## Hardy-Weinberg Made Easy: A Seventh Way

Jack Doepke
1994 Woodrow Wilson Biology Institute

#### Teacher Instructions

Target Age: High School (9-12) Student/Class time required: 40 minutes

The purpose of this lesson is to slowly introduce the Hardy-Weinberg Law and population genetics to your students after you have completed Mendelian genetics. Using this format, you ease the students into the concept by relying on the knowledge they already have.

Yogi Bear decided one year that for future conservation plans regarding the usage of the park and its equipment, it would be important for him to gather some data about the bears that inhabit the park, so he petitioned the use of some of the other animals in the park and sent them out to gather some data. A week later the survey was completed and tabulated. It showed that 360 brown bears and 640 black bears resided in the park. The data also showed that the bears mated regardless of color, but that when brown bears mated with brown bears only brown cubs were produced, but when black bears mated with other black bears sometimes brown cubs were produced. Yogi also noticed that there did not appear to be any obvious survival value to having one color or the other.

The first question that Yogi wanted answered was which trait, black or brown, is dominant and which is recessive. Can you help Yogi figure this out with the information provided?

Hint: To determine the answer set up a cross using all possible combinations of coat colors and look at the expected results. The answer will become obvious.

In making plans for purchasing new band uniforms for the Fourth of July parade, Yogi thought it would be nice if the brown bears and black bears had different color ties so he next wanted to know if the percent of bears having brown coat color would be the same for the next generation. So he called upon the wise old owl, Doc Cronkite, for he was the wisest of all the animals in the forest.

'Doc,' he asked, 'using the information that I gathered in my survey, can I determine if the coat colors of the bears here in Jellystone will be the same in future generations to come?'

'Yes, Yogi, thanks to two very smart men by the names of Hardy and Weinberg, I think we can extract that information for you from your survey. But first we have to go back and look at our old friend the Punnett square from our studies in Mendelian genetics. We are going to modify the way we use the square slightly to suit our purposes. First of all, instead of thinking in terms of a single cross between two mating individuals, we are going to think in terms of the whole population of bears.

'First we will change this model slightly to fit our data:'

'Now remember to put the male gametes across the top and the female gametes down the side:'

'We will put all the gametes on the top coming from all of the males and we will put all the gametes from the females down the side. We will calculate these by working backwards or from what we can deduce from what we know about what is inside the box.'

First help Yogi to calculate the percent of gametes coming from the male and female population that was required to produce 360 brown bears. Hint: First think in terms of percent rather than 360 bears.

Now notice that some number B (male gametes) must have been multiplied by some number 2 (female gametes) to produce our 36% of brown bears. Help Yogi to calculate that number.

Notice that the frequency of the recessive gene for all of the 360 brown bears (36%) has to be .6 (60%) for both the male and female population. We refer to this as the gene frequency for the recessive gene and we assign the letter q to it. Now to calculate the frequency of the dominant gene in the population we simply subtract from 1 (100%). Thus p + q = 1. This gives us a value of .4 (40%) for the dominant gene.

From this we can see that :

• p2 = (.4x.4) .16 or 16%
• 2pq = (2 x .4 x .6 ) .48 or 48%
• q2 = (.6 x.6 ) .36 or 36%

p2 + 2pq + q2 = 1 is the other part of the Hardy-Weinberg Equation that represents the genetic percentages of the offspring. Do not confuse this with the gene frequency in the population or gene pool.

Tired and hungry from all of this math, Yogi and Doc took a break and walked down by the pool and had some cookies and milk. This was relaxing and fun for Yogi, but all Doc wanted to do was count the number of chocolate chips in the cookies. Yogi guessed that Doc must have inherited a mathematical gene from a parent. Probably his mother. Rested ,they began anew.

'Doc, I'm ready to tackle my next question, if you are. How do I tell if the next generation of my bears will be the same color?'

'Of course they will be the same color, Yogi. What you want to know is, will they be in the same genetic ratio as before.'

'Yeah, that's what I meant.'

'For that, Yogi, we have to ask ourselves, what kind of gametes can the bears that we have now produce and in what proportion?'

'How do we do that, Doc?'

'Well, you remember from your study of meiosis, don't you, that each parent carries two genes or alleles for a trait, but they only contribute one to their offspring.'

'Sure I remember that, Doc. That is pretty obvious, otherwise our chromosome number wouldn't stay constant from one generation to the next.'

'That's right, Yogi, but do you remember which controls what gene goes into a gamete?'

'Does it have something to do with dominance and recessiveness?'

'No, Yogi, it is strictly a matter of chance.'

'Oh! So our job should be easy then. We just need to go back to our original percentages and work from there.'

Can you help Yogi do this?

16% BB + 48% Bb + 36% bb = 100%

16% BB can produce what kind of gametes_________________________

48% Bb can produce what two kind of gametes _________ + _________

36% bb can produce what kind of gametes _________________________

Results:

• .16 B +.24 B/.40 B
• .24 b +.36 b/ .60 b

From this we can see that if we fill in the Punnett square our percentages for this new generation will be exactly the same as the present generation. This is a fundamental principle of the Hardy-Weinberg Equation.

Gene frequencies will remain constant from one generation to the next in a population not undergoing natural selection.

#### Hardy-Weinberg Equilibrium Introduction

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