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it depends on their ability adopt in new teritory. and if they adopt swimmingly the diversity index of another species could decline and diversity of invasive species will invrease
Okay, so a diversity index is usually based on two aspects (a) the species richness at that site and (b) the "evenness" of species at that site (tell me if you don't know what this means and I will explain it :) ) If a site becomes less species rich the diversity index will go down similarly the more "even" the species at the site the higher the index. If a species is "invasive" it would correct to infer that it would invade the site and may become dominant. Usually (but not always) the invasion of another species leads to a decline in richness due to the loss of native species. Also if this invasive species becomes dominant this would effect the evenness of the species at that site, how do you think this would effect the evenness, would it go up or down? and so how do you think this would effect the diversity index?