Reproductive traits such as number of stillborn piglets (SB) and number of teats (NT) have been evaluated in many genome-wide association studies (GWAS). Most of these GWAS were performed under the assumption that these traits were normally distributed. However, both SB and NT are discrete (e.g. count) variables. Therefore, it is necessary to test for better fit of other appropriate statistical models based on discrete distributions. In addition, although many GWAS have been performed, the biological meaning of the identified candidate genes, as well as their functional relationships still need to be better understood. Here, we performed and tested a Bayesian treatment of a GWAS model assuming a Poisson distribution for SB and NT in a commercial pig line. To explore the biological role of the genes that underlie SB and NT and identify the most likely candidate genes, we used the most significant single nucleotide polymorphisms (SNPs), to collect related genes and generated gene-transcription factor (TF) networks. Comparisons of the Poisson and Gaussian distributions showed that the Poisson model was appropriate for SB, while the Gaussian was appropriate for NT. The fitted GWAS models indicated 18 and 65 significant SNPs with one and nine quantitative trait locus (QTL) regions within which 18 and 57 related genes were identified for SB and NT, respectively. Based on the related TF, we selected the most representative TF for each trait and constructed a gene-TF network of gene-gene interactions and identified new candidate genes. Our comparative analyses showed that the Poisson model presented the best fit for SB. Thus, to increase the accuracy of GWAS, counting models should be considered for this kind of trait. We identified multiple candidate genes (e.g. PTP4A2, NPHP1, and CYP24A1 for SB and YLPM1, SYNDIG1L, TGFB3, and VRTN for NT) and TF (e.g. NF-κB and KLF4 for SB and SOX9 and ELF5 for NT), which were consistent with known newborn survival traits (e.g. congenital heart disease in fetuses and kidney diseases and diabetes in the mother) and mammary gland biology (e.g. mammary gland development and body length).