Prediction of genetic gains in body weight, egg production and shell quality traits in the Brown Tsaiya laying duck (Anas platyrhynchos)

(Anas platyrhynchos). Les gains genetiques attendus et les reponses genetiques predites du poids de l'oeuf et du poids corporel a l'âge de 40 semaines (EW40, BW40), du nombre d'oeufs pondus jusqu'a l'âge de 52 semaines (NEGG52 ), de la solidite de la coquille aux âges de 30 et 40 semaines (ES30 ou ES40) chez la cane pondeuse Tsaiya Brune selectionnee pendant cinq generations ont ete calcules. La selection par niveaux independants etait basee sur un premier choix des 50% meilleures femelles d'apres leurs valeurs individuelles d'un indice de selection massale sur les trois caracteres EW40, BW40, NEGG52 et sur un deuxieme choix portant sur les valeurs individuelles de ES30 (deux premieres generations) puis de ES40 a partir de la troisieme generation. Les reproducteurs mâles etaient choisis de facon comparable a partir de l'information sur leurs soeurs. Au total, 3482 femelles et 2093 mâles ont ete etudies. Pendant les quatre premieres generations, en moyenne 25,6% des femelles et 12,2% des mâles furent selectionnes. A partir des parametres genetiques de la population de base, les gains genetiques attendus ont ete calcules. Les reponses genetiques par generation ont ete estimees par ailleurs a partir des moyennes des predicteurs de valeurs genetiques du BLUP modele animal, en calculant la regression des moyennes en fonction du numero de generation. Les reponses par generation sont de + 0,177g (EW40); de + 8,029g (BW40); de + 0,935 oeufs (NEGG52); de + 0,017 kg/cm 2 (ES30); de + 0,014 kg/cm 2 (ES40). Ces valeurs correspondent au gain genetique attendu pour NEGG52, elles sont plus fortes pour BW40 et plus faibles pour ES30 and ES40. Il est montre que, par rapport a la methode de selection qui a ete appliquee et avec la meme intensite de selection chez les canes (i = 1 1 , 271), la selection avec contraintes sur un indice de selection massale ou un indice genetique sur quatre caracteres pourrait multiplier le gain genetique attendu de NEGG52 par 3,5 et 5,7 respectivement, tout en maintenant constant le poids de l'oeuf (EW40) et le poids corporel (BW40).

(Received 13 June 1995; accepted 16 August 1996) Summary -An evaluation was made of the expected genetic gain and predicted genetic responses for egg weight and body weight at 40 weeks of age (EW40, BW40), number of eggs laid up to 52 weeks of age (NEGG52), eggshell strength at 30 or 40 weeks of age (ES30 or ES40) in Brown Tsaiya laying ducks selected for five generations by independent culling levels, first on a linear phenotypic index for the first three traits, and then on ES30 or ES40. The genetic parameters estimated in the base population were used to calculate the expected genetic gains in one generation of selection. The genetic responses per generation were evaluated by averaging the multitrait best linear unbiased prediction (BLUP) animal model predictors and regressing them on generation number. The per generation genetic responses were +0.177 g (EW40); +8.029 g (BW40); +0.935 eggs (NEGG52); +0.017 kg/cm 2 (ES30); + 0.014 kg/ CM 2 (ES40). These values fit the expected genetic gains for NEGG52, but they are higher than those for BW40 and lower than those for ES30 and ES40. It was shown that, compared to the selection method which has been used and with the same selection intensity in female ducks (i = 1.271), constrained selection based on a phenotypic selection index or a genetic index could increase the expected genetic gains in NEGG52 by a factor of 3.5 or 5.7, respectively, while maintaining constant EW40 and BW40. genetic gain / selection / laying duck / restricted selection index Résumé -Prédiction des gains génétiques sur des caractères de poids corporel, de production d'oeufs et de qualité de la coquille chez la cane pondeuse Tsaiya Brune (Anas platyrhynchos). Les  puis de ES40 à partir de la troisième génération. Les reproducteurs mâles étaient choisis de façon comparable à partir de l'information sur leurs soeurs. Au total, !482 femelles et 2 093 mâles ont été étudiés. Pendant les quatre premières générations, en moyenne 25,6% des femelles et 12,2% des mâles furent sélectionnés. À partir des paramètres génétiques de la population de base, les gains génétiques attendus ont été calculés. Les réponses génétiques par génération ont été estimées par ailleurs à partir des moyennes des prédicteurs de valeurs génétiques du BL UP modèle animal, en calculant la régression des moyennes en fonction du numéro de génération. Les réponses par génération sont de + 0,177g (EW40); de + 8, 029 g (BWl, 0); de + 0, 935 ceufs (NEGG52); de + 0, 017 kg/cM 2 (ES30); de + 0, 014 kg/cm 2 (ES40). Ces valeurs correspondent au gain génétique attendu

INTRODUCTION
The native breed Brown Tsaiya (Anas platyrhynchos) is a major breed of laying duck in Taiwan. A selection for the four traits of egg weight and body weight at 40 weeks of age (EW40 and BW40), number of eggs laid up to 52 weeks of age (NEGG52), eggshell strength at 30 weeks of age (ES30, first two generations) and at 40 weeks of age (ES40, from generation three) has been conducted at the Ilan Branch of the Taiwan Livestock Research Institute since 1984. The selection was made by independent culling levels, first on the values of a restricted phenotypic selection index for three traits EW40, BW40, NEGG52 and then on the ES30 or ES40. There was no unselected control population. Cheng et al (1995) estimated the genetic parameters in the base population by REML applied to a multiple trait animal model based on data of the first five generations of selection. The selection goals of this breeding program at present are to maintain EW40 and BW40 at their current genetic levels, to increase as much as possible the genetic level in NEGG52, while getting a positive genetic response on ES30 and ES40. It is therefore useful at this stage to evaluate the genetic responses and to determine the most efficient multitrait selection index in order to get the desired gains.
From early research it is now well known that theoretically the selection index for several traits is more efficient than the independent culling levels procedure; the superiority may depend on the number of traits, the economic weights and the genetic correlations (Minvielle, 1990). Since Hazel (1943), the conventional selection index for multiple trait has been extended by several workers to take into account information from relatives (Henderson, 1963;Rouvier, 1969ab, 1977. One of the classical selection indices with restrictions for egg size, body weight and egg production rate in poultry selection was presented by Hogsett and Nordskog in 1958. The theory of restricted selection indices (Kempthorne and Nordskog, 1959) or indices for desired gains has been further developed (Mallard, 1972;Itoh and Yamada, 1987). When the means are unknown and the estimated variances and covariances used are not very different from their true values, multiple trait evaluation by best linear unbiased prediction (BLUP) can be used Schaeffer, 1984;Ducrocq, 1994). Some applications with an animal model have been made recently by Hofer et al (1992) and Ducos (1994) for genetic evaluation in swine, and by Besbes (1993) for laying hens. A restricted BLUP, the BLUP counterpart of restricted selection index, has been derived by imposing restrictions on the multitrait mixed-model equations (MME) Henderson, 1984). Lin (1990) gave a unified procedure for computing both a restricted BLUP and a restricted selection index for multiple trait (MT).
The purpose of this study was to predict the breeding value by an MT-BLUP procedure using an animal model in order to evaluate the genetic responses and to study the expected genetic gains calculated by the conventional methods. The results would then be used to discuss the possible application of a restricted genetic selection index for MT and maximum gain on the number of eggs laid up to 52 weeks of age.

Selection method
A restricted selection index h based on egg weight at 40 weeks of age in grams (EW40), body weight at 40 weeks of age in grams (BW40) and number of eggs laid up to 52 weeks of age (NEGG52) was first applied to select 50% of the female ducks. This restricted selection index was constructed with conventional estimated genetic parameters (table I) to increase the number of eggs while holding egg weight and body weight constant in Brown Tsaiya (Tai et al, 1994). As the heritabilities of ES30 and ES40, and their genetic correlations with the three previous traits were unknown, among these 50%, the top 50% of the best female ducks was selected for ES30 in the first and second generations (Gl and G2) and for ES40 from the third generation (G3) of selection by independent culling levels. Eggs laid over five consecutive days at 30 and 40 weeks of age were weighed and measured by eggshell meters (unit: kg/cm 2 ) for the average of ES30 and ES40. The drakes were chosen within sire using information from four full sisters: first 35% of them on the averages of h and then 35% on averages of ES30 or ES40. On average in G1 up to G4, 12.2% of the drakes and 25.6% of the female ducks were selected. In G1 up to G5, the data from 3 482 female and 2 093 male offspring were recorded (Cheng et al, 1995; table II).

Computation of breeding values and predicted genetic responses
Theoretically, an MT animal model which accounts for covariances among traits should reduce the prediction error variance of predicted breeding values (Schaeffer, 1984;Thompson and Meyer, 1986). Therefore, the same data for the five traits (EW40, BW40, NEGG52, ES30 and ES40), the heritabilities and phenotypic and genetic correlations estimates for these five traits were taken from Cheng et al (1995) for computation of breeding values (table I). The pedigree information was traced to the founder animals (GO) which were assumed to be unrelated (table II). Hatch batches (26 levels) and sexes (for BW40) were assigned as fixed effects. Predicted breeding values of the five traits were calculated by an MT-BLUP animal model that accounts for inbreeding using the PEST program (Groeneveld, 1990;Groeneveld and Kovac, 1990;Groeneveld et al, 1992). The genetic responses for each trait were estimated from the regression of the MT-BLUP breeding values of female ducks on generation number. The phenotypic selection differentials for each trait were calculated in female ducks only.
Multitrait selection index and expected genetic gains The expected genetic gains for one generation which correspond to the applied selection index, have to be calculated in order to compare them with the predicted genetic response. They also have to be calculated when selecting on multitrait selection index to make possible improvement of the selection efficiency. The expected genetic gain in each traits was based on the regression of its additive genetic value on the selection differential in the selection index.

Selection on individual phenotypic values
In the present case the selection was based on a restricted phenotypic selection index h = b'y for the three traits EW40, BW40 and NEGG52. The vector b was chosen in order to fit the restrictions of no genetic change for EW40 and BW40.

Selection on the predicted individual breeding values
If g is the vector of predictors of breeding values for each of the n traits of an animal, it is straightforward, according to the classical theory (Rouvier, 1969ab, 1977Mallard, 1972), to combine them in a genetic index Ig = a'g where a is the vector of coefficients for the n breeding values, a' is a transposed, and g is the vector of predictors of breeding values for each of the n traits, calculated as the multiple regression of g on all the phenotypic predictors.
Following Lin (1990) the vector of the coefficients in the restricted genetic index 1 2 = v'g has been calculated with constraints of 0.0 and 0.013 kg/cm 2 for genetic gains in EW40, BW40 and ES40 respectively and maximum gain in NEGG52 (with a selection intensity i = 1).
The matrix of additive genetic variances and covariances of the n traits was assumed to be known. The matrix E(g g') = B was approximated by B, the variance-covariance matrix of the MT-BLUP breeding values in an animal model. Table III gives the expected genetic gains for female ducks in one generation for EW40, BW40, NEGG52, ES30 and ES40 when selecting by independent culling level on the index h with p = 50%, and on ES30 or ES40 with p = 50%. Since h and ES30 or ES40 are phenotypically uncorrelated, the formulas of Young and Weiler (1961) simplify to calculate the selection intensities which are i = 0.789 for h and the same for ES30 or ES40. In total 25% of the female ducks are theoretically selected with this procedure. The expected genetic gains for male ducks in one generation are similar, being + 0.595, + 0.490 for EW40, + 5.245, -1.290 for BW40, + 0.974, + 0.993 for NEGG52, + 0.051, +0.040 for ES30, + 0.058, + 0.063 for ES40, when selecting in the second step for ES30 or ES40 respectively. The overall expected gains can be obtained by averaging the second figures with the corresponding ones in the last two lines of table III. Table IV gives the average phenotypic values in Brown Tsaiya female ducks for EW40, BW40, NEGG52, ES30 and ES40 for the five generations (G1 to G5). It also gives the phenotypic values of the selected animals and the achieved phenotypic selection differential. The genetic responses in female ducks for MT-BLUP animal model prediction are shown in figure 1 and table V.

Genetic selection indices
The (co)variances of the predicted breeding values for EW40, BW40, NEGG52 and ES40 were calculated for males and females in the generation to be selected (fifth generation, table VI). From these parameters, the restricted genetic selection indices I 2 were calculated separately for male and female ducks of G5. The results are shown in table VII for the coefficients of the predictors of breeding values and the expected genetic gains in each trait, by a truncation selection with selection intensity i = 1. The expected gains for a similarly restricted phenotypic selection index (-1 3 ) are also included in table VII.

DISCUSSION
When there is no control population, the genetic response per generation can be obtained by the regression of the average predicted genetic values of the ducks of the same generation on generation number. This method to estimate genetic trends is unbiased because the genetic evaluation is based on a multitrait animal model (Henderson, 1975;Sorensen and Kennedy, 1984;Kennedy et al, 1988;Ducrocq, 1994). The predicted genetic response depends on the genetic parameters which have been used (Thompson, 1986). These were obtained by Cheng et al (1995) as unbiased estimates in the base population. These estimates were assumed to be not very different from the true values.
As far as we know, there is no published data from a selection experiment for such laying traits in laying female ducks. Recently, Besbes (1993) estimated the genetic trends in two strains of laying hens selected for egg production, egg quality and body weight traits, by the regression of the average values of the predictors of breeding values above ten separate generations with several hatch fixed effects in each one.
The model of analysis was based on the prediction of the additive genetic values, without taking account dominance effects. In case of dominance, as for egg number traits in this population (Tai et al, 1989), the genetic response might be overestimated (Johansson et al, 1994).
In order to discuss in retrospect the efficiency of the selection method which was applied and to predict the efficiency of a new one to reach the current selection goals, the predicted genetic responses and the expected genetic gains were calculated. This second method can be applied in only one generation to predict the efficiency of the selection method. The first one takes into account the realized selection differentials and is unbiased by the selection.
The average genetic response per generation for the number of eggs laid up to 52 weeks of age (NEGG52) represents 9.4% of the additive genetic standard deviation. It is close to the expected genetic gain (0.953 to 0.967 eggs). Nevertheless, the phenotypic trend for NEGG52 is negative dropping from 208.6 eggs in Gl to 198.8 eggs in G5, This could be explained by an adverse environmental effect especially in G5 with larger change of climate in the open feeding system (it was 217 eggs in G6).
On the other hand, the increase in inbreeding coefficient is rather small, the mean ± standard deviation being 0.0485 t 0.0255 in G5. The founder animals are assumed to be neither inbred nor related (table II). The genetic response in EW40 represents 6.1% of the additive genetic standard deviation of the trait. This slight increase may be due to the selection for ES30 and ES40, which are positively correlated to EW40 (rg = 0.583 and rg = 0.483, respectively). The genetic response in BW40 (8.6% of the additive genetic standard deviation) was higher than the expected genetic gain. When selecting for ES30 or ES40, there was a correlated positive response on BW40 which counteracted the effects of the selection on h. As has already been observed by Lee et al (1991Lee et al ( , 1993, the eggshell strength depended on the age of the ducks and ES40 was weaker on average than ES30. From G3 the selection criterion ES30 was replaced by ES40 (Lee et al, 1992). The genetic responses per generation in ES30 ( + 0.017 kg/cm 2 ) and in ES40 ( + 0.014 kg/cm 2 ) were lower than the expected ones. The genetic responses per generation in ES30 and ES40 were 9.3 and 6.3% respectively of the additive genetic standard deviations of the traits.
More than 90% of eggs produced is used for egg processing such as salted eggs and century eggs in Taiwanese markets. Economically speaking, a small body size of female duck is desirable to reduce maintenance requirements and egg weight has to be maintained at the current level (around 65 g) to meet market requirements, ES30 and ES40 must not be decreased in order to maintain a low incidence of broken eggs. Thus, NEGG52 has to be increased without negative correlated response on these two traits. The genetic correlations between NEGG52 and ES30 or ES40 are small and negative (rg = -0.194 and rg = -0.203, respectively). The selection method applied was rather efficient for the desired gains in ES30 and ES40 and there was a positive genetic response in EW40 and BW40. The method however was not efficient for improving NEGG52. This could be explained by the independent culling on ES30 and ES40 of 50% of female ducks selected for h. According to the heritabilities and the genetic correlations, this independent culling induces a negative correlated genetic response in NEGG52 and a positive correlated genetic responses in EW40 and BW40 (table III). This is similar for the male duck selection.
Since ES40 is measured before NEGG52, it would be possible to use a multitrait selection index based on the four traits of EW40, BW40, NEGG52 and ES40 such as the phenotypic selection index 1 3 (table VII). This selection index should improve the efficiency of the selection method. With i = 1.271 (25% of selected female ducks), the expected genetic progress on NEGG52 would be multiplied by a factor of 3.5 compared with the current selection method.
A simple computation procedure was derived to calculate a genetic multitrait selection index with restricted traits 1 2 = v'g using the multitrait predictors (g) of breeding values. The performance data of the 3 482 female ducks and 2 093 males (for BW40) of the five generations were taken into account for calculating the matrix B of variances and covariances of the predicted breeding values of all the animals in G5 (1112 females and 624 males), separately for males and females with the assumption E(B) = B. This assumption is more valid when there is a large number of animals. Theoretically, the variances of each predictor for each animal depend on the coefficients of relationship with its relatives which are not the same for each animal. So the approximation of one unique average B has to be made. The results revealed (table VII) that with i = 1.271 the expected genetic gain for NEGG52 was multiplied by the factor 5.7, when compared with selection by independent culling levels. This extra gain compared to I 3 is explained by the increase in accuracy of the prediction of breeding values and of the multitrait genetic selection index. The application of this method would lead to variance-covariance matrix of the MT-BLUP animal model predictors of breeding values calculated separately for males and females in the generation to be selected.

CONCLUSIONS
The selection method applied for five generations in laying Brown Tsaiya ducks has resulted in a predicted genetic response per generation of + 0.935 eggs for the number of eggs laid up to 52 weeks of age. It is the only trait for which the genetic response fits the expected genetic gain. The genetic responses were higher than expected for BW40, but lower than expected for ES30 and ES40. Assuming that the estimates of the genetic parameters in the base population were accurate, it was shown that a restricted selection index based on phenotypic values of four traits EW40, BW40, NEGG52 and ES40 would fit the breeding objectives better than the independent culling level method; EW40 and BW40 could be maintained at their current genetic level, the expected genetic gains in NEGG52 should be much higher and the expected genetic gains on ES30 and ES40 should be positive as desired. Due to the increased accuracy of the predictors of breeding values using an MT-BLUP animal model, a restricted genetic selection index will given even larger expected genetic gain for NEGG52 compared to a conventional restricted selection index. So this selection procedure could be recommended.