Final answer:
Mendel's principle of independent assortment and the process of random fertilization significantly increase genetic variation. The way alleles assort into gametes during meiosis and combine randomly during fertilization leads to many potential genotypic and phenotypic combinations in offspring.
Step-by-step explanation:
Independent Assortment and Random Fertilization
Mendel's laws, including the principle of independent assortment and the law of segregation, dictate how alleles for different genes segregate and assort into gametes. During the formation of gametes in meiosis, alleles of different genes segregate independently from each other, which is the essence of the principle of independent assortment. In the dihybrid cross example of pea plants, one with green, wrinkled seeds (yyrr) and the other with yellow, round seeds (YYRR), both parents produce gametes that reflect these traits (yr and YR). The F1 generation will all have the genotype YyRr, displaying both traits.
For the F2 generation, the law of segregation ensures that each gamete has one and only one allele of each gene (either R or r, and Y or y). According to the law of independent assortment, these alleles assort into gametes irrespective of one another, resulting in four equally likely combinations of gametes when the F1 heterozygote is self-crossed: YR, Yr, yR, yr. Laying these out in a Punnett square predicts the genotypic and phenotypic ratios of the F2 generation.
Moreover, random fertilization adds to genetic variation by ensuring that any sperm can fuse with any egg, increasing the allelic combinations in the resulting zygote. With humans, for example, random fertilization and independent assortment make it possible to have millions of genetically distinct offspring.