Invasions often accelerate through time, as dispersal-enhancing traits accumulate at the expanding range edge. How does the dispersal behaviour of individual organisms shift to increase rates of population spread? We collate data from 44 radio-tracking studies (in total, of 650 animals) of cane toads (Rhinella marina) to quantify distances moved per day, and the frequency of displacement in their native range (French Guiana) and two invaded areas (Hawai’i and Australia). Here we show that toads...