Two true-breeding pea plants are crossed. One parent is round, terminal, violet, constricted, while the other expresses the contrasting phenotypes of wrinkled, axial, white, full. The four pairs of contrasting traits are controlled by four genes, each located on a separate chromosome. In the F₁ generation, only round, axial, violet, and full are expressed. In the F₂ generation, all possible combinations of these traits are expressed in ratios consistent with Mendelian inheritance.
How often is either P₁ phenotype likely to occur in the F₂ generation?

Verified step by step guidance

1. Identify the traits and their dominant/recessive relationships based on the F1 generation phenotypes. Since the F1 shows round, axial, violet, and full, these are the dominant traits, and the contrasting traits (wrinkled, terminal, white, constricted) are recessive.
2. Assign letters to each gene for clarity. For example, let R = round (dominant), r = wrinkled (recessive); A = axial (dominant), a = terminal (recessive); V = violet (dominant), v = white (recessive); F = full (dominant), f = constricted (recessive).
3. Determine the genotypes of the P1 parents. Since they are true-breeding, one parent is homozygous dominant for all dominant traits (RR AA VV FF), and the other is homozygous recessive for all recessive traits (rr aa vv ff).
4. Understand that the F2 generation results from self-crossing the F1 heterozygotes (Rr Aa Vv Ff). Each gene segregates independently, so the phenotypic ratio for each trait follows a 3:1 dominant to recessive ratio.
5. Calculate the probability of each P1 phenotype appearing in the F2 by multiplying the probabilities of each trait combination. For example, the probability of the all-dominant phenotype (like the first P1) is the product of the probabilities of dominant phenotypes for all four traits, and similarly for the all-recessive phenotype (like the second P1).

Key Concepts

Mendelian Inheritance and Independent Assortment

Mendelian inheritance describes how traits are passed from parents to offspring through dominant and recessive alleles. Independent assortment states that genes on different chromosomes segregate independently during gamete formation, leading to various combinations of traits in the offspring.

True-Breeding and F1/F2 Generations

True-breeding plants are homozygous for specific traits, producing uniform offspring. Crossing two true-breeding parents yields the F1 generation, which is heterozygous and shows dominant traits. The F2 generation results from self-crossing F1 individuals, revealing phenotypic ratios based on allele segregation.

Calculating Phenotypic Ratios in Dihybrid and Multihybrid Crosses

When multiple genes assort independently, the probability of specific phenotypes in the F2 generation is the product of individual trait probabilities. For four traits, each with dominant and recessive forms, the chance of obtaining a parent phenotype (all dominant or all recessive) is (1/4)^4 = 1/256 for each, since each trait segregates in a 3:1 ratio.