HHMI Evolution in Action Statistics

N AME : P ERIOD : INTRODUCTION In 1973, Princeton University evolutionary biologists Peter and Rosemary Grant began studying the finches of the Galápagos archipelago, a group of islands about 600 miles off the coast of Ecuador. They collected thousands of measurements every year to track changes in the physical characteristics of finch populations over time. One of their major goals was to collect enough data to identify associations between environmental and evolutionary changes in finch populations. For their study, the Grants focused on the medium ground finch ( Geospiza fortis ), a seed-eating species of finch on the island of Daphne Major. Every year, the Grants measured physical characteristics like wing length, body mass, tarsus length (the section of leg between the ankle and knee), and beak depth for hundreds of individual medium ground finches. Small changes in these structures can be important for survival in different environments. In addition, these traits tend to vary widely within populations. In early 1977, a drought began on Daphne Major. The drought lasted for 18 months and caused the type and abundance of food available to the finches to change rapidly. Medium ground finches prefer to eat the small, soft seeds of the bushy plant chamaesyce ( Chamaesyce amplexicaulis ), but the supply of chamaesyce seeds was extremely limited as a result of the drought. As the drought progressed and the hungry finches quickly ate the small, soft chamaesyce seeds, one of the only remaining food sources for the medium ground finch became the seeds of a plant called caltrop ( Tribulus cistoides ). Caltrop seeds are much larger and harder than those of the chamaesyce and are covered with pointed spines. Fewer than 20% of the 1,200 medium ground finches on the island survived the drought of 1977. The Grants were interested in determining whether there were any differences between the finches that survived the drought and the finches that did not—and in particular, whether any physical characteristics were key to survival. To answer this question, they compared the average value of different characteristics in the finches that survived the drought to the average values of the same characteristics in those that did not survive. They then applied statistical methods to determine whether the differences they found between the two groups were likely to be real or merely occurred by chance. You now have the opportunity to statistically analyze data collected by the Grants. MATERIALS ● Scientific calculator if not using a computer with a spreadsheet program like Excel or Google spreadsheet ● Graphing paper if not using a computer ● Colored pencils for graphing if not using a computer ● Ruler for graphing if not using a computer PROCEDURE Table 1 (on the next page) shows body measurements from 100 medium ground finches living on Daphne Major in 1976. Fifty of those birds did not survive the 1977 drought (nonsurvivors) and 50 did (survivors). These data are also provided in an Excel spreadsheet; use either the data in Table 1 or in the Excel spreadsheet to construct several graphs as outlined in the following pages . The Origin of Species: Beak of the Finch Revised December 2017 www.BioInteractive.org Page 1 of 6

Evolution in Action: Statistical Analysis Table 1. Morphological measurements (body mass, wing length, tarsus length, and beak depth) taken from a subsample of 100 medium ground finches ( Geospiza fortis ) before the drought began on the island of Daphne Major in 1977. Half of the birds in the sample ( n = 50) did not survive the drought (Nonsurvivors) and half ( n = 50) did (Survivors). Nonsurvivors Survivors Band # Body Mass (g) Wing Length (mm) Tarsus Length (mm) Beak Depth (mm) Band # Body Mass (g) Wing Length (mm) Tarsus Length (mm) Beak Depth (mm) 9 14.50 67.00 18.00 8.30 309 18.00 71.00 20.20 9.80 12 13.50 66.00 18.30 7.50 560 14.00 67.00 19.10 8.50 276 16.44 64.19 18.47 8.00 572 18.00 70.00 20.20 10.30 278 18.54 67.19 19.27 10.60 618 17.50 68.00 20.70 9.90 283 17.44 70.19 19.27 11.20 623 15.00 67.00 19.00 8.80 288 16.34 71.19 20.27 9.10 673 18.00 72.00 19.00 10.10 293 15.74 67.19 17.57 9.50 685 14.50 67.00 18.00 8.20 294 16.84 68.19 18.17 10.50 891 15.00 65.00 18.60 8.00 298 15.54 68.19 18.57 8.40 931 14.50 65.00 19.60 8.90 307 17.50 70.00 20.00 8.60 943 15.00 66.00 19.30 9.10 311 15.00 67.00 18.40 9.20 1452 16.24 68.19 18.47 9.80 315 17.00 70.00 19.90 8.80 1477 17.34 70.19 20.57 10.10 321 15.00 66.00 19.10 8.50 1528 17.09 68.19 19.32 8.55 342 15.00 66.00 18.40 8.00 1587 17.64 72.19 20.57 9.30 343 15.00 67.00 18.00 9.70 1592 17.24 71.19 18.87 10.00 345 16.50 67.00 20.10 8.40 1599 18.04 72.19 19.77 10.70 346 13.00 64.00 17.60 7.90 1635 15.84 68.19 20.07 9.10 347 16.00 71.00 19.60 9.30 1643 15.24 65.19 20.17 8.80 352 13.50 65.00 18.40 7.70 1850 16.14 66.19 19.07 10.40 356 16.00 69.00 18.50 8.50 1861 20.19 72.69 19.32 10.70 413 14.00 65.00 17.90 8.20 1884 16.24 67.69 17.97 9.15 420 15.00 65.00 19.80 9.70 1919 21.24 72.19 19.47 11.20 422 19.00 70.00 19.40 10.30 2206 17.44 72.19 20.07 10.50 428 17.00 72.00 20.10 10.20 2211 16.94 70.19 19.27 9.70 452 15.00 68.00 20.00 8.90 2226 14.74 65.19 18.27 8.90 456 16.50 68.90 18.50 9.60 2887 17.34 69.19 19.07 10.10 457 14.75 64.20 17.05 7.85 8136 15.54 68.19 18.07 8.90 458 16.00 73.00 19.60 9.60 616 19.00 70.00 20.00 9.60 461 17.00 68.00 20.00 9.80 1248 15.40 66.00 19.50 8.50 462 15.00 68.00 19.60 8.80 2210 16.34 68.01 18.96 10.08 468 16.00 68.00 19.00 9.00 2242 15.41 72.94 18.26 9.45 503 14.50 65.00 18.90 9.10 2939 15.37 67.95 19.41 8.31 506 17.00 69.00 18.60 9.20 354 17.50 67.00 20.30 9.80 507 16.00 70.00 19.00 8.80 678 16.50 71.00 18.20 9.70 509 17.00 70.00 20.00 9.20 1418 17.94 71.01 18.76 10.38 511 14.50 66.00 19.10 8.80 1426 21.22 71.45 21.01 10.61 512 15.50 67.00 20.30 9.40 1527 17.04 68.01 18.46 8.38 519 14.50 67.00 19.10 8.30 1659 17.74 71.01 19.16 10.78 522 15.50 66.00 18.20 8.40 2244 18.87 71.95 20.16 11.01 561 16.50 70.00 20.00 10.20 2249 18.44 74.01 20.06 10.68 564 14.00 66.00 18.80 9.30 2940 15.14 70.01 17.86 8.78 605 15.50 71.00 19.90 10.20 3642 17.84 71.01 19.16 10.28 609 16.50 69.00 19.60 10.50 8191 19.63 70.41 20.81 10.86 610 14.00 66.00 18.80 9.00 1019 20.82 70.45 19.86 11.21 611 16.00 66.00 18.90 9.80 1372 16.64 69.01 18.16 9.48 619 14.00 65.00 18.00 9.30 1797 16.67 69.45 19.21 9.31 621 15.50 67.00 18.50 7.60 2378 18.07 70.95 21.06 9.86 674 18.50 70.00 20.50 10.50 8190 15.60 69.47 18.36 9.28 676 17.00 72.00 20.00 9.70 316 17.55 67.50 19.55 9.85 687 14.00 66.00 18.90 8.60 710 15.00 69.00 19.00 10.00 Mean 15.71 67.79 19.04 9.11 Mean 16.99 69.30 19.35 9.67 Var (s 2 ) 1.842 5.181 0.701 0.775 Var (s 2 ) 3.087 5.448 0.735 0.709 The Origin of Species: Beak of the Finch Revised December 2017 www.BioInteractive.org Page 2 of 6

Evolution in Action: Statistical Analysis PART B: Graphing the Data 5. On a separate sheet of graph paper or on your computer, construct four bar graphs that compare the means of nonsurvivors and survivors for each physical characteristic (body mass, wing length, tarsus length, and beak depth). Label both axes of each graph and use error bars to show the 95% CI (+ or - two SEM ). An example of a well-constructed bar graph is shown below (Figure 1). Mean Dorsal Fin Height Among Male and Female Orca Whales 6. Once you complete your four bar graphs, describe in the space below any differences between nonsurvivors and survivors you observe in each graph. Be sure to use the error bars to assess whether the differences are significant or not. In each graph, all four measurements from the surviving birds are greater than the measurements for the non surviving birds. Even though there is overlap between the two groups of birds' 95% confidence ranges for tarsus length, for body mass, wing length, and beak depth, the error bars show that the 95% confidence intervals for the survivors and nonsurvivors do not overlap, indicating that the difference between the two groups may be significant. PART C: Calculating t -Test Statistics In Figure 1, the means are different and the error bars do not overlap, suggesting that there might be a difference between the two mean fin heights. But a statistical test is required to confirm that the difference is significant. The appropriate statistical test for comparing two means is the Student’s t -test for independent samples (the t -test). The t -test can assess whether any observed differences between the means of two samples (i.e., nonsurvivors and survivors) occurred simply by chance, by determining the probability (p) of obtaining a more different result if the null hypothesis is correct. You will calculate the t statistic called “observed t ” ( t obs ) and then compare it to the critical t statistic ( t crit ). This critical t -value is a cutoff value that determines whether you can reject the null hypothesis that the mean of the population from which the first sample came is equal to the mean of population from which the second sample came, or = . If your observed t -value ( t obs ) is less than the critical value ( t crit ), then you cannot reject the null 𝑥 1 𝑥 2 hypothesis . If the calculated statistic is larger than the critical value, then we have enough evidence to reject The Origin of Species: Beak of the Finch Revised December 2017 www.BioInteractive.org Page 4 of 6

Evolution in Action: Statistical Analysis the null hypothesis and support the alternative hypothesis that the means are significantly different , or ≠ 𝑥 1 𝑥 2 . If t obs is greater than t crit we can conclude that the means ARE significantly different. The t crit for your sample size of 50 is 1.98. This is the t -value that could occur 5% of the time for a sample size of 50 if the null hypothesis is true. 7. Calculate t obs to compare the mean values of each physical characteristic between survivors and nonsurvivors. a. Use the following online t-test calculator to calculate t obs : https://www.socscistatistics.com/tests/studentttest/default.aspx Cut and paste the two sets of data you want to compare. Select .05 significance level. Select 2 tails. Remember to record the absolute value of the t value calculated. Mean body mass: t obs = 4.08 Mean wing length: t obs = 3.27 Mean beak depth: t obs = 3.27 Mean tarsus length: t obs = 1.82 b. How do your t obs for each pair of measurements compare to the critical t -value ( t crit ) of 1.98? Answer with GREATER or LESS. Mean body mass: Greater Mean wing length: Greater Mean beak depth: Greater Mean tarsus length: The Origin of Species: Beak of the Finch Revised December 2017 www.BioInteractive.org Page 5 of 6