$ 9 Emphasis appendix provides the formula [Equation A.1] for calculating variances) Substitutions Left Substitutions Right Replicate 1 12 2 9 2 3 8 7 4 4 7 5 10 5 6 7 9 7 6 10 8 6 9 9 8 7 10 6 12 Average 7.6 7.7 Heading Heading Variance The variance is a statistic that measures the spread of a distribution around the mean. Evolution dep critically on variation, and so variance plays a central role in evolutionary biology. Variance is repre by the symbol o o (x x) Where is the sum of each (x-2) Where N is the sample size (in our case the sample size is 10 for 10 replicates) Adapted from Evolution 4e, Sinauer Associates, Inc. I Question 5 What were the mean and the variance for the number of substitutions for the left lineage? For the right lineage? Were the means of the left and right lineage approximately equal? You can fill out the tables b to help you calculate variance. Left lineage: (12+9+8+4+....) Mean for the left lineage = 7.6 Variance for left lineage = 5.3 Dinks Fina DOO F4 % MacBook Air F5 F6 & 434 F7 FB Question 5 What were the mean and the variance for the number of substitutions for the left lineage? For the right lineage? Were the means of the left and right lineage approximately equal? You can fill out the tables bel to help you calculate variance. Left lineage: (12+9+8+4+....) Mean for the left lineage=7.6 Variance for left lineage=5.3 Right lineage: (9+2+7+7+....) Mean for the right lineage=7.7 Variance for the right lineage=7.8 Yes, the means of the left and right lineage were approximately the same. Replicate Substitutions Left -average left Square the previous column Substitutions Right-average right Square the previous column 1 231 4 5 6 7 8 9 10 SUM Divide the SUM by the sample size (N=10) to find the variance for that lineage. 1 $ 000 F4 B 96 85 MacBook Air F5 F6 66 & 27 3 F7 D11 F8 8 V V |AaBbCcDdEx AaBbCcDd AaFC Da Emphasis Heading 1 Heading 2 Replicate 1 2 Substitutions Left Substitutions Right 7 5 3 5 3 7 11 4 4 2 5 2 9 6 4 1 7 3 8 8 5 10 9 3 2 10 5 6 Average 4.6 5.6 Left lineage: (7+3+7+4+....) Mean for the left lineage=4.6 Variance for left lineage=4.2 Right lineage: (5+5+11+2+....) Mean for the right lineage=5.6 Variance for the right lineage = 12.0 Replicate Substitutions Left -average left Square the Substitutions Square the previous column Right-average previous right column 1 23451 6 7 8 9 10 SUM Question 6 What are your results? How do they compare with the results obtained in Question 5? MacBook Air DO F4 F5 F6 V F7 411 FB Emphasis Heading 1 Heading 2 Set time to 15 (for 15 million years) and run the simulation ten times. For each replicate, record the n of substitutions. Calculate the mean and the variance. Replicate Substitutions Left Substitutions Right 1 12 12 2 13 15 3 9 13 4 12 17 5 14 11 6 14 17 7 11 7 8 13 14 9 16 13 10 10 12 Average 12.4 13.1 Left lineage: (12+13+9+12+....) Mean for the left lineage=12.4 Variance for left lineage=4.2 Right lineage: (12+15+13+17+....) Mean for the right lineage=13.1 Variance for the right lineage=8.7 Replicate Substitutions Left Square the Substitutions Square the -average left previous Right-average previous column right column 1 2 3 4 5 6 7 8 9 10 SUM Question 7 888 F4 MacBook Air 034 D F5 F6 F7 FB Ev Ev Ev 2 AaBbCcDdEe AaBbCcDd ABCDE >> Emphasis Heading 1 Heading 2 Styles Dictate Pane Graph the mean number of substitutions (use open circles for the left and closed circles for the right lineage data points) against time (in million of years). Question 8 What does your graph look like? Based on your graph, provide the average substitution rate per nucleotide per million years. Remember there are 100 nucleotides in the sample. Question 9 Based on your estimate of the substitution rate, how many substitutions would you predict will accumulate between the ancestral and each descendant lineage in 50 million years? Test your prediction by running 10 replicates with the time set at 50 million years. For each replicate, record the number of nucleotide changes that occurred along the left and the right lineages. Compute the mean for each. I Replicate Substitutions Left Substitutions Right 1 32 44 2 50 39 3 29 39 4 36 41 5 42 38 6 34 37 7 34 50 8 46 48 9 41 48 10 39 48 Average 38.3 43.2 $ $ 4 Left lineage: (32+50+29+36+....) Mean for the left lineage = 28.3 8880 F4 R % 85 F5 F G 6 MacBook Air F6 Y 27 & H F7 U Focus DII FB 44 F9 k 8 9 K C 0