In 1948 two researchers looked at polyploidy (additional sets of chromosomes) in 175 weedy species in California and found about equal numbers of diploid and polyploid weeds. They concluded that polyploidy had little to do with weediness in general, but might be useful in more specific comparisons within families or genera (Heiser and Whitaker, 1948).
Polyploidy can lead to a plant having different growth and reproductive characteristics and often leads to plants either being sterile or to becoming a different species that is no longer able to breed with the parent species. Some polyploids are able to hybridize with other related species that the diploid parent wasn’t able to cross with.
You can read all the details about why a polyploid might be expected to be more successful as an invader in an article by Beest et al. (2011). It has to do with some polyploids producing more seeds or more vegetative propagules, becoming adapted to new environmental conditions, and a host of other factors.
In the case of spotted knapweed, Centaurea stoebe, diploid and tetraploids exist in its native Europe, but only tetraploids occur in its invasive range in the United States. In a common garden experiment, tetraploids from the US had much greater seed production and seedling establishment and therefore a high population growth rate, than either European diploids or tetraploids. This indicates that it isn’t ploidy level, but rather some other evolutionary driver that makes American populations so successful (Hahn et al., 2012).
Although polyploidy certainly can increase the probability of invasiveness, it clearly isn’t the cause in every case. Who ever said ecology had easy answers though?!
Beest, Mariska te, Johannes J. Le Roux, David M. Richardson, Anne, K. Brysting, Jan Suda, Magdalena Kubešová and Petr Pyšek. 2011, The more the better? The role of polyploidy in facilitating plant invasions. Annals of Botany doi: 10.1093/aob/mcr277. Available online: http://aob.oxfordjournals.org/content/early/2011/10/30/aob.mcr277.full
Hahn, M. A., Buckley, Y. M., Müller-Schärer, H. (2012). Increased population growth rate in invasive polyploid Centaurea stoebe in a common garden. Ecology Letters, 15: 947–954. doi: 10.1111/j.1461-0248.2012.01813.x
Heiser, Charles B. Jr. and Thomas W. Whitaker. 1948. Chromosome number, polyploidy and growth habit in California weeds. American Journal of Botany 35 (3): 179-186.