BIOL 101L: Principles of Biology Laboratory

Transcription

1 BIOL 101L: Principles of Biology Laboratory Sampling populations To understand how the world works, scientists collect, record, and analyze data. In this lab, you will learn concepts that pertain to these important activities. In particular, you will record and summarize data describing the physiology of fruit flies (Drosophila melanogaster). In lecture, we will use these data to test a hypothesis. In general, a hypothesis represents an educated guess about how the world works in some respect. Finally, you will select a subset of the flies from your experiment, and your lab instructors will breed these flies for a future lab (Week 3: Artificial Selection). Definitions of terms You will need to master the following terms for today s lab: Observation a measurement taken on the smallest sampling unit. In this lab, an observation is some measurement of an individual fly. Variable a property represented by each observation. In this lab, you will be measuring the cold tolerance of flies. Specifically, you will observe how long a fly needs to recover from exposure to a freezing temperature. The observation is the duration of recovery (in seconds) and the variable is called cold tolerance. Another property of each observation is the population from which the fly was taken. You will have three groups, each containing ten flies. Therefore, group can also be considered a variable. Scientists distinguish variables based on their beliefs about cause-and-effect. For example, in lecture, we will hypothesize that flies from different groups possess different cold tolerances. Because we hypothesize that cold tolerance depends on the group, we call cold tolerance the dependent variable. By contrast, group identity (1, 2 or 3) should be independent of cold tolerance. Thus, we call group the independent variable. Sample a collection of observations representing a certain population of objects. In this lab, you will have three samples (groups), each one representing a population of flies. Population the collection of all possible objects that can be measured or observed. In other words, the population comprises more individuals than you have measured in your sample of observations. In fact, the population includes all other observations you could have made in addition to your sample. In this lab, the population contains thousands of flies, which were raised in the laboratory since July. Note that this use of the term population can differ from the more typical use in biology, where population refers to a collection of organisms belonging to the same species. Population mean the average value of a variable for the entire population. You can t measure this value unless you can sample the entire population (usually an impossible

2 task). Nevertheless, you can estimate the population mean by calculating the sample mean. Sample mean the average value of a variable for a sample of a population. Methods Today, you will measure the cold tolerance of fruit flies using a standard assay. Many insects either resist or survive freezing, and thus recover fairly quickly from a short exposure to freezing temperatures. Insects that recover quickly are said to be more tolerant of cold than insects that recover slowly. You will expose flies to a temperature of 0 C for 20 minutes. This exposure will cause the flies to enter a coma-like state, in which they will be immobile and unresponsive. After which, you will record the time required for the flies to recover their mobility. You will measure the cold tolerances of three samples of flies (groups 1, 2 and 3). For each sample, you will use a computer program (J Watcher) to record your data. Then, you will import these data into the computer program Excel to calculate sample means and create histograms. Materials: 1 container if ice 3 Petri dishes of flies 1 small paint brush 1 stopwatch 1 roll of colored tape 1 ball-point pen or permanent marker 1 laptop computer pre-loaded with software (J Watcher and Excel) Measuring Cold Tolerance of Flies: 1) Form a group of 3-4 people. At the front of the room, you will find plastic containers filled with ice and some Petri dishes containing flies (10 per dish). Someone from your group must get a container of ice and 3 dishes of flies. Another person in your group should open the J Watcher program on his/her laptop computer. Using a pen/marker and a piece of tape, label the Petri dishes as groups 1, 2, and 3. This distinction will be important for your analyses and for determining what to do with your flies after you have completed your measurements. You will measure cold tolerance of one group of flies at a time. Thus, you will need to complete three trials to measure the tolerance of all groups. Each trial will begin by placing flies on ice for a period of 20 minutes; you will use a stopwatch to time the exposure to ice. After the 20 minutes, you will transfer the flies to a sheet of paper, on which you will be able to observe the activity of the flies.

3 To begin, bury a Petri dish of flies in the bucket of ice; be sure the dish comes in contact with ice on all sides and push a layer of ice on top (about 2 inches). Start recording time with the stopwatch as soon as the dish is covered with ice. After the flies have been on ice for 20 minutes, quickly but carefully remove the dish from the ice and empty the dish of flies on the sheet of paper. At the same time, one person in your group should start the timer in J Watcher. While the timer is running, use a small brush to move each fly to the center of a circle (the circles are labeled 1 through 10). The flies will remain on their side or backs for a few minutes before they begin to stir. As each fly recovers consciousness, it will try to walk around. When a fly leaves the circle, call out its number to the person recording the data in J Watcher. This person will enter the number, followed by any letter; the letter will show up in the data file and will help you to distinguish data for individual flies. As you call out the number of the fly, cover the fly with a one half of a Petri dish to prevent its escape. Once all of the flies have recovered, you will return three of the flies to the Petri dish and discard the remainder of the flies in jar of mineral oil. The three flies that you will keep will differ for each group: Group 1: Keep the 3 flies that recovered first Group 2: Keep the 3 flies that recovered last Group 3: Keep 3 flies chosen at random Note that you will need to use Excel to randomly choose 3 flies from Group 3 prior to measuring the cold tolerance for this group. Your TA will show you how to use the Help menu of Excel to learn useful functions. One of these functions, the random function, generates random numbers between 0 and 1. Importing Data in Excel: 1) Open an Excel workbook by either double-clicking on the Excel icon, or by going to the Start button in the lower left corner of the screen, clicking the following: Start Programs Excel. 2) Open the file called Group 1, which is stored in C:\Program Files\JWatcher\. Because this is a text file, Excel will ask you to specify how you would like to import the data. Choose delimited and then mark the box that indicates the data are comma delimited. Immediately save the workbook in the Excel format with a descriptive name, such as Group 1 data. You can save the workbook by going to the menu, and clicking File Save As. Then you will be given a dialog box where you type in the name. 3) Notice that the workbook has several spreadsheets already available to you, labeled Sheet 1, Sheet 2, and Sheet 3. If you click on the tabs at the bottom of the worksheet, you will move to that particular sheet. For now, just use sheet 1. 4) The number in the left-hand column correspond to the time (in milliseconds) at which you made each keystroke (a number or letter). You should convert these data from milliseconds to seconds by entering the appropriate formula into an empty column. Now you can cut and paste the time for each fly into a new column. These are the

4 observations you will need for your analysis (there should be 10 in total). You should label the column Cold tolerance of Group 1 by typing text into row 1. 5) Repeat these steps to import data for the other groups of flies. Using an Excel function to Analyze Data: You can use Excel to calculate certain parameters from your data, such as the sample mean and standard deviation. You can also make Excel grab the numbers you entered into cells D11, E34, A6, and add them, multiply them, factorial them, or perform any other function with them that you want. Excel can either use data from single cells (e.g., cell B12) or from ranges of cells (e.g., all cells between B12 and E34). We will do this here: Sample Mean 1) Click in a cell at the bottom of the column of measurements for flies in Group 1. Skip a cell between the data and your calculation so that you don t confuse the sample mean with your data (e.g., use row 13 if you have one row as a header and ten rows of data). 2) Type an equals sign =. This tells Excel that you are about to enter a function or a formula. 3) Immediately after the equals sign type the name of the function, in this case it is just average (without the quotation marks). 4) Immediately after average type an open parenthesis (. 5) Next, enter the range of cells that you want included in the calculation for average. You can do this in several ways: a) Type the cell reference of the first measurement (such as c2 ), followed by a colon : followed by the cell reference for the last measurement (such as c11 ). b) An easier way is to highlight the range: click on the first cell of data in the column (such as c2), and while holding down the mouse button, drag the mouse to the last cell of data (such as c11). Then release the mouse button. Notice that as you click in cells and drag the mouse, the cell references appear in the formula after the open parenthesis. 6) Without clicking mouse anywhere else, just hit Enter. If you do click the mouse before hitting enter (after highlighting a range), the cell that you click in may become part of the calculation, and you don t want that. 7) At this point, the cell should contain a formula, such as =average(c2:c11). Either lower case or upper case is acceptable. 8) After hitting Enter, the result for the average calculation should appear in the cell into which you typed the formula. This calculated the average of the numbers you entered in cells C2 through C11. 9) Repeat steps 2-8 for the column of data for the other groups. 10) It might be handy to label the sample mean that you just calculated. Move your cursor to the cell just to the left of the calculated average (Cell A13 is a good choice), and type in the word mean (not the excel function, just the word). This is a label that will let you know what the number at the bottom of the column represents. You may

5 want to make the label a bold font, so that it is easy to distinguish from the rest of the spreadsheet. Variation in traits Imagine that you got the following measurements for two groups of flies: Group 1: 65, 65, 65, 65, 65, and 65 s Group 2: 50, 80, 65, 80, 50, and 65 s What are the mean measurements for these samples? Group 1 Mean: Group 2 Mean: If you did your math correctly, you should have found that both of these samples have the same mean; however, the two samples are obviously very different. The observations from Group 1 are all equal to their mean, whereas some of those from Group 2 are quite different from their mean. We can use another statistical parameter (the variance) to quantify how wildly the observations deviate from the mean. Variance The variance may be an unfamiliar concept to you. It basically represents how far away from the mean the average observation lies. With the flies that you measured, few of them (more likely none of them) had a cold tolerance equal to the sample mean. Different flies probably deviated from the mean by different amounts. Such variation is common among living things. We can represent this variation by the descriptive statistic, variance. As with the mean, each population has a variance that summarizes the degree of deviation of all individuals from the population mean; but we can t know the population variance with certainty unless we can measure all of the flies in the population. Fortunately, we can estimate the population variance by calculating a sample variance. Sample Variance To calculate the sample variance we start by finding the deviation of each observation from the sample mean, and then we square that deviation. Why do we square it? For one thing, squaring the deviation converts everything to positive numbers (some of the deviations will be negative). If we tried to find the average deviation without squaring, it would equal zero no matter what your data actually were, which would not be very useful. In addition, there happen to be useful properties of squared deviations that permit us to perform statistical tests, which we will take up in a later lab. After squaring the deviations, we next find the average of the squared deviations; or rather we find something that is almost the average. For reasons you will learn about in lecture, we calculate the sample variance by dividing the sum of squared deviations by N - 1, where N is the number of observations in the sample (or sample size). The reason has to do with the fact that we are calculating a sample variance, rather than a population variance. Calculating a variance by hand can be painful, so let s get Excel to do it for us.

6 Calculating the Sample Variance 1) To find the sample variance, you need to know the deviation (squared) of each observation from the sample mean. In the cell beneath the one labeled Cold tolerance of Group 1, enter the label sqdev so you know what is contained in that column. The formula for the squared deviation is the mean minus the observation, squared. For example if the observation were in cell C2, simply click on the cell to the right of this observation and enter the following: =(mean-c2)^2 without the quotation marks and putting the actual mean of your observations in the place of the word mean. The inverted V symbol (^) represents raised to the power of, so you have raised the deviation to the power of 2; in other words, you squared the deviation. 3) You need the square the deviations of all ten observations, not just the first one. However, you don t need to type the equation all over again for each one. Click on the cell where you entered the formula for the first squared deviation. Notice that the border around the cell that you clicked has become thick and dark; this indicates which cell you are working with at the moment. At the bottom right corner of this border is a tiny black square. If you move your mouse cursor over this little black square, you will see it change shape slightly. Click on this little black square, and without releasing the mouse button, drag the mouse cursor down to last cell. Then release the button. The thick black border should have been dragged down with the cursor, and all the cells you dragged the thick border through should now be filled with numbers. You have copied the equation for the squared deviation into each of these new cells, and Excel has calculated the squared deviations for each of your sunny observations for you. If you were to click on these cells, you would see that Excel updated the cell references in each formula to reflect the new location of the formula (for example, if your observation were cell C6 and the sample mean was 65 seconds, the formula in cell in D6 would be =(65-c6)^2). That s a lot easier than retyping the equation, isn t it? 4) Repeat this process for the observations of the other groups of flies. 5) Now that you have your squared deviations, you can calculate your sample variances. In an empty cell below the squared deviations, enter formula =sum(d2:d11)/9 without the quotations. This adds together the values in cells D2 through D11, then divides the sum by 9, which happens to equal your sample size (10) minus one. Thus, you just calculated the sample variance of your data! Now calculate the sample variance for the other groups in the same way. 7) Save your work because you will use these data in a future lab. Also, a copy of the data to your lab instructor before you leave lab today. Your instructor will forward these data to Dr. Angilletta, who will review the data in lecture. Do not leave your data on one of the lab computers because these computers will erase such files when they reboot. Examining the variation graphically Although means and variances play a crucial role in the interpretation of data, most people prefer to visualize these parameters in the form of a graph. In particular, a histogram shows the distribution of data, which gives you a feel for the central tendency

7 of the data (the mean) and their dispersion around the mean (the variance). Use the Help menu of Excel to search for instructions on making histograms. Try to plot a histogram of the data for each group. Once you have obtained these plots, examine them for unusually high or low values. These extreme observations are referred to as outliers, because they lie outside the range of most of the data. Outliers may be caused by real biological factors or they may reflect typographical errors or biases in your procedure. Because you selected the most extreme flies in groups 1 and 2 for future breeding, you should make sure these flies do not represent outliers caused by typographical or experimental errors. Such errors would negatively influence the analysis of your data in the coming weeks. Check before Leaving Lab 1) Make sure you understand the methods used to quantify cold tolerance. You will need to summarize these methods in a homework assignment. 2) Make sure you understand the statistical concepts defined above. These concepts will be used throughout the semester in lab and lecture. 3) Make sure you can calculate a mean and variance in Excel. You will need to make these calculations again in future labs. 4) Make sure you know how to create a histogram and identify extreme values, such as outliers. 5) Make sure you have given the selected flies to your lab instructor. These flies will be bred to create new flies for the Artificial Selection Lab (week 3). 6) Make sure you have saved your data to your own hard drive or have ed these data to yourself. Also, make sure you have ed a copy of your data to your lab instructor.