Hi Craig, this is a very interesting topic and one which I am actively involved in studying. First and foremost, the speciation process and the multitude of definitions of "species" is lineage dependent, and somewhat controversial.  One reason is that many taxonomists and systematic biologists might agree that the species designation is at least a somewhat artificial rank, and may not actually exist in all lineages in the same fashion, therefore I prefer to talk about rates of adaptation, ecological and morphological change in the introduced lineages relative to these characteristics in the natural range. The other main point to consider is the challenge of evolutionary and geologic time, versus the way humans view time.  New species can arise relatively rapidly, but that is "relatively" and still takes more time than even the longest PhD program NSF funding cycle, etc. We are looking at evolution and adaptation of introduced Jackson's chameleons in Hawaii, and let's say they have been here for 45 generations or so, and we are seeing subtle changes in head shape,  horn morphology and color signaling. We attribute these changes to the phenomenon of selective release, relating to differences in the Hawaiian versus East African montane ecosystems. 

I know that it is the case in some trees, however everything becomes even more complicated when you talk about species (because next logical question what is species). But they are evolving for sure and you certainly can look how far they are diverged from the population of origin. 

Since the Age of Discovery, plants and, sometimes, insects have been transported and naturalized all over the world. While the factors they exploit to thrive in their new environment may be different from those in the land of origin, I do not know of any case where the naturalized plants or insects have been described as valid new species. Of course, there is, as Oleksandr points out, the rather delicate question of what exactly constitutes a species, but despite that, there do not seem to have been any attempts to erect new taxa for exotic species.

The answer will depend on the species and the timeframe involved.  For example, bacteria and fungi can also be considered invasive species and due to their typically short generation length, can rapidly evolve away from their source population because more mutations can accumulate in a short space of time.  However, higher plants and animals will usually need a longer timeframe to genetically diverge from their source population.  That is not to say that they can't display profound behavioural differences - one unifying character of invasive species is that they tend to be adaptable!  As alluded to by Oleksandr, whether invasive species can eventually be considered new endemic species depends on how you define species (is it morphological differences, genetic divergence or behavioural adaptation, etc.).

When we consider a species as a new one that it has difference in three state: Genetically, Morphologically and ecologically different.  Although sometimes these differences are not very large. But if only different limited to behavior, (lifestyle) I think it is not true to use new species.

Here is one citation, you will find more if you will follow references and additionally search for other papers in the topic. I am aware about similar studies on lizards of genus Podarcis. Then there is kind of common knowledge that plants, which prone to polyploidy can get reproductive isolation instantly and due to fast evolution in novel habitats give rise to a new species. If you look on endemic island species you will find the lower threshold in terms of  level of divergence and minimum time of isolation needed for "species" level. Again, depends on definition of species. One could treat new population of species on other continent as such which will never fuse with those it is originating from, so eventually it will be a new species and it is very subjective to say when it will happen. 

Joanna M. Buswell, Angela T. Moles and Stephen Hartley Is rapid evolution common in introduced plant species? Journal of Ecology 2011, 99, 214–224

Thanks for all of your answers so far.  Perhaps there is a genetic component within each exotic species, in that the broadness of its genome helps it become naturalized in a new environment?  

Then conversely, perhaps removing the exotic plant or animals from  from the environmental constraints that were the evolutionary pressures that created the species in the first place, let's call that the "bottle", then letting the genome out of the bottle so-to-speak, could allow for unrestrained genetic changes to be expressed?

On the other side of the coin, say am exotic grass species gets established in California over a wide range of environmental conditions, and in order to do so, has to express its genome in different ways that end up getting fixed over time>>Ecotypes evolving into species, for example.    

I had a group of New Zealand grass seed company scientists visiting California looking among the introduced wild populations of European pasture grasses that had been introduces over 100 years ago, for a more drought resistant strain that had evolved to survive with only 60 cm or less of annual rainfall instead of the European varieties that need a meter or more, for example.  

That would be a drought-resistant genetically fixed ecotype and not a separate species yet, but maybe that is one road towards a new species?

To address your second question, only those species with the flexibility to adjust to the new circumstances would survive, so there might not be a need to modify genes in such cases, rather, it would be merely matter of using existing generic components, don't you think? The ones that would need major changes to adjust might die out in due course?

Evolution can happen and that too in a very different ecological condition can make some drastic variation.  In long course of time characters very different  from the original species in home land may also get exhibited.  May end up in formation of a new species.  Even in homeland if the characters exhibited are so different and inherited,  speciation can happen.

First, to the question of how introduced species adapt, it may not be alien that does the adaptation, it may be potential symbiotes.  For example, legumes obviously benefit from associations from diazotrophic bacteria.  Their relationships with plants are not only specific, they are strain specific.  Such potential symbiotes are not introduced maternally; they must come from the soils into which the seed is introduced. 

It is known that some introduced species do require a period of time before they become virulent and it is here where the question of adaptation becomes effective. It should be fairly obvious that the genetics of these introduced species are more narrowly distributed and have few generations for classical Darwinian "mutation" making that an unlikely adaptive mechanism.  Rhizobial bacteria, on the other hand, do breed rapidly and are capable of horizontal gene transfer, a much more powerful mechanism capable of greater distance than random mutation and selection.  It may be that either the encoding in the plant or its associates found on the seed coat or in its tissue supply genetic fragments liberated during mastication and incubation by ruminants or by shearing forces due to trampling in mud, thus facilitating a recombination rate sufficient for adaptation for the purposes of fixing nitrogenase. Poof!

As to your example of drought tolerance developed in introduced grasses, I would expect that to be a preexisting and internally coded form of epigenetic adaptation. One would rationally posit that endemic species would be capable of responding to cyclical variations in climate fairly rapidly.

Sorry for the typos, the last message should read 

"On the other side of the coin, say an exotic grass ..." and

"...pasture grasses that had been introduced.."

What I have been looking at here in California, are the environmental conditions that form plant ecotypes, that in turn can form new species, and have attached how the local ecotypes of one native grass species sorts out, with the new species budding out from the main genetic population.

Dear Sir,

Species and their speciation  is a continuum process of evolution. Environmental factors can  bring variability in the gene pool so every thing is possible. However, it might be more feasible in those organisms wherein possibility of reproduction  by several means and time for  life span is very short. In that condition, rate of modification according to the abiotic factors, can go faster. Recently, due to climatic variability, entry and elimination of  some species (plants and animals) in the various parts of the world has been attracted more attention. It is true, if the climate of the whole geographical areas of the world  become as one habitat then  exotic and native species would have very thin distinction.

Ideally, in each habitat, a set of driver of that particular ecosystem fond which control species and speciation. When entry of any particular new species emerge in  a new environment, that species try to communicate with the ecosystem driver for function but associated other organisms  already do not like to communicate each other. Therefore, a barrier creates in between native and exotic range  and competition for food and resource utilization starts in monotonically. In brief, it might be possible for the formation of a new species ecologically. 

Check out some stories in Calandra weevils. I'd also look at Drosophila fruit flies.

http://www.cabdirect.org/abstracts/19460500044.html;jsessionid=C006AB9529A8A641F49EA592AC9ACA41

Hi Craig, this is a very interesting topic and one which I am actively involved in studying. First and foremost, the speciation process and the multitude of definitions of "species" is lineage dependent, and somewhat controversial.  One reason is that many taxonomists and systematic biologists might agree that the species designation is at least a somewhat artificial rank, and may not actually exist in all lineages in the same fashion, therefore I prefer to talk about rates of adaptation, ecological and morphological change in the introduced lineages relative to these characteristics in the natural range. The other main point to consider is the challenge of evolutionary and geologic time, versus the way humans view time.  New species can arise relatively rapidly, but that is "relatively" and still takes more time than even the longest PhD program NSF funding cycle, etc. We are looking at evolution and adaptation of introduced Jackson's chameleons in Hawaii, and let's say they have been here for 45 generations or so, and we are seeing subtle changes in head shape,  horn morphology and color signaling. We attribute these changes to the phenomenon of selective release, relating to differences in the Hawaiian versus East African montane ecosystems. 

Hi! I'm  studying a system similar to the example of the New Zealand pasture grass you mentioned utilizing invasive Brachypodium sylvaticum (slender false brome) in Oregon. In order to tell if your grass species has actually evolved towards being genetically fixed for drought resistance would require a common garden study, otherwise the drought resistance within the populations you are viewing could be  phenotypic plasticity representative of genetic variation already present within the species prior to invasion. I'm not sure if you have performed this type of study already.

look at the genus Oenothera (Onagraceae). In Europe many species was described after introduction from America. I do not know if only for splitting or for effective changes.

In the historical reconstructions it is common. Please write in Google search: "Beringia Bridge" and you will obtain enough species formed as a result of a single population spread in both directions between Asia and America. I think the same for other temporary bridges between continents, and continents and islands.

Perhaps ANY plant or animal, once disconnected from its country of origin for a long enough period of time, so that it is no longer exchanging genes with the original population, can spin off in isolation to evolve not only new species, but entirely new genera, like how the silversword and two other Hawaiian plant genera evolved from their California tarweed ancestor, that you can read about at http://www.sherwincarlquist.com/tarweed-silversword.html