lab 5

Hardy Weinberg Equilibrium Punnett squares (like those in our last lab) are used to make statistical predictions about the outcome of reproduction in a specific pair of individuals. What if we aren’t interested in just one pair of individuals? What if we are interested in making predictions about reproduction in an entire population of individuals. As long as we make some assumptions, for example, that the members of the population don’t choose sexual partners based on a knowledge of their genotype (this is called random mating), we can use the same statistical principles as we did for Punnett squares. This is called population genetics . Population Genetics: Lets Practice Probability in Punnett Squares In individuals, we know that everyone has two alleles and that they each have a 50% chance of being passed into the fertilized egg (zygote). The probability that the offspring will have one allele from one parent is 50% AND another allele from the other parent is 50%. 0.50 X 0.50 =0.25 That’s why each square of the punnett square corresponds to a 25% chance of a particular genotype. See this demonstrated visually in the Punnett square below for two heterozygous parents. Parent #1 (Aa) A (0.50 probability) a (0.50 probability) Parent #2 (Aa) A (0.50 probability) AA (0.50*0.50=0.25 probability) Aa (0.50*0.50=0.25 probability) a (0.50 probability) Aa (0.50*0.50=0.25 probability) aa (0.50*0.50=0.25 probability)

1. What is the probability that these two heterozygous parents will have a homozygous dominant offspring (hint: review last week’s lab as a reminder if needed). 2. What is the probability that these two heterozygous parents will have a heterozygous offspring (hint: remember to add up the probabilities from any square that represents a heterozygous offspring ). Allele Frequencies We can use the same principle to make predictions about populations, except there is one problem. In individuals, we know each allele has a 50% chance of being passed on. In populations, the probability that an allele is passed on is based on how frequent that allele is in the population to start with. So instead of using 0.50 to build our square, we have to use the frequency of the allele. Let’s imagine we have two alleles, “A” and “a” just like above. The allele frequency is the number of one type of allele divided by the total number of alleles in the population. freq (A) = Number of “A” alleles freq (a) = Number of “a” alleles Total Number of Alleles (A+a) Total Number of Alleles (A+a) Because there are only two alleles, the two frequencies must add to 1. freq (A) + freq (a) = 1

(p*q) (q*q= q 2 ) Each square corresponds to a prediction about the frequency of a genotype in the population. Remember that frequencies must add to 1, which leads to an important mathematical model known as the Hardy-Weinberg equation . p 2 + 2pq + q 2 =1 Each portion of the equation represents a genotype frequency: p 2 = genotype frequency of homozygous dominant 2pq = genotype frequency of heterozygous q 2 = genotype frequency of homozygous recessive Let’s practice: 5. What two letters represent the frequency of the dominant and recessive alleles in the population? Freq of the dominant allele = Freq of the recessive allele = 6. If the frequency of the dominant allele (p) is 0.70, what is the frequency of the recessive allele (q)? (Hint: remember that they must add to 1.) 7. What portion of the Hardy-Weinberg equation represents the homozygous dominant genotype frequency ?

8. If the frequency of the dominant allele (p) is 0.70, what is the frequency of the homozygous dominant genotype ? (Hint: Look at the Punnett square, the homozygous dominant square is p 2 . You know what “p” is, you just have to plug it in.) The Hardy Weinberg Law of Equilibrium The Hardy-Weinberg equation is an important way to make predictions about animal populations based on statistical probability. But you might notice that it never changes….if the allele frequency is 0.70, it will always return the same predictions for the genotype frequencies. In fact, the H-W equation describes only animal populations in a state called equilibrium , which means that their allele and genotype frequencies are staying the same year after year, generation after generation. In biology, evolution is defined as genetic change in a population through time. If a population is in Hardy-Weinberg equilibrium, then it is NOT evolving. That means we can use the H-W equation to identify evolution in species. If we compare the genotype frequencies predicted by the Hardy-Weinberg equation to the observed (actual) genotype frequencies in the population, we can see if the population is changing. If the observed frequencies are the same as the predicted frequencies then the population is in equilibrium (NOT evolving). If the observed frequencies are different from the predicted frequencies then the population is evolving . The How-To Guide below will guide you through the process of calculating observed allele and genotype frequencies in a population and compare them to H-W predictions.

Step 3: Calculate the expected genotype frequency using the allele frequencies above and the Hardy Weinberg mathematical formula p 2 + 2pq + q 2 = 1 . (.3) 2 + 2pq + q 2 = 1 ____ .09 _____ = p 2 P 2 + 2(.3)(.7) + q 2 = 1 ____ .42 _______ = 2pq P 2 + 2pq + (.7) 2 = 1 ____ .49 _______ = q 2 The combined frequencies should add up to one. _ 1.0 ____ Step 4: Calculate the observed genotype frequency within the population. Number of TT genotypes / Number of people = __ 15 ___ / __ 200 __ = __ .075 ___ This represents P 2 . Number of Tt genotypes / Number of people = _ 90 ___ / __ 200 __ = __ .450 ___ This represents 2pq. Number of tt genotypes / Number of people = _ 95 __ / __ 200 __ = __ .475 ____ This represents q 2 . The combined frequencies should add up to one. __ 1.0 __ Step 5: Compare the expected genotype frequency to the observed genotype frequency . If the frequencies are the same when comparing each, then the population is in equilibrium. If they are different, then the population is evolving. Does each of the values shown look similar to each other when comparing the p 2 , pq, and q 2 values? Are they different from each other? Answer: These values are different from one another. This population is evolving, not in equilibrium.

Exercise 1: Part A Fill in the chart to determine the number of alleles for the people on a small island. The trait being evaluated is Darwin’s tubercle, a dominant trait which is expressed as a small point on the ear cartilage. Phenotype Genotype Number of people #T alleles #t alleles Total Alleles Darwin’s Tubercle TT 250 Darwin’s Tubercle Tt 400 No tubercle tt 350 Total People 1,000 Calculate the observed allele frequency within the population. Round all calculations to the nearest hundredth (e.g. two decimal places. 3.141 will round to 3.14) Number of T alleles / Total alleles in population / = This represents p. Number of t alleles / Total alleles in population / = This represents q. The combined frequencies should add up to one . Calculate the expected genotype frequency using the allele frequencies above and the Hardy Weinberg mathematical formula p 2 + 2pq + q 2 = 1.

Compare the expected genotype frequency to the observed genotype frequency. Is the population in equilibrium or does it appear to be evolving? Exercise 1: Part B Fill in the chart to determine the number of alleles present in the people on the same small island. Dimples are inherited as a dominant trait. Phenotype Genotype Number of people #D alleles #d alleles Total Alleles Dimples DD 100 Dimples Dd 430 No dimples dd 470 Total People 1,000 Calculate the observed allele frequency within the population.Round all calculations to the nearest hundredth (e.g. two decimal places. 3.141 will round to 3.14) Number of D alleles / Total alleles in population / = This represents p.

Number of d alleles / Total alleles in population / = This represents q. The combined frequencies should add up to one . Calculate the expected genotype frequency using the allele frequencies above and the Hardy Weinberg mathematical formula p 2 + 2pq + q 2 = 1. = p 2 = 2pq = q 2 The combined frequencies should add up to one. Calculate the observed genotype frequency within the population. Number of DD genotypes / Number of people = / = This represents p 2 . Number of Dd genotypes / Number of people = / = This represents 2pq

Year Number of students with EE genotype Number of students with Ee genotype Number of students with ee genotype Total Number of students 2005 250 250 500 1000 2010 300 300 400 1000 2015 300 400 300 1000 The Forces of Evolution There are no exercises for the table below, but you are responsible for the terms, definitions, and their significance for Exam 1. Evolution is defined as a change in allele (and therefore gene) frequencies in a population over time. In our last lab, we learned how to use the Hardy-Weinburg equation to identify when a population was evolving. In reality, it is very rare to find animal populations in equilibrium. That is because there are a number of natural processes that can disrupt the equilibrium by changing the allele frequencies. We call these processes forces, or mechanisms, of evolution. Each of these following four forces is responsible for changing allele frequencies over generations. Evolutionary Force Types Impact on population Mutation Only mechanism that creates new genetic material within populations, changes alleles present within population

Gene Flow Introduction of alleles from one population into another, increases the diversity within a population Genetic Drift Population bottleneck, Founder Effect Random changes in genetic frequencies A population bottleneck can limit the diversity of genetic material that is passed down. The founder effect , due to limited diversity of the parental gene pool, creates a new gene pool with even less diversity. Natural Selection Sexual selection Genes for preferential characteristics increase, changing the allele frequencies within the population. Surviving members have higher rates of reproductive fitness. Sexual selection usually impacts sexual dimorphism. Concept Review 1. Sickle cell anemia is caused by one base in the DNA strand being entered incorrectly. Which force of evolution created sickle cell anemia? 2. Can we predict the outcome of genetic drift on a future population? Why or why not?