Even within the on-rushing waves of a looming biological invasion, there is variation. And variation matters.
Invasions have edges. Few, if any, invasive species can be said to be ubiquitous (maybe dandelion?). To spread, a species generally must adapt to the environmental conditions at the margins of its range. This is possible when there is ecologically relevant variation within a species for selection to act on. Within an invasive species, things are not as monotypic as they might first appear. Amongst populations of a given species in the invaded range, genetic and phenotypic diversity can sometimes be nearly as high as in the native range. Local adaptation to habitats at an invasion’s leading edge may be key to whether or not the invasion can advance.
In some cases, genetic constraints limit how much a species can adapt to the new habitat at the invasions edge. For example in purple loosestrife, Colautti et al. found evidence that a genetic constraint is holding populations back at the northern most edge of the invasion. Using models and three common gardens (one greenhouse, two field. Whoa!), they demonstrated a latitudinal cline in the quantitative genetic variation of flowering time and plant size. The larger a plant is when it flowers, the more seeds it can produce, making it advantageous to grow for as long as possible. But as the invasion pushes north into habitats with shorter growing seasons, natural selection favors earlier and earlier flowering, before frost can kill the plant. And populations on the northern fringe have adapted, resulting in a 23-fold difference in seed production between northern (average 57 fruits/plant) and southern populations (average 1325 fruits/plant). But this can’t go on forever – plants have to reach a minimum threshold size before they can flower. And all that selection has led to a decline in genetic variance with populations. This constraint can explain why purple loosestrife appears to have reached its northern most range limit. For the moment.
In other cases, it’s just a matter of time before the invading species adapts to marginal habitats. Looking at one of the most noxious invaders of western North America, cheatgrass, Leger et al. used a reciprocal transplant across an altitudinal limit up a mountain in the Great Basin to assess the ability of cheatgrass to adapt to marginal habitats. They found that survival was quite low on the margin, regardless if the individual plant originated from a habitat high up the mountain or a more benign valley habitat. So for now, there is no evidence that the marginal populations are specifically adapted to their 
harsh environments. Further, they found abundant genetic variation, even in the marginal populations. This could mean that, like in purple loosestrife, cheatgrass, though it has some genetic variation, lacks variation for ecologically-relevant traits, and the current altitudinal edge represents a stable range limit. Or perhaps these populations will eventually be able to adapt, and push the invasion up the mountain. It could just be biding its time at the mountains edge, waiting for the right altitude-tolerant genotype to come along. Or perhaps, climate change will make conditions more pleasant for an invasion.
On a side note, these two studies are perhaps especially impressive for their breadth. To really tackle their questions they use a broad span of techniques and methods, from modeling, to greenhouses, field experiments, and molecular work. Wow! That’s crazy! How do they do all these things?!
Colautti, R., Eckert, C., & Barrett, S. (2010). Evolutionary constraints on adaptive evolution during range expansion in an invasive plant Proceedings of the Royal Society B: Biological Sciences, 277 (1689), 1799-1806 DOI: 10.1098/rspb.2009.2231
LEGER, E., ESPELAND, E., MERRILL, K., & MEYER, S. (2009). Genetic variation and local adaptation at a cheatgrass (Bromus tectorum) invasion edge in western Nevada
Molecular Ecology, 18 (21), 4366-4379 DOI: 10.1111/j.1365-294X.2009.04357.x
Alien Plantation 