The story of barberry
Common barberry (Berberis vulgaris) was introduced to New England from Eurasia intentionally by colonists who enjoyed certain properties of the plant: it makes a nice hedge, has lot of berries, and looks pretty. However, the plant spread rapidly across the landscape, displacing native plants wherever it went. They realized that common barberry is an alternate host for black stem rust, which is a disease that affects wheat crops, so common barberry was mostly eradicated in the early 1900’s. Japanese barberry (Berberis thunbergii) was promoted as an appropriate alternative that is very similar, but doesn’t host the disease. Since then, Japanese barberry has been planted all over the place, and it turns out it is invasive too! Now Japanese barberry is one of the most ubiquitous non-native shrubs in New England. [1,2]
The story of many invasive organisms is familiar: It was innocuous in its homeland, and was introduced accidentally or purposely to a new area, where it spread and multiplied until it became a nuisance. Sometimes introduced organisms degrade the ecosystems they invade and can cost us money.
It might seem like poor planning to have introduced the non-native barberry species to New England, especially the second time. But to their credit, not all non-native species become invasive. Most do not. Many, many plants have been introduced to new areas for agriculture, horticulture, ornamentals, etc., without a problem.
Check out wikipedia for more on the different meanings of the words introduced, native and invasive.
So what makes some plants invade, while others never do?
Invasive plants seem to have a few things in common. [3,4]
- They produce seeds or berries prolifically, which are often bird-dispersed
- They are “generalists,” meaning that they can grow in many different conditions
- They grow quickly
- They lack enemies, in that not many animals will eat them and few diseases affect them in their new environment
However, these are just a few generalizations, and it is still quite a puzzle as to why some species invade and some don’t . It may also have something to do with the environment the plants find themselves in, or more fundamental characteristics of the species on the genetic level.
In a review study, Prentis et al. explore the ability of invasive plants to adapt rapidly to a new environment. They found that this ability could come from inherent genetic variation rather than new mutations in the species. In other words, the species has the genetic potential to adapt quickly, perhaps more so than other species. 
Similarly, another paper suggests that the adaptability of invasive plants lies in their quick genetic changes in a new environment, rather than the species’ inherent ability to tolerate many conditions .
The genetics, evolution and ecology of invasive plants is an interesting field with lots of room for future research!
 Invasive Plant Atlas of New England. Berberis vulgaris. http://www.eddmaps.org/ipane/ipanespecies/shrubs/Berberis_vulgaris.htm
 Gucker, Corey L. (2009). Berberis vulgaris. In: Fire Effects Information System. U.S. Department of Agriculture, Forest Service. http://www.fs.fed.us/database/feis/plants/shrub/bervul/all.html
 US Forest Service (2009). Invasive Species. http://www.fs.fed.us/pnw/invasives/
 Simberloff, Daniel (2013). Invasive Species: What Everyone Needs to Know. Oxford University Press, USA.
 Prentis, Peter J., John R.U. Wilson, Eleanor E. Dormontt, David M. Richardson, Andrew J. Lowe (2008). Adaptive evolution in invasive species. Trends in Plant Science, Volume 13, Issue 6, June 2008, Pages 288–294 http://dx.doi.org/10.1016/j.tplants.2008.03.004
 Lee, Carol Eunmi (2002). Evolutionary genetics of invasive species. Trends in Ecology & Evolution, Volume 17, Issue 8, 1 August 2002, Pages 386–391 http://dx.doi.org/10.1016/S0169-5347(02)02554-5