Fall 22 (50 minute) Activity - Shark Teeth

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University of Maryland, Baltimore County *

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142

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Statistics

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Jan 9, 2024

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Shark Evolution All graphs and this assignment must be in a Blackboard submission (found in this week’s folder) by the end of class. Background The purpose of this assignment is to teach you how to create a histogram graph of data and how to calculate basic statistics from a set of biological data. These activities will prepare you for this week's module and help ensure that you can complete the module activities during class time. Introduction: The scientific method that we use to answer any biological question usually requires that we: ● Make observations about some natural phenomena ● Ask questions based on these observations ● Generate testable hypotheses ● Design appropriate experiments / additional observations that will allow us to test the hypotheses ● Gather data to test hypotheses ● Analyze the data and draw conclusions about hypotheses Once data are gathered, the first thing scientists do is to plot the data. This gives us a visual description of two important aspects of most data sets 1) the central tendency of the data (e.g., the average, median or mode of the data) and 2) the spread of the data around the center of the distribution (e.g., standard deviation and variance which is the squared standard deviation). There are many ways to graph data, but in this activity, we are going to make a histogram plot. Histograms are graphs that convert continuous data like height and weight, into different groups or bins that are shown as bars on the graph. In these graphs the different heights of the bars indicate how frequently a group of observations occurs in a data set. See figure 1 for an example of a histogram of the weights of newborn bird chicks. The graph has many components that ALL graphs need. The x-axis and y-axis are labeled, and the units of measurement are given. In this case, the unit of measurement on the y-axis is the number of birds whose weight (or mass) fell within the size class of each bar on the x-axis. The

unit of measurement on the x-axis is the mass of each bird in grams that fell within a particular size class. Note that each bar, which is the frequency of each group, is bounded by a "(" on one side and a "]" on the other (“]“ means that number is included). For example, the values beneath the second bar are given as (31, 41]. This means that all chicks that weigh between 31 grams (not including) and 41 grams (including) are included in the calculation of the frequency of that size class. If a bird weighs 31 grams, it would be found in the [21, 31] bin. In this example only one bird falls in the [21,31] size class which you can see on the y-axis. Exercise 1: Making a Shark Histogram (Pre-Active Learning) Natural selection is one of the major forces of evolution acting on populations. The major requirements for selection to occur are that 1) traits (or phenotypes) vary among individuals in populations, 2) some of this variation among individuals is due to genetic differences among individuals, and 3) that variation in traits affects some aspect of fitness. If scientists know the distribution of a trait over time, they can identify changes in the population as a result of a change in the environment. Selective pressures can act on the variance. of a population to result in stabilizing, disruptive, or directional selection. One way to diagram the variation is using a histogram. In today’s lab, we will look at the mean and variation of shark tooth length in a population of sharks. The length of a tooth can be related to many factors such as size of shark, typical size of prey, difficulty in catching prey, or sexual selection. We will then examine how natural selection can change the mean and variance of shark's teeth in a population and use these changes to interpret what type of selection may have occurred. First, open the Excel spreadsheet called SharkTeeth.xlsx. On sheet one you will find the length of 52 shark teeth. The first thing we need to do is identify the highest and lowest values from the dataset. Highlight the data values and then select the sort button (shown here on the left) to arrange your values from smallest to largest. This will give us a range of values for the X-axis on our graph. Include units. ● Lowest number, rounded: 20 mm ● Highest number, rounded: 44 mm 4. Calculate the range of data (the highest value – the lowest value). Include units. ● Range: 24 mm 5. The next step is to put the data into different bins. There is no general rule for how many bins, or bars, to create. Since we will have 52 data points, the bin size should ensure that the histogram has at least 6 data points on average per bin. # data points / data points per bin = # bins (round down) range / # bins = bin size (round up) Include the units. Note that we always round UP to create the matching bin size.

● Bin size: 3mm 6. Next, fill out the frequency table below using your bin sizes and the data you sorted in Excel. For example, if your first bin starts at 20mm, and your bin size is 3mm, then your first bin values would be [20mm - 23mm]. Fill in the number of data points that fit within that bin. Remember, the bracket indicates you include the value it’s next to, while the parenthesis indicates you only include values greater than what it’s next to. Bin Values (min # - max #) Number of Data Points in Bin [20mm - 23mm] 2 (23mm - 26mm] 3 (26mm - 29mm] 10 (29mm - 32mm] 9 (32mm - 35mm] 12 (35mm - 38mm] 3 (38mm - 41mm] 6 (41mm - 44mm] 7 The next step is to calculate some basic statistics on your data set: mean (or average) and standard deviation. The mean measures the central tendency of the data and the standard deviation measures the spread of the data around the mean. 7. We will use Microsoft Excel to calculate these values for us instead of by hand. In your spreadsheet, type “Mean” in an empty cell. In the cell below it type “ =AVERAGE(A2:A53)” and hit enter. This formula tells excel to calculate the average of all the values between cell A2 and A53. You could also simply type “=average”, then highlight the data you want averaged. The average length of shark teeth in this data set is (include units) 32.9 mm 8. Next, use excel to find the standard deviation. In an empty cell, type “Standard Deviation”, and in the cell below it, type “ =STDEV(A2:A53) ”, or highlight the data you want to include. The standard deviation is (include units) 5.87 mm 9. Now let’s make the histogram. Follow the tutorial in the document in the blackboard folder. Remember that you must include: Axes labels, axes units, and a descriptive title. We will not be lenient for titles from this lab on.

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EXERCISE 2 13. This population of sharks is experiencing an environmental change. Below, each group has been assigned a form of selective pressure that is being enacted on the population of sharks. Stabilizing: Tables 1, 5, 9, 13, 17, 21 Disruptive: Tables 2, 6, 10, 14, 18 Directional to smaller: Tables 3, 7, 11, 15, 19 Directional to larger: Tables 4, 8, 12, 16, 20 ● Assigned selective pressure: Stabilizing Selection 14. Describe a scenario that uses natural selection to explain why the length of sharks’ teeth would change to reflect the selective pressure assigned to your group. Think about predation. In shark habitat, there were originally large, medium, and small fish. Then, the large and small fish went extinct, only leaving the medium fish to be left in the habitat/environment where the sharks live. The best type of teeth to consume these fish were medium sized teeth. Over generations, stabilizing selection occurred and made the frequency of sharks with medium teeth to be the average.

15. Open a new worksheet (tab) in Microsoft Excel and rename it to “Exercise 2”. Copy and paste the shark tooth data into this new worksheet. 16. Change this data to simulate the selective pressure that has occurred in this population. To do so, delete ~20% of the data points (10 data points). How many data points can you delete? Always keep the highest and lowest values (44mm and 20mm). Don’t delete the lowest or highest values in your 20% (duplicate lowest/highest values are okay to delete). Why did you delete the data points you deleted? We deleted the five points from each extreme, not including the extremes. In stabilizing selection, we decrease the extremes of phenotypes and makes the average the more prevalent. This means the graph will me more concentrated in the middle, with less outliers. 17. Next, make a new histogram. Use the same bin size and bin values as before (#4-7) . 19. Calculate the mean and standard deviation of this data set within excel and list them below The mean = 32.8mm The Standard Deviation = 4.947 mm

20. Calculate the percent change in the mean and standard deviation from the original dataset. Negative values are ok! % change = (new value - old value) / old value % Standard Deviation change= -15.7% = -0.157 = (4.947 – 5.87) / 5.87 % Mean change= -0.33% =-0.0033 = (32.8 – 32.91) / 32.91 REPORT OUT 21. Now, copy and paste your first histogram of the shark population and your second histogram with the environmental change side by side. Write a brief summary of your explanation of this change (#14), and how the average and standard deviation changed and the direction of the change (e.g., it got bigger, smaller). Describing how much the mean and standard deviation changed (if at all ). You’ll submit BOTH graphs AND this worksheet in a Blackboard submission (found in this week’s folder) by the end of class. In the graph without stabilizing selection, there was more outliers and there was more variation. The graph with stabilizing selection had less outliers and the mean/average was more concentrated in the middle. The standard deviation decreased in the stabilizing selection since there was less variation in the data. This is all because the sharks that were good at eating medium sized fish increased in the population, while other sharks that were not good at eating medium sized fish decreased. The lengths of shark teeth was less varied. 22. Use the space below to write about the other selection types. Briefly, for each type of selection, what could cause this type of selection? How does the average and standard deviation change? You should be explaining all three other types of selection in your answer.

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Directional Selection: There would be favoring an extreme. For example, if the medium and small fish died out, the large fish would be the only source of food, which means large teeth will be favored in the population. This causes the graph to be skewed right. The large teeth phenotype will be favored more, and the mean will be closer to this. The standard deviation deviation would decrease, because there would be a more concentrated area on the graph (the favored phenotype). Disruptive Selection: There be favoring both extremes. For example, there would only be large and small fish, causing them to be the only sources of food. The sharks that eat medium fish would be removed over time, and the teeth length that favor eating large and small fish will be most prevalent in the population. There will be a large standard deviation since there are two extremes on either side of the graph. The mean will be the same.

Fall 22 (50 minute) Activity - Shark Teeth

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