Natural Selection in Teddy Grahams



Natural Selection in Teddy Grahams

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Before we can begin eating our bears, we need to understand how population genetics are calculated.

The allelic frequencies in a population are determined through the following equations. This is known as the Hardy-Weinberg equation.

Hardy Weinberg

p2 + 2pq + q2 = 1 and p + q = 1

p = frequency of the dominant allele in the population

q = frequency of the recessive allele in the population

p2 = percentage of homozygous dominant individuals

q2 = percentage of homozygous recessive individuals

2pq = percentage of heterozygous individuals

4 simple rules for calculating the equations:

1) Find what q2 and q are first. Q2 are the homozygous recessive phenotypes, and q are the actual number of recessive alleles in the population. They can be determined through the information given to you in a problem.

2) Once you find what q is, you subtract that number from 1. p + q = 1. That will give you p, or the number of dominant alleles in a population.

3) Square the p number. This will give you the number of homozygous dominant individuals in a population.

4) Now that we have p2, p, q2, and q, put those numbers into the Hardy-Weinburg equation. That number should be equal to 1. This gives you the allelic frequencies in a population.

Now lets practice before we begin the lab.

PROBLEM #1.

You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:

A. The frequency of the "aa" genotype.

B. The frequency of the "a" allele.

C. The frequency of the "A" allele.

D. The frequencies of the genotypes "AA" and "Aa."

E. The frequencies of the two possible phenotypes if "A" is completely dominant over "a."

PROBLEM #2.

There are 100 students in a class. Ninety-six did well in the course whereas four blew it totally and received a grade of F. Sorry. In the highly unlikely event that these traits are genetic rather than environmental, if these traits involve dominant and recessive alleles, and if the four (4%) represent the frequency of the homozygous recessive condition, please calculate the following:

A. The frequency of the recessive allele.

B. The frequency of the dominant allele.

C. The frequency of heterozygous individuals.

PROBLEM #3.

The ability to taste PTC is due to a single dominate allele "T". You sampled 215 individuals in biology, and determined that 150 could detect the bitter taste of PTC and 65 could not. Calculate all of the potential frequencies.

The Hardy-Weinburg equation relies on the fact that there is no change in the population. The following must be met for the equation to be reliable.

1. Large population. The population must be large to minimize random sampling errors.

2. Random mating. There is no mating preference. For example an AA male does not prefer an aa female.

3. No mutation. The alleles must not change.

4. No migration. Exchange of genes between the population and another population must not occur.

5. No natural selection. Natural selection must not favor any particular individual.

Introduction [pic]

You are a bear-eating monster. There are two kinds of bears that you like to eat: happy bears and sad bears. You can tell the difference between them by the way they hold their hands. Happy bears hold their hands high in the air, and sad bears hold their hands down low. Happy bears taste sweet and are easy to catch. Sad bears taste bitter, are devious and hard to catch. Because of this you only eat happy bears. The happy trait in bears is caused by the expression of a recessive allele. The homozygous recessive condition is being happy. The sad trait is caused by a dominant allele. New bears are born every year (when they are hibernating in their den, the cardboard box), and the birth rate is one new bear for every old bear left from last year.  

Materials: Teddy Grahams, pencil, ruler

Procedure:

1. Obtain a population of 10 bears and record he number of happy and sad bears and the total population number. Using the equation for Hardy-Weinberg equilibrium, calculate the frequencies of both the dominant and recessive alleles and the genotypes that are represented in the population. Example: If 5 of the 10 bears are happy, then 10 out of 20 alleles would be happy alleles. Therefore the q2 number would be 0.5. You must then determine the q number by taking the square of 0.5.

2. Now, go hunting! Eat 3 happy bears. (If you do not have 3 happy bears then eat the difference in sad bears.)

3. Once you have consumed the bears obtain a new generation from your den (the box). You should only remove seven additional bears from the den for a total of 14 bears.

4. Repeat the procedures again. Be sure to record the number of each type of bear and the total population.

 Table:  

|Generations |P2 (sad) |2pq (sad) |q2 (happy) |P |q |

|1. Initial |  |  |  |  |  |

|2. |  |  |  |  |  |

|3. |  |  |  |  |  |

|4. |  |  |  |  |  |

 

Questions:

1. Describe what is happening to the genotype and allele frequencies in the population of Teddy Grahams?

 

2. What would you expect to happen if you continued the selection process for additional generations?

 

3. How would the frequencies change if you were to now select for the sad bears?

 

4. Why doesn’t the recessive allele disappear from the population? How is it protected?

5. A river dries up between two previously geographically separated species of wolves. How does this affect the Hardy-Weinberg method of finding allelic frequencies in a population and why?

6. A species of finch with longer beaks are able to reach nectar inside of flowers better than their relatives. How does this affect the Hardy-Weinberg equation and why?

7. The males of caribou in a forest find the females with a darker coat more attractive. The darker coat is a recessive allele. How does this affect the Hardy-Weinberg equation and why?

8. The food source for a population of cougars has diminished. The population was reduced from 75 to 30 in a few months. How does this affect the Hardy-Weinberg equation and why?

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