How does crossing over ensure that organisms living in isolated populations will have genetic variation?

For example, a population with many different alleles at a single chromosome locus has a high amount of genetic variation ... crossing over (or recombination) between chromatids of homologous chromosomes during meiosis.

Genetic variation can be caused by mutation (which can create entirely new alleles in a population), random mating, random fertilization, and recombination between homologous chromosomes during meiosis (which reshuffles alleles within an organism's offspring).