A dihybrid cross of two contrasting pure-breeding organisms involves crossing two individuals that are homozygous for different alleles at two different gene loci. This means they are "pure-breeding" for two different traits, and each individual possesses two identical alleles for each trait.

What a dihybrid cross does:

1. Reveals the inheritance patterns of two traits simultaneously: It allows you to study how two different genes, each with two different alleles, are inherited together.

2. Demonstrates the principle of independent assortment: It shows that alleles for different traits segregate independently of each other during gamete formation. This means that the inheritance of one trait does not influence the inheritance of another.

3. Produces a phenotypic ratio of 9:3:3:1: In a typical dihybrid cross, the offspring will exhibit a phenotypic ratio of 9:3:3:1. This means that 9 out of 16 offspring will express both dominant traits, 3 will express one dominant and one recessive trait, another 3 will express the other dominant and one recessive trait, and 1 out of 16 will express both recessive traits.

Example:

Let's say we are crossing a homozygous tall, round pea plant (TT, RR) with a homozygous short, wrinkled pea plant (tt, rr).

* Parental generation (P): TT RR x tt rr

* Gametes: TR x tr

* F1 generation: TtRr (all tall, round)

* F2 generation: 9 tall, round : 3 tall, wrinkled : 3 short, round : 1 short, wrinkled

In summary: A dihybrid cross allows you to observe the simultaneous inheritance of two traits, demonstrating independent assortment and producing a characteristic phenotypic ratio. This information is crucial for understanding how genetic variations are passed down from one generation to the next.