The Origin Of Species The Making Of The Fittest: The .

fFinchtheFittest:TheBeakof theNaturalSelectionandAdaptationSTUDENT HANDOUTNaturalSelectionandAdaptationEVOLUTION IN ACTION: STATISTICAL ANALYSISINTRODUCTIONIn 1973, Princeton University evolutionary biologists Peter and Rosemary Grant began studying thefinches of the Galápagos archipelago, a group of islands about 600 miles off the coast of Ecuador. Theycollected thousands of measurements every year to track changes in the physical characteristics of finchpopulations over time. One of their major goals was to collect enough data to identify associationsbetween environmental and evolutionary changes in finch populations.For their study, the Grants focused on the medium ground finch (Geospiza fortis), a seed-eating speciesof finch on the island of Daphne Major. Every year the Grants measured physical characteristics likewing length, body mass, tarsus length (the section of leg between the ankle and knee), and beak size forhundreds of individual medium ground finches. Small changes in these structures can be important forsurvival 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 typeand abundance of food available to the finches to change rapidly. Medium ground finches prefer to eatthe small, soft seeds of the bushy plant chamaesyce (Chamaesyce amplexicaulis), but the supply ofchamaesyce seeds was extremely limited as a result of the drought. As the drought progressed and thehungry finches quickly ate the small, soft chamaesyce seeds, one of the only remaining food sources forthe medium ground finch became the seeds of a plant called caltrop (Tribulus cistoides). Caltrop seedsare much larger and harder than those of the chamaesyce and are covered with pointy spines. Morethan 80% of the 1,200 medium ground finches on the island did not survive the drought of 1977.The Grants were interested in determining whether there were any differences between the finchesthat survived the drought and the finches that did not—and in particular, whether any physicalcharacteristics were key to survival. To answer this question they compared the average value ofdifferent characteristics in the finches that survived the drought to the average values of the samecharacteristics in those that did not survive. They then applied statistical methods to determine whetherthe 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.Table 1 (on the next page) shows body measurements from 100 medium ground finches living onDaphne 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 inthe Excel spreadsheet to construct several graphs as outlined in the following pages.www.BioInteractive.orgUpdated September 2015Page 1 of 7

fFinchtheFittest:TheBeakof dAdaptationSTUDENT HANDOUTTable 1. Morphological measurements (wing length, body mass, tarsus length, and beak size) takenfrom a subsample of 100 medium ground finches (Geospiza fortis) before the drought began on theisland 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 ted September 2015Page 2 of 7

fFinchtheFittest:TheBeakof dAdaptationSTUDENT HANDOUTPart A: Calculating Descriptive StatisticsAs you complete steps 1-3 below, enter your calculations in Table 2 for the mean, standard deviation,standard error of the mean, and/or 95% confidence interval as assigned by your instructor.Table 2. Descriptive statistics for morphological measurements taken from 100 medium groundfinches (Geospiza fortis). The data are presented in two groups: birds that did not survive the 1977 drought(Nonsurvivors) and birds that survived the drought (Survivors).DescriptiveStatisticsMeanVariance (s2)StandardDeviationStandardError of vivorsWingTarsusLength 7753.087SurvivorsWingTarsusLength Length(mm)(mm)5.4480.735BeakDepth(mm)0.7091. For the data in Table 1, calculate the mean for each physical characteristic in the nonsurvivor andsurvivor group.2. Calculate the standard deviation for each set of data. The standard deviation measures the meandifference between each individual measurement and the mean of the entire population. Standarddeviation is a way to quantify how spread out a set of measurements is compared to the mean.(Note: To calculate the standard deviation for a sample, simply calculate the square root of the variance(s2) for that sample. In Table 2, the variance has already been calculated.)3. Calculate the standard error of the mean for each set of data.Because you are analyzing random samples of 50 birds taken from the entire medium ground finchpopulation living on Daphne Major, it is not possible to know for certain that the mean you havecalculated for each sample is the same as the mean of the entire medium ground finch population. Oneway to show how close the sample mean is to the population mean is to calculate the standard error ofthe mean (SEM). If you take many random samples, the SEM is the standard deviation of the differentsample means. About 68% of sample means would be within one standard error of the populationmean.Use the formula below to calculate the SEM:SEM !!www.BioInteractive.orgUpdated September 2015Page 3 of 7

fFinchtheFittest:TheBeakof dAdaptationSTUDENT HANDOUT4. Calculate the 95% confidence interval for each set of data.Confidence limits serve the same purpose as SEM. The 95% CI provides a range of values within whichthe mean of the entire population is likely to be found.As an approximation, use the simplified formula below to calculate the 95% confidence interval (95%CI), which is roughly twice the SEM:95% CI !(!)!Part B: Graphing the Data5. On a separate sheet of graph paper or on your computer, construct four bar graphs that comparethe means of nonsurvivors and survivors for each physical characteristic (wing length, body mass, tarsuslength, and beak size). Label both axes of each graph and show either the SEM or 95% CI as error barsdepending on your instructor’s directions. An example of a well-constructed bar graph is shown below(Figure 1).Mean dorsal fin height (m)Mean Dorsal Fin Height Among Male and Female Orca WhalesFigure 1. An example of a well-constructed bar graph: Mean dorsal fin height in meters (m) for 36 female and 36 male orca whales(Orcinus orca). In this case, error bars indicate 95% confidence intervals.6. Once you complete your four bar graphs, describe in the space below any differences betweennonsurvivors and survivors you observe in each graph.Part C: Calculating t-Test Statisticswww.BioInteractive.orgUpdated September 2015Page 4 of 7

fFinchtheFittest:TheBeakof dAdaptationSTUDENT HANDOUTIn Figure 1, the means are different and the error bars do not overlap, suggesting that there might be adifference between the two mean fin heights. But a statistical test is required to confirm that thedifference is significant. The appropriate statistical test for comparing two means is the Student’s t-Testfor independent samples (the t-Test). The t-Test can assess whether any observed differences betweenthe means of two samples (i.e., nonsurvivors and survivors) simply occurred by chance, by determiningthe probability (p) of obtaining a more different result if the null hypothesis is correct.You will calculate the t statistic called “observed t” (tobs) and then compare it to the critical t statistic (tcrit).This critical t-value is a cutoff value that determines whether you can reject the null hypothesis that themean of the population from which the first sample came is equal to the mean of the population fromwhich the second sample came, or 𝜇! 𝜇! . If your observed t value (tobs) is less than the critical value(tcrit), then you cannot reject the null hypothesis. If the calculated statistic is larger than the critical value,then we have enough evidence to reject the null hypothesis and support the alternative hypothesis thatthe means are significantly different, or 𝜇! 𝜇! .The tcrit for your sample size of 50 is 1.98. This is the t value that could occur 5% of the time for a samplesize of 50 if the null hypothesis is true.7. Calculate tobs to compare the mean values of each physical characteristic between survivors andnonsurvivors.a. Use a graphing calculator, a spreadsheet program (e.g., Excel: function “T.TEST”), or an online t-Testcalculator (many are available) to calculate tobs.Mean body mass: tobs Mean wing length: tobs Mean beak depth: tobs Mean tarsus length: tobs b. How do your tobs for each pair of measurements compare to the critical t-value (tcrit) of 1.98?Mean body mass:Mean wing length:Mean beak depth:Mean tarsus length:8. Analyze your four bar graphs, their associated error bars, and the results of your t statisticcalculations. For each characteristic, make a claim about the differences you observe between survivorsand nonsurvivors. Support your claim with evidence from the graphs and statistics.Mean body mass:Mean wing length:Mean beak depth:Mean tarsus length:www.BioInteractive.orgUpdated September 2015Page 5 of 7

fFinchtheFittest:TheBeakof dAdaptationSTUDENT HANDOUT9. Based on what you saw in the film, identify the adaptive trait that is most important to survival underthe environmental conditions presented by the drought and suggest a reason for the differencesbetween the measurements taken from the birds that died during the 1977 drought and the birds thatsurvived.www.BioInteractive.orgUpdated September 2015Page 6 of 7

fFinchtheFittest:TheBeakof dAdaptationSTUDENT HANDOUTExtension Activity: Evaluating Associated Variables1.2.3.Using the data in Table 1, construct and label a scatter plot using a computer program orhand-graphing that illustrates the association between beak depth and wing length for thebirds that survived the drought of 1977.Draw a trend line either by hand on your graphing paper or automatically by right-clicking onyour data plot in Excel and choosing “add trendline.” If you are doing this exercise in Excel, awindow will pop up after you choose “add trendline.”Calculate thecoefficient of determination, or r2, using your calculator or spreadsheet program.This value represents the proportion of the variation in the y variable that is explained by thevariation in the x variable. Values vary from 0 to 1; values near 0 mean there is little relationshipbetween x and y. For example, if r2 is 0.90, the x variable “explains” 90% of the variation in the yvariable.4.Based on these results, comment on the presence or absence of a relationship between beakdepth and wing length in this population of medium ground finches.5.Suggest a reason for the presence or absence of a relationship between beak depth and winglength in this population.6.Based on your observations regarding beak depth and wing length, predict what mighthappen to body mass in the medium ground finch population over a few generations if small,soft seeds returned in abundance after the end of the drought in 1978, and explain youranswer.AUTHORSWritten by Paul Strode, PhD, Fairview High School, Boulder, ColoradoEdited by Laura Bonetta, PhD, HHMI, and Ann Brokaw, Rocky River High School, OhioReviewed by Brad Williamson, University of Kansas; Peter Grant, PhD, and Rosemary Grant, PhD, Princeton Universitywww.BioInteractive.orgUpdated September 2015Page 7 of 7

The Origin of Species The Beak of the Finch Table 1. Morphological measurements (wing length, body mass, tarsus length, and beak size) 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