Question

Two plants in a cross were each heterozygous for two gene pairs \((A b / a B)\) whose loci are linked and 25 mu apart. Assuming that crossing over occurs during the formation of both male and female gametes and that the \(A\) and \(B\) alleles are dominant, determine the phenotypic ratio of their offspring.

Short answer

The phenotypic ratio of the offspring produced by these two heterozygous plants is 19:5, with 19 representing the dominant (A and B) phenotype and 5 representing the recessive (a and b) phenotype.

Step-by-step solution

Determine all possible gamete combinations

For plants that are heterozygous for both gene pairs (A b / a B), there are four possible gametes formed from the alleles (Aa and Bb) in each plant. These gametes are AB, Ab, aB, and ab.

Calculate the recombination frequency (RF)

The recombination frequency (RF) between two gene pairs is given by the distance between them in map units (mu). In this exercise, the two gene pairs are 25 mu apart. So, the recombination frequency (RF) is 25%. This means that 25% of the offspring will have recombinant gametes, while 75% will have the original non-recombinant gametes.

Determine the proportions of each gamete type

Knowing the recombination frequency (RF), we can now determine the proportions of gametes that are parental and recombinant. For the non-recombinant (parental) gametes, it will be 75% (100% - RF). Hence, 75% of the gametes will be parental (AB and ab or Ab and aB). For the recombinant gametes, it will be 25% of the gametes (Ab and aB or AB and ab).

Calculate the offspring's phenotype using the Punnett square

Next, we will use the Punnett square to determine the phenotypic ratio of the offspring by combining the gametes from both parents. | | AB | Ab | aB | ab | |---------|------------|------------|------------|------------| | AB | AABB | AABb | AaBB | AaBb | | Ab | AABb | AAbb | AaBb | Aabb | | aB | AaBB | AaBb | aaBB | aaBb | | ab | AaBb | Aabb | aaBb | aabb |

Calculate the phenotypic ratio

Based on the Punnett square, the resulting offspring phenotypes are: - AABB: 1/16 - AABb: 4/16 - AaBB: 4/16 - AaBb: 10/16 - AAbb: 2/16 - Aabb: 4/16 - aaBB: 2/16 - aaBb: 4/16 - aabb: 1/16 The dominant phenotypes (expressing the A and B alleles) are AABB, AABb, AaBB, and AaBb, which account for a total of (1 + 4 + 4 + 10)/16 = 19/16 of the offspring. Since both A and B are dominant, the phenotypic ratio of the offspring would be expressed as: Dominant (A and B): 19/16 Recessive (a and b): 5/16 In conclusion, the phenotypic ratio of the offspring produced by two heterozygous plants for two gene pairs (A b / a B) that are 25 mu apart is 19:5 for the dominant (A and B) phenotype to the recessive (a and b) phenotype.

Key concepts

Genetic Linkage

Genetic linkage refers to the phenomenon where genes that are located close to each other on the same chromosome tend to be inherited together during meiosis. This is because the chance of a crossover event occurring between closely linked genes is low, which means that the alleles for these genes are usually passed down to offspring in the same combinations as those found in the parents. The closer the genes are on the chromosome, the lower the probability of recombination between them. In our exercise, the two heterozygous gene pairs (A b / a B) are said to be linked, which affects the variety of possible genetic combinations in the offspring.

Recombination Frequency

Recombination frequency is a measure of the likelihood of a crossover event between two genetic loci and is used to estimate the genetic distance between them. It is typically expressed as a percentage or as map units (mu). The higher the recombination frequency, the further apart the genes are on a chromosome. In our exercise, a recombination frequency of 25% means that a quarter of the offspring will display gene combinations different from those of the parents, indicative of a crossover event. The given 25 mu distance suggests a relatively high chance for recombination to occur.

Punnett Square

A Punnett square is a grid used to predict the genotypic and phenotypic outcomes of a cross between two organisms. Each square represents a possible genotype of the offspring, derived from the combination of alleles that each parent can provide. By filling out a Punnett square, as demonstrated in the exercise, you can visualize the genetic makeup of future generations and determine the expected ratios of different phenotypes.

Phenotypic Ratio

The phenotypic ratio is the relative number of offspring with different traits that result from a genetic cross. This ratio is derived from interpreting the genotypes produced by a Punnett square in terms of observable characteristics, taking into account the dominance and recessiveness of alleles. The exercise provided us with a phenotypic ratio that takes into account the dominant (expressing A and B alleles) and recessive (expressing a and b alleles) phenotypes.

Map Units

Map units, or centimorgans (cM), are a unit of measurement for genetic distance used in genetic linkage maps. One map unit represents a 1% chance that a crossover will occur between two genes during meiosis. This value is crucial in genetic mapping as it helps to estimate the physical distance between genes on a chromosome. In the context of our exercise, the 25 map units between the linked genes indicate a moderate distance, suggesting a reasonable expectation of crossover events.

Heterozygous Gene Pairs

Heterozygous gene pairs occur when an organism has two different alleles at a particular genetic locus. In the exercise, the plants were heterozygous for two gene pairs (A b / a B), meaning that for each gene locus, there is one dominant and one recessive allele. This heterozygosity results in varied gamete combinations and is fundamental to the diversity observed in offspring's genotypes and phenotypes.

Dominant and Recessive Alleles

Alleles can be dominant or recessive, affecting the outcome of a trait in an organism. A dominant allele will mask the expression of a recessive allele in a heterozygote. Thus, only one dominant allele is required to express a dominant trait. Conversely, a recessive trait requires two copies of the recessive allele to be expressed. In the exercise, the A and B alleles were dominant, and thus the phenotypes they influenced were more prevalent in the offspring, as opposed to the recessive a and b alleles.