College

A geranium can be red [tex]$(R)$[/tex] or white [tex]$(r)$[/tex]. A horticulturist has a red geranium with an uncertain genetic makeup. She crosses this red geranium with a white geranium and generates offspring in which half of the plants have red flowers and half have white flowers.

[tex]
\[
\begin{tabular}{|c|c|c|}
\hline
& r & r \\
\hline
? & Rr & Rr \\
\hline
? & rr & rr \\
\hline
\end{tabular}
\]
[/tex]

What does this combination of offspring tell her about the genotype of the red geranium?

Answer :

To determine the genotype of the red geranium, let's break down the information provided about the offspring:

1. Flower Color and Genetic Representation:
- Red flowers are represented by the dominant allele [tex]\( R \)[/tex].
- White flowers are represented by the recessive allele [tex]\( r \)[/tex].

2. Crossbreeding Outcome:
- A red geranium is crossed with a white geranium (genotype [tex]\( rr \)[/tex]).
- The offspring consists of half red-flowered and half white-flowered plants.

3. Analyzing Offspring Results:
- The results show a 1:1 ratio of red to white flowers.
- For the white-flowered offspring to appear (genotype [tex]\( rr \)[/tex]), each parent must contribute one [tex]\( r \)[/tex] allele. Since the white geranium is [tex]\( rr \)[/tex], it contributes one [tex]\( r \)[/tex] allele, meaning the red geranium must contribute the other [tex]\( r \)[/tex] for these white flowers to appear.

4. Determining the Red Geranium’s Genotype:
- A plant with at least one [tex]\( R \)[/tex] allele has red flowers. Since half the offspring are red, the genotype of the red flowers must be [tex]\( Rr \)[/tex], where the dominant [tex]\( R \)[/tex] from the red geranium combines with the [tex]\( r \)[/tex] from the white geranium.
- Thus, this 1:1 ratio indicates that the red geranium's genotype must be [tex]\( Rr \)[/tex], meaning it is heterozygous (one dominant [tex]\( R \)[/tex] and one recessive [tex]\( r \)[/tex]).

Therefore, the genotype of the red geranium is [tex]\( Rr \)[/tex].