PRECALCULUS NAME___________________

DESIGNER GENES

Suppose Blondie has blonde hair and her spouse Dagwood has brown hair. What are the chances that their children will have brown hair?

PUNNETT SQUARES

Hair or eye color are traits that are genetically determined. You get one gene from your mother and one gene from your father. For many of your traits you have either two dominant genes (called homozygous dominant), two recessive genes (called homozygous recessive), or one of each type (called heterozygous or hybrid). A dominant gene is usually denoted by a capital letter, say B, and a recessive gene for the same trait is denoted by a lower case letter, say b. So,

BB is homozygous dominant,

bb is homozygous recessive, and

Bb is heterozygous dominant.

	B	b
B	BB	Bb
b	Bb	bb

We can set up what is called in biology a Punnett square to help determine the probability of getting brown hair. Historically, we know that brown hair is dominant to blonde hair. Thus, a Punnett square for this scenario might look like this.

So there are four possible outcomes. Three of these (BB, Bb, Bb) will result in brown hair, and one (bb) will result in blonde hair. Thus, the probability of brown hair is ¾ , and the probability of blonde hair is ¼.

	2	1
2	4	3
1	3	2

We can set up a simulation to help determine this probability by using the randint command on your calculator. First we need to numerically code each of the possible genes. Let B = 2 and b = 1. Then we need to decide how to describe the joining of the genes in a numerical way. Using addition seems reasonable. So the numbered “Punnett square” might look like this:

Thus, getting a sum greater than 3 would result in brown hair.

SIMULATIONS

To design a simulation of this situation, generate a list of 100 random integers between 1 and 2 inclusive in L1. Do the same in L2. Create L3 so that it is L1 + L2. Display your results from L3 in a histogram using an appropriate window. Draw your histogram below.

What do you notice about the frequency distribution? Is it close to what you would expect from the theoretical probability?

Generating a simulation for such a small Punnett square seems to be more cumbersome than actually writing the square itself. However, when considering two or more traits, the Punnett square can be rather unwieldy to form. Now your are ready to answer the question originally posed at the top of this page. “What is the probability that a person would have brown hair and blue eyes with a mother who has blonde hair and blue eyes and a father who has brown hair and brown eyes?” (Note that blue eyes are recessive to brown eyes.) Try to use a simulation to model your scenario.

TEACHER’S NOTES FOR DESIGNER GENES LAB

1. This is an activity to link random simulations to biology. You may want to do this as a whole class rather than in groups or individually.
2. The frequency distribution for the 2 by 2 Punnett square should have 3 intervals, with the first and third frequencies about the same, and the middle one about double the smaller ones. This would lend credence to the ¾ and ¼ probabilities.
3. Note that the parents with brown hair in the 2 by 2 Punnett square were chosen to be heterozygous. But they could have been homozygous dominant to result in Punnett squares that looks like these:

	B	B
B	BB	BB
B	BB	BB
	B	B
B	BB	BB
b	Bb	Bb

100% brown hair 100% brown hair

4. Setting up the second simulation is a bit more complicated.

• The mother could be denoted by bbee with the father as BbEe, where E = brown eyes and e = blue eyes.
• The Punnett Square would look like this: