Science at a Distance

Mendelian Genetics

Solving Genetic Problems

What is a Genetic Problem?

A genetic problem is a type examination question that involves both a knowledge of Mendel's experiments, and an analysis of data produced during one of his genetic crosses. In the question the solver is presented with information concerning the genotypes and phenotypes of individuals involved in a genetic cross, and the genotypes and phenotypes of their offspring. Some of this critical information is missing, and the solver's task is to supply that missing data.

Example #1.... A red flowered plant is fertilized with pollen from a plant of unknown phenotype. 62 seeds are collected, planted the next year and grow into the F1 offspring. 16 of these offspring have white flowers and the rest have red flowers. What was the phenotype and genotype of the unknown parental plant?

The Four Steps

Almost all the genetic problems used in Core Biology 8.1 can be analyzed and solved using four basic steps, or processes.

(1) Use Your Course Work

From information give in the lecture part of the course and from information given in these Web pages, write down what you already know about this situation.

Flower color is controlled by a single gene.
The dominant form of this gene is often written R
When ever the R gene is present in the genotype of a plant, the flower color is always red.
The mutant form of this gene, which is recessive, is often written r.
Plants with the genotype RR or Rr have red flowers.
Plants with the genotype rr have white flowers.

(2) Use the Information in the Question

Every question includes a lot of valuable information (some of it not so obvious - think for a moment). Take this information and write it out in a logical sequence as it appears in a typical genetic cross. See what you have and what is missing.

Phenotypes and Genotypes of parents
- Parental Genotypes ... unknown, but the red flowered parent must have contained at least one R gene, with a genotype of RR or Rr.
- Parental Phenotypes ... one red flowered, one unknown
Genotypes of all possible gametes from each of the parents
- NOTE: The pollen grains used in this cross came from the unknown plant, and the egg cells came from the red flowered plant. The pollen grains contain the male gametes, and the egg cells (in the red flowered plant) are the female gametes.
- Male gametes ... genotypes unknown (these came from the unknown male plant)
- Female gametes ... At least half the gametes must have been R for the plant to have red flowers. (see above)
Genotypes and Phenotypes of Offspring (F1 generation)
- The data given was for 62 F1 offspring.
- Phenotypes: 16 white flowers, 46 red flowers.
- Genotypes: all 16 white flowered plants = rr. All red flowered plants = R?

(3) Reduce all raw data to ratios

Not all genetic problems involve raw data, but in those that do, use Mendel's approach and reduce all such raw numbers to ratios. In classical one factor and two factor crosses, there are only three ratios that matter.

Heterozygous x Heterozygous
Aa x Aa
which gives a ratio of 3:1 among the offspring.
Heterozygous x Homozygous recessive
Aa x aa
which gives a ratio of 1:1 among the offspring.
Heterozygous x Heterozygous (two factors)
Aa.Bb x Aa.Bb
which gives a ratio of 9:3:3:1 among the offspring.
There are, of course, other combinations of genes, but their results can usually be reduced to one or other of these ratios.

If you learn (know or even understand) how these ratios arise during a genetic cross, you can often go straight to the final answer in many genetic problems. Even if it is not possible to deduce the correct answer directly from these ratios, they are valuable clues.

(4) Diagram and Fill in the Blanks

Once you have assembled the evidence, write it out in a typical genetic cross diagram. Use question marks (?) when you encounter something you cannot fill in yet.
Often the missing parts of the puzzle will be obvious once you have done this, but even if they aren't, a short trial and error session filling in the missing pieces will give the right answer after one or two tries.

In the example we have worked on so far ...

Parents R? x ??
(the genotype of the second parent, the male, is the whole point of the problem)

Gametes R and ? (female) x ? and ? (male)

Punnett Square

Gametes	R	?
?	R?	R?
?	R?	rr

NOTE: In the above Punnett Square a genotype of rr has been entered for one quarter of the offspring; why?
Well, this was part of the data given in the question. The data said that 16 out of 62 F1 offspring had white flowers. White flowered plants can only have the genotype rr. The raw numbers were reduced to the ratio of 3:1 in step 3. So one quarter of the F1 offspring (one box in the Punnett Square) must hold the genotype rr.
Also, each of the other three offspring must have at least one R gene. This was also given in the data and deduced in step 3, so much of the Punnett Square can be filled in from what is already known.

Now fill in the blanks.

If it is not obvious from the Punnett Square, work backwards. Since some of the offspring have white flowers (genotype rr), the gametes that formed them must have been r. So the only arrangement that would give this result is ...

Gametes	R	r
?	R?	R?
r	R?	rr

Now most of the gametes are filled in along the sides of the Punnett Square, some of the missing genotypes can also be filled in ...

Gametes	R	r
?	R?	Rr
r	Rr	rr

This only leaves one gamete and one F1 genotype unresolved. There are only two choices for the missing gamete; R or r. Putting a recessive, r gamete in place of the question mark does not give the right answer, so the missing gamete must be R.

So the complete Punnett Square is ...

Gametes	R	r
R	RR	Rr
r	Rr	rr

With the Punnett Square complete, it is now possible to answer the original question.

ANSWER ... The genotype of the unknown male plant must have been Rr (a fact deduced from the two gametes this plant must have provided for the Punnett Square to work). The phenotype of this plant must have been - red flowers.

Your Turn

Now it is your turn. Use similar logic and process to deduce the answer to the following genetic problems.

Question 2 ... A red flowered plant was crossed with a white flowered plant. Out of 124 offspring, 65 had red flowers, the rest had white flowers. What was the genotype of the red flowered parent plant?

Question 3 ... Long-pod ribbon plants when crossed with one another always give long-pod ribbon plants. However, when long-pod ribbon plants are crossed with short-pod ribbon plants, the F1 offspring sometimes contain a mixture of short- and long-pod plants. What is the genotype of the long-pod ribbon plants?

Mendelian Genetics - Topic Outline