Dikerogammarus villosus, a visitor to this country so unpopular that even the Environment Agency calls it the killer shrimp, turned up recently in Cardiff Bay and two freshwater reservoirs. It must be the only shrimp in history to have been given its own "wanted" poster by the government. Striped and suitably vicious-looking, the creature, which likes to kill its prey without eating it, has arrived from the Black Sea intent on wiping out northern Europe's rather meeker amphipods. And it is not alone.

Yesterday, it was reported, monk parakeets became the latest invasive species to be targeted by the government. The grey and green birds stand accused of building huge communal nests and causing power blackouts, and the 150 or so that have established themselves in Britain are to be shot (or, if you can offer a secure cage, perhaps rehoused). The much larger population of ring-necked parakeets – a familiar sight in south-west London and found as far north as the Clyde – is harder to control, since it is so well-established, though the GB non-native species secretariat (a sort of biological border patrol) advocates limiting its numbers and is investigating chemical sterilisation.

Is this ecological xenophobia? Take evolutionary theory to its limit and you might think Britain is well-placed to encourage a free for all, with the fittest plants and birds free to survive while others perish. Advocates of open borders and open economies should perhaps not blanch when nature applies the principle of globalisation, too. Homo sapiens arrived in Britain as a migrant about 12,000 years ago and has been bringing new land animals and plants to the country ever since. A diet of purely native species would be unhealthy and limited.

Scientists agree, up to a point. "We must not think that all non-native species are bad," they say. But they also point out that some migrants are far worse than others. There is an official blacklist of invasive non-native species, defined as ones able to damage the "environment, the economy, our health and the way we live". Many thrive here because they lack natural regulation or predators (rather like the global banks that did so much harm in the City). They include such creatures as the African clawed-toad, the leathery sea squirt and the edible dormouse (best served with honey and poppy seeds, according to an ancient Roman recipe). Some, such as the notorious Japanese knotweed, do immense harm. The best response is to limit the arrival and spread of new species. But sometimes eradication is necessary. That's tough for the ruddy duck – an American import culled to 120 birds from 4,400 – but good news, perhaps, for the white-headed duck, otherwise facing extinction.