How effective are bioclimatic models in projecting vegetative species diversity changes? What algorithms are used to reduce effect of other environmental factors?
... Yes, it can be done. You may want to use a complex of bio-climatic and phytoclimatic different algorithms to test if results converge, and then comparing the expansions-contractions of species and/or populations in relation to trends of combined climate variables. However, it needs to have medium-long term monitoring data or you may use proxies provided that you test them for reliability very accurately.
There used to be a theory that centers of diversity were the centers of origin. However, when I worked with cultivars of the family Cucurbitaceae I noticed that most of them had a center near China in an Area disputed between Russia and China, and another in Africa. The Eastern USSR was definitely not the origin of the species (or of cultivation). However, a literature survey might help you identify the centers with the most diversity. Then you might have some sort of baseline to find more literature, or for suitable hypothesis concerning weather. Notice that such research requires the researcher to get up to date with the relevant statistics. YouTube lectures by Roger Peng might be a leas into (via his more advanced stuff) the statistics principles you would need to know. I would also advise using the R language if you are not already deep into other software.