GENETICS. R. P. Savegnago,* S. L. Caetano,* S. B. Ramos,* G. B. Nascimento,* G. S. Schmidt, M. C. Ledur, and D. P. Munari* 1

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1 GENETICS Estimates of genetic parameters, and cluster and principal components analyses of breeding values related to egg production traits in a White Leghorn population R. P. Savegnago,* S. L. Caetano,* S. B. Ramos,* G. B. Nascimento,* G. S. Schmidt, M. C. Ledur, and D. P. Munari* 1 *Departamento de Ciências Exatas, Faculdade de Ciências Agrárias e Veterinárias Universidade Estadual Paulista, Jaboticabal, São Paulo, Brazil; and Embrapa Suínos e Aves, , Concórdia, Santa Catarina, Brazil ABSTRACT The objectives of this paper were to identify the phenotypic egg-laying patterns in a White Leghorn line mainly selected for egg production, to estimate genetic parameters of traits related to egg production and to evaluate the genetic association between these by principal components analysis to identify trait(s) that could be used as selection criteria to improve egg production. Records of 54 wk of egg production from a White Leghorn population were used. The data set contained records of the length:width ratio of eggs at 32, 37, and 40 wk of age; egg weight at 32, 37, and 40 wk of age; BW at 54 and 62 wk of age; age at first egg; early partial egg production rate from 17 to 30 wk and from 17 to 40 wk of age; late partial egg production rate from 30 to 70 wk and from 40 to 70 wk of age; and total egg production rate (TEP). The estimates of genetic parameters between these traits were estimated by the restricted maximum likelihood method. Multivariate analyses were performed: a hierarchical cluster INTRODUCTION Chicken eggs and meat are 2 primary poultry products whose consumption has been increasing rapidly (Scanes, 2007). To increase productivity without increasing the physical space, the selection of birds is carried out by taking into account the traits of economic interest, such as egg production. In poultry breeding programs, egg production, age at first egg (AFE), egg weight, and egg size are included in breeding goals. The estimates of genetic parameters provide support to analyze the genetic associations between traits in a data analysis, a nonhierarchical clustering analysis by the k-means method of weekly egg production rate to describe the egg-laying patterns of hens, and a principal components analysis using the breeding values of all traits. The highest heritability estimates were obtained for BW at 54 wk of age (0.68 ± 0.07) and age at first egg (0.53 ± 0.07). It is recommended that a preliminary clustering analysis be performed to obtain the population structure that takes into account the pattern of egg production, rather than the TEP, because hens may have the same final egg production with different patterns of egg laying. Early partial production periods were not good indicators for use in improving total egg production because these traits presented an overestimated genetic correlation with TEP because of the part-whole genetic correlation component. Egg production might be improved by selecting individuals based on TEP. Key words: cluster analysis, egg production, genetic correlation, heritability, principal components analysis 2011 Poultry Science Association Inc. Received March 10, Accepted June 3, Corresponding author: danisio@fcav.unesp.br 2011 Poultry Science 90 : doi: /ps set. These estimates could be used to decide on the selection method and to choose what birds could be selected to attain the breeding goal (Ledur et al., 1993). Poultry data sets have many traits measured on the same bird, and this allows the use of multivariate statistical analysis for various purposes. These methods can be used to analyze phenotypic records or the breeding values of traits. Nonhierarchical cluster analysis is a multivariate technique that uses a k-means algorithm to partition individuals into groups, where k denotes the number of clusters. To conduct a k-means analysis, the number of clusters needs to be specified at the start (Rencher, 2002). This could be used to separate the patterns of egg production within a population of hens. Principal components analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to reduce a set of correlated variables into a set of 2174

2 uncorrelated variables called principal components. It is a means of identifying patterns in the data by their similarities and differences and a method to compress the data information (i.e., by reducing the number of dimensions) without much loss of information (Hair et al., 2009). The objectives of this paper were 1) to identify the phenotypic egg-laying patterns of a White Leghorn line mainly selected for egg production, 2) to estimate the genetic parameters of traits related to egg production, and 3) to evaluate the genetic associations between these traits by PCA to identify trait(s) that could be used as selection criteria to improve egg production. Birds GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES MATERIALS AND METHODS A data set from a White Leghorn layer population, named CC, developed and maintained under multitrait selection for 7 generations by Embrapa (Empresa Brasileira de Pesquisa Agropecuária) Swine and Poultry National Research Center, Concórdia, Santa Catarina, Brazil, was used in this study. The CC is a pure line mainly selected for egg production and for egg weight, feed conversion, hatchability, sexual maturity, fertility, viability, egg quality, and reduced BW (Figueiredo et al., 2003; Rosário et al., 2009). Data on 1,569 layers from 3 hatches were analyzed. The eggs were collected over 5 d of the week. According to Wheat and Lush (1961), this measure shows a correlation of 0.99 with weekly egg production. Bird Phenotype Measurement The following traits were studied: total egg production rate (TEP) from 17 to 70 wk of age (totaling 54 wk of egg production); early partial egg production rate from 17 to 30 wk of age (EP1730) and from 17 to 40 wk of age (EP1740); late partial egg production rate from 30 to 70 wk of age (EP3070) and from 40 to 70 wk of age (EP4070), with all egg production rates measured as a percentage); AFE, measured as the number of days until the first laying egg; BW at 54 and 62 wk of age (BW54 and BW62), measured in grams; egg weight at 32, 37, and 40 wk of age (EW32, EW37, and EW40), measured in grams; and the length:width ratio of eggs at 32, 37, and 40 wk of age (RLW32, RLW37, and RLW40). The length:width ratio of eggs at the ith week of age (RLW i ) was determined by the following formula: Cluster Analysis of TEP All the cluster analyses were done by considering the weekly production rate of 1,579 laying hens. The aim of this procedure was to characterize the population through this trait. This was done by using the 2 different approaches described below. First Clustering Analysis: Previous Group Division by TEP Nonhierarchical clustering by the k-means method is a multivariate exploratory analysis that can be applied when there is any previous group classification of cases. The focus of this analysis is on grouping individuals, to minimize the variance within groups and maximize the variance between groups (Hair et al., 2009), for identification of the weekly egg-laying pattern of hens. The phenotypic records of weekly egg production rate (17 to 70 wk of egg production) were used in this analysis. This cluster method requires a previous division of the data set into groups. The hens were divided into 5 groups (G1 to G5) according to TEP class: G1, TEP <20%; G2, 20% TEP < 40%; G3, 40% TEP < 60%; G4, 60% TEP < 80%, and G5, TEP 80%. This predivision of the groups by the class of TEP was done to verify that the criteria used to group the hens was appropriate. Second Clustering Analysis: Previous Group Division by Hierarchical Clustering 2175 Hierarchical cluster analysis by the Ward algorithm was performed to find a suitable number of groups within the population. After the number of clusters was chosen by the hierarchical clustering method, a nonhierarchical k-means cluster analysis was carried out to compare the pattern of clusters with the previous k-means analysis. The first nonhierarchical k-means clustering method (previous group division by TEP) and the second nonhierarchical k-means clustering method (previous group division by hierarchical clustering with the Ward algorithm) were compared to verify the best criterion to divide hens into groups: a preliminary division into groups by the class of TEP or the pattern of egg production rate. It used the phenotypic records of weekly egg production rate (17 to 70 wk of age) in both the hierarchical and nonhierarchical cluster analyses. All cluster analyses were carried out using Statistica 7.0 software (StatSoft Inc., 2007). RLW i = ELL i /ESL i, where ELL i and ESL i are the long and short lengths (diameters) of each egg at i weeks of age, respectively. A trait similar to RWL is generally found in the literature, namely, the egg shape index (ESI), which equals 1/RLW, for purposes of comparison with the literature. Estimates of Genetic Parameters To estimate the genetic parameters, records of hens presenting a TEP of less than 25% were excluded to eliminate birds that died or those that had subclinical infections affecting egg production (Fairfull and Gowe, 1990). Seventeen hens were excluded from the

3 2176 Savegnago et al. data set according to this criterion because hens that died or had fertility problems would have an atypical pattern of posture within the population and could affect the estimates of genetic parameters. In addition, hens with lost information on the other traits (cited above) were excluded to enable the estimation of SE of genetic parameter estimates. This excluded 263 hens to obtain balanced data. After this edition, the data set included 1,289 hens and the pedigree contained 12,132 birds from 7 generations. The fixed effect of hatch was significant (P < 0.01) for all traits, using the GLM procedure (SAS Institute Inc., 2004). Variance and covariance components were estimated by the restricted maximum likelihood method in a 2-trait bird model using the MTDFREML (multipletrait derivative-free restricted maximum likelihood) program, as described by Boldman et al. (1995). The convergence criterion was met when the variance of the simplex ( 2log likelihood) was less than The bird model included hatch as a fixed effect and additive genetic and residual as random effects. The heritability estimates presented in this study were the median estimates from the 2-trait analysis. PCA of Breeding Values of the Studied Traits The main objective of the PCA is to reduce the information on the breeding values for 14 variables to a smaller number of orthogonal latent variables, called principal components, with a minimal loss of information (Hair et al., 2009). The reduction of the multidimensional distribution of breeding values of traits was done to provide information to understand the genetic associations between the studied traits. The standardized breeding values of 1,289 hens of all traits (BVEP1730, BVEP1740, BVEP3070, BVEP4070, BVTEP, BVBW54, BVBW62, BVEW32, BVEW37, BVEW40, BVRLW32, BVRLW37, and BVRLW40, where BV is breeding value) were used in the PCA. The breeding values were standardized using the formula x x z =, S where z is the standardized value of x, x is the mean of a trait, and S is the respective SD. Principal components are calculated by linear combinations of the original variables with eigenvectors. The absolute value of an eigenvector determines the importance of the traits in a principal component. Each eigenvector is calculated from an eigenvalue from the correlation matrix of the data. Eigenvalues are related to the variance in each principal component (Rencher, 2002). The first principal component (PC1) explains the largest percentage of the total additive genetic variance. The second principal component (PC2) explains the second largest percentage and so on, until the whole variance is explained. In a data set with p variables, the ith principal component is given by PC i = a i1 X 1 + a i2 X a ij X j, (i = 1, 2,,13; j = 1, 2,,13), where a ij is the jth eigenvector and X j is the jth value of the original variable. Breeding values for TEP were used as a supplemental variable; that is, this variable had no influence on the correlation matrix used for construction of the principal components. It was not used as an active variable because BVTEP represented information already included in other variables. The reason for adding a supplemental variable in this analysis was to help the interpretation of results. Thus, it is possible to interpret the relationship between the breeding values of other variables in each principal component and BVTEP. The Kaiser criterion (Kaiser, 1958) was used to choose principal components that explained most of the variation in the data set. This criterion obtains principal components with eigenvalues greater than unity, that is, the principal components that explain most of the variation in the data set. This analysis was done using Statistica 7.0 software (StatSoft Inc., 2007). Descriptive Statistics RESULTS The means, SD, CV, and minimum and maximum values of the traits are shown in Table 1. All traits had the same number of records (i.e., data were balanced). The frequency of TEP is shown in Figure 1. We observed that 46% of the hens in the population had a TEP of 80 to 90%. First Clustering Analysis: Previous Group Division by TEP The 5 egg-laying patterns obtained by nonhierarchical cluster analysis using the k-means method are shown in Figure 2. The means and 95% CI for TEP in the 5 groups and 5 clusters are shown in Figure 3. The number of individuals previously classified into the 5 groups (G1 to G5) according to the class of TEP is shown in Table 2, and the number of individuals in the 5 clusters is shown in Table 3. Differences were observed among the 5 groups and 5 clusters with respect to the mean egg production rate and the number of hens. Second Clustering Analysis: Previous Group Division by Hierarchical Clustering There are several ways to divide a population into groups when the hierarchical method is used, but we

4 GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES 2177 Figure 1. Frequency distribution of the total egg production rate of 1,569 laying hens. chose to divide the population into 3 groups, using a Euclidean distance of 120 (Figure 4). A disadvantage of this method is that it is not possible to determine an optimal number of clusters. The choice of the division into groups should be the choice of the researcher. After the choice of the 3 groups, the nonhierarchical cluster analysis was conducted by using the k-means clustering method, and the egg-laying patterns of the 3 clusters were observed (Figure 5). The number of hens, mean, and SD for each cluster are shown in Table 4. Estimates of Genetic Parameters The median estimates of additive genetic and environmental variances are shown in Table 5. Median heritability estimates and genetic correlations are shown in Table 6. The lowest and highest estimates of heritability were 0.09 ± 0.04 and 0.68 ± 0.07, for EP4070 and BW54, respectively. The highest negative genetic correlation was between EP1730 and AFE. The length:width ratio of eggs had a negative genetic correlation with TEP and a positive genetic correlation with BW and egg weight. Body weight measures presented the highest positive genetic correlation with egg weight (Table 6). There was a part-whole genetic correlation component when breeding values of partial period records of the laying cycle were correlated with breeding values of total period records of egg laying, and there was a part-part genetic correlation component when breeding values of partial period records of the laying cycle were correlated with themselves (Figure 6). Table 1. Mean, SD, CV, and minimum and maximum values of 14 traits of 1,289 layers 1 Trait 2 Mean SD CV (%) Minimum Maximum BW54 (g) 1, , , BW62 (g) 1, , , EW32 (g) EW37 (g) EW40 (g) RLW RLW RLW AFE (d) EP1730 (%) EP1740 (%) EP3070 (%) EP4070 (%) TEP (%) The data set was balanced. 2 BW54 and BW62 = BW at 54 and 62 wk of age, respectively; EW32, EW37, and EW40 = egg weight at 32, 37, and 40 wk of age, respectively; RLW32, RLW37, and RLW40 = egg length:width ratio at 32, 37, and 40 wk of age, respectively; AFE = age at first egg; EP1730, EP1740, EP3070, EP4070, and TEP = egg production rate from 17 to 30 wk, 17 to 40 wk, 30 to 70 wk, 40 to 70 wk, and 17 to 70 wk of age, respectively.

5 2178 Savegnago et al. Figure 2. Nonhierarchical k-means cluster analysis of the weekly mean egg-laying pattern from 17 to 70 wk of age (54 wk of egg production) according to the previous classification of individuals by total egg production rate. PCA of Breeding Values of the Studied Traits An alternative way to analyze the variance-covariance between traits (Table 6) was shown by the PCA. Four principal components were chosen to explain most of the variation in the data set (Figures 7 and 8) because these attended the Kaiser criterion when eigenvalues were higher than one (Kaiser, 1958). The relationships between the breeding values of the traits are shown by the PCA (Figure 8). Four principal components explained 80.04% of the total additive genetic variation of the traits (Table 7). The most important relationships between breeding values were explained in PC1, PC2, and PC3 (Figure 8). The PC1 PC2, PC1 PC3, and PC2 PC3 graphics (Figure 8) show the multidimensional structure of the breeding values of 14 traits in 3 principal components. However, 2 graphs (PC1 PC2 and PC1 PC3) were sufficient to explain the most important genetic associations in relation to egg production traits, despite the fact that the fourth principal component met the Kaiser criterion. The linear correlation coefficients (Table 8) indicated the importance of each trait in the respective principal component. Principal component 1 explained 32.30% of the total additive genetic variation of the traits; it is a latent variable related to the breeding values of egg weight, BW, and the length:width ratio of the eggs. The breeding values of egg weight (BVEW32, BVEW37, BVEW40), the breeding values of the length:width ratio (BVRLW32, BVRLW37, BVRLW40), and the breeding values of BW (BVBW54, BVBW62) had high negative correlations with PC1, indicating that these traits had a similar contribution to PC1. This was verified by the variables that had a greater length of vectors and that were nearest to the PC1 axis (Figure 8a). Principal component 2 explained 18.71% of the additive genetic variation; it is a latent variable related to the breeding values of AFE (BVAFE) and egg production traits (BVEP1730, BVEP1740, BVEP3070, BVEP4070, and BVTEP). The breeding values of egg production traits had a high positive linear correlation with PC2. The BVAFE had a high negative linear correlation with PC2, indicating that BVAFE had a negative genetic association with egg production traits (Figure 8a and Table 8). Principal component 3 explained 16.58% of the additive genetic variation and had a high linear correlation with the same traits as PC2, except with BVEP1740. There was a high, positive genetic association of BVAFE, BVEP3040, and BVEP4070 with BVTEP in PC3. The genetic association between BVEP1730 and PC3 was high and negative, indicating that in this dimension, BVEP1730 had a negative genetic association with the other traits in this principal component (Figure 8b and Table 8). DISCUSSION The means of EP1730 and EP1740 observed in this study were similar to those reported by Francesch et al. (1997), who obtained egg production rates to 39 wk of age ranging from ± to ± 17.79% in 3 poultry lines selected for egg production. This suggests that the egg production of the CC line was high, as it should be in a line selected for this purpose.

6 GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES 2179 Figure 3. Means and 95% CI for mean total egg production (panel a) of the 5 groups previously classified by total egg production rate (TEP; panel b) into 5 clusters created by the k-means method. The means of EW37 and EW40 were slightly higher than those reported by Francesch et al. (1997), who obtained mean egg weights ranging from ± 5.00 to ± 4.63 g at 39 wk of age. The length:width ratios of eggs in this study were similar to those reported by Ledur et al. (1998), who found 1.35 ± 0.01 at 36 wk of laying for the same line. The use of cluster analyses enabled verification of the egg-laying patterns within the population. The first nonhierarchical cluster analysis (Figure 2) showed that the previous subdivision of the groups based on TEP was not an appropriate criterion for division into groups of hens. The mean and CI of the classes of groups previously classified by TEP (G1 to G5) were different from the mean and CI of the clusters built by the nonhierarchical k-means method (Figure 3). Thus, it is recommended that a preliminary clustering analysis be performed to obtain a population structure (Figure 4) that takes into account the pattern of egg production, rather than the TEP, because hens may have the same final egg production with different patterns of egg laying. Classification through the hierarchical method resulted in 3 groups (Figures 4 and 5) instead of the 5 groups in the previous classification based on egg production rate (Figure 2). According to Table 4, this population has many hens with a high laying performance, maintaining the persistence of egg laying after the peak.

7 2180 Savegnago et al. Table 2. Number of hens per group (G1 to G5) previously classified by total egg production Hens G1 G2 G3 G4 G5 No % Table 3. Number of hens per cluster created by the nonhierarchical k-means method Hens Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 No % Figure 4. Classification of laying hens by the cluster hierarchical method using Ward s algorithm based on weekly egg production rate from 17 to 70 wk of age. The x-axis represents the names (codes) of the 1,569 layer hens. Figure 5. Nonhierarchical k-means cluster analysis of the weekly mean of egg-laying pattern of hens from 17 to 70 wk of age (54 wk of egg production) according to the previous classification of individuals by the hierarchical clustering method using Ward s algorithm.

8 GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES 2181 Table 4. Number of laying hens and mean ± SE of the mean total egg production rate in each cluster created by k-means after previous group division by the hierarchical method Item Cluster 1 Cluster 2 Cluster 3 Hens (No.) 322 1, Mean ± SE ± ± ± The highest median heritability estimates in this study were AFE (0.54 ± 0.07), BW54 (0.68 ± 0.07), and BW62 (0.63 ± 0.06), indicating that these traits had a great influence on additive genes. Munari et al. (1992) found heritability estimates for AFE of 0.57 ± 0.05 for the same CC line, similar to the AFE heritability estimates in the present study. The median heritability estimates for EW32 (0.37 ± 0.06), EW37 (0.31 ± 0.06), and EW40 (0.34 ± 0.06) were lower than those found in the literature. Francesch et al. (1997) found heritability estimates for egg weight at 39 wk of age ranging from 0.48 ± 0.05 to 0.59 ± 0.06 in 3 layer breeds. Sabri et al. (1999) obtained heritability estimates of 0.46 ± 0.17 for egg weight between 26 and 30 wk of laying and of 0.50 ± 0.19 for egg weight between 50 and 54 wk of laying. Ledur et al. (1998) reported heritability estimates of 0.44 ± 0.05 (female fullsister intraclass correlation) and 0.37 ± 0.08 (female half-sister intraclass correlation) for egg weight at 36 wk of age for the same strain. The authors carried out analyses using a different method to estimate genetic parameters, which resulted in different estimates from those in the present study. The median heritability estimates for RLW32, RLW37, and RLW40 (Table 6) were lower than those reported by Ledur et al. (1998), who found a heritability estimate of 0.26 ± 0.04 for the egg length:width ratio at 36 wk of age. However, these estimates were close to that reported by Begli et al. (2010), which was 0.18 ± 0.07 for the ESI (the rate between the short and long diameters of each egg). The length:width ratio of eggs showed a high positive genetic association with egg weight. The median heritability estimates for EP1730 were higher when compared with heritability estimates of other egg production periods, and they were similar to those related by Sabri et al. (1999) and Francesch et al. (1997) of 0.27 ± 0.17 and 0.20 ± 0.06 to 0.33 ± 0.05, respectively. Munari et al. (1992) found heritability estimates of 0.33 ± 0.04 for egg production rate from 18 to 40 wk, 0.31 ± 0.04 from 18 to 50 wk, 0.40 ± 0.04 from 18 to 70 wk, 0.26 ± 0.04 from 40 to 50 wk, 0.38 ± 0.04 from 50 to 70 wk, and 0.40 ± 0.04 from 40 to 70 wk of age. Hagger and Abplanalp (1978) and Sabri et al. (1991) suggested that the maximum genetic potential of egg production and related traits is expressed during peak laying, from 11 to 15 wk of egg production. Environmental effects are minimal during this period when compared with subsequent periods of the production cycle. Studies with random regression that consider the monthly number of eggs produced showed that the highest heritability estimates for egg production are at the beginning of the egg-laying period. After the third month, these heritability estimates decreased until the sixth month, when they started to increase again, forming a U-shaped curve (Anang et al., 2002; Wolc and Szwaczkowski, 2009). These heritability estimates are more accurate than those estimated by the multi-trait model because the month of egg production can be analyzed as repeated measures of the same feature, in which the covariance matrix is taken into account in the statistical model, suggesting that the major additive gene action occurs at the beginning of the laying cycle. Other authors have reported estimates of genetic parameters for cumulative weekly egg production and monthly egg production for a broiler dam line (Luo et al., 2007), cumulative monthly egg production in turkeys (Kranis et al., 2007), and the fortnightly rate of egg production (Wolc et al., 2011) through the use of random regression. These authors found a gradual increase in heritability estimates over time in the egglaying cycle, possibly because of a decrease in the residual variance and an increase in the additive genetic variance over time. The genetic correlations between egg production and egg weight in this study were similar to those obtained by Ledur et al. (1993) and Francesch et al. (1997). The low negative association between them indicated that these traits had a low additive genetic association. The genetic correlation between the length:width ratio of egg and egg weight was high and positive. This result was not in agreement with those reported by Zhang et al. (2005), Lwelamira et al. (2009), and Begli et al. (2010), who obtained low estimates of genetic correlation between ESI and egg weight. The length:width ratio of eggs is more appropriate to show a genetic association of this trait with egg weight. The length:width ratio of eggs and egg weight do not present strong genetic correlations with AFE and with egg production in all the studied periods, implying that genetic changes in the AFE or in egg production traits would have little genetic influence on the length:width ratio of eggs and egg weight. The genetic correlation between EP1740 and EW40 ( 0.20 ± 0.16) was similar to that reported by Fairfull and Gowe (1990) in a White Leghorn control line. Similar results were also reported by Besbes et al. (1992), Wei and van der Werf (1993), Hagger (1994), Mielenz

9 2182 Savegnago et al. Table 5. Additive genetic ( 2 σ a ) and environmental ( 2 σ e ) variances of the studied traits 1 Item EP1730 EP1740 EP3070 EP4070 TEP AFE EW32 EW37 EW40 BW54 BW62 RLW32 RLW37 RLW , , , , σ a 2 σ e 1 Variances are the median estimates from the bi-trait analysis. BW54 and BW62 = BW at 54 and 62 wk of age, respectively; EW32, EW37, and EW40 = egg weight at 32, 37, and 40 wk of age, respectively; RLW32, RLW37, and RLW40 = egg length:width ratio at 32, 37, and 40 wk of age, respectively; AFE = age at first egg; EP1730, EP1740, EP3070, EP4070, and TEP = production rate from 17 to 30 wk, 17 to 40 wk, 30 to 70 wk, 40 to 70 wk, and 17 to 70 wk of age, respectively. et al. (1994), Jeyarubau and Gibson (1996), and Francesch et al. (1997). In the present study, the genetic correlation between EW37 and AFE was 0.12 ± According to Danbaro et al. (1995), the genetic correlation between egg weight at 37 wk and AFE measured in 5 broiler female lines ranged from 0.21 to Studying the first egg production cycle in a White Leghorn population, Schmidt and Figueiredo (2004) obtained genetic correlations of 0.20 between AFE and BW at 40 wk of age, 0.22 between mean egg weight and AFE, 0.31 between mean egg weight and BW at 40 wk of age, 0.27 between mean egg weight and the length:width ratio of eggs, and 0.13 between the length:width ratio and BW at 40 wk of age. The authors found no genetic correlation between AFE and the length:width ratio of eggs. These results differ from the present study in terms of the magnitude of the correlations but were similar in terms of the sign of the correlation. According to Begli et al. (2010), egg weight has a strong genetic correlation with internal egg content (albumen and yolk quantity), and according to Nurgiartiningsih et al. (2002), the egg weight is negatively correlated with egg production. The results of the present study are consistent with those found by the latter authors, suggesting that EW32, EW37, or EW40 should be used as a selection criterion in a weighted way so that they do not decrease the egg-laying performance. Another possibility for studying the genetic relationship between egg weight and the other traits would be to use random regression models because egg weight is a trait that can be measured over time. Thus, it would be possible to select birds weighted by the mean and the egg weight and BW curves. Regarding egg production, EP1730 and EP1740 would be advantageous as selection criteria to improve TEP because they had the highest egg production heritability estimates compared with the other egg production traits (EP3070, EP4070, and TEP). Selecting birds based on EP1730 or EP1740 performance would genetically increase the total egg production but would reduce the AFE because the genetic correlations between EP1730 with AFE and between EP1740 with AFE were 0.85 ± 0.05 and 0.56 ± 0.12, respectively. This selection criterion could diminish the generation interval for selecting birds until 40 wk of age. However, it could reduce the AFE, causing an increase in the frequency of small eggs because of the incomplete sexual development of young hens. Moreover, this selection criterion disregards the expression of genes related to natural molting and brooding, which are related to late partial egg production periods, and could cause a decrease in the performance of total egg production when the entire egg cycle is not considered in breeding programs. Furthermore, it is important to evaluate and select poultry by taking into account late partial egg production periods to favor the persistence of egg laying.

10 GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES 2183 Table 6. Heritabilities 1 (diagonal), genetic correlations (above the diagonal), and environmental correlations (below the diagonal) ± SE between the studied traits 2 Item RLW32 RLW37 RLW40 BW54 BW62 EW32 EW37 EW40 AFE EP1730 EP1740 EP3070 EP4070 TEP RLW ± 0.83 ± 0.74 ± 0.37 ± 0.24 ± 0.71 ± 0.75 ± 0.77 ± 0.21 ± 0.21 ± 0.17 ± 0.15 ± 0.19 ± 0.01 ± RLW ± 0.13 ± 0.95 ± 0.30 ± 0.15 ± 0.70 ± 0.75 ± 0.77 ± 0.00 ± 0.25 ± 0.26 ± 0.29 ± 0.30 ± 0.34 ± RLW ± 0.25 ± 0.15 ± 0.14 ± 0.00 ± 0.70 ± 0.74 ± 0.66 ± 0.15 ± 0.21 ± 0.03 ± 0.47 ± 0.46 ± 0.37 ± BW ± 0.15 ± 0.13 ± 0.68 ± 0.98 ± 0.57 ± 0.49 ± 0.42 ± 0.05 ± 0.05 ± 0.02 ± 0.22 ± 0.24 ± 0.18 ± BW ± 0.16 ± 0.18 ± 0.73 ± 0.63 ± 0.47 ± 0.42 ± 0.36 ± 0.08 ± 0.07 ± 0.08 ± 0.15 ± 0.17 ± 0.15 ± EW ± 0.21 ± 0.17 ± 0.01 ± 0.08 ± 0.37 ± 0.99 ± 0.97 ± 0.08 ± 0.13 ± 0.13 ± 0.02 ± 0.00 ± 0.05 ± EW ± 0.56 ± 0.20 ± 0.15 ± 0.17 ± 0.38 ± 0.31 ± 0.94 ± 0.12 ± 0.15 ± 0.19 ± 0.24 ± 0.25 ± 0.28 ± EW ± 0.24 ± 0.53 ± 0.17 ± 0.22 ± 0.38 ± 0.39 ± 0.34 ± 0.10 ± 0.15 ± 0.20 ± 0.26 ± 0.25 ± 0.28 ± AFE 0.06 ± 0.01 ± 0.07 ± 0.03 ± 0.00 ± 0.06 ± 0.05 ± 0.02 ± 0.54 ± 0.85 ± 0.56 ± 0.06 ± 0.04 ± 0.25 ± EP ± 0.08 ± 0.14 ± 0.13 ± 0.06 ± 0.24 ± 0.13 ± 0.13 ± 0.51 ± 0.29 ± 0.94 ± 0.37 ± 0.31 ± 0.67 ± EP ± 0.10 ± 0.18 ± 0.06 ± 0.05 ± 0.19 ± 0.11 ± 0.16 ± 0.34 ± 0.81 ± 0.25 ± 0.60 ± 0.54 ± 0.82 ± EP ± 0.01 ± 0.00 ± 0.06 ± 0.02 ± 0.02 ± 0.01 ± 0.07 ± 0.05 ± 0.15 ± 0.39 ± 0.11 ± 0.99 ± 0.94 ± EP ± 0.01 ± 0.04 ± 0.06 ± 0.03 ± 0.01 ± 0.02 ± 0.05 ± 0.06 ± 0.06 ± 0.21 ± 0.97 ± 0.09 ± 0.92 ± TEP 0.08 ± 0.02 ± 0.03 ± 0.02 ± 0.01 ± 0.07 ± 0.01 ± 0.09 ± 0.07 ± 0.36 ± 0.54 ± 0.98 ± 0.93 ± 0.15 ± Median estimates from the bi-trait analysis. 2 BW54 and BW62 = BW at 54 and 62 wk of age, respectively; EW32, EW37, and EW40 = egg weight at 32, 37, and 40 wk of age, respectively; RLW32, RLW37, and RLW40 = egg length:width ratio at 32, 37, and 40 wk of age, respectively; AFE = age at first egg; EP1730, EP1740, EP3070, EP4070, and TEP = production rate from 17 to 30 wk, 17 to 40 wk, 30 to 70 wk, 40 to 70 wk, and 17 to 70 wk of age, respectively.

11 2184 Savegnago et al. Figure 6. Genetic correlation between partial periods and whole periods of egg production. BVEP1730, BVEP1740, BVEP3070, and BVEP4070 = breeding value of the egg production rate from 17 to 30 wk, 17 to 40 wk, 30 to 70 wk, and 40 to 70 wk of age, respectively; BVTEP = breeding value of total egg production. Genetic parameter estimates of longitudinal records, treated as different traits, should be analyzed with caution because the literature indicates the existence of correlations between partial period records of a production cycle, termed part-part genetic correlations, and between partial period records and whole period records, termed part-whole genetic correlations. According to Fairfull and Gowe (1990), genetic correlations between partial periods of egg production and whole periods of egg production are part-whole correlations; that is, the data of the partial records make up a substantial proportion of the egg production of the whole record. Thus, the part-whole genetic correlation is greater when long partial records of egg laying are correlated with the total egg production period. This causes an overestimation of genetic correlations between the part-whole periods. According to the same authors, a part-part genetic correlation also exists when the genetic correlation between early partial records and late partial records is estimated. The genetic correlation is Figure 7. Eigenvalues (y-axis) and percentage of original variation stored in each of the 13 principal components (x-axis).

12 GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES 2185 Figure 8. Principal components analysis using BVEP1730, BVEP1740, BVEP3070, BVEP4070, BVAFE, BVBW54, BVBW62, BVEW32, BVEW37, BVEW40, BVRLW32, BVRLW37, BVRLW40, and *BVTEP (supplemental variable). Panel a) Principal components 1 and 2 (PC1 PC2); panel b) principal components 1 and 3 (PC1 PC3); panel c) principal components 2 and 3 (PC2 PC3). BVEP1730, BVEP1740, BVEP3070, and BVEP4070 = breeding value of egg production rate from 17 to 30 wk, 17 to 40 wk, 30 to 70 wk, and 40 to 70 wk of laying, respectively; BVAFE = breeding value of age at first egg; BVBW54 and BVBW62 = breeding values of BW at 54 and 62 wk of age, respectively; BVEW32, BVEW37, and BVEW40 = breeding value of egg weight at 32, 37, and 40 wk of age, respectively; BVRLW32, BVRLW37, and BVRLW40 = breeding values of length:width ratio at 32, 37, and 40 wk of age, respectively; BVTEP = breeding value of total egg production rate. lower when 2 distant periods of egg production are correlated and vice versa, indicating that these 2 different periods are expressed by different genetic factors. A part-whole genetic correlation was observed in the present study as the genetic correlation between BVEP1730, BVEP1740, BVEP3070, BVEP4070, and BVTEP was higher when early partial periods and late partial periods were higher (Table 6 and Figure 6). A part-part genetic correlation was also observed (Table 6 and Figure 6) as the genetic correlation decreased when the partial periods were far longer (BVEP1730 with BVEP4070) than when they were closer (BVEP1730 with BVEP3070). In this case, the use of random regression was able to model the covariance structure between measurements from different periods of the same trait, avoiding the inflation of genetic correlations.

13 2186 Savegnago et al. Table 7. Eigenvalue of each principal component (PC), cumulative eigenvalue, proportion of total variation of the data set explained in each PC, and cumulative total variation PC Eigenvalue Cumulative eigenvalue Proportion of total variation (%) Cumulative total variation (%) Table 8. Linear correlation of variables within each principal component (PC1 to PC3) 1 Trait PC1 PC2 PC3 BVEP BVEP BVEP BVEP BVAFE BVBW BVBW BVEW BVEW BVEW BVRLW BVRLW BVRLW BVTEP BVBW54 and BVBW62 = breeding values of BW at 54 and 62 wk of age, respectively; BVEW32, BVEW37, and BVEW40 = breeding value of egg weight at 32, 37, and 40 wk of age, respectively; BVRLW32, BVRLW37, and BVRLW40 = breeding values of length:width ratio at 32, 37, and 40 wk of age, respectively; BVAFE = breeding value of age at first egg; BVEP1730, BVEP1740, BVEP3070, and BVEP4070 = breeding value of egg production rate from 17 to 30 wk, 17 to 40 wk, 30 to 70 wk, and 40 to 70 wk of laying, respectively. 2 Numbers indicated show the highest (>0.50 or < 0.50) magnitude of the correlation within each PC. 3 BVTEP = breeding value of total egg production, which was used as a supplemental variable for the PC analysis. Principal components analysis was used to reduce the dimensions of original variables without a loss of information. By definition, the correlation between the principal components is zero; that is, the variation explained in PC1 is independent of that explained in PC2 and so on. This definition implies that the selection of birds for any principal component will not cause a correlated response in terms of other principal components (i.e., they are orthogonal). Kirkpatrick and Meyer (2004) and Meyer (2005) suggested a direct estimation of genetic principal components instead of an estimation of genetic parameters of each trait in a data set. According to those authors, this method has 3 advantages. First, the principal components generate parsimonious models with fewer parameters to be estimated. Second, changes in sampling tend to increase with the number of estimated parameters. If the principal components do not take into account eigenvalues close to zero, the bias in estimates attributable to this omission is negligible. Third, as the number of desired parameters to be estimated increases, the computational demand also increases. However, our objective was to estimate genetic parameters for all traits in the data set to gain a greater understanding of the genetic structure between these traits. We wanted to estimate genetic parameters for all traits measured in different periods in the age of hens. In the present work, the PCA was used to reduce the size of the matrix of genetic values consisting of 14 traits and 1,289 laying hens and to study the multidimensional distribution within each principal component selected. The practical consequence when the genetic correlations between 2 traits tended to zero was that these were separated into 2 different principal components. Vectors of variables tended to show the same sign in PC1 and were close to this axis. This suggests that hens with a positive breeding value for EW37 (BVEW37) also present positive breeding values for EW32, EW40, BW54, BW62, RLW32, RLW37, and RLW40 (BVEW32, BVEW40, BVBW54, BVBW62, BVRLW32, BVRLW37, and BVRLW40, respectively), and vice versa (Figure 8). The PC2 presented the tendency for hens that had a higher BVTEP also to have higher breeding values for the early and late partial egg production periods and to have lower breeding values for AFE (Figure 8). The PC3 presented the tendency for hens that had a higher BVTEP also to have higher breeding values for the late partial egg production periods (BVEP3070 and BVEP4070) for AFE and to have negative breeding values for BVEP1730. These results suggest there may be at least 2 major genetic relationships between egg production and the AFE within the population. Hens with a high TEP were early and reached AFE at a younger age (Figure 8a). However, there were hens with a high egg production rate in the final portion of the cycle, a late AFE,

14 GENETIC PARAMETERS, AND CLUSTER AND PRINCIPAL COMPONENTS ANALYSES and hence a low production of eggs in the initial period of the cycle (Figure 8b). The relationships of BVTEP with BVEP3070 and of BVTEP with BVEP4070 had the same pattern (Figure 8a and 8b), suggesting that high genetic values associated with the persistence of egg laying (late partial egg production periods) contributed to high genetic values for TEP. This may also be explained by the fact that the length of the laying period after peak egg production was higher than the laying period preceding this peak. The selection of hens can be made based on scores generated for each bird (based on the sum of the product between a weight and the respective breeding values of all traits for each bird; values not shown) in PC1 (the principal component associated with the breeding values of BW, egg weight, and the length:width ratio of the eggs) and PC2 (the principal component associated with the breeding values for egg production and AFE). Each weight was obtained by dividing the eigenvector of the trait into the principal component by the square root of the eigenvalue of the principal component (Hair et al., 2009). Thus, the traits of a principal component can be selected without causing genetic changes in the traits of the other principal component because of its orthogonality. In conclusion, early partial production periods (EP1730 and EP1740) were not good indicators for use in improving total egg production because these traits presented an overestimated genetic correlation with TEP because of the part-whole genetic correlation component. Egg production might be improved by selecting individuals based on TEP. ACKNOWLEDGMENTS Financial support was provided by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo; Brazil) and Embrapa Suinos e Aves (Empresa Brasileira de Pesquisa Agropecuária; Concordia-SC, Brazil). R. P. Savegnago was granted scholarships from FAPESP and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Brasilia-DF, Brazil). S. L. Caetano and S. B. Ramos were granted scholarships from FAPESP, and G. B. Nascimento received a scholarship from CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico; Brasilia-DF, Brazil). 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