Native bees are the answer

Many struggle with colony collapse, mites, sugar feeding, etc but the majority of these issues are due to the fact you bought non-local bees.  Most bees bought by commercial and residential beekeeper are Italian honey bees.  In mediterranean climates nectar is available 10 months out of the year, where you reside is likely quite different.  In addition, the rainfall in mediterranean climates is is likely far different than your climate.  What this means is you are now in a uphill battle trying to keep your bees alive.  But no one is keeping your local wild bees alive with chemicals and sugar water, why?  Simply because the bees in your climate are adapted to that climate.  Even mites, in my climate the Ozarks, we get a drought almost every summer, this kills off most of the bees food sources.  The queen stops her brooding cycle for a bit during this time, which in turn starves the varroa mites and disrupts their reproduction cycle, essentially weakening the mites so that they are not a threat.  Feeding sugar water is no longer necessary because the bees understand they have to overwinter for 5 months in the Ozarks instead of 2 in Italy.  So if you want the most success (failures are part of learning and you will still get lessons) try to start your colonies with local bees or at least a local queen.  Try swarm traps, or if you have a friend with some native bees try an artificial swarm.  Happy Beekeeping!

You do not have to buy Italians. There is Carniolan - better adapted to cold and able to quickly increase population to cater to shorter vegetative period. There is also Russian and then hybrids of all these breeds and more.

Do bees reproduce in a way that a population, with enough time, it could become locally adapted?

Cristo: True, you can buy bees from anyone that sells them, my point is the majority of store bough bees are italian and that's actually the main issue.

Timothy:  From what I have been told and found, bees take a minimum of 5 years to adapt genetics to their local conditions.  So yes, even italian bees can truly adapt, given they survive long enough.