Abstract Around the world, the number of species establishing outside of their native range has and continues to increase rapidly. Some of these non‐native species are invasive and can cause negative environmental, economic, and social impacts, including declines in native biodiversity. Species can become established either through natural dispersal or with intentional or inadvertent human assistance, but the relative importance of these two modes over time has been little studied. We compiled data on 116 moth species that became established in Great Britain (GB) between 1900 and 2019. We classed each species as either an immigrant, which had colonised naturally, or an adventive, which had colonised through human assistance, and categorised species as feeding on either native or non‐native larval host plants. We found that the rate of moth species establishment has accelerated steadily, at 21% increase per decade, showing no signs of saturation. Immigrant species showed a steady rate of establishment between 1900 and 1935, followed by a significant acceleration of 11% per decade thereafter, which most closely matches the rate of immigrants that feed on native host plants. Immigrants that feed on non‐native host plants show a slower increase across the whole time period compared to all species, of 13% per decade. Adventive species show a similar rate of increase in establishment to all moth species, at a rate of 26% per decade. Adventives on non‐native host plants show a similar trend, but we find evidence for a post‐1980s increase in the rate of establishment for adventives that feed on native host plants. Our results indicate that the global case for enhanced biosecurity, around both the monitoring of natural colonisations and for the horticultural trade, remains very strong as non‐native colonisations are showing no signs of saturation with ongoing environmental and economic change.
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