Knowledge about population structure and connectivity of waterfowl species, especially mallards (Anas platyrhynchos), is a priority because of recent outbreaks of avian influenza. Ringing studies that trace large-scale movement patterns have to date been unable to detect clearly delineated mallard populations. We employed 363 single nucleotide polymorphism markers in combination with population genetics and phylogeographical approaches to conduct a population genomic test of panmixia in 801 mallards from 45 locations worldwide. Basic population genetic and phylogenetic methods suggest no or very little population structure on continental scales. Nor could individual-based structuring algorithms discern geographical structuring. Model-based coalescent analyses for testing models of population structure pointed to strong genetic connectivity among the world's mallard population. These diverse approaches all support the conclusion that there is a lack of clear population structure, suggesting that the world's mallards, perhaps with minor exceptions, form a single large, mainly interbreeding population.