Question

What is the chance of producing a child with the dominant phenotype from each of the following crosses? (pages \(469-70\) ) a. \(A A \times A A\) b. \(A a \times A A\) c. \(A a \times A a\) d. \(a a \times a a\)

Short answer

a. The probability of producing a child with the dominant phenotype from the cross \(A A \times A A\) is 100% or 1. b. The probability of producing a child with the dominant phenotype from the cross \(A a \times A A\) is 100% or 1. c. The probability of producing a child with the dominant phenotype from the cross \(A a \times A a\) is 75% or \(\frac{3}{4}\). d. The probability of producing a child with the dominant phenotype from the cross \(a a \times a a\) is 0% or 0.

Step-by-step solution

Cross a. \(A A \times A A\)

Since both parents are homozygous dominant (having identical dominant alleles), their genotypes are represented as \(A A\). If we create a Punnett square for this cross, all the offspring will have the same genotype, which is \(A A\), and since \(A\) is the dominant allele, they all will show the dominant phenotype. So the probability is 100% or 1.

Cross b. \(A a \times A A\)

In this cross, one parent is homozygous dominant (having identical dominant alleles) \(A A\), and the other is heterozygous (having one dominant and one recessive allele) \(A a\). If we create a Punnett square for this cross, all the offspring will have dominant allele \(A\), which means they all will show the dominant phenotype. So, the probability is 100% or 1.

Cross c. \(A a \times A a\)

In this cross, both parents are heterozygous (having one dominant and one recessive allele) \(A a\). If we create a Punnett square for this cross, we get the following genotypes: \(\frac{1}{4} A A, \frac{1}{2} A a, \frac{1}{4} a a\). The offspring that have at least one dominant allele \(A\) will show the dominant phenotype. So, the probability is \(\frac{1}{4} + \frac{1}{2} = \frac{3}{4}\) or 75%.

Cross d. \(a a \times a a\)

In this cross, both parents are homozygous recessive (having identical recessive alleles) \(a a\). If we create a Punnett square for this cross, all the offspring will have the same genotype, which is \(a a\), and since there is no dominant allele \(A\), none of them will show the dominant phenotype. Therefore, the probability is 0% or 0.

Key concepts

Punnett square

A Punnett square is a handy tool used in genetics to predict the probability of different genotypes in the offspring resulting from a particular cross. It's essentially a visual grid that helps you see how alleles from each parent can combine. You draw a box, usually a 2x2, for a monohybrid cross and list the alleles from one parent on the top and those of the other parent on the side. Then, you simply fill in the squares to see the possible genotypes of the offspring.

For example, if we use a Punnett square to match allele combinations from parents with genotypes AA and Aa, the offspring's genotypes can be easily calculated. This allows us to visualize and predict traits like a dominant phenotype. Remember, it's named after Reginald Punnett, who popularized its use.

dominant phenotype

A dominant phenotype is the physical expression of a dominant allele in an organism. In terms of genetics, an organism with at least one dominant allele (such as "A" in a genotype like AA or Aa) will display the dominant phenotype. This is because dominant alleles mask the effect of recessive alleles, if present.

For instance, in a cross of Aa x Aa, where 'A' is a dominant allele, the phenotypic ratio would show that 75% of the offspring will express the dominant trait, while only 25% will express the recessive phenotype aa. It's important to note that the dominant phenotype does not imply better or more common, but simply that it is expressed in the presence of the dominant allele.

homozygous dominant

When an individual has two identical dominant alleles for a particular gene, they are considered homozygous dominant. This is shown as "AA" if "A" is the dominant allele. Homozygous dominant organisms will always exhibit the dominant phenotype because there are no recessive alleles to mask the effect.

For example, in a cross like AA x AA, all offspring will also be homozygous dominant and thus will have a 100% probability of showing the dominant trait. This concept helps explain how certain traits can be consistently passed on if both parents exhibit homozygosity for dominant alleles.

heterozygous

An organism is termed heterozygous when it possesses one dominant and one recessive allele for a specific gene, such as "Aa". In genetics, heterozygosity is important because it often results in the manifestation of the dominant phenotype, due to the presence of the dominant allele.

In crosses involving heterozygous individuals, like Aa x Aa, we can predict a variety of possible outcomes: 25% AA, 50% Aa, and 25% aa. Hence, while 75% of the offspring will express the dominant phenotype, only 25% will express the recessive phenotype. Understanding heterozygosity is crucial in predicting the likelihood of different traits appearing in the offspring.