4) How many alleles does each individual carry? 5) How many total alleles do we need to create this population?

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1 SC135 Introductory Biology Hardy-Weinberg and Natural Selection with M & M s Lab Objectives: Understand the concepts of allele frequency, genotype frequency and phenotype frequency in a population. Understand the concept of a Hardy-Weinberg population. Understand the principle of Natural Selection. Part 1 Hardy-Weinberg Populations 1) Separate out the brown and red M & M s from the bag (you could use any two colors I m just choosing brown and red). 2) Each M&M represents one allele for a color gene in a population. Let s say that there are 2 allele types red and brown! We can also make the assumption that brown is dominant to red. 3) We will create a population of 50 individuals. 13 individuals are homozygous brown, 25 individuals are heterozygous brown and 12 individuals are red. 4) How many alleles does each individual carry? 5) How many total alleles do we need to create this population? 6) Lay out pairs of alleles on a table which represent each individual in the population. 7) How many brown alleles are there in the population altogether? 8) What proportion of total alleles is this? (divide the total number of brown alleles by the total number of alleles). This number is p in the Hardy-Weinberg equation. 9) p =. This is the allele frequency of brown alleles in your population. 10) How many red alleles are there in the population altogether? 11) What proportion of total alleles is this? (divide the total number of red alleles by the total number of alleles). This number is q in the Hardy-Weinberg equation. 12) q =. This is the allele frequency of red alleles in your population. 13) The proportion of brown alleles (p) and the proportion of red alleles (q) should equal 1. Check to see that your values of p + q = 1. 14) In a Hardy-Weinberg population, random mating is assumed. This means that what an individual looks like or behaves like has no bearing on the chances that their alleles are

2 represented in the next generation. In essence then, the individuals do not exist! A population is literally, a collection of alleles. To represent this, take all the alleles from the individuals in front of you and put them in a paper bag. This bag is your population! It is all the alleles that exist in the population regardless of how they are arranged in individuals. 15) Without looking, draw an allele out of the bag. What color did you draw? 16) Put the allele back and shake the bag. Draw another allele. What color did you draw? 17) Repeat the last two steps a number of times. Do you have a feel for what the chances of drawing a particular color allele is? What is the probability of drawing a red allele? 18) What is the probability of drawing a brown allele? 19) Notice that these probabilities are the same as p and q! Allele frequencies in a population are also the probability of the allele being drawn from the population! 20) Drawing 2 alleles at random is equivalent to random mating in the population. Alleles combine at random in the population to make the next population. Try this by drawing 2 M & M s from the bag. This allele pair represents an individual in the next generation! 21) Hardy-Weinberg says that you can predict what the chances of having any one particular genotype being drawn from the allele pool. The chances of drawing a homozygous brown individual is the probability of drawing a brown allele (p) and the probability of drawing a 2 nd brown allele (p). Mathematically, the probability of drawing 2 brown alleles is (p x p) or (p 2 ). This value also represents the genotype frequency of homozygous brown individuals in the next generation! 22) For your example: p 2 =. 23) Likewise: the chances of drawing a homozygous red individual is the probability of drawing a red allele (q) and the probability of drawing a 2 nd red allele (q). Mathematically, the probability of drawing 2 red alleles is (q x q) or (q 2 ). This value also represents the genotype frequency of homozygous red individuals in the next generation! 24) For your example: q 2 =. 25) Now let s consider the probability of drawing a heterozygote. Here there are 2 possibilities. Either you draw a brown allele first (p) and then a red allele (q) or you draw a red allele first (q) and then a brown allele (p). Mathematically, the probability of drawing a heterozygote is (p x q) and (q x p) or (2 x p x q). This value also represents the genotype frequency of heterozygous individuals in the next generation! 26) For your example: 2pq =.

3 27) The probability of pulling any pair of alleles should equal 1 (or 100%). This means that p 2 + 2pq + q 2 = 1. Check to see if your values add up to 1. 28) What this means is that for any population that you know the allele frequencies for, you know what proportion of the population is homozygous dominant, heterozygous, and homozygous recessive! Of course, this is provided that the population in a Hardy- Weinberg population. 29) There are 5 conditions under which populations conform to Hardy-Weinberg. What are they? (Hint: look at your lecture notes.) a. b. c. d. e. Part 2 Natural Selection 30) Let s see what happens if your population experiences natural selection. What is the definition of natural selection? 31) Let s assume that the red individuals (phenotypes) are easy prey and that the brown phenotype blends in with the environment so is protected. In any one generation, 50% of the red individuals fall prey to the predator (in other words they die and cannot reproduce!) 32) To model what happens in the first generation, you want to remove ½ of the individuals who are red. a. How many individuals are killed? b. How many alleles must be removed from the population? c. What alleles exactly are removed? [You can be the predator and eat those individuals!!] 33) Now we have to replace those individuals so our population is back up to 50. Let s say that the remaining individuals mate randomly. Select two alleles for the first individual

4 from the bag. Then select two more alleles for the next individual from the bag. (You should have one of the following crosses: BB x BB, BB x Bb, Bb x Bb, BB x bb, Bb x bb, bb x bb). 34) Write the cross that you have. 35) Each parent passes one of their two alleles on to their child. Decide which allele in each parent will be heads in a coin toss and which will be tails. Flip your coin once for each parent. What color allele does mom pass on? 36) What color allele does dad pass on? 37) Those two alleles represent the genotype for the new child. Write the genotype of the child. 38) Place the parent s alleles (all 4) and 2 more M&M s for the child s alleles in your bag. This represents adding the child to the population. 39) Repeat the mating game for 5 more kids. This should replace the 6 individuals killed by the predator!! Write the genotypes that you added to the population. 40) Your population is now at the next time period (or generation). You should have a total of 50 individuals. How many of each genotype do you have in your population? (this should be the original number of BB and Bb, ½ the number of original bb plus whatever the kids were). 41) How many alleles are in your population? 42) Count the number of each color allele in your bag. 43) What is your new value of p (remember this is a proportion)? 44) What is your new value of q? 45) What proportion of BB is there in your population? (this should be the number of BB individuals divided by 50 (the total number of individuals)). 46) What proportion of Bb is there in your population? 47) What proportion of bb is there in your population? 48) Does the proportion of BB = p 2? 49) Does the proportion of Bb = 2pq? 50) Does the proportion of bb = q 2?

5 51) If the proportions are not equal to Hardy-Weinberg, the population is evolving! In this case it should be evolving due to natural selection. 52) Repeat the experiment with your new population. Start by having ½ of the red individuals die. 53) For each generation, keep track of the numbers of each genotype in the table below. 54) What kind of selection have you just demonstrated? (hint its one of the 3 types you studied in Chapter 18.) Generation Homozygous brown Heterozygous brown Homozygous red (bb) (BB) (Bb)