What are the roles of variation, reproductive isolation, and geographical isolation in speciation?

Hi. Think variation in environment.

It's a key element in evolution, and comes about through modifications of an organism's DNA via radiation, chemical poisoning, or simple mischance in cell replication.  The daugther organism can inherit the modified DNA, and it may - or may not - give some advantage toward survival and subsequent reproduction.

Existing variation is the basis by which populations adapt most quickly.

Reproductive isolation can be simple.  If by variation, one subpopulation of insect does best feeding from apple trees and another off of chestnuts, they are most likely to mate with another insect from the same tree.  Eventually the subpopulations may specialize on the two different trees to the extent that they become separate species.  Similarly, flowers blooming early in the season are unlikely to crosspollinate with flowers that bloom late in the season.  Eventually, the early flowers and the late flowers will tend towards traits that favor the average conditions when they bloom.

Geographical isolation means that evolution will take place independently.  Marsupials dominated Australia.  A variety of unusual creatures evolved in the Galapagos Islands.  Most notably, from a single set of finches, a variety of bird species evolved to fill the available niches determined by feeding habits.  The danger is that small areas have less competition and when a species is introduced from a larger, more competitive area is introduced, it may overrun the ecosystem devastating food supplies and adversely affecting every creature in the food chain above below and in its niche.