Will a Sourdough starter from one locale change to yeasts of current locale over time?

Short answer: YES, a sourdough culture can change when moved to a different location. But the amount and types of shifts are unpredictable, and other factors (feeding schedule and regimen, kitchen conditions like temperature, nutrients from flour, etc.) can also cause significant changes. Also, environmental conditions can include not only microorganisms in the air, but also contaminants from kitchen surfaces, baker's hands, etc., which can all contribute to or detract from the stability of the culture.

In your case, unless you've kept your five starters apart with laboratory-level hygiene and precision, it's very likely that many of them have interacted or become similar in various ways.

Long answer:

This is one of those questions that comes up periodically, because it gets at a more fundamental question of where exactly the organisms come from in sourdough -- do they come from the air, the flour, the water, the baker's hands, the surfaces of other kitchen equipment that come in contact with the dough, etc.? There are literally hundreds of scientific articles in food science journals about sourdough microorganisms, and the precise answer is still not fully determined.

What we do know is that there are many factors which influence how a starter initially develops and how stable an existing starter is. Changing the flour, for example, may introduce new microorganisms that could come to dominate and/or change the nutrients available (which may starve old microorganisms while giving new foods to others). Changing the feeding schedule, temperature of fermentation, or other aspects of the feeding regime may stress various microorganisms while allowing others to flourish.

That said, starters in many artisan bakeries have shown to be remarkably stable over years or even decades. Of course, in most of these situations we can assume a more-or-less consistent procedure for propagating the starter, somewhat consistent ingredients, and a consistent environment surrounding the starter.

It's that last factor that gets to this question. A recent review article from 2014 summarized a few related experiments that may shed some light. One experiment took seven traditional sourdough cultures and propagated them for 80 days in a laboratory while they were also propagated in their home bakery environment. Some bacterial species thrived in both environments, while others died out gradually or quickly in the lab:

Permutation analysis based on bacterial diversity, assessed through culture-dependent and -independent methods, showed that in five out of seven cases, sourdoughs propagated at artisan bakery and those propagated in the laboratory diverged. This may be explained probably by incomplete control of relevant factors and by the influence of house microbiota, whose level of contamination is supposed to be much higher in the bakery than in the laboratory.

Another notable observation is the fact that baker's yeast often shows up in bakery starters (presumably because it is present in the bakery in various places, even if never deliberately added to the sourdough starter), but it will die out in lab conditions.

In another experiment discussed in the review article that studied bacteria, various species present in the starters were detected in the air of the storage and work rooms, on benches and the dough mixer, on the hands of the baker, and in the flour of the bakery. (Different bacterial species tended to show up in different places, suggesting different media contributed different species for transmission to the dough, whether the flour, the air, the baker's hands, or the equipment.)

In concluding this section of the review:

Despite the use of different flour batches and possible variations in flour characteristics during subsequent propagation of the sourdoughs analysed, those strains appeared to persist in the doughs over at least 3 years of sampling. This persistence may be the result of the continuous use of the same fermentation parameters and of significant contamination from the environment of propagation.

Overall, the results of this study suggest that bakery environment, because of its usually high level of microbial contamination, may be the source not only of yeasts, but also of LAB [lactic acid bacteria] that, by virtue of their intrinsic capacities, may or may not dominate traditional sourdough.

There seems to be conclusive scientific evidence in a number of studies that a specific baking environment can have a significant effect on the stability of a sourdough culture. But the amount of variation will vary significantly from case to case. Most home bakers, for example, may not bake often enough or use their equipment regularly enough to transmit bacteria and yeast on the scale that happens in a bakery. And certain strains of bacteria and yeast tend to remain dominant in cultures even when moved out of their "home environment," while others may die off, thus making some cultures inherently more stable than others. Given that the concentration of microorganisms on surfaces and in ingredients is significantly higher than in the air in general, it is often likely that your specific home environment will play a greater role in your sourdough culture than the general region you live in.

In summary, baking environment is a factor in culture stability, but its contribution in particular cases will vary.

I too have read a lot of websites where this has been debated, but I've never seen a definitive answer. My guess is that no one has ever bothered to do an objective examination of the ratios of specific strains of microorganisms found in a given starter pre- and post-move.

My personal experience with cultures that I got from Sourdoughs International 10 years ago is that they will keep their distinct characteristics as long as they are maintained and kept active through regular feeding. If you let the culture get too weak, the naturally occurring microbes on the flour may have a chance of colonizing the starter and changing its character.