At first it begins with the migration into new spaces by a few, then, slowly, increasing numbers. Local insects may at first be mildly concerned, but soon it is a battle for existing food resources, which the invaders can more effectively utilise. Over time, natural selection works its magic, and the populations change, by demographic displacement:
https://www.dailystar.co.uk/news/latest-news/786417/britain-asian-hornets-killer-human-sting-fatal-venom-nests-channel-islands
“BRITAIN is braced for an invasion of “killer” Asian Hornets as 80 queens have already been found in the UK. The insects – which can grow up to 1.6 inches – have powerful stings which can be fatal to humans with just a single strike if the person is allergic. Record numbers of nests have been found on Jersey as there are fears they will move onto the mainland. The fight is on-going on the Channel Island and is seen as a crucial battle-ground to stop the spread. Just one of the foreign menaces can eat up to 50 bees a day and their impact on honey production could be devastating.”
Along with colony collapse disorder, the life of bees, and human food production is numbered.
http://www.futuredirections.org.au/publication/no-bees-no-food-the-potential-implications-for-australian-food-security/
https://theconversation.com/ten-years-after-the-crisis-what-is-happening-to-the-worlds-bees-77164