College

A horticulturalist wants to produce geraniums with specific characteristics. She knows that the trait of red flowers is governed by the allele [tex]R[/tex] ([tex]RR[/tex] and [tex]Rr[/tex]), and the trait of white flowers is governed by the allele [tex]r[/tex] ([tex]rr[/tex]).

The horticulturalist crosses two geraniums from the F1 generation. Look at the Punnett square to see this cross.

[tex]
\[
\begin{array}{|c|c|c|}
\hline
& R & r \\
\hline
R & RR & Rr \\
\hline
r & Rr & rr \\
\hline
\end{array}
\]
[/tex]

Which ratio of red-to-white flowering plants would she expect to see in the phenotypes of the F2 generation?

Answer :

To solve the problem, we first note that the trait for red flowers is dominant (allele [tex]$R$[/tex]) and the trait for white flowers is recessive (allele [tex]$r$[/tex]). Since the geraniums in the F1 generation are heterozygous, both have the genotype [tex]$Rr$[/tex]. When two heterozygotes are crossed, the mating is:

[tex]$$
Rr \times Rr
$$[/tex]

We can determine the genotypes of the offspring using a Punnett square. First, list the gametes each parent can produce:

- The first parent can produce gametes: [tex]$R$[/tex] and [tex]$r$[/tex].
- The second parent can also produce gametes: [tex]$R$[/tex] and [tex]$r$[/tex].

The Punnett square is set up as follows:

[tex]$$
\begin{array}{c|cc}
& R & r \\
\hline
R & RR & Rr \\
r & Rr & rr \\
\end{array}
$$[/tex]

From the Punnett square:

1. The top-left square is [tex]$RR$[/tex].
2. The top-right square is [tex]$Rr$[/tex].
3. The bottom-left square is [tex]$Rr$[/tex].
4. The bottom-right square is [tex]$rr$[/tex].

Since red is dominant, both [tex]$RR$[/tex] and [tex]$Rr$[/tex] will have red flowers. Only [tex]$rr$[/tex] will have white flowers.

Counting the outcomes:
- Red-flowering plants: [tex]$RR$[/tex] (1 outcome) + [tex]$Rr$[/tex] (2 outcomes) = 3 outcomes.
- White-flowering plants: [tex]$rr$[/tex] = 1 outcome.

Thus, the ratio of red-to-white flowering plants in the F2 generation is:

[tex]$$
3:1.
$$[/tex]

This completes the step-by-step solution.