University of Lethbridge Biology 2200 Fall 2024 Lab Manual PDF

University of Lethbridge BIOLOGY 2200 Principles of Ecology Laboratory Introductory Information Fall 2024 All of the lab exercises used in Biology 2200 were compiled and...

University of Lethbridge BIOLOGY 2200 Principles of Ecology Laboratory Introductory Information Fall 2024 All of the lab exercises used in Biology 2200 were compiled and edited by: K. Mendez, J. Burke, M. Robinson, K. Gill, R. Laird Department of Biological Sciences University of Lethbridge Student Name: I.D. Number: Lab Section: Day: Time: Room: Instructor’s Name: Office: Email address: Telephone: Office Hours: Biology 2200 LAB SCHEDULE Fall 2024 Week Lab Topic Sept. 9 - 13 Lab 1: The Naturalist in Ecology Sept. 16 - 20 Lab 2: Ecological Sampling and Data Handling I Sept. 23 - 27 Lab 3: Phenotypic Variation and Adaptation (Assignment 1; 7%) Sept. 30 - Oct. 4 No labs – National Day for Truth and Reconciliation Oct. 7 - 11 Lab 4: Ecological Sampling and Data Handling II Oct. 14 - 18 Lab 5: Optimal Foraging Theory (Assignment 2; 7%) Oct. 21 - 25 Lab 6: Predation and Functional Response Oct. 28 – Nov. 1 Lab 7: Competition (Assignment 3; 7%) Nov. 4 - 8 Lab 8: Soil Ecology and Decomposition Nov. 11 - 15 No labs – Reading Week Nov. 18 - 22 Lab 9: Measuring Biodiversity (Assignment 4; 7%) Nov. 25 - 29 Study Period, appointments with instructors as needed Dec. 2-4 Final Lab Exam - Moodle (12%) Any questions concerning your laboratory experience should be first directed to your lab instructor. After discussion with your lab instructor, if you need further direction you can contact the Biology 2200 lab coordinator, Katrina Mendez (SA9228, [email protected], 403-329-2125). Biology 2200 Lab Instructors – Contact Information Eric Chan [email protected] Lauren Edison [email protected] Emma Neigel [email protected] Kristin Olson [email protected] Erik Vilu [email protected] Scheduled Labs: Fall 2023 Lab # Day Time Room Instructors 1 Tuesday 12:00-14:45 SA7108 Lauren Edison and Erik Vilu 2 Wednesday 12:00-14:45 SA7108 Kristin Olson and Erik Vilu 3 Friday 12:00-14:45 SA7108 Emma Neigel and Eric Chan 1 LAND ACKNOWLEDGEMENT Our University’s Blackfoot name is Iniskim, meaning Sacred Buffalo Stone. The University of Lethbridge acknowledges and deeply appreciates the Siksikaitsitapi peoples’ connection to their traditional territory. We, as people living and benefiting from Blackfoot Confederacy traditional territory, honour the traditions of people who have cared for this land since time immemorial. We recognize the diverse population of Aboriginal peoples who attend the University of Lethbridge and the contributions these Aboriginal peoples have made in shaping and strengthening the University community in the past, present, and in the future. As we study ecology in this place, we acknowledge all the many First Nations, Métis, and Inuit whose footsteps have marked these lands for millennia. INTRODUCTION The nature of ecological study makes looking at any one given question, sampling, analyzing data and making a conclusion about that question a difficult task for a single 3-hour lab period. Thus, the Biology 2200 labs are designed with two basic objectives: 1) to teach students the research methodology used by ecologists (and other biologists) in designing and conducting experiments, summarizing and evaluating results, and communicating findings, and 2) to explore selected topics in ecology that are covered in lecture, and to present students with the opportunity to explore examples of these topics in full or in part. The lab exercises are inquiry based, and cover quantitative topics (taking measurements, summarizing and analyzing results), as well as focus on ecological hypotheses. The labs are designed to assist students in acquiring research skills through active participation in the lab exercises, and even more importantly, active thinking about the concepts that underlie them. The lab manual is designed to direct your inquiry rather than provide rote answers. Your own notes and answers to questions asked within the manual (along with the understanding you gained along the way) will be critical to excelling in lab. Your laboratory Experience: As noted above, you will get much more out of your Biology 2200 lab experience if you participate actively in the exercises and discussion. The lab exercises are simple, but the concepts and skills they teach will require time and effort to absorb. If you put little into the lab, you are likely to take little out. Below are some tips on how to approach the lab. Do the assigned readings before completing the lab. Read the lab exercise through before beginning any exercises or simulations. Take active part in group discussions. Ask questions, both inside and outside the lab meetings. Work through all the questions in the lab manual, including the thought problems at the end of each lab. Seek clarification on any aspects that are unclear. Make connections with lecture. Your lectures in Biology 2200 (and other courses) will introduce you to important experiments. Try to see how the researchers who conducted these experiments applied the same principles you are learning in lab. Some lab exercises require moderate physical activity and trips outside around the university campus. If you have extenuating circumstances that make these activities difficult, contact your lab instructor prior to the lab so alternative arrangements can be made to allow you to complete the lab safely and comfortably. Remember to prepare yourself adequately for the field activities (wear comfortable, closed-toed shoes, wear clothing appropriate to the weather and field conditions, take along a small pack for your lab manual, notebook, water bottle, etc.). 2 Attendance Attendance at each lab is expected. If you are unable to come to your regularly scheduled lab period, you may contact the instructor about attending a different lab section that week (see Lab Schedule on page 1 for list of all sections). Grading The lab portion of Biology 2200 is worth 40% of your total mark in the course. These marks will be broken down as follows: Lab Assignments (4) 28% Final Lab Exam 12% Total 40% Assignment guidelines will be posted to Moodle and will include the specific deadlines. If you miss an assignment deadline you must contact your lab instructor within 24 hours of the missed deadline. Extensions without penalty will be granted on a case-by-case basis. Assignments that are handed in late without an approved excuse will have the following reductions in total possible marks: 10% penalty if on the same calendar day, 25% penalty if late by one calendar day, 50% penalty if late by two calendar days, and 100% penalty if late by more than two calendar days. Computer related problems and poor time management are not acceptable excuses for late assignments, so make sure to complete your assignments well enough before the deadline and back-up often. Grading Review It is the student’s responsibility to review grading feedback as soon as possible. Concerns about grading must be brought to the lab coordinator’s attention within 7 days of receiving the graded work. Grade changes will not be made after that point. Background Readings Each week’s lab has a set of required readings, reflecting the goals of the labs. For background information on research methodology and scientific writing, the Biology 2200 lab uses The Science Toolkit: http://people.uleth.ca/~steyqj/science-toolkit/ Background readings on ecological topics are from the required text for the course, Ecology: The Economy of Nature (Canadian Ed., Ricklefs, Relyea, & Richter, 2015) Plagiarism The written assignments to be submitted as part of the requirements of this lab must be the individual work of the student. Any evidence to the contrary will be treated as plagiarism, which is an academic offense (consult the Student Discipline Policy in the University of Lethbridge Calendar for details). Ideas or information from any source that are used in writing the assignments must be acknowledged with an appropriate citation. Failure to cite sources also constitutes plagiarism. Turnitin This course uses the services of turnitin.com, an online plagiarism detection system to which the University of Lethbridge subscribes. All Biology 2200 written material must be submitted to turnitin.com in order to be graded. Failure to submit your work to Turnitin results in a grade of zero for the assignment. Please be aware that turnitin.com is a site that verifies the originality of your work; as such your work will be stored in Turnitin’s database and may be checked against future submissions. If you have concerns with storage of your written work in Turnitin, please consult the University of Lethbridge Assessment of Student Learning Policy and Procedures document. 3  GUIDELINES FOR SAFETY PROCEDURES Students enrolled in laboratories in the Biological Sciences should be aware that there are risks of personal injury through accidents (fire, explosion, exposure to biohazardous materials, corrosive chemicals, fumes, cuts, etc). The guidelines outlined below are designed to minimize the risk of injury by emphasizing safety precautions and clarify emergency procedures should an accident occur. EMERGENCY NUMBERS: City Emergency 911 Campus Emergency 2345 Campus Security 2603 Student Health Centre 2484 (Emergency - 2483) THE LABORATORY INSTRUCTOR MUST BE NOTIFIED AS SOON AS POSSIBLE AFTER THE INCIDENT OCCURS. EMERGENCY EQUIPMENT: Your lab instructor will indicate the location of the following items to you at the beginning of the first lab period. Closest emergency exit Closest emergency telephone and emergency phone numbers Closest fire alarm Fire extinguisher and explanation of use Safety showers and explanation of operation Eyewash facilities and explanation of operation First aid kit GENERAL SAFETY REGULATIONS: Eating and drinking is prohibited in the laboratory. Keep pencils, fingers and other objects away from your mouth. These measures are to ensure your safety and prevent accidental ingestion of chemicals or microorganisms. Personal protective wear is mandatory. Lab coats and closed-toed shoes must be worn at all times when working in the lab. When working outside on campus long pants and closed-toed walking shoes must be worn. Coats, knapsacks, briefcases, etc. are to be hung on the hooks provided, stowed in the cupboards beneath the countertops, or placed along a side designated by your instructor. Take only the absolute essentials needed to complete the exercise with you to your laboratory bench. When working outside be aware of physical hazards, wildlife, etc. in the area. If possible work with a partner or group (while practicing appropriate social distancing). At least one person in each group should carry a cellphone. Always wash your hands prior to leaving the laboratory. Report any equipment problems to instructor immediately. Do NOT attempt to fix any of the equipment that malfunctions during the course of the lab. Contain and wipe up any spills immediately and notify your lab instructor (see SPILLS below). Heed any special instructions outlined in the lab manual, those given by the instructor or those written on reagent bottles. Long hair should be restrained to prevent it from being caught in equipment, chemicals, etc. You are responsible for leaving your lab bench clean and tidy. Glassware must be thoroughly rinsed and placed on paper toweling to dry. 4 SPILLS: Spill of SOLUTION/CHEMICAL/SPECIMENS: Contact instructor immediately. In the ecology labs, most spills can be cleaned up with ordinary paper towel and water, without wearing PPE, but your instructor may prefer to try to salvage any specimens that may have been spilt. DISPOSAL: Broken glass, microscope slides, coverslips and Pasteur pipets are placed in the upright white ‘broken glass’ cardboard boxes. Petri plates, microfuge tubes, pipet tips should be placed in the orange biohazard bags. The material in this bag will be autoclaved prior to disposal. Liquid chemicals should be disposed of as indicated by the instructor. DO NOT dispose of residual solution in the regent bottles. In case of any uncertainty in disposal please consult the lab instructor. HEALTH CONCERNS: Students who have health concerns or physical limitations that may make the lab or outdoor components of the exercises difficult should inform their lab instructor ahead of time so that appropriate precautions can be taken or modifications made where necessary. CERTIFICATES: You must possess valid WHMIS and U of L Lab Safety training certification to participate in labs on campus. Submit your certificates to the appropriate Crowdmark assignment posted to Moodle prior to the second week of your scheduled lab. By participating in the lab exercises you acknowledge that you have read and understand the safety rules that appear in this manual. You recognize that it is your responsibility to observe them, and agree to abide by them throughout this course. 5  LAB 1: THE NATURALIST IN ECOLOGY In every walk with nature one receives far more than he seeks. (John Muir, Scottish-American naturalist) NOTE: This lab has a field component. We will meet in the lab, but will be outside around the campus for 1-2 hours. Long pants and closed-toed shoes are required. Wear clothing appropriate for the weather and bring other gear as you see fit (e.g. water bottle, binoculars, camera). Lab Objectives 1. Make natural history observations and recognize some of the major themes in ecology. 2. Identify some common prairie organisms to different taxonomic levels. 3. Recognize the level of detailed observation necessary when identifying organisms and making natural history notes. 4. Carry out the first steps of the scientific method. 5. Describe the central tendency and variation of measurements using the mean and standard deviation. Readings Science Toolkit {http://people.uleth.ca/~steyqj/science-toolkit/} Scientific method: What is Science? Scientific method: Data Analysis: Descriptive statistics: Central tendency and Variation Ricklefs, Relyea, & Richter, 2015: Detailed Contents, pg v-xiv Chapter 1, all INTRODUCTION Ecologists study a very broad range of organisms and processes, asking questions about the interconnectedness of these in relation to each other and environmental conditions. The term ecology was coined in 1873 by the German zoologist, Ernst Haeckel, to describe the study of the complex interactions between organisms and their environments that were presented by Darwin in his book, The Origin of the Species. Ecological research inherently begins with observations of the natural world. Before the term ecology existed, the individuals who dedicated their time and efforts to studying and becoming experts on plants and animals in the field were (and are still today) termed naturalists. Naturalists make observations of the natural world and are experts in natural history (what is the organism, what does it do, when does it do them, what does it interact with, where is it found, etc.). They study flora and fauna, but also nonliving parts of the natural world such as fossils. You likely recognize the names of many famous naturalists, both historical (e.g. von Humboldt, Darwin, Audubon, Grey Owl) and contemporary (e.g. David Attenborough, Steve Irwin, John Acorn). As students of biology, we all have something of the naturalist in us, and understanding natural history is imperative to answering ecological questions. In this lab you will complete activities as naturalists, and at the same time learn how an appreciation of the natural world can raise ecological questions and lead to ecological study. Exercise 1: #IAmANaturalist - Notes on Common Campus Plants (work in groups of 4) When making observations of nature, it is important to know the identity of the organisms you are observing. This exercise is designed to familiarize you with a few common plants, and maybe start you on the journey to becoming a naturalist. A naturalist is interested in knowing about the plants and wildlife in an area, the natural history of those organisms, and often also the geologic history, weather, 6 and climate. A good ecologist is likely a good naturalist (but a good naturalist doesn’t necessarily make a good ecologist). 1. Field component: This portion of the exercise will help you get a feel for how a naturalist goes about observing, identify and recording information about an organism under their study. a) Choose a plant: Select one of the marked plant species in the area indicated by your instructor. b) Describe the plant: Prepare a field notes entry about your plant by listing some of the plant’s characteristics. Your description should include the life form, approximate height, arrangement of the leaves, the shape and size of the leaves, the texture of leaf surfaces, flower characteristics (colour, number of petals), fruit characteristics (berry, dry fruit, shape), or anything else that you observe. Think about what might distinguish this plant from the others you see around you. Take a few pictures of the plant showing identifying characteristics to include in your field notes entry. Use the plant identification guides posted to Moodle, an app like Seek or LeafSnap, or reverse image search in Google to try to identify the plant. Note your best guess of its scientific name and common name in your field notes. c) As you work, pay attention to the characteristics of the plant that are necessary for identification purposes. This attention to detail is important anytime you try to identify an unknown organism. d) Once you have completely detailed your chosen plant, use the same methods to identify at least 2 more marked plant species to practice your identification and observational skills. Make field note entries for each plant, showing the species name and include some natural history observations about the plant using the field guides as a reference. Remember that field notes entries should follow the guidelines in the “Field Notebook Guidelines” section of the lab manual and must include the following information: identification (to species when possible), where observed (GPS coordinates and local landmark reference), and natural history details such as structure, size, body plan, life stage, behaviour, etc. (the following space is left empty to complete your “field note” entries for Exercise 1, part 1) Plant 1: 7 (the following space is left empty to complete your “field note” entries for Exercise 1, part 1) Plant 2: Plant 3: 8  2. Homework component: After you have completed your lab today, find time to go out on campus again to observe an organism of your choice. The organism must be naturally-occurring (i.e. not planted as an ornamental by grounds staff; not someone’s pet). Provide a complete field notebook entry on the plant, animal, or fungus you choose. Your field notes may include a sketch of the organism and must provide the following information: identification (to species if possible), where observed (GPS coordinates and local landmark reference), and natural history details such as structure, size, body plan, life stage, behaviour, etc. This homework component will be incorporated as a portion of your first assignment. If you have a twitter or Instagram account, you are encouraged to post about your naturalist experience today by posting comments/pictures of your plants or field notes using #IAmANaturalist. There is a very interesting series of blog posts on the Ecological Society of America’s webpage about the use of the name ‘naturalist’ which you may also like to check out (links available on Moodle). (the following space is left empty to complete your “field note” entry for Exercise 1, part 2) 9 The Naturalist as Ecologist: The Scientific Method As naturalists seek to learn more about the intricate details of the organisms they encounter, they will likely be curious about the “why, where, and how” of things they observe. A desire to understand the answers to those questions often leads to further research, leading us to the scientific method. Scientific Method Astute observations and curious minds lead to interesting research questions, which are the first step in the scientific method (Figure 1). After coming up with a clearly defined research question, the next logical step is to speculate on what the answer might be. A possible answer to the question is called a hypothesis. Potentially, there could be several hypotheses to answer one question. The concept of hypotheses and how to derive them will be further discussed in subsequent labs, as will the other elements in the scientific method illustrated in Figure 1. Information: Observation Testing the hypothesis Experiment increases the pool of Model information that can be used to Scientific literature change or refine questions and hypotheses Question Hypothesis not supported: Hypothesis change hypothesis in light of new data Prediction Hypothesis supported: Conduct additional tests of the hypothesis using original or new prediction Test of hypothesis: Observational study Experiment Modelling Data: Collecting measurements Display (figures) Descriptive statistics Statistical anlaysis Accept/reject hypothesis Figure 1. Flowchart summary of the scientific method. Figure slightly modified from Molles and Cahill, Ecology: Concepts & Application, 2006. Review: Summarizing measurements with mean and standard deviation In today’s lab we will be collecting some measurements. When we take a series of measurements, we often wish to summarize the results with summary statistics. This makes them easier to understand and interpret. This week we will look at two simple ways to summarize a series of measurements – the mean and the standard deviation. The mean tells us where the middle of the measurements falls (formally called the central tendency). It is calculated by adding up all the measurements and dividing by the number of measurements taken (Equation 1). 10  åi=1 x i n x= Equation 1 n The mean is usually (but not always) what people mean by the average. It is identified in a variety of ways, but a common one is the symbol: x. Standard deviation tells us how far apart the individual measurements tend to fall, or the variation about the central tendency. If they are clustered tightly together, we will have a small standard deviation, and if they are further apart, we will have a larger standard deviation. Standard deviation can be calculated by several formulae. The simplest to use, especially for larger sets of data, is Equation 2. æç n ö÷ 2 2 è åi=1 x i ø åi=1 x i - n n s= Equation 2 n -1 Standard deviation is often abbreviated as “SD” but is more correctly identified by the letter “s”. Most calculators and computer spreadsheet programs will quickly calculate both mean and standard deviation for a series of numbers. If you use these programs, make sure you use the formula for standard deviation of a sample, not a population. Throughout the semester, calculating means and standard deviations will be the first step in summarizing data we collect. You should be comfortable with calculating these quickly and accurately in Excel. Exercise 2: Natural History Observations (work in groups of 4) In today’s lab exercises, you are asked to make natural history observations around the U of L campus. In preparation for this activity, review the wide range of themes and topics covered in your textbook by referring to the detailed table of contents. While some of these topics are difficult to observe in the time period and geographic area of our lab activity, we may be able to make observations such as variation in the environment (chapters 2, 3, and 4), adaptations (chapter 7), life history strategies (chapter 8), social interactions within a population (chapter 10), the distribution and structure of populations (chapter 11), interactions between species such as herbivory, predation and competition (chapter 14-17), community structure (chapter 18), or nutrient regeneration in ecosystems (chapter 21). 1. Field component: Spend a few minutes exploring and observing the surrounding natural landscape and all the organisms it contains. Come up with two natural history observations and record these below. Remember that ecological systems occur on a hierarchical scale (Figure 1.1 in Ricklefs, Relyea, and Richter, 2015); you can make observations about individual organisms, populations, communities, or about the broader ecosystem. If you don’t know where to start, you could try making an observation about the plant species you have just learned in Exercise 1. 2. Lab component: Revisit the natural history observations you noted above. Do they fit into one or more of the ecological themes outlined in the textbook table of contents, and if so, where? Provide an example of how you could use one of your natural history observations as the starting point for scientific investigation into a specific ecological question. 11  Observation 1: Ecological Theme: Observation 2: Ecological Theme: Exercise 3: Taking a natural history observation through the scientific method (work as a group of 4) As you were identifying plants and looking around for natural history observations, you may have noticed that there seems to be a lot more pasture sage on the tops of the hills in our observation area than in the bottom of the hilly area. As a naturalist making the observation, you might be curious as to why this is the case. Imagine you decide it has something to do with the specific microclimate preferences of the species. Turning that “why?” moment into a scientific question, then a hypothesis, based on which you can design an experiment or study, makes a naturalist an ecologist. For this exercise, we will work with the hypothesis that pasture sage prefers the dry, arid soils at the hill top more than the moist, cool soils in the valley. We might then predict that if we count the abundance of sage plants we should find more on hill tops then in the valleys. In groups of 4, your instructor will assign you to a random 2x2 meter area on a hill top or in the valley. 1. Field component: Count the number of pasture sage plants in your assigned area and note the habitat type assigned. Habitat: # of sage plants: 2. Lab component: Provide your group’s habitat type and plant number to the lab instructor for inclusion in the class data set. Your instructor will post the class data set to the Moodle lab page. Download this data set to continue along with your instructor. Can we learn anything useful by looking at the table of raw data? What could we do to better understand the data? 12  3. Work as a class to complete the summary statistics for the abundance of plants in each habitat type. Statistic Habitat Type Hilltop Valley Mean SD Based on the calculated summary statistics, do you think the populations we have sampled are different or the same? Is there more variation within one of the environments? Which numbers will you need to compare to answer this question? Can we be sure any difference we see in these data are due to the reason we set forth in our hypothesis? Assume that based on our summary results we conclude that pasture sage requires the hotter, well-drained soils of hill tops to promote growth. What are two problems with this conclusion? What other explanations are possible for the difference we observed in the means? 13 Exercise 4: Natural History Observations of Preserved Specimens (work in groups of 4) Naturalists generally prefer to leave nature as they found it and observe organisms in their natural habitat without any manipulation. However, sometimes due to the nature of the observations being made, particularly in biological or ecological research, it is often essential to collect and preserve sample specimens. Samples can be used to increase identification accuracy, to prepare a voucher collection, to keep repositories of genetic material for study and conservation purposes, etc. In today’s lab you will continue to practice your naturalist skills by observing, identifying and making notes about preserved specimens. In future labs, you will have the opportunity to learn various collection techniques and preservation methods. 1. Lab component: Images and information sheets for several specimens from a variety of plant and animal taxa have been provided. Use the keys and field guides provided on Moodle to practice identifying plants and animals. Prepare field note entries for at least three of the specimens, including your identifications and some natural history notes about the preserved organisms based on field guide and website information. Pay special attention to the characteristics necessarily observed for identification, as you will need to consider these as you make research quality field notes for your assignment. (the following space is left empty to complete your “field note” entries for Exercise 3) 14 (the following space is left empty to complete your “field note” entries for Exercise 3) 15 Thought Questions 1. Define the term natural history as it applies to biological study. Breaking the term down into its two roots and beginning with their definitions may help with your definition. 2. List some important qualities for a naturalist to possess as they set about describing the natural history of an organism. 3. Based on the process of the scientific method, do observations of natural history alone provide evidence in support of hypotheses about those observations? Why or why not? 4. Many animal rights groups say that scientists should not kill and preserve animals for study. Provide 3 reasons you could use to rebut their argument. 16  LAB 2: ECOLOGICAL SAMPLING AND DATA HANDLING I “What we observe is not nature itself, but nature exposed to our method of questioning.” (Werner Heisenberg, German physicist) NOTE: This lab has a field component. We will meet in the lab, but will be outside around the campus for 1-2 hours. Long pants and closed-toed shoes are recommended. Wear clothing appropriate for the weather (i.e. rain gear, hat, etc.). Bring other gear as you see fit (water bottle, binoculars, camera). Lab Objectives 1. Learn common field sampling techniques for plants. 2. Understand the theory behind sampling of populations. 3. Explain the effect of bias, variability of population, and sample size on reliability of statistics. 4. Describe some of the practical problems involved in collecting field data and discuss important sources of error in these data. 5. Define, and distinguish between data types: nominal, ordinal, and ratio/interval data, discrete vs. continuous. Readings Science Toolkit: Scientific Method: Designing Studies: Types of Studies Scientific Method: Designing Studies: Sampling Scientific Method: Designing Studies: Variables and Data Ricklefs, Relyea, and Richter, 2015: Chapter 11, pg. 249-259. INTRODUCTION Sampling Populations Most of the questions ecologists are interested in answering involve large numbers of organisms. If we are measuring the length of crayfish in the campus pond, we won’t be content to know about one crayfish, or even a few crayfish; we want to be able to draw general conclusions about the length of all the crayfish in the pond. This is the population we are interested in. Populations are unwieldy to deal with directly. The first problem would be getting the measurements. Trying to catch every crayfish in the pond would be enormously time-consuming and expensive. We get around this problem by measuring only some of the crayfish and using this sample to make inferences about the entire population. A second problem is describing the population we have measured in some understandable way. Imagine we record the weights of 50 crayfish. A table with 50 weights is not likely to be very informative (at least for most of us). Instead, we characterize the population by using parameters, such as mean or standard deviation. These values are descriptive statistics. The mean tells us what a typical crayfish weighs (the middle of the population) and the standard deviation tells us how much variation there is from crayfish to crayfish. Because we only measure a sample from the population, the mean or standard deviation of our sample is called a statistic. We use our sample statistic to estimate the population parameter, and our goal will be to make the best estimate we can. The better our estimate, the closer our statistic will be to the parameter (e.g. the closer our calculated mean will be to the true population mean). In this week’s lab, you will explore some ways to make your sample better. 17 Replication and pseudo-replication The simplest way to make our sample better is to take more measurements. It makes intuitive sense that the more of the population we include in the sample, the better we can estimate what is going on in the population. This is known as replication. Sample size (n) is an important aspect of any sample. We will take sample size directly into account when estimating how much confidence to have in our sample (see formula for standard error below). Because we assume that increased sample size gives us a better estimate, it is important that we don’t artificially inflate our sample size through pseudo-replication. The most extreme example of pseudo- replication is to count the same organism more than once. Let’s suppose we’re interested in knowing the mean weight of cherries in an orchard. If we weigh the same cherry 100 times, we won’t learn nearly as much as if we measure 100 different cherries selected from around the orchard. Our 100 measurements tell us only how much random error exists in our measurements (i.e. the precision of our weight), and nothing about variation that exists among different cherries. A less extreme but much more common type of pseudo-replication is to take measurements which are not independent of one another, but rather are connected in some way. (Most of the statistical tests we will learn this semester assume that all our measurements are independent.) For example, suppose we want to study the behavior of monkeys, and decide to use a troupe of 20 monkeys in a local zoo. Are measurements of these monkeys likely to be independent? If the monkeys have been raised in the zoo, they are likely genetically closely related, and living together, they have probably learned many of their behaviors from one another. A sample of 20 monkeys from this troupe may not be representative of the behavior of all monkeys of this species. Random samples and bias Any time we sample a population, we want to replicate our measurements as much as we reasonably can. Unfortunately, time and money for sampling limit how many measurements we can make. Ecologists want to get the best estimate possible for the effort invested, and thus need to have some way of deciding when a sample is large enough to be representative of the larger population. Every member of the population should have an equal chance of ending up in the sample. The simplest way to do this is with a random sample, ensuring that every member in the population has an equal chance of being sampled by avoiding bias. For example, if we were measuring the mass of fish in a lake, and we used a net that only extended 1 m below the surface of the water, we would not be catching any of the fish deeper in the lake, which might be larger than those near the surface. Our sample would not reflect the entire population, and so our estimate would be inaccurate. Accuracy measures how close our estimated mean comes to the true value. We often don’t know what the ‘true’ mean is, but by eliminating bias we are more likely to be closer to this value. Bias can be extremely subtle. No matter how hard we strive to be objective, our pre-conceived ideas about the outcome can influence our decisions during an experiment and affect the outcome. For this reason, it is often best to let random chance decide the organism or location to be measured. For example, in well-designed drug studies neither the doctors nor the patients know which patients receive the drug being tested and which receive a placebo. This way doctors don’t unconsciously give the drugs to healthier patients, or evaluate patients receiving the drug differently, and patients don’t report feeling better because they believe they are receiving a drug (the “placebo effect”). Note also that individual measurements can be subject to biases introduced by the observer. Think about what effect this might have if two or more observers are involved in taking the measurements. If we sample only part of our population, the effect is like having a smaller sample. Let’s go back to our example of looking at cherries in the orchard. Imagine that there are 100 trees in the orchard, and cherry size varies from tree to tree. If we took 100 cherries all from the same tree, we would not have a 18 representative sample of the orchard. Our sample size is really one, not 100, because our measurements are not independent. More cherries from the same tree give us a better estimate of the true mean of that tree but tell us nothing about the mean of all trees. Ultimately, how we should sample depends on the population we are interested in knowing about. If we want to know about only one tree, 100 cherries from that tree is a representative sample. If we want to know about all 100 trees, we need to collect from many different trees, and make sure each tree has an equal chance of being chosen. In an ideal world, we would collect at least a few cherries from each tree we sampled, allowing us to learn about variation in size within a tree, and also variation between trees. The real world is even more complex. Cherries might be bigger in sunny parts of the tree; different parts of the orchard might have different soil or moisture, etc. The field ecologist must design his/her study carefully to make sure the sample is as representative as possible, and also take care when reporting results to consider what population was really sampled. Drawing conclusions about a larger population than you have really sampled is a common, but serious, failure in a research paper. Notice that we have two types of “error” in our measurements: bias, which we need to control with careful experimental design; and random variation from measurement to measurement. This random variation will be due in part to random measurement errors (if you measure the exact same thing twice, the measurements won’t necessarily be identical), but will mainly reflect real variation from organism to organism in the population we are measuring. Standard deviation and standard error will help us understand how variable our population is, and we can use this information to help draw conclusions when making comparisons between populations. Standard error The standard error helps us to quantify how much confidence we should have in our estimate of the mean of a population (formally called “standard error of the mean” and abbreviated SE). The smaller the standard error associated with the mean, the more confidence we can have in the mean, as the standard error gives an estimate of how far the sample mean is from the true mean for the population. Standard error is calculated by dividing standard deviation (s) by the square root of sample size (n). s SE = n Types of Measurements Ecologists record a vast number of different types of measurements, but these measurements (or data) must all fall into one of three categories, depending on how much information we obtain. Nominal data: used for labeling mutually exclusive variables without any quantitative value. Frequency data are a common way of dealing with nominal measurements (e.g. We could go out and look at the trees around the university, and assign each one to the appropriate species - poplar, ash, spruce. Without further information, we couldn’t put the species in any kind of order. All we could do is count the number of individuals in each species). Ordinal data: categories are ranked according to some criteria. However, with ordinal data we still don’t know how far apart the measurements are (e.g. We might know that poplars have the largest leaves, ash next, and spruce the smallest. We know that poplars have bigger leaves than ash, but not how much bigger). 19 Interval data: quantitative measurements in which we know not only the ranking of the measurements, but also the interval between them. However, interval scales do not have a true zero (e.g. You can’t measure ‘no temperature’ – 0 degrees Celsius is an arbitrary value, making this an interval scale). Without a true zero, it is impossible to compute ratios. With interval data, we can add and subtract, but cannot multiply or divide. Ratio data: quantitative measurements, distinguished from interval data by the presence of a physically meaningful zero on the scale. The measurements we are most familiar with, such as height, weight, length, and area, fall into this category of measurements. (e.g. We measured and know that poplar leaves, at 20 cm long, are twice as long as ash leaves, at 10 cm long). Data can also be separated into discrete and continuous scales. In discrete scales, only certain values are possible (typically whole numbers). If we are counting number of bird eggs in a nest, we won’t find 3.75 eggs. With other measurements, such as height and weight, any value is possible (within the limits of natural variation, of course) and so these scales are said to be continuous. Nominal and ordinal data by their nature tend to be discrete, while interval/ratio data may be discrete or continuous. Sampling Methods The physical way we sample any given population depends greatly on the type of organism being studied, the environment in which the samples will be collected, and the question being asked about the population. Today we will simply practice several different sampling methodologies. In future lab exercises, the data we collect will be used to answer some questions about how both abiotic and biotic affect the distribution of organisms over a small spatial scale on the U of L campus. Understanding distribution patterns of organisms is a central focus of ecology. There are several different ways ecologists can evaluate distribution: Geographical range: where the organism is present and where it is absent Abundance: how many individuals of a particular organisms are in a certain area Dispersal: has a population of organisms been in an area for a long time or recently arrived Survival and reproduction: how long the organisms live and how often, how much, when they reproduce. Distribution patterns can be affected by both abiotic factors (the physical and chemical characteristics of the environment) or biotic factors (the influence of other organisms through competition, predation, etc.). Each of these factors can also be analyzed on many different spatial scales, from the global to the local. A few examples may help to show how these different approaches are applied in real studies. European starlings (Sturnus vulgaris) were first introduced to North America in 1890 in New York City. In a little more than a century, they have spread across most of the continent. Ecologists have tracked their dispersal into each new environment, and the factors that have aided their invasion (primarily an ability to outcompete many native bird species, particularly in urban environments. These studies examined the geographical range of the starling on a broad spatial scale, examining both dispersal over time, and survival as affected by biotic factors (competition). At the other end of the spatial scale, we could look down into the river valley in Lethbridge, and ask why the cottonwoods (Populus spp.) grow only on the valley bottom and not on the slopes a few metres away. This question of microhabitat is likely explained by an abiotic factor – water in the soil. 20 Exercise 1: Field Sampling of Plants (work in groups of 4) Note: Some details of the sampling protocol are subject to conditions during the summer growing season and will be discussed by your instructor at the start of lab. The class will move as a group to an area on campus that is typically mowed near prairie that is typically left to grow naturally. Because microclimates in the area might affect plant growth, we want to get a sample that is representative of the whole patch. A transect is a good way to do this. A transect is a line running through the population to be sampled, often along some sort of gradient in the environment. Measurements can be taken randomly or at regular intervals along the transect. A very common tool used to estimate the distribution or population size of sedentary organisms is a quadrat. A quadrat is an easily transportable plot that is laid down on the surface being studied to define a standard sampling area. It can be essentially any shape and size, chosen based on the organism being studied. 1. Lab component: Each pair of students should generate two random numbers, one between 0 and 50 and one between 0 and 5. Use a stopwatch to generate these numbers. Start the watch and then stop it again a few seconds later without looking at the screen. The decimals (tenths and hundredths of a second) will be essentially random. If the decimals are less than 0.50, use this as your first random number. If the decimals are > 0.50, subtract 0.50 and use this as your random number. For example, if your watch read 5.69 seconds, you would use 0.69-0.50 = 0.19, so 19 would be your random number. Now repeat the same process using only the hundredths of a second to generate a random number between 0 and 5 (subtract 5 if the number is higher than 5). These two numbers will define your sampling location. Record them in your field notebook - the first number will define a distance up the path and the second will define a distance away from the path. One pair of students in your group of 4 will use their coordinates to measure to the left of the transect, and the other pair of students will use their coordinates to measure to the right of the transect. Habitat type Random # b/w 0-50 Random # b/w 0-5 # of non-grasses Distance Up the Distance away from transect Transect Mowed grassland Un-mowed grassland 2. Field component: A 50 m tape measure will be extended in each patch and serve as a transect. Use your randomly generated coordinates to locate your sampling location along the transect. We will record the density of any non-grass plants using a circular quadrat. Record the number of non-grass plants you counted in each habitat type (mowed or un-mowed) in the table above. Provide your results to your instructor for inclusion in the class dataset. 3. Data analysis component: a. Before looking at the class data, begin by coming up with a hypothesis about how you might expect the disturbance of mowing to affect the density of weedy species in the natural area. Hypothesis: 21  b. Using the class dataset uploaded to Moodle and working in Excel, calculate means and standard deviations to determine if mowed prairie is more is more or less “weedy” than unmowed prairie. Prepare a completely formatted graph showing the summary data for this field study. c. Based on your graphed summary statistics, provide a conclusion about the effect of mowing on weedy plant density. Conclusion: Exercise 2: Field sampling of invertebrates (work in groups of 8, divide into two subset groups for the two microhabitats) Note: Some details of the sampling protocol are subject to conditions at the time of sampling and will be discussed by your instructor during the lab. Collection of invertebrate samples is a common tool in ecological study to answer many questions, either about specific invertebrate taxa themselves or about the overall health of a given environment because invertebrates are highly sensitive to even minor environmental changes. Terrestrial Invertebrate Collection: Trapping of terrestrial invertebrates can be carried out using a number of different methods, such as sweep netting, pitfall traps, malaise traps, Berlese funnels, barrier traps, light traps, etc. This week we will use pantraps, which are relatively shallow dishes, with wide surface openings (hence, ‘pan’), of various colours to attract flying insects. These are laid on the ground and partially filled with water or, if traps can’t be emptied every day, a preservative such as ethylene glycol or saltwater. A drop of dish soap is used to break the surface tension of the trap liquid. For collection, the trap contents are poured through a fine mesh then rinsed into a jar containing 70-80% ethanol. Prior to this week of lab, your instructor set pantraps along transects in two different habitat types. 1. Field component: Each group of students will be assigned a trap number and will collect the pantrap contents from both microhabitats. Divide your group into two subsets to increase efficiency of collection. a. Pantrap contents should be poured through the mesh sieve into a collection jar. Be sure to collect all specimens from the trap and from the sieve (use the squeeze bottle for rinsing). After the specimens have been removed from the trap, replace the trap liquid into the pantrap. If the volume of the trap liquid has diminished significantly inform you instructor to replenish the liquid. 2. Lab component: Once back in lab, transfer the specimen samples from your collection jar to an observation pan to sort and identify. Using the identification skills learned in the first lab, identify the specimens collected from each trap. While the pantrap samples will likely have many small to tiny organisms in them, we will focus only on the “macroinvertebrates” (those easily observed and identified with the naked eye) and we will only identify them to the Order level in the classification hierarchy. Complete frequency counts on the numbers of specimens of each order 22  that were collected in your group’s sample. This data should be provided to the lab instructor for inclusion in the class dataset. Once identified and counted you can throw away your specimens. 3. Data analysis component: We will use these data in a future lab on biodiversity measurements (completed in Lab 9). 23  Thought Questions 1. Does the mean provide a more accurate estimate than a single measurement? Why or why not? 2. Was there any degree of pseudo-replication in our sampling? If so, explain. 3. In Exercise 1, we considered two variables – habitat type (mowed or unmowed) and plant density. a. What type of variable is habitat type? nominal / ordinal / ratio / interval. b. What type of variable is plant density? nominal / ordinal / ratio / interval. 4. Rank the three basic types of measurement (nominal, ordinal and ratio/interval) based on the amount of information they provide. 5. Could you convert ratio/interval data to ordinal data, or vice-versa? Why might you want to do this? 6. The bar graphs you produced in this lab should have displayed error bars. If you were plotting nominal data as raw counts, would your graph have error bars? Explain your answer. 7. a) Which experiment would be better: one in which you group your independent variable treatments into three ranked categories (e.g. low, medium, high temperature), or one in which you collect a range of quantitative values for your independent variable (e.g. several treatments measured from 0-20°C)? Why? b) Why might a researcher carry out the weaker experiment above? 8. Is looking at calculated central tendencies (i.e. means) sufficient to make a conclusion about a given hypothesis? Why or why not? 24 9. A larger sample will almost invariably give a better estimate of population parameters. Does this mean it will always be worth taking a bigger sample if time and resources permit? (Hint: assuming SD is 10, what happens to SE when you collect 10 replicates vs. 20, 100, 500, 1000, 2000, etc.?) 10. a) You are comparing two samples of mean leaf area. You obtain the following means ± SE. Sample 1: 15 ± 5 cm2; Sample 2: 20 ± 5 cm2. How much confidence should you have that the two populations have different means? Explain your answer. b) Now compare the following samples of leaf area (mean ± SE). Sample 1: 15 ± 1 cm2; Sample 2: 20 ± 1 cm2. How much confidence should you have that the two populations have different means? Why has your answer changed from the part ‘a’? What possible explanations are there for the lower SE in the second set of samples? 25  LAB 3: PHENOTYPIC VARIATION AND ADAPTATION “Natural selection has, through all its long history, shown a mighty open-mindedness toward any idea that works.” (Robert Ardrey, American science writer) Lab Objectives 1. Describe the different sources of phenotypic variation within a species. 2. Define a scientific hypothesis. 3. Understand how previous knowledge is used to develop plausible hypotheses. 4. Recognize and distinguish between hypotheses and predictions in scientific literature. 5. Define and distinguish between the null and alternative hypothesis and explain the usefulness of these concepts in inferential statistics. 6. If given a question and a set of data, be able to follow a flowchart to choose the appropriate statistical test. 7. Understand and explain the meaning of a p-value. 8. Carry out a simple statistical test: the t-test using Microsoft Excel, interpret the results appropriately, and extract the appropriate information for describing the results of the test in a research paper. 9. Distinguish between peer-reviewed and non-peer-reviewed journals. 10. Understand and explain the role of peer-reviewed journals in the research process. 11. Search the peer-reviewed literature for articles relevant to your own research. 12. Understand the structure of the introduction to a research paper. Be able to name the four main elements of an introduction and identify them in a paper. Readings: Science Toolkit: Scientific Method: Hypotheses: Building a Hypothesis and Searching the Scientific Literature Science Writing: Research Papers: Introduction Scientific Method: Data Analysis: Inferential Statistics Science Writing: Research Paper: Results Science Writing: Research Papers: Citations and Literature Cited U of L Library website How To Articles: (https://library.ulethbridge.ca/biology/home) Articles & Databases (Search Techniques and Strategies video) Research, Writing & Citation Evaluating Your Sources Ricklefs, Relyea, & Richter, 2015: Chapter 4, pg. 89-91 (phenotypic variation) INTRODUCTION One of the first steps in answering a question about the natural world is to come up with a plausible answer to the question – an answer that we can then test. But testing hypotheses is typically expensive and time-consuming, and we want to spend our time and money as efficiently as possible. This means we want to choose hypotheses that are plausible – ones that make sense based on what we already know about the topic. Science is a process of building on existing knowledge, and whatever the subject we are interested in, it is likely that others have asked similar questions in the past (although the similarity may 26 not be immediately obvious). An important starting point in any research project is to sift through the huge mass of previously published research (commonly called “the literature”) in search of information that will give us clues to the answer to our own question. Computers have made the process of searching this immense body of information much faster and easier, but searching the literature remains a skill that must be learned and practiced to achieve proficiency. What is a Hypothesis? In essence, the hypothesis is no more than an educated guess about the answer to a researcher’s question. But, there are important distinctions between a scientific hypothesis, and casual speculation about how things work. The first relates to making the guess “educated”. Scientists don’t simply pick their ideas out of the air, they try to come up with ideas that make sense based on both their own observations and logic, and on the research of others. A great deal of the immense power of science comes from constantly building on existing knowledge – using previous research as a lever to help us keep learning new things about nature. Think of the world as a giant jigsaw puzzle that we are trying to put together. We use the parts of the picture we can see so far to help us puzzle out where the next pieces should go. Sometimes we will try a piece that doesn’t fit, but not as often as if we were just putting in pieces at random. This allows us to be vastly more efficient in our research. The second key aspect of the hypothesis relates to research as well. The hypothesis must be testable. Science is only concerned with ideas that can be tested. For example, you might speculate that fairies exist, but they are simply not visible to any of our senses or instruments. This could be true, but it could never be the subject of a scientific investigation, since we could never demonstrate through any experiment that the fairies don’t exist. If study after study failed to find evidence for fairies, it could still always be argued that they exist, but simply don’t show up on any of our instruments. Notice that the key test for science is to be able to disprove or falsify the hypothesis. We can never prove any hypothesis with 100% certainty because however well our current hypothesis fits the facts we have gathered so far, we can never be sure that another theory wouldn’t fit equally well, or that new facts will come to light which don’t fit the hypothesis. However, to present our idea as a scientific hypothesis, we must be willing to say: If this experiment doesn’t come out the way I expect it to (the prediction(s) of the hypothesis), I will accept that my hypothesis is wrong. Developing a Hypothesis There are two basic starting points in developing a hypothesis. The first is to begin with an observation of nature, and then to attempt to explain it. For example, we might observe that tigers have stripes and ask: What is the function of these stripes? Additional observations and a bit of reading might suggest that the stripes provide camouflage in the tiger’s normal habitat. This approach is known as inductive logic. The other way to begin, is with some general theory and then generate new predictions which can be tested. For example ecologists have been quite successful in explaining bright colouration and long tails in male birds as a product of sexual selection – these ornaments make the males more attractive to females. Today researchers are going on to use the same ideas to attempt to understand differences between the sexes in some insects. This is known as deductive logic. Modern science depends more heavily on this approach, and so the scientific method is sometimes called a hypothetico-deductive process. Whichever approach we use to begin, we will need to follow up our original idea with some research in the library. We need to find what is already known about our topic, and whether our initial idea makes any sense. Remember from above that we are constantly trying to build on existing knowledge. With ecological hypotheses, we typically need both some general theory and some specifics of the organism we are studying in order to develop reasonable hypotheses. The general theory helps us understand how this type of question has been answered in other organisms. The details of our study organism’s 27 physiology and natural history will help us see which theory might best apply to our specific situation and how it applies. Our own logic and ingenuity will help us make connections between theory and a real organism. Peer-Reviewed Literature The most important body of information that the researcher draws on is primary literature (also called refereed journals or peer-reviewed journals). These journals are important because they publish original research papers written by the researchers themselves. In the primary literature we are hearing the results and what they mean directly from those who conducted the study. Every time this information is read and copied by others, some important information may be left out, and small (or even large) errors may creep in. Secondary sources are a bit less complete and a bit less reliable than the original papers, and so must be treated with some caution (although many remain excellent resources, especially in the early stages of your library research). A second strength of the primary literature is the process of peer-review. Before any research paper is published in these journals, the editors of the journal will send it out to two or three other researchers in the same field (“peers” of the paper’s author) and ask their opinions. Some papers are flatly rejected for publication on the basis of the reviewers’ comments, and so some poorly done research is blocked from publication. More commonly, the reviewers offer some suggestions for further experiments, additional data analysis, or editorial changes, which make the paper stronger before it is published. Unfortunately, no simple and foolproof set of rules for recognizing peer-reviewed journals is possible due to the huge number and variety of journals. Some are commercially published, and some are run by academic societies. One thing to look for is papers published in the standard research format known as IMRAD (for the main sections of the paper – introduction, methods, results and discussion) with citations in the text and a Literature Cited section at the end. Most of the journals lack advertising (although the highly regarded journals “Science” and “Nature” are exceptions to this rule) and are aimed at a specialized audience rather than a mass market. If you are in doubt about any specific journal, your lab instructor can help you determine if it is peer-reviewed or not. Over time you will begin to know most of the useful journals in your field and will get a “feel” for identifying primary sources. Exercise 1: Recognizing Hypotheses and Predictions Access the three research papers posted to the Lab 3 toggle on your Biol 2200 Lab Moodle page. Go through the introductions of the papers and for each find the hypothesis and the prediction(s) tested in the paper. This exercise is helpful every time you read scientific articles as it will help to direct your focus in your readings to determine what background studies best apply to the question you have at hand. You should practice this skill each time you read articles for the assigned Research Readings. Note the hypotheses and predictions for each of the three papers we reviewed today and record them here or highlight them in your copy of the paper. 28 Ecology Concept: Phenotypic Variation An ecological topic that we will explore in more detail in this week’s lab is phenotypic variation. An organism’s phenotype is all of its physical and behavioral characteristics. Because ecologists are often interested in specific taxa and will make observations of many individuals within those taxa, they may start to notice distinct variations in phenotypic traits, or phenotypic variation, between individuals of a single species. Phenotypic differences might be a result of random variation, which refers to unexplainable, unpredictable differences from one individual to another. However, when we are referring to phenotypic variation, it is generally assumed that we are referring to the non-random differences from one individual to another within a species, or the variation among individuals due to the environment. This variation is the result of underlying genotypic and/or environmental influences. It is extremely common for individuals of the same species to vary from one environment to another. This can be observed as phenotypic plasticity, the ability of a single genotype to exhibit variable phenotypes as a response to different environments. The way a given genotype is expressed phenotypically across various environments is described as a reaction norm, which can be visualized by graphing environmental condition against some phenotypic value. There are several ways in which prevalent environmental conditions influence phenotypic variation. Some of those are defined below: a) Tolerance – Optimal conditions result in a ‘healthy’ phenotype and marginal conditions result in a ‘stressed’ phenotype. This is a non-adaptive form of phenotypic plasticity in which one phenotype is most beneficial in all environments, but is not produced in all environments. This occurs when the conditions may simply be better for growth in one environment. For example, as you move up a mountain, trees of a particular species become smaller and less healthy, before disappearing altogether. The trees are stressed by the increasing cold and tend to be stunted near the edge of their geographical range. b) Acclimation – Reversible physiological changes that allow better function under local conditions. This plasticity is adaptive, in that the different phenotypes are each beneficial in the environment in which they are found. For example, humans who spend time at high elevations begin to produce more red blood cells, to cope with the lower levels of oxygen in the air. c) Developmental responses can produce different body forms as a result of cues in the current environment. This is an example of adaptive, non-reversible phenotypic plasticity. For example, depending on what food items are available, spadefoot toad larva will develop into one of two body forms – an omnivore-morph, or a carnivore-morph. d) Ecotypes are different genetic strains of the same species. Each ecotype is best adapted to the conditions in its local environment. There is no genetic obstacle to interbreeding between ecotypes, however due to the differences in genetic strain, migration to other environments by natural selection is prevented. Several flowering plants possess high-elevation versus low- elevation ecotypes, for example, and moving the high-elevation plant to a low-elevation area will not change its growth form. Exercise 2: Observation leads to Hypothesis 1. Scenario: A naturalist who has stopped to make notes about some snowberry bushes along her favorite coulee hiking trail notices that the bushes in low, shaded areas on north facing slopes seem to have differently sized leaves than those in higher, full-sun areas on south-facing slopes. 29  Generate a hypothesis for this observed difference in leaf size and record it here. Given your hypothesis, write a prediction for the leaf size of snowberry bush leaves on north- versus south-facing coulee slopes. 2. Field component: Using class data, we will look for evidence of phenotypic variation between leaves of snowberry on campus. The phenomenon we will observe can be seen in several species of trees and shrubs. Proceed to the field area with your instructor. In pairs, find and measure the length and width of three “sun” and three “shade” leaves. Choose leaves that are 3 or 4 nodes down on the stem of the plant. Record your measurements below. Leaf North-Facing Slope South-Facing Slope Measurement Leaf 1 Leaf 2 Leaf 3 Leaf 1 Leaf 2 Leaf 3 (cm) Length Width Do you notice any qualitative difference in size? 3. Data analysis component: Once back in the lab, multiply the length and width of each leaf sample to give a rough estimate of leaf area. Average the 3 rough leaf area measurements together. Provide your pair’s data to the lab instructor for inclusion in the class data set, which will then be posted to the Lab 3 toggle in Moodle. Slope Aspect Leaf Area (cm2) (l x w) Average Leaf Leaf 1 Leaf 2 Leaf 3 Area calculated North-Facing Slope South-Facing Slope 4. We will now use the data to make some interpretations about our original prediction and hypothesis. The first thing we need to do is summarize our data with descriptive statistics and graphs, to make the trend more visible (raw data are generally not very informative, and so are almost never included in a research paper.) Together with the class, calculate the mean leaf areas and standard deviations from each treatment (slope aspect). Prepare a properly formatted bar graph illustrating the summary statistics for the difference in leaf area for the two microhabitats. Be sure to save a copy of this graph, as it may be requested in an upcoming assignment. 30 5. Answer the following questions based on the class findings: a) Do you think there is evidence that shrubs produce larger leaves in a cooler, shaded environment than in a hot and dry, sunny one (or vice-versa)? What factor(s) give you confidence in your conclusion? What factor(s) might make you doubt your conclusion? b) Conduct an appropriate statistical test to determine if the variation in leaf area is significant. Report the results here as you would in a published scientific paper. c) Is there more variation within one of the environments? (What numbers will you need to compare?) d) What possible explanations are there for the variation you see among measurements within each environment? e) What possible explanations are there for the variation you see among measurements between environments? f) Suppose you concluded that snowberry leaf size is different in the two locations. Which type of phenotypic variation do you think is most likely (refer to the four types listed in the introduction)? Can you say with certainty which type is responsible for any variation? Why or why not? 31 Interpreting Experimental Results In the previous labs we have qualitatively compared our two samples to see if they were different. We then asked ourselves if the populations (from which the samples were derived) were also different. Up to now, we haven’t really been able to answer this question in a satisfactory way. No matter how well designed our experiments are, we can’t be sure that the difference between our samples isn’t just the result of random chance. As a simple example, think about flipping two coins 20 times each. One coin comes up heads 12 times, and the other comes up heads 6 times. Are the two coins really different, or could the difference be simply chance? Inferential statistical tests will help us to answer this question. They get their name because they help us make inferences about populations based on our samples. Our statistical tests will never give us complete certainty, but they help us to know how likely we are to make a mistake if we conclude there really is a difference between our samples. Null and alternative hypotheses: Inferential statistics are designed to help us answer questions, so we need to begin with a clear understanding of the exact question we are interested in. We state this in the form of two mutually exclusive alternatives called the null and alternative hypothesis. Remember that we normally set out looking for a difference or a correlation between two (or more) populations. The alternative hypothesis (HA) will be that the expected difference or correlation does exist. The null hypothesis (H0) will be that there is no difference or correlation. If you remember that null means nothing, you won’t have any trouble keeping HA and H0 straight. The null hypothesis says nothing is going on. One common error is to think of the null hypothesis as the opposite of the alternative, but this isn’t quite right. When we ask whether snowberry plants have bigger leaves in shady areas than hotter areas, the alternative hypothesis is that leaves from moist, cool areas are bigger than leaves from hot, dry areas. The opposite of this would be that leaves from wet areas are smaller than leaves from dry areas, but this is not a null hypothesis. The correct null hypothesis would be that leaves from the two areas are the same size (no difference). There are always two alternative hypotheses for each null hypothesis – one in each direction. It turns out that when doing our statistical tests we can usually lump these two alternatives together and consider only the general HA that a difference exists. This is known as a “two-tailed test” (because we consider that the difference could be in two directions) and generally is more conservative than considering only one direction (a “one-tailed test”). The data will tell us the direction of the effect if it exists. We set our questions up in the form of HA and H0 because our statistical tests do not allow us to prove anything. We proceed only by disproving (or falsifying) hypotheses. If we can disprove the null hypothesis, this provides support for the alternative hypothesis. Typically, the HA in an experiment is a predication made by some more general hypothesis, and so we can provide support for this broader hypothesis. Keep in mind, however, that we can’t even disprove anything with complete certainty. Our statistical tests will only give us answers in terms of probabilities. Specifically, they tell us the probability of getting the results we did, if the null hypothesis is true. If this probability is small, we are confident in concluding the null hypothesis is false (i.e. rejecting H0). Types of Error We ask a question that has two possible answers: either the null hypothesis is true, or the alternative is true. Whichever conclusion we draw, we may be right or wrong (See Fig. 1). If we are right, all is well, but if we are wrong, we need to consider what type of error we have made. If we conclude that the null hypothesis is false, and it is really true, we have made a Type I error. If we conclude the null hypothesis is true, and it is really false, we have made a Type II error. Most simple inferential statistical tests only tell us our chance of making a Type I error. If we want to know our probability of making a Type II 32 error, we must do a more sophisticated type of test called power analysis (Power is defined as our chance of not making a Type II error). Power analysis is beyond the scope of this course. H0 is true H0 is false Reject H0 Type I error We are correct Fail to reject H0 We are correct Type II error Figure 1. A truth table can be used to distinguish between Type I and Type II errors. Interpreting Results of Tests The final result of most statistical tests is a number called P or the p-value. As noted above, this number is the probability of getting the results we did in our samples, if the null hypothesis is true. Put another way, P is the probability that our results can be explained purely by random chance. For a concrete example, let’s assume we are comparing crop yield from two different varieties of wheat. Our null hypothesis will be no difference in yield between the two varieties. If we see a difference in the mean yields in our samples, there are two possibilities. First, the difference reflects a real difference between the two varieties (our populations). This is the alternative hypothesis. Second, the two varieties produce equal yield, and the differences we see in our sample are simply due to random chance (null hypothesis). If we get a p-value of 0.01 in our statistical test, that will tell us that there is only one chance in 100 of seeing a sample difference as big as ours due to random chance. Since this probability is small, it makes more sense to conclude that the two varieties really are different. This is analogous to a court case, in which we must prove the defendant (the null hypothesis) guilty beyond a reasonable doubt before reaching a guilty verdict. There’s one difference, however, scientists define exactly what is “reasonable.” By convention, we use a probability of 0.05 (one chance in 20) as our cutoff. If there is more than one chance in 20 that our results could be due to random chance, we will not reject this possibility. Notice that we are biased toward not rejecting the null hypothesis. If there is even a one in 10 chance that H0 explains our results, we will not conclude that there is anything else going on. In most areas of theoretical science, this conservative attitude makes sense. We don’t want to jump to incorrect conclusions. We would rather wait and study the matter further. In some fields of applied science we need to be equally concerned about missing a pattern that is really there. An example would be testing a new drug that might save many lives. In these situations, power analysis is essential. Choosing a Statistical Test Memorizing all statistical tests available, and when they should be used, is not necessary. But you should be familiar with the type of information that is used to decide on an appropriate stats test. This can be broken down into two main questions. 1. What question are we trying to answer? Remember that typically we are looking for a difference or a correlation. If we are looking for a difference, we can compare many different statistics (e.g. mean, variance, distribution). 2. What type of data do I have? Statistical tests are designed to be applied to specific types of data. For example, some tests can only be used with ratio/interval data, while others are designed for use with nominal or ordinal data. Some tests are designed to compare only two treatments, while others can compare more than two treatments. Some tests require data collected in pairs (for 33  example a test on the same animal before and after some drug is given). Some tests are only designed to use data that are parametric (or normally distributed). If your data don’t follow a bell curve, you can’t use a parametric test. However, in some cases you may be able to transform your data by applying the same mathematical formula to each point, resulting in a more normal distribution of data points. Practice using the flowchart on the Science Toolkit until you are comfortable using this approach to choosing a statistical test. Together with the instructor, the class will use the flowchart in the Science Toolkit to choose the appropriate statistical test for our snowberry data and alternative hypothesis. You can assume the data are parametric. Once the appropriate test is chosen your instructor will walk through carrying out the test using Excel’s Data Analysis Toolpak. Record the pertinent information from the test, along with the appropriate conclusion. Test statistic: Degrees of freedom: p-value: Conclusion based on these results: Was the prediction supported by the data? Presenting Results Research results are almost always presented in a stereotypical format designed to provide the reader with a great deal of information as concisely as possible. It must be clear to the reader what the specific alternative hypothesis in the test is. However, statement of this hypothesis can often be combined with the statement of conclusion, to save space and time for your reader. Note that the null hypothesis is NOT stated. The reader can easily infer the appropriate null hypothesis from our alternative hypothesis, and so there is no need to state the obvious. This is true for most results. A conclusion in this form based on the results of an inferential statistical test can also be called a trend. Ultimately, looking for trends in the data is what research is all about. Note also that if we looked for a correlation or difference and failed to find one, this should also be reported, in exactly the same way, and is still considered an important trend. Remember, also, that we want to draw conclusions about the populations we are studying, not just the samples we looked at. Our statistical test allows us to reject the null hypothesis and conclude that there is a real difference in the data sets. The results are very unlikely to be the result of a fluke in our study data. We need to indicate this formal conclusion to the reader, but we can do it more concisely than by stating that “we reject the null hypothesis”. Instead we simply say that the difference is significant. “Significant” is used in a results section only to indicate that a p-value < 0.05 has been obtained, and the 34 null hypothesis can therefore be rejected. Avoid using this word in any other sense in your results section, or you may confuse your reader. Six pieces of information are normally needed for each result being described. Alternative hypothesis (prediction) being tested. Statistical test being used. The test statistic calculated. The degrees of freedom calculated. The P-value estimated. The conclusion drawn (i.e. significant or not). The results of the statistical test are typically provided in a compact phrase enclosed in parentheses and immediately following the statement of the result. Example: “We found blue fish in Seuss Lake to be significantly longer red fish (t-test: t38=3.61, p