Question

In pea plants, round peas \((R)\) are dominant to wrinkled peas ( \(r\) ). You do a test cross between a pea plant with wrinkled peas (genotype \(r r)\) and a plant of unknown genotype that has round peas. You end up with three plants, all which have round peas. From this data, can you tell if the parent plant is homozygous dominant or heterozygous?

Short answer

Based on the provided information, it could be inferred that the genotype of the parent plant with the unknown genotype is most likely homozygous dominant (\(RR\)), as all the offspring present the dominant trait, which is round peas. However, to confidently predict the genotype of the parent plant, a larger sample size would be needed.

Step-by-step solution

Understand the Genetics Involved

In this scenario, we know that round peas (\(R\)) are dominant over wrinkled peas (\(r\)), and that the genotype of one of the parent plants, the one with wrinkled peas, is homozygous recessive (\(rr\)).

Understand the Unknown Genotype

The genotype of the plant with round peas is unknown. It could either be homozygous dominant (\(RR\)) or heterozygous (\(Rr\)). Given that all of the plants produced from the cross are round, we know that this plant must at least be heterozygous, in order to pass on the dominant trait.

Analyze the Results

All the offspring plants have round peas. If the parent plant was heterozygous (\(Rr\)), there would be a 50% chance that an offspring could receive both recessive alleles and present as a wrinkled pea plant. Since all the offspring have round peas, it is most likely that the parent plant is homozygous dominant (\(RR\)).

Validate the Observations

The number of plants used in this cross may not be enough to statistically verify the hypothesis. The real validation of the assumption would require a higher sample of plants, to confidently predict the genotype of the parent plant.

Key concepts

Mendelian inheritance

Mendelian inheritance is a key concept in genetics that explains how traits are passed from parents to their offspring. Named after Gregor Mendel, the father of genetics, this principle relies on the idea that genes come in pairs and are inherited as distinct units, one from each parent. Mendel demonstrated this through his experiments with pea plants, where he discovered that certain traits follow a predictable inheritance pattern.
Mendel's laws consist of the Law of Segregation and the Law of Independent Assortment. The Law of Segregation states that during the formation of gametes (egg and sperm), the two alleles for a trait separate so that offspring receive one allele from each parent. The Law of Independent Assortment suggests that alleles for different traits are distributed to gametes independently.
Understanding Mendelian inheritance helps clarify why, in some crosses, certain traits appear more frequently or exclusively in the offspring, as illustrated by the round and wrinkled pea plants experiment.

dominant and recessive traits

Dominant and recessive traits are crucial aspects of genetics that help explain how different characteristics are expressed. In the case of the pea plants example, round peas are considered a dominant trait, while wrinkled peas are recessive. A trait is dominant if it can appear in the offspring even if only one parent contributes the allele for that trait. Conversely, a recessive trait is only expressed when both parents contribute the allele for that trait.
For instance, if one parent carries the round pea allele ( R ) and the other does not, the round shape will still manifest in the presence of any recessive alleles ( Smart ), shown as ( Rr ). In contrast, wrinkled peas appear only if both alleles are recessive ( rr ). This dynamic allows for the varied presentation of inherited traits depending on the combination of alleles passed on from the parents.
Understanding dominant and recessive traits offers valuable insight into how genetic variation can occur, and how certain features become either prevalent or recessive in a population over time.

homozygous vs heterozygous

The terms homozygous and heterozygous refer to the genetic makeup of an organism concerning a particular trait. Simply put, homozygous means that an individual has two copies of the same allele, while heterozygous means they have two different alleles for a trait.
When it comes to the pea plant example, a plant can be homozygous dominant ( RR ) or homozygous recessive ( rr ). A "homozygous dominant" pea plant will always produce round peas, as both alleles are dominant. On the other hand, a homozygous recessive ( rr ) plant will yield wrinkled peas since both alleles are recessive.
A heterozygous plant ( Rr ), which contains one dominant and one recessive allele, will exhibit the dominant trait, resulting in round peas. When breeding plants like in the given exercise, knowing if a plant is homozygous or heterozygous for a particular trait helps in predicting the types of offspring that may be produced, thus illuminating Mendelian inheritance patterns.