How could species have evolved from an ancestor such as Archaeopteryx?

When the population of a species is separated, each group is put under different selection pressures due to differing environments. In each population there is genetic variation, and more offspring are produced than can survive. This means that only those the best adapted to the respective environments would survive and pass on favourable traits. The species would therefore diverge as different alleles were passed on, making the populations distinct and unable to interbreed successfully.