Question

What genotypes, and in what frequencies, will be present in the offspring from the following matings? a. \( A A B B \times\) aa \(B B\) b. Aa \(B b \times\)aabb c. Aa \(B B \times A A B b\) d. Aa \(B b \times\)AaBb

Short answer

a. All AaBb (100%), b. AaBb (25%), Aabb (25%), aaBb (25%), aabb (25%), c. AABB (50%), AaBB (50%), d. AABB (1/16), AABb (1/8), AaBB (1/8), AaBb (1/4), AAbb (1/16), aaBB (1/16), aaBb (1/8), aabb (1/16).

Step-by-step solution

Determine Genotypes of Offspring for Cross a

To find the genotypes for the cross between individuals with genotypes AABB and aabb, write down each possible gamete these individuals can produce. The first individual can only produce AB gametes, while the second can only produce ab gametes. When these gametes combine, all offspring will have the genotype AaBb.

Determine Genotypes of Offspring for Cross b

For the cross between AaBb and aabb, list all possible gametes from the first individual (AB, Ab, aB, ab) and the second individual (ab). Each gamete from the first individual can combine with the ab gamete from the second individual, resulting in the following offspring genotypes: AaBb, Aabb, aaBb, and aabb, each occurring with equal frequency or 25%.

Determine Genotypes of Offspring for Cross c

For the cross AaBB x AABB, identify possible gametes. The first individual can produce AB or aB gametes, and the second can only produce AB gametes. Combining these gives two possible genotypes for the offspring: AABB and AaBB. The frequencies will be 50% for each genotype.

Determine Genotypes of Offspring for Cross d

For the cross AaBb x AaBb, list all possible gametes for each parent (AB, Ab, aB, ab). The combination of these gametes results in nine possible genotypes: AABB, AABb, AaBB, AaBb (x2), AAbb, aaBB, aaBb, and aabb, with the frequencies being 1:2:1:4:2:1:1:2:1 respectively.

Key concepts

Punnett Square

A Punnett square is a graphical tool used in genetics to predict the possible genotypes of offspring from a particular genetic cross. It's a grid that simplifies the process of determining which alleles from each parent can combine when they reproduce. To create a Punnett square, you write the possible gametes (combinations of alleles for each gene) of one parent along the top and those of the other parent down the side. Then, you fill in the grid by combining these alleles.

For example, if we look at cross a from the exercise, we have one parent with the genotype AABB and the other with aaBB. The first parent can only produce gametes with the alleles AB, and the second can only produce gametes with the alleles ab. When you set up a Punnett square, every single cell of the grid will result in the genotype AaBb as there’s only one option for each allele from each parent. This visual tool is immensely helpful in visualizing genetic outcomes and helps students understand the process of inheritance.

Mendelian Genetics

Mendelian genetics is founded on the principles set forth by Gregor Mendel in the 1860s. At its core, it's about understanding how traits are inherited through the mechanisms of dominant and recessive alleles. In the case of pea plants, which Mendel famously studied, these principles can be straightforward. However, in more complex organisms, traits can be influenced by multiple genes, which is referred to as polygenic inheritance.

In our Punnett square exercise, Mendelian genetics helps to simplify the genetic cross by allowing us to predict offspring genotypes based on the dominant and recessive states of the alleles involved. Understanding that each parent contributes one allele for each gene to their offspring is a fundamental principle of this discipline, and applying it correctly can help clarify the outcomes in genetic crosses.

Genetic Cross Outcomes

The outcomes of a genetic cross depend on the allele combinations from both parents. We can define outcomes in terms of the offspring's physical characteristics (phenotype) or genetic makeup (genotype). In Step 4 of solving cross d (AaBb x AaBb), using the rules of Mendelian genetics, we see that there are nine possible genotypes. However, these genotypes don't all occur with the same frequency.

Using concepts from probability, we can determine that the genotype AaBb is more likely to occur than AABB or aabb, for instance, because there are more combinations of parental alleles that result in AaBb. Understanding this concept assists students in grasping why certain traits may be more prevalent in a population due to the genetic variance and probabilities of certain allele combinations.

Allele Combinations

Alleles are different versions of the same gene, and their combinations determine the genetic variation seen in offspring. Every individual has two alleles for each gene, one inherited from each parent. In genetics, we commonly refer to these as homozygous if the alleles are the same (AA or aa), or heterozygous if they differ (Aa).

Each parental combination of alleles has the potential to produce multiple types of gametes, as shown in cross b (AaBb x aabb), resulting in different allele combinations and thus different genotypes in their offspring. The allele combinations are the heart of genetic diversity and are crucial for understanding heredity. By focusing on how these combinations come together, students can better predict genetic variations and understand the fundamental concepts of genetics.