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Abstract Background The most prolific duck genetic resource in the world is located in Southeast/South Asia but little is known about the domestication and complex histories of these duck populations. Results Based on whole-genome resequencing data of 78 ducks (Anas platyrhynchos) and 31 published whole-genome duck sequences, we detected three geographic distinct genetic groups, including local Chinese, wild, and local Southeast/South Asian populations. We inferred the demographic history of these duck populations with different geographical distributions and found that the Chinese and Southeast/South Asian ducks shared similar demographic features. The Chinese domestic ducks experienced the strongest population bottleneck caused by domestication and the last glacial maximum (LGM) period, whereas the Chinese wild ducks experienced a relatively weak bottleneck caused by domestication only. Furthermore, the bottleneck was more severe in the local Southeast/South Asian populations than in the local Chinese populations, which resulted in a smaller effective population size for the former (7100–11,900). We show that extensive gene flow has occurred between the Southeast/South Asian and Chinese populations, and between the Southeast Asian and South Asian populations. Prolonged gene flow was detected between the Guangxi population from China and its neighboring Southeast/South Asian populations. In addition, based on multiple statistical approaches, we identified a genomic region that included three genes (PNPLA8, THAP5, and DNAJB9) on duck chromosome 1 with a high probability of gene flow between the Guangxi and Southeast/South Asian populations. Finally, we detected strong signatures of selection in genes that are involved in signaling pathways of the nervous system development (e.g., ADCYAP1R1 and PDC) and in genes that are associated with morphological traits such as cell growth (e.g., IGF1R). Conclusions Our findings provide valuable information for a better understanding of the domestication and demographic history of the duck, and of the gene flow between local duck populations from Southeast/South Asia and China.