In the datura plant, purple flower color is controlled by a dominant allele, P. White flowers are found in plants homozygous for the recessive allele p. Suppose that a purple-flowered datura plant with an unknown genotype is self-fertilized and that its progeny are 28 purple-flowered plants and 10 white-flowered plants.
If one of the purple-flowered progeny plants is selected at random and self-fertilized, what is the probability it will breed true?

Verified step by step guidance

1. Step 1: Understand the genetic basis of the problem. The purple flower color is controlled by the dominant allele P, while the white flower color is controlled by the recessive allele p. A plant with genotype PP or Pp will have purple flowers, and a plant with genotype pp will have white flowers.
2. Step 2: Analyze the progeny data from the self-fertilized purple-flowered plant. The progeny consists of 28 purple-flowered plants and 10 white-flowered plants. This ratio suggests a segregation pattern consistent with a heterozygous genotype (Pp) for the parent plant. Use the Mendelian ratio of 3:1 (purple:white) to confirm this.
3. Step 3: Consider the genotype of the purple-flowered progeny. Purple-flowered progeny can have either the PP or Pp genotype. To determine the probability of breeding true (producing only purple-flowered offspring), focus on the PP genotype, as it will always produce purple flowers when self-fertilized.
4. Step 4: Calculate the probability of selecting a PP genotype from the purple-flowered progeny. Since the parent plant was heterozygous (Pp), the purple-flowered progeny will consist of 1/3 PP and 2/3 Pp, based on Mendelian inheritance patterns.
5. Step 5: Use the probability of selecting a PP genotype to determine the likelihood of breeding true. A PP plant will always produce purple-flowered offspring when self-fertilized, so the probability of breeding true corresponds to the probability of selecting a PP genotype from the purple-flowered progeny.

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It involves understanding dominant and recessive alleles, where dominant alleles mask the expression of recessive ones. In this case, the purple flower color (P) is dominant over white (p), which is crucial for predicting the offspring's traits.

Genotype and Phenotype

The genotype refers to the genetic makeup of an organism, while the phenotype is the observable physical or biochemical characteristics. In the datura plant example, the genotype of the purple-flowered plant could be either homozygous dominant (PP) or heterozygous (Pp). Understanding the relationship between genotype and phenotype is essential for determining the probability of offspring traits.

Punnett Square

A Punnett square is a diagram used to predict the genetic outcomes of a cross between two organisms. It helps visualize the possible combinations of alleles from the parents. In this scenario, constructing a Punnett square for the purple-flowered progeny will allow us to calculate the probability of obtaining a homozygous dominant plant (PP) that breeds true for purple flowers.