## 1 Introduction  
In poultry production, enhancing reproductive performance has always been a key objective. However, selective breeding for reproductive traits faces several obstacles. Firstly, reproductive traits are typically complex polygenic traits influenced by multiple genes and environmental factors [1]. The genetic mechanisms underlying these traits are complex and difficult to elucidate, making effective improvement by traditional phenotypic selection methods challenging [2]. The collection of phenotypic data is costly and time-consuming, requiring prolonged monitoring and recording and involving significant labor and resource investment. Traditional pedigree and phenotypic selection methods have limited performance in improving reproductive traits, with slow selection response and low precision. The main reason for this is that the reproductive performance of individuals of opposing sexes can almost only be replaced by records of full siblings. Genomic selection, utilizing whole-genome information, enhances selection efficiency and accuracy, overcoming the limitations of traditional methods [3; 4; 5]. Genomic selection methods, such as GBLUP (Genomic Best Linear Unbiased Prediction), ssGBLUP (Single-step Genomic Best Linear Unbiased Prediction), and Bayesian approaches, have significantly increased breeding precision and efficiency [6; 7; 8]. Genomic breeding value estimation allows an accurate assessment of the genetic potential of individuals of opposite sexes, improving the efficiency of breeding plans. Genomic selection can be used to improve reproductive performance in agricultural animals such as rainbow trout [9], sheep [10], and dairy cattle [11]. However, widespread application still faces several challenges, including the complexity of genomic data and the diversity of breeding objectives. By integrating advanced genomic selection technologies with traditional breeding methods and leveraging big data and precision breeding tools, it is possible to gradually overcome these challenges and achieve the effective improvement of reproductive traits [12; 13]. For meat ducks, as for other meat birds, selection indices focus on growth rates and feed conversion efficiency. Selection also continues for meat quality or fat traits to meet market needs. Selection for egg laying traits is carried out to further improve breeding efficiency. Most selection for these traits is carried out by phenotypic or sibling selection, with genomic selection becoming more common. The Pekin duck is famous for its tender meat and high-quality eggs, occupies an important position in the poultry industry, and is a world-famous standard breed. As the consumption of duck meat and eggs increases year by year, the need for high-quality domestic duck breeds is becoming more and more urgent. Compared to pigs, chickens, and cows, the application of genomic selection technology to ducks is only just getting started. In our previous study, we found that genomic selection methods have high accuracy in the assessment of duck meat yield and growth traits [6]. However, research on genomic prediction in ducks remains limited and has mainly focused on meat quality traits [14], carcass traits [15], and growth and breast morphological traits [6]. The application of genomic selection techniques in duck reproductive traits has not yet been thoroughly explored. Therefore, this study aimed to estimate the genetic parameters of reproductive traits (age at first egg and number of eggs between 25 and 44 weeks) and egg quality traits (average egg weight at 40 weeks and egg shape index) in multiple consecutive generations of Pekin ducks. Additionally, we evaluated the selection progress of age at first egg and number of eggs between 25 and 44 weeks over several generations using BLUP, GBLUP, and ssGBLUP models. We also assessed the genomic prediction performance of different models through 10-fold cross-validation.