BIO D2 Transmission Gen & Probability

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305

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Dec 6, 2023

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1 Discussion 2 Bio 305 – Genetics Winter 2022 Transmission genetics and probability The goal of today's activity is to improve your familiarity and confidence with basic probability and chi- squared tests. These skills are used extensively for genetic analysis. We will be working with the following phenotypes of students: Handedness and Birth Month Part 1: Gather Data In the tables on the white board, place a hatch mark in each table indicating your dominant writing hand, and the quarter of the year you were born in. Record the composite date from the entire class in the middle row of the tables below. (Q1= Jan-March, Q2=Apr-June, etc). Left Handed Right Handed Ambi- dextrous Total Frequency Part 2 - Calculating Probabilities of two Events The probability of a single event happening expresses the likelihood of the desired outcome or group of outcomes out of the total possible outcomes. That probability may be predicted by a null hypothesis or estimated from real data using frequencies. When considering multiple events, such as date of birth and handedness of individuals, the outcome of one event may influence or be determined by the other. If two desired events are mutually exclusive (meaning on or the other can occur but not both), we use the sum rule to determine their collective probability. When two desired outcomes are independent, we use the product rule to determine their collective probability. In your group Calculate the frequency of students in each group for the tables above (handedness or quarter of birth) and write it down in the bottom row of the table above. For example, p(Ambidextrous) = 2/20 = 0.1 or p(Q1) = 8/20 = 0.4. Answer the following questions using the frequencies calculated AND assuming that handedness is independent of birth quarter. 1. Given the above frequencies, what is the probability the instructor will randomly call on a right handed student born in the second quarter of the year? What rule(s) are you using? 2. What is the probability the instructor will call on a student born in the first half of the year? What rule(s) are you using? 3. What is the probability the instructor will call on a student (any handedness) born in the first quarter of the year or left handed student born in the last quarter of the year ? What rule(s) are you using? Q1 Q2 Q3 Q4 Total Frequency
2 Part 3 – Chi-squared tests Chi-squared tests are used to evaluate whether data are consistent with a null hypothesis. The null hypothesis proposes that there is no relationship between two events, no association among groups. You will use the data collected today to evaluate null hypotheses about enrollment in this discussion section. In each case, the null model proposes that the data are random. Assuming random distribution, you would predict an equal number of people born in each quarter of the year in class, and a distribution of handedness that mirrors that of the population as a whole, i.e. ~89% righties, ~10% lefties and 1% ambidextrous). You can then use this prediction to calculate the deviation of the real data from that of a null distribution, the chi-square distribution, using the formula: where O = observed number, E = expected number, and 6 represents the summation of all of the samples in all categories. This sum is then compared to the list of critical values of the chi-square distribution (see appendix) to determine whether the null model can be rejected. The critical value depends on the degrees of freedom, which is equal to the number of categories minus 1 (df=c-1). In your group Use the class data and chi-squared tests to evaluate one of the following 2 null hypothesis: Null hypothesis #1. “The people in this discussion are equally likely to be born in any quarter of the year.” Null hypothesis #2: “There is no difference in the distribution of handedness between this discussion section and the general US population” (A) calculate the chi-squared value (B) How many degrees of freedom are there for the birth month data? (remember df =c - 1) (C) use the table below to determine the approximate p-value for this comparison. (D) Given the p value you determined in (C) should you reject or fail to reject the null hypothesis? When you finish with the test(s), discuss the following question: Regardless of the outcomes of your tests, discuss possible reasons why the class data could cause you to reject the null hypothesis used in each case?
3 Part 4: Meiosis review, Independent assortment and the probability of inheritance: 1. What stage of the cell cycle, and in what type of cell, does the below image depict? A. Mitosis in a haploid cell B. Mitosis in a diploid cell C. Meiosis in a haploid cell D. Meiosis in a diploid cell E. Not enough information to decide 2. What stage of the cell cycle, and in what type of cell, does the image to the left depict? A. Meiosis II, haploid B. Meiosis II, diploid C. Meiosis I, haploid D. Meiosis I, diploid E. C and D only 3. Consider a single germ cell of a heterozygote with the genotype A/a; B/b undergoing meiosis. Which of the following are possible genotypes the set of four gametes resulting from this single cell (assuming no nondisjunction, no crossing over, and the A and B genes are on separate chromosomes)? A. A, a, B, b B. Ab, Ab, aB, aB C. AB, Ab, aB, ab D. Aa, AA, BB, bb E. Aa, Aa, Bb, Bb 4. How many genotypes will result from selfing a pentahybrid (penta=5 genes)? A. 243 B. 64 C. 32 D. 60 E. 212 5. If the genotype AaBbCcDdEeFf was selfed, what is the probability of getting the following offspring genotype: AABbCCDdEEff? A. 1/8 B. 1/16 C. 1/1024 D. 1/256 E. 1/512
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4 6. You have collected tardigrades from nature and sorted them as follows into growth chambers: Growth chamber 1 500 blue & 500 splotchy Growth chamber 2 200 pink & 800 spotchy Growth chamber 3 800 tan & 200 splotchy If you blindly select one tardigrade from each jar, what is the probability that you remove one that has coloration (blue, pink, tan) and two that are splotchy? Note that they are not mating and producing progeny, and tardigrades are either colored or splotchy, but not both. A. 0.50 B. 0.12 C. 0.32 D. 0.42 E. 0.20 7. How would you state the null hypothesis for allele assortment given Mendel’s laws? Appendix – Basic Probability rules and Chi-Squared Table The multiplication rule for AND questions: If you want to know the probability of two independent events BOTH happening, then multiply the individual probabilities together. Example: The probability of drawing a heart from a well-shuffled deck is ¼. The probability of drawing a 10 is 1/13. The probability of drawing a 10 AND drawing a heart (i.e. the 10 of hearts) is ¼ * 1/13 = 1/52. *Note that suit and value are independent events. The addition rule for OR questions: If you want to know the probability of ONE OR THE OTHER of two mutually exclusive events happening, then add the individual probabilities together. Example 1: The probability of drawing a heart from a well-shuffled deck is ¼. The probability of drawing a spade is 1/4. The probability of drawing a heart or a spade ¼ + ¼ = ½. Example 2: The probability of drawing a heart from a well-shuffled deck is 1/4. The probability of drawing a jack is 1/13. The probability of drawing a heart OR a jack is ¼ + 1/13 – (1/4 x 1/13) = 16/52 = 4/13. *Note that while suit and value ARE NOT mutually exclusive (e.g. a card can be a club, and be some value), but that the possible phenotypes within each trait ARE mutually exclusive events, ie when considering suits, a card may not be both a heart and a club.
5 Table 1. Critical Chi Square Values P Values Degrees 0.99 0.90 0.50 0.10 0.05 0.01 0.001 of Freedom 1 - 0.02 0.46 2.71 3.84 6.64 10.83 2 0.02 0.21 1.39 4.61 5.99 9.21 13.82 3 0.11 0.58 2.37 6.25 7.82 11.35 16.27 4 0.30 1.06 3.36 7.78 9.49 13.28 18.47 P values for additional degrees of freedom can be found in your textbook on page 51.

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