Dynamic species invasions network: sender nodes are species and receiver nodes are regions as defined in the FirstRecords database. The dataset covers four taxonomic groups (i.e., mammals, birds, plants, insects) and a fixed time-frame [1880–2005] over which the invasion process of the species occurs into the regional set of the 272 pre-specified regions. The dataset includes 16,403 invasion events recorded for 4,835 species (615 birds, 186 mammals, 3,920 plants, and 114 insect species). The average number of invasion events per taxonomic group is ~5 records per insect species, ~4 per bird and mammal species, and ~3 recorded events per plant species. On average, ~46 invasion events are recorded per region, ranging from 1 to 1,685 events. 157 regions had less than 15 observations, with 33% of these regions located in Africa; 36 regions had more than 100 records.