During my research on invasive aliens in this part of the world (Article with further reference attached) I have not come across research on biodiversity versus invasion of aliens. You may have found an interesting and publishable topic. Some observations that may help you to conceptualize your research. In my research of Chromolaena, the tree layer species diversity of the forest does not differ between invaded and non-invaded portions of the forest and the botanical diversity is found among trees; the tree cover is more open in the invaded forest. When I look around here in my plot, I see two invasive alien plants, Lantana camara on the slopes and Arundo donax at the valley bottom. Lantana may smother indigenous trees if uncontrolled, but will not become a transformer. Arundo donax has transformed the wetland. Consequently, smaller herbs have no chance here. The number of wetland plant species may have declined at the 100-1000 msq resolution. However, the bird diversity has been increased at 1000 m sq resolution by the addition of reeds to the structural diversity. Walking from my house I meet with the next km two invasive cacti, one of them is Opuntia. The Opuntia may be a transformer at the 1000 m sq resolution and competing out Aloes, but not at the km sq resolution. First of all such diversity and density of invasives would be hard to find anywhere in Europe. Secondly, I wonder about the chicken and egg question. Did the plant biodiversity decline first and invasion followed or vice versa. Concluding, the spatial resolution of the diversity observations, the land use legacy and the range of organisms studied are relevant for the research design and the answer to your question. Hope it stimulates.

Article Invasion of an alien shrub across four land management regim...

I tried determine the degree of Impatiens glandulifera influence on the habitat and native elements of the flora. You can see the article "NETÝKAVKA ŽLIAZKATÁ (IMPATIENS GLANDULIFERA ROYLE) V OJCOWSKOM NÁRODNOM PARKU (JUŽNÉ POĽSKO) " (in english) on my profile.

Sorry the title is in english: "purple jewelweed impatiens glandulifera royle in the ojcow national park"

https://www.researchgate.net/publication/216389305_purple_jewelweed_impatiens_glandulifera_royle_in_the_ojcw_national_park_%28southern_poland%29?ev=prf_pub

Article PURPLE JEWELWEED IMPATIENS GLANDULIFERA ROYLE IN THE OJCÓW N...

Interesting case of an invasive alien plant following river valleys and without transforming native vegetation. Does the European Impatiens noli-tangere occur anywhere near the research area?

You have to consider population structure and regeneration potential of native species in the areas affected by invasive species. If it is a deciduous forest habitat, open canopies, forest fires, fragmentation and edge effects may provide chance for invasive species to colonise and then massive spread. If it is aquatic habitat, eutrophication may favour dominance of invasive species.

To make your case that an invasive alien effects biodiversity (positively or negatively) you need to compare biodiversity in adjacent invaded and non-invaded areas under similar environmental conditions. Finding such situations is a great challenge. In my previously attached paper, I present such situation for the invasion after searching for years. However, we did not test alternative hypothesis for impact of invasions on biodiversity among natives. Ana (above) did so and found no impact.

The second, practical issue is whether control/eradication of the alien restores the biodiversity among the natives. I have found very little scientific evidence for effective biodiversity restoration by control of invasive alien plants in the literature. Often the alien returns sooner or later. An example is attached.

Article Efficacy of Chromolaena odorata control in a South African c...

Thanks for your answer

Being able to measure the mathematical interactions between the exotic plant and native plant species is the important parameter that I use to find the relationships between species.

From my research in allelopathy, I think that the allelopathic interaction play an important role in invasive-native plant relationship. Allelochemicals from invasive or alien species considered as an effective weapons against the native species

Allelopathic effects that exotic plants add to an ecosystem are extremely important. These are herbicides that are macro-antibiotic-like substances produced by those plants--one of the main methods that helps them clear room to invade.  

The Journal of Chemical Ecology has articles on this effect, starting with Dr. Liu's studies of the chemicals produced by barley in 1993 and 1994, at http://link.springer.com/article/10.1007/BF00979659.  

Also,a DVD is the PBS NATURE series: "What Plants Talk About"--the section on knapweed shows how the  allelochemicals kill native grasses, so the knapweed can cover millions of acres in Montana.  

The US Forest Service report at http://www.nps.gov/plants/alien/fact/pdf/cest1.pdf says that knapweed has been spreading at the rate of 27% per year since 1920.  So an exotic plant armed with allelochemicals can be like a slow burning fire, causing permanent spatial extinction wherever it grows. 

thanks for valuable answers

I have studied the effect of allelopathic and physical effective of native plant (Acacia trees) against the invasive grass (mission grass). Paper is attached for your information.

Article Acacia holosericea (Fabaceae) litter has allelopathic and ph...

In this reference my articles on RG viewed.