Reproductive barriers may arise haphazardly, or occassional reproductive contact with sister species may select for reproductive isolating mechanisms. When non-geographic isolating mechanisms are in place geographic isolation is no longer necessary. Opportunities for Geographic isolation may be more common that you think. Shouldn't chains of islands have more species than isolated islands. When individuals multiply their chromsome sets 2n to 4n, 4n to 8n, etc.
Polyploids behave like ordinary diploids in meiosis.
For two polyploids to reproduce sexually then must both have the same chromosome number. For example, a single 4n individual that arises via an error in meiosis can't breed with the parental 2n population, but can reproduce sexually via selfing. This form of speciation does not require geographic separation. Bread Wheat is a famous example of hybridization combined with polyploidy. We often this think of microevolution are a consistent gradual process.