Genetic parameters of body weight, egg production and shell quality traits in the Brown Tsaiya laying duck

Parametres genetiques des caracteres de poids corporels, de production d'œufs, et de qualite de la coquille chez la cane pondeuse Tsaiya Brune. Les heritabilites et correlations genetiques ont ete estimees pour 5575 pondeuses Tsaiya Brune, sur la base de performances concernant les 5 premieres generations d'une experience de selection par la methode du REML-MM (maximum de vraisemblance restreinte-multivariate multimodele) appliquee a un modele animal sur 12 caracteres: la longueur de la plume a l'âge de 20 sem (FL20), le poids corporel a 20 et 40 sem (BW20; B W40), l'âge au premier œuf (AGE1EGG), les nombres d'œufs a 40 et 52 sem (NEGG40; NEGG52), la solidite de la coquille a 30 et 40 sem (ES30; ES40), le poids des œufs a 30 et 40 sem (EW30; EW40), le poids des jaunes d'œufs a 40 sem (EYW40) et le rapport du poids de l'œuf au poids corporel a 40 sem (EW40/BW40). Les femelles adultes etaient plus lourdes que les mâles (BW40: 1 391 vs 1 310 g). ES40 etait inferieure a ES30 (3,5 vs 3,8 kg/cm 2 ). Les valeurs d'heritabilite d'ES40, ES30, NEGG52, NEGG40, FL20, EYW40 et AGE1EGG etaient faibles: 0,094; 0,107; 0,118; 0,160; 0,169; 0,191 et 0,201 respectivement. Elles etaient de 0,327; 0,329; 0,353; 0,425 et 0,499 pour EW40/BW40, EW40, EW30, BW20 et BW40. Cinquante correlations genetiques sont tabulees. NEGG52 etait fortement correle avec NEGG40 (rg = 0, 948), mais n'etait pas correle avec les poids corporels et etait correle negativement avec AGE1EGG (rg = -0, 749), EW40 (rg = -0, 323), EW30 (rg = -0,200), EYW40 (rg = -0,340), ES30 (rg = -0,194), ES40 (rg = -0,203), FL20 (rg = -0,131) et EW40/BW40 (rg = -0, 259). Les poids des œufs, les poids corporels et les caracteres de la solidite de la coquille etaient positivement correles entre eux. Les resultats suggerent qu'une selection sur un index lineaire pour NEGG52 avec des contraintes pour EW40, BW40 et ES40 pourrait etre efficace pour ameliorer les performances de la production d'œuf de la cane Tsaiya Brune.

genetic correlations for the traits to be selected showed that NEGG52 was highly positively correlated with NEGG40 (rg = 0.948), uncorrelated with the body weight and was negatively correlated with AGELEGG (rg = -0.749), EW40 (rg = -0.323), EW30 (rg = -0.200), EYW40 (rg = -0.340), ES30 (rg = -0.194), ES40 (rg = -0.203), FL20 (rg = -0.131) and EW40/BW40 (rg = -0.259). Egg weights, body weights and eggshell strength traits were positively genetically correlated among themselves. The results suggest that a linear selection index for NEGG52 with constraints for EW40, BW40 and ES40 could be an efficient tool for improving the efficiency of egg production with this small body type laying duck. heritability / genetic correlation / animal model / laying duck Résumé -Paramètres génétiques des caractères de poids corporels, de production d'oeufs, et de qualité de la coquille chez la cane pondeuse Tsaiya Brune. Les héritabilités et corrélations génétiques ont été estimées pour 5 575 pondeuses Tsaiya Brune, sur la base de performances concernant les 5 premières générations d'une expérience de sélection par la méthode du REML-MM (maximum de vraisemblance restreinte-multivariate multimodèle) appliquée à un modèle animal sur 12 caractères : la longueur de la plume à l'âge de 20 sem (FL20), le poids corporel à 20 et 40 sem (BW20 ; BW40), l'âge au premier ceuf (AGEIEGG), les nombres d'ceufs à 40 et 52 sem (NEGG40; NEGG52), la solidité de la coquille à 30 et 40 sem (ES30 ; ES40), le poids des ceufs à 30 et 40 sem (EW30 ; EWl,O), le poids des jaunes d'oeufs à 40 sem (EYWl!O) et le rapport du poids de l'ceuf au poids corporel à 40 sem (EW401BW40). Les (Tai et al, 1994). Not much is known about the genetic parameters and especially the genetic correlations for these traits in ducks. Tai et al (1989) estimated heritabilities for 8 of these traits in the first generation. Lee et al (1992) estimated genetic parameters in each of the first 4 generations, using variance component estimation method applied to a hierarchical relationship structure. On the other hand, the best linear unbiased prediction (BLUP) (Henderson, 1988) has been increasingly applied to an animal model for predicting the genetic merit of candidates for selection in most species of farm animals. For this purpose estimates of the genetic parameters in the base population are required. Some simulation research has shown that the use of maximum likelihood (ML) or minimum variance quadratic unbiased estimation (MIVQUE) methods on selected data can lead to unbiased estimates of additive genetic variance in the base population (Rothschild et al, 1979;Meyer and Thompson, 1984;Sorensen and Kennedy, 1984). It has been shown that when the method of restricted maximum likelihood (REML, Patterson and Thompson, 1971) is applied to an animal model, in particular when all the information contributing to selection is included in the analysis and a large number of additive loci is assumed, it can provide unbiased estimation in selected populations (Kennedy, 1990;Meyer, 1990Meyer, , 1991. Consequently, REML has recently been applied in animal breeding for estimating variance and covariance components in selected populations (Hofer et al, 1992;Besbes, 1993;Ducos et al, 1993;Hagger, 1994;Mielenz et al, 1994;Poujardieu et al, 1994). As far as we know, it has not yet been used to estimate genetic parameters in laying ducks.
The purpose of this study was to estimate and discuss genetic parameters for the 12 traits recorded for the first 5 generations in a selection experiment for laying Brown Tsaiya ducks.

Data description
The ducks were collected from 4 different locations around Taiwan. Sires came from 4 breed farms and dams from another 4 egg-production farms. With 4-by-4 mating, each origin of sire was mated to the 4 origins of dams (5 ducks per drake) and then progeny was assigned to mating groups depending on the sire origins. Twelve traits were individually measured and recorded as follows: FL20: feather length at 20 weeks of age (except in 2nd and 4th generations) in both sexes.
BW20, BW40: body weight at 20 and 40 weeks of age respectively in both sexes.
AGE1EGG: age at first egg.
NEGG40, NEGG52: number of eggs laid up to 40 and 52 weeks of age, respectively.
ES30: eggshell strength at 30 weeks of age (except in 4th and 5th generations). ES40: eggshell strength at 40 weeks of age (except in 1st and 2nd generations).
EYW40: egg yolk weight at 40 weeks of age (except in first generation). EW40/BW40: the ratio of egg weight to body weight at 40 weeks of age.
Eggs laid over 5 consecutive days at 30 and 40 weeks of age were weighed and measured by eggshell strength meters for the average of EW30, EW40, ES30 and ES40.
The structure of the selection experiment (without control strain) is described in table I for the number of ducks (males and females) and the hatching date of each generation. Population size was increased from the third generation mainly in order to maintain an optimal population size for long-term selection (Lee et al, 1992). A 2-stage selection was carried out. First, 50% of the female ducks were selected on a linear phenotypic selection index: Among these selected females, the top 50% were selected for ES30 (first and second generations) or ES40 (third to fifth generations). The drakes were similarly chosen taking into account the performances of their full and half sisters.

Statistical analysis
All records were analysed by an SAS univariate procedure to test normal distribution, and some extreme and abnormal data were discarded (less than 3 depending on the trait). Skewed distributions were observed for the AGE1EGG, NEGG40 and NEGG52 variables. They were thus transformed using a power distribution (Box and Cox, 1964;Besbes et al, 1993) in order to satisfy the classical hypotheses for normally distributed traits. This transformation relies on a single parameter t as shown previously for laying hens (Ibe and Hill, 1988;Besbes et al, 1992). The following formula was used: where ! is the geometric mean of the original observations. The parameter t was empirically chosen is such a way that skewness became close to zero and there was a low residual sum of squares in the genetic model used to describe the data. The t values were 3.8, 3.0 and -1.2, respectively, for NEGG52, NEGG40 and AGE1EGG. Analysis of FL20, BW20 and BW40 was based on the following linear model: where for AGEIEGG, NEGG40, NEGG52, ES30, ES40, EW30, EW40, EYW40 and EW40/BW40 the following model was used: where y2!xl and Y i kl are the ijklth and iklth observations respectively, ! is the population mean, H is the fixed effect for the ith hatch, S is the fixed effect for the jth sex, az!x and a ix are the random additive genetic effects of the ijkth and ikth animals respectively, and e2!xl and e iki are the residual effects.
Sires from the 4 origins were considered to belong to the same population. The data for the 4 lines were pooled. Heritabilities and genetic correlations were estimated by the restricted maximum likelihood method (REML) applied to an animal model. A derivative-free REML algorithm (Graser et al, 1987) from the DF-REML program of Groeneveld and Kovac (1990a,b) as adapted by Boichard (1994) and the VCE multivariate multimodel REML (co)variance component estimation (MM-REML) program of Groeneveld (1994a) were used for all trait analyses.

Computing strategy
The general linear model is as follows: where y = vector of observations for the trait; (3 = vector of fixed effects; u = vector of animal effects; e = random vector of residual effects; X, Z are incidence matrices relating observations to the effects in the model, G = A (9 Go; A is the numerator relationship matrix; Go is the (co)variance matrix for additive genetic effects among traits; R = L e &reg; Rro; I e is the identify matrix; R o is the residual (co)variance among traits; (9 = the Kronecker product. The mixed-model equations (MME) are then (Henderson, 1963(Henderson, , 1973: The logarithm of the restricted, multivariate, normal likelihood function to be maximized is as follows (Groeneveld, 1994b): where LV is proportional to the logarithm of the likelihood function; W = (X!Z); b° is the solution vector of the MME; C * is the inverse of the coefficient matrix of the MME; na = the number of animals; and n = the number of observations. The log likelihood value was maximized by a Downhill-Simplex procedure or a Quasi-Newton algorithm method and MME were solved by Cholesky factorization using a super-nodal block factorization (Groeneveld, 1994a,b).
The number of levels for fixed effects was 26 for hatch and 2 for sex. Heritabilities and genetic correlations were estimated with an animal model, taking all ducks which had at least one observation. The selected traits EW40, BW40, NEGG52, ES30 and ES40 were included together in the MM-REML analysis to obtain heritabilities and genetic correlations for the 5 traits selected. Each of the secondary traits was then added to study correlations between selected traits and 7 secondary traits. Finally the 7 secondary traits were analyzed together for genetic correlations.
All relationship coefficients were calculated from the founder stock (GO) and all duck measurements from G1 to G5 were considered.

Management
The same management system described by Tai et al (1989) was applied throughout the 5 generations of selection in this study.

RESULTS
Tables II and III give the number of animals, and the means and standard deviations of phenotypic values for the 12 traits over 5 generations. EW40/BW40, EW40, EW30, BW20 and BW40, respectively. FL20 was genetically positively correlated with AGE1EGG, body weight and egg weight traits, and slightly positively correlated with eggshell strength and EYW40, but slightly negatively correlated with egg production traits and EW40/BW40. Body weight traits were highly genetically correlated between themselves (rg = 0.988), and were positively correlated with egg weights, EYW40 and eggshell strength, but were not correlated with AGE1EGG and NEGG52. Age at first egg was negatively correlated with egg production traits, positively correlated with EYW40 and egg weight traits, and slightly positively correlated with ES40 and EW40/BW40. The 2 egg production traits were highly genetically correlated (rg = 0.948) between themselves and were negatively correlated with all other traits except BW40. ES30 and ES40 were highly correlated between themselves (rg = 0.845) and also EW30 and EW40 (rg = 0.979). EYW40 was highly positively correlated with egg weight (rg = 0.870&mdash;0.914). Egg weight and EYW40 were positive correlated with eggshell strength (rg = 0.318-0.585). EW40/BW40 was highly negatively correlated with body weight (rg = -0.686 to -0.748) and slightly negatively correlated with egg production traits and ES30, but was not correlated with EW40. It was positively correlated with EW30 and ES40. If computer facilities had not been limited, the MM-REML method could have been applied to take the whole selection process into account simultaneously and related genetic information could thus have been seen more clearly.

DISCUSSION
Unlike for poultry, very little data is available on the genetic parameters of laying duck traits. Pingel (1990) (1992) were the closest to our results for Brown Tsaiya.
A sex effect was introduced in the model of analysis for body weight and feather length, because males Brown Tsaiya are significantly lighter than females. This is quite unusual if we compare them with Muscovy ducks where there is a very large sexual dimorphism for body weight in favor of males, but also with Pekin ducks, in which the males are 10% heavier than the females.
Taking all the information from the selected traits enables the best use of MM-REML in an animal model in order to get unbiased estimates of the genetic parameters in the base population. Owing to limited computing facilities, we calculated the genetic parameters for the 5 selected traits included together in the MM-REML analysis. It was assumed that the genetic parameters should be consistent at least for these traits and also the genetic correlations of these 5 selected traits along with the 7 secondary trait ones. The heritability values calculated by univariate or multivariate REML are very close and the maximum difference is only 3%.
The estimates of the heritabilities of the 12 traits and their genetic correlations could provide a basic knowledge of the genetic parameters in the base population of this laying Brown Tsaiya line selected for 5 generations. The main purpose of breeding could be to increase additive genetic value for egg production traits while getting a moderate body weight and keeping egg weight and eggshell quality at optimum levels according to market requirements. ES40 is lower on average than ES30. So it seems better to take ES40 as a selection criterion for eggshell strength. Heritability values of egg production traits in Brown Tsaiya are small but there is some additive genetic variation, and selection for NEGG52 is possible. The same is true for eggshell quality traits. NEGG40 and NEGG52 are slightly negatively correlated with ES30 and negatively correlated with ES40. They are negatively correlated with EW40 and EYW40, and slightly negatively correlated with EW30. EW40 is highly correlated with EYW40 and behaves as if it were the same trait. BW20 and BW40 behave genetically as the same trait, with BW20 being slightly negatively correlated with egg production up to 52 weeks of age, but BW40 showing no genetic correlation with egg number. Thus selection for egg number up to 40 or 52 weeks of age alone should be antagonistic to genetic progress in EW40 and ES40. Constraints for these 2 traits could be introduced into a selection index, the aim of which should be to increase egg number while maintaining EW40, BW40 and ES40 at their current levels.
In fact EW40/BW40 was found to be strongly influenced by body weights, with highly negative genetic correlations. When compared with laying hens, the Brown Tsaiya showed a good ratio of egg weight to body weight at 40 weeks of age (0.0489 vs 0.0316 (Liljedahl et al, 1979)). The Brown Tsaiya ducks already have quite a moderate body weight. In order to improve egg production, egg weight/body weight ratio and feed efficiency by limiting maintenance cost, it seems that ducks of small body type should be considered. Besbes et al (1992) also showed a genetic correlation of -0.14 (line A) or -0.22 (line B) between egg number and egg weight, 0.32 (line A) or 0.33 (line B) between egg weight and body weight and 0.25 (line A) or -0.12 (line B) between egg number and body weight. The results indicated that different lines could exhibit different genetic correlations between egg number and body weight. Hagger (1994) estimated that genetic correlations between NEGG40 and EW40 was -0.267 and that between NEGG40 and male and female BW40 were -0.161 and -0.036, respectively, with the genetic correlations between EW40, male and female BW40 being 0.338 and 0.294, respectively. Mielenz et al (1994) reported genetic correlations among egg number up to day 270, egg weight and body weight at day 215 were -0.11 and 0.07, respectively, and 0.39 between egg weight and body weight at day 215. Obviously, the genetic correlations between egg number and body weight can vary according to line and sex as found in laying hens, whereas Brown Tsaiya showed no genetic correlations between them. It could be concluded that in laying hens most of the heritabilities estimated by the REML animal model showed higher values for egg number than in Brown Tsaiya, and the genetic correlations reported among traits were also different.
Once the heritabilities and genetic correlations in the base popultion are known, the breeder can define a selection strategy by selecting for a linear combination of the predicted breeding values of the 4 traits EW40, BW40, NEGG52 and ES40. The optimal linear combination can be chosen according to the expected correlated responses for the several traits.