter yield deviations in dairy cattle breeding. J Appl Genet 49: Wada Y, Kashiwagi N, Selecting statistical models with information statistics. J Dairy Sci 73: Wolc A, Lisowski M, Szwaczkowski T, Heritability of egg production in laying hens under cumulative, multitrait and repeated measurement animal models. Czech J Anim Sci 52: