Final answer:
Independent assortment occurs during anaphase I of meiosis I and to some extent during metaphase II and anaphase II, leading to the formation of gametes with diverse combinations of paternal and maternal chromosomes.
Step-by-step explanation:
Independent assortment of chromosomes occurs during meiosis, a critical process for producing genetically diverse gametes in eukaryotic organisms. Specifically, this event takes place during anaphase I of meiosis I, where bivalent chromosomes separate, and again, although indirectly, during metaphase II and anaphase II as sister chromatids segregate. During the phase of prophase I, chromosomes align randomly at the metaphase plate, setting the stage for the independent assortment. The physical basis for the law of independent assortment lies here, as different homologous pairs line up in random orientations, allowing any combination of paternal and maternal chromosomes to segregate into each gamete, thus increasing genetic variation.
Additionally, recombination or chromosomal cross-over during meiosis further increases genetic diversity by producing new combinations of alleles. At the end of meiosis II, four different gametic combinations are produced, each containing a haploid set of chromosomes. As the number of chromosomes increases, the number of possible assortment combinations increases dramatically, leading to a vast potential for genetic diversity.