Final answer:
The alleles of one trait separate independently from the alleles of another trait during gamete production because of Mendel's law of independent assortment, which ensures every possible combination of alleles is equally likely to occur in the gametes.
Step-by-step explanation:
In gamete production, the alleles of one trait separate independently from the alleles of a second trait. This principle is best explained by Mendel's law of independent assortment, which states that genes do not influence each other with regard to the sorting of alleles into gametes, and every possible combination of alleles for every gene is equally likely to occur. During gamete formation, the two alleles for a given gene segregate, so that each gamete carries only one allele for each gene. This results in the F1 generation inheriting different combinations of alleles from both parents, allowing for genetic diversity.
For instance, in the case of pea plants, each parent might contribute a different allele for seed color and seed texture, with the possible combinations of alleles being segregated into gametes independently. This segregation and assortment ensure that the resulting offspring have diverse genotypes and phenotypes.