Question

What is the chance that an \(A a\) individual will be produced from an \(A a \times A a\) cross? a. \(50 \%\) b. \(75 \%\) c. \(0 \%\) d. \(25 \%\) e. \(100 \%\)

Short answer

a. \(50\%\)

Step-by-step solution

Identify the parents' genotypes

First, we need to recognize the genotypes of both parents, which are Aa for both of them.

Set up a Punnett square

Create a 2x2 Punnett square, representing the possible genetic combinations resulting from the cross between two Aa individuals.

Fill the Punnett square

Fill the Punnett square according to the parental genotypes: The first row will be a combination of A and the parent's alleles, and the first column will be a combination of a and the parent's alleles. The resulting Punnett square should look like this: | - | A | a | |-----|-----|-----| | A | AA | Aa | | a | Aa | aa |

Calculate the probability of the desired genotype

Now, count the number of Aa individuals (the desired genotype) in the Punnett square. There are 2 Aa individuals. Then count the total number of outcomes (there are 4 possible genotypes in the Punnett square). The probability of getting an Aa individual is the ratio of Aa individuals to the total genotypes: \(P(Aa) = \frac{Number\: of\: Aa}{Total\: number\: of\: Genotypes}\)

Final Answer

Using the ratio from Step 4, the probability of obtaining an Aa individual is: \(P(Aa) = \frac{2}{4} = \frac{1}{2} = 50\% \) So the correct answer is: a. \(50\%\).

Key concepts

Understanding Genotype Ratios

When studying genetics, a genotype ratio is a critical concept that helps us predict the likelihood of offspring inheriting specific gene combinations from their parents. A genotype refers to the genetic makeup of an organism, the blueprint that determines a trait, such as eye color or blood type. In a genetic cross between two individuals, the genotypes of their offspring can be represented in ratios, which tell us the proportion of different genotypes produced.

For example, in the Punnett square exercise provided, two parents with a heterozygous genotype (Aa) can produce offspring with genotypes AA, Aa, or aa. The genotype ratio resulting from this monohybrid cross is 1:2:1, meaning for every one AA offspring, there are two Aa offspring, and one aa offspring. This ratio is crucial for predicting the distribution of traits in the future generation and is a direct application of Mendelian genetics principles.

Fundamentals of Genetic Inheritance

Genetic inheritance is the process by which traits are passed from parents to their children through genes. Each parent contributes one allele for each gene, which combine to form the offspring's genotype. There are different modes of inheritance, but the most basic is Mendelian inheritance.

In Mendelian inheritance, traits are controlled by single genes on different chromosomes with only two alleles: a dominant allele and a recessive allele. If an organism has at least one dominant allele (represented as 'A' in the provided exercise), the dominant trait will be expressed. Only when an organism has two recessive alleles (represented as 'aa'), will the recessive trait appear. This creates a predictable pattern of inheritance, which can be visualized using a tool called the Punnett square. Understanding how alleles interact and segregate during reproduction is key to mastering the concept of genetic inheritance.

Exploring Mendelian Genetics

Mendelian genetics is named after Gregor Mendel, who is considered the father of modern genetics. His experiments with pea plants laid the groundwork for our understanding of how traits are inherited through generations. Mendel's laws of inheritance include the law of segregation and the law of independent assortment. The law of segregation states that during the formation of reproductive cells (gametes), the two alleles responsible for a trait separate from each other so that each gamete carries only one allele for each gene. The law of independent assortment states that the alleles of two (or more) different genes get sorted into gametes independently of one another.

Application in the Punnett Square Exercise

The exercise showcases the law of segregation, where each parent has a 50% chance of passing on either the dominant allele 'A' or the recessive allele 'a' to their offspring. When we fill out the Punnett square, we see the possibilities of these alleles combining, resulting in the different genotypes. Mendelian genetics allows us to predict the genotypic and phenotypic outcomes of a cross, giving us a powerful tool for understanding human genetics, agriculture, and even some diseases.