Final answer:
To demonstrate Mendel's Law of Independent Assortment, at least two loci are needed in a cross. This can be shown through a dihybrid cross, where parental homozygous traits produce an F1 generation with heterozygous pairs that create gametes independently, resulting in varied offspring.
Step-by-step explanation:
To demonstrate Mendel's Law of Independent Assortment, a minimum of two loci are required in a cross, such as those used in a dihybrid cross, which involves organisms that are heterozygous for two different traits. This will enable the observation of the independent segregation of two sets of alleles into gametes, which is central to the law. By using a dihybrid cross in which the parental generation has homozygous alleles for the traits being observed (for example, RRYY x rryy), we can see the creation of an F1 generation that is heterozygous for both traits (RrYy).
During the formation of gametes in the F1 generation, the law of segregation ensures each gamete receives one allele per gene, while the law of independent assortment assures the alleles sort independently of each other. This results in four types of gametes, RY, Ry, rY, and ry, leading to a variety of combinations in the F2 generation, which can be demonstrated by the phenotypic ratio of 9:3:3:1 typical of a dihybrid cross. To observe independent assortment, it is imperative to track two or more genes that are on different chromosomes or so far apart on the same chromosome that they assort independently due to cross-over.