Practical ecology lab manual 2014 lortie


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Here is a new second-year ecology lab manual for ecology. The focus has been shifted more extensively to technique development, critical scientific thinking, and independent and structured inquiry.

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Practical ecology lab manual 2014 lortie

  1. 1. practical ecology The way of the ecologist is quantitative, creative, and meditative. Christopher J. Lortie 2014
  2. 2. 2 Schedule wk dates practice module lab exercise 1 Sept 8-12th no labs 2 sept 15-19th Techniques & data introduction intro to groups, publishing data, intro to sampling designs: product publish fun dataset on figshare (0% just practice) 3 sept 22-26 Techniques & data field training field sampling training plants: product publish dataset with meta-data & methods (5%) 4 sept 29-oct 3 Techniques & data field training field sampling training animals: product publish dataset with meta-data & methods (5%) 5 oct 6-10th Experimental design experimental design training meet in lab, plan & design experiment for next two weeks: product hand in experimental design proposals (5%) 6 oct 13-17th Experimental design field experiment field experiment by each group 7 oct 20-24 Experimental design field experiment field experiment by each group 8 nov 3-7th Big Data experimental analyses training Statistics tutorial in lab with your experimental datasets & the write-up: product publish final dataset with meta-data & methods (5%) 9 nov 10-14th Big Data Big Data Ecology Big Data Lab on published ecological dataset from funded research 10 nov 17-21 Critical thinking skills Critical thinking training Hand in lab report (20%) then Critical scientific thinking in ecology 11 nov 24-28 Critical thinking skills Critical thinking training Critical scientific thinking in ecology 12 dec 1-5 Critical thinking skills Critical thinking Critical scientific thinking in ecology & in-lab exercise (10%)
  3. 3. 3 Purpose of practical ecology exercises Learning outcomes: The primary objective of the labs is to provide you with a solid introduction to the skills needed to effectively conduct environmental research. Here are the learning outcomes associated with the activities included herein. 1. To become familiar with ecological data collection, meta-data, and data sharing. 2. To be able to design an ecological experiment. 3. To develop scientific writing skills in methodological and meta-data description and report writing. 4. To critically appreciate the strengths of an ecological perspective and the scientific literature in general. Skills: (1) Data collection, data entry, meta-data description, and data publishing/sharing. (2) Experimental design for natural systems. (3) Critical thinking skills in reading, writing, and processing scientific literature. Products & evaluation: Individual datasets with meta-data & methods x 3 (5% each) 15% Experimental design 5% Lab report 20% Critical thinking exercise 10% Total (course) 50%
  4. 4. 4 Techniques & data module
  5. 5. 5 WK2. Techniques & data: introductory lab Location: Lab Tasks: Group delineation, tutorial on data & data sharing, collect a fun dataset, publish dataset Products: Dataset – NOTE worth 0% this week, but it is your chance to get ready for all other submissions worth 5% each. Skills Collect data Write meta-data and methods description Publish data Steps 1. Form into groups of four for subsequent fieldwork in upcoming weeks. 2. Tutorial by teaching assistant on data, meta-data, and data-sharing. 3. Collect dataset individually in or out of the lab. Number of individuals with different eye colours by gender for instance. Anything in or out of the lab that includes at least two variables (i.e., gender and eye colour) and takes only 15 minutes to collect. 4. Return to lab and enter data into laptop or tablet. If you do not have a device with you, ensure you have recorded all data into your notebook to enter this evening. 5. Set-up account. Use whatever name/handle you like if you prefer to be anonymous. However, provide your teaching assistant with your name so that she/he can check your work this term as dataset sharing is worth 20% of final grade in the course. 6. Publish/share you dataset with methods and meta-data. You can write the methods and meta-data details in a word doc and pasted into the description box. You can directly upload the dataset you entered into excel for instance. Use two worksheets in Excel one for the data and one for the meta-data. NOTE the teaching assistant will check and mark this every week after this week. 7. Ensure you use the following tags for the dataset: York University, BIOL2050, Lortie, introductory lab, ecology. Please also use additional tags for whatever your dataset was about such as eye colour, gender, plant presence, number of squirrels, backpacks versus bags etc. Tags enable others to find your dataset.
  6. 6. 6 Techniques & data introductory resources (read if you need) Data “Data are the underpinning of the scientific method. Without data to back up theory, science becomes ungrounded conjecture” (Heidron 2008 in Library Trends). Admittedly, this is a bit extreme, but it is not an uncommon philosophy held by many ecologists. Data (plural) are one of the fundamental outputs of the scientific process. Data are not the only product nor always the most important but are nonetheless a substantiate form of evidence. Importantly, data shared allows other to explore your interpretations and promotes open, transparent, and reproducible science. Data are a set of measurements recorded from a natural system in ecology and are frequently stored in tables. Every set of elements/attributes explored is called variables and can be both quantitative and qualitative. Quantitative variables are numeric, and qualitative variables are usually text. There are many forms of data collected in ecology. A brief tour of any major data repository with ecological data will provide with you a sense of the scope of data we collect. There are many terms you will encounter in the ecological literature and datasets. Here is shorthand for a few of the most common ones. Predictors or factors or independent variables are the groups of subjects recorded that likely predict/drive/shape/influence the other variables in your dataset. For instance, diameter of tree trunk can sometimes predict size of leaf canopy or distance to nearest neighbour. If we do not have a sense of the potential causation in an ecological system, we model the dataset as a set of variables and explore patterns of covariation. This is entirely legitimate and can be important in promoting discovery and shaping future experiments. Every variable in a dataset will have its own distribution and properties, and it is extremely useful to consider the implications of these properties. For instance, size of an organism in an ecological system can be recorded/modeled as continuous (i.e. we measure height in centimeters), ordinal (i.e. we use size-classes such as 1,2,3, & 4), or categorical (i.e. small, medium, large trees or as binomial with only two classes such as saplings & adults). There are trade-offs associated with the type of the data measured. Height as a continuous variable is the more rich, powerful form but also the most time consuming to collect and we will certainly measure fewer trees relative to zipping around a woodlot and eyeballing the height as 1-4 or as sapling and adults. The scope of inference or purpose of the experiment will determine your decisions for each variable as you will have at least two variables to measure, and in ecology, we must always balance covering more a system with detail. The main goal of current ecological research is explore the relationship between several sets of variables and interactions are always
  7. 7. 7 important in ecology both biotic and abiotic and between different levels of the factors (i.e. high-water and low-light etc.). Consequently, a critical practical skill in ecological and environmental research is to be able to assess the datasets of others and infer the trade-offs they decided upon and in designing your own experiments, whether mensurative or manipulative, ensuring that you best capture the ecological process in question. Here are two examples of ecological/environmental data repositories: However, is also a popular repository for datasets and is the sharing tool we will be using in this course. Here is my profile with a collection of both datasets and visualizations of datasets/concepts that I have shared for feedback and collaboration with other scientists. Here is a favorite of mine: Quick summary: data are tables of numbers and words that capture your ecological system.
  8. 8. 8 Meta-data Meta-data are the data about the data. Typically in ecology, we are describing both how we collected the data (the methods) and what each variable in a dataset means. Check out published ecological datasets to get a feel for the incredible and often unfortunate variation in the meta-data that are published. Go to DataONE and check out the education module on meta-data: but a simple best practice is that someone else unfamiliar with your experiment or survey should be able to read the meta-data (description box in figshare) and understand what you did and what every variable means. As a quick guide, I create a sheet in my excel data file entitled ‘meta-data’. Then I cut and paste every column heading from the primary data sheet into rows and write a brief description of what each means. This provides the reader/user of my data file, a synopsis and clear statement of even very simple things like plant height (in metres, tape to ground to nearest flat surface, measured to highest point in plant even if it was a leaf or flower and not the woody stem – i.e. it is plant height in this column not stem length etc.). Practice, practice and reading the meta-data of others and realizing you have no idea what they are talking about dramatically improves your own descriptions. You must also include a general description of how you collected data, when, the instrumentation, and the collaborators. This is typically not in the meta-data sheet in the excel file but in notes that you paste into the description field in the figshare tool. Quick summary: meta-data are the data about the data – the descriptors – that allow others to understand the meaning of every variables in a dataset and how the experiments was done. For this course, use a separate sheet in your excel file entitled ‘meta-data’ and describe every column heading (variable) in your dataset, what they mean, and what any categories within a variable also mean. Use the description box in figshare for the general description. Use tags so that others can find it (and mark it). Meta-data = (1) every variable described within data file in separate sheet, (2) the general description of methodology as short-paragraphs pasted in figshare description box, (3) tags that described the dataset in keywords so that others can find it. Data sharing Open science is the most important ‘innovation’ in the scientific process. Science has always been open to some extent in that historically we published papers after the research was complete for others to read and sometimes repeat or test. However, we now publish our workflows, figures, ideas, and datasets at whatever point in the process makes the most sense to accelerate discovery or seek collaborations. There are many ways to share data but emailing
  9. 9. 9 them to colleagues or posting to personal websites makes it difficult, if not impossible, for others to find them and reuse them. Consequently, a data repository is the most effective means of sharing data. All include a unique identifier for each dataset (i.e. a doi), tags, search tools, licensing, standard meta-data guidelines/languages, and a means to contact the author. In ecology, this is likely one of the most important skills you will practice that can benefit you as a scientist of professional or scientific literate citizen that uses evidence to make informed decisions. It sounds trivial, upload excel file, paste in description, and publish. It is in almost all respects, it really is that simple. However, building your portfolio of scientific products sooner versus later in your education careers is extremely useful. You are also expanding the products you share. Instead of just term papers, you are producing and sharing primary scientific evidence (even the beer and scientific productivity dataset is used by others). Finally, sharing data is easy, but writing clear meta-data is hard. Structuring datasets (the tables/matrices you build) to ensure usability is also a critical skill. Excel and tables Tables are formatted with rows and columns. Usually, each column is a variable and rows are independent samples or replicates. As a best practice, also include a column entitled ‘replicate’ to make it clear to the reader/user that each row labeled 1,2,3, etc. is a new instance or subject measured. Avoid use of colours, use clear labels, avoid abbreviations (but if you must use them describe in meta-data sheet), and label each sheet with excel file. It is also a good idea to add data columns if you repeated an experiment in the following week and a column listing the researchers (your lab group members just as initials). Excel is not the best tool (total understatement) but is a common tool. More information here on how to use it:
  10. 10. 10 WK3. Techniques & data: field training with plants (traits, transects, and quadrats) Location: York University grasslands and woodlots. Tasks: Collect 4 datasets as groups to familiarize with sampling tools, publish dataset individually Products: Individual dataset worth 5%. Skills Sample plant populations & communities with quadrats, transects, and trait sampling techniques Collect field data Write meta-data and methods description Publish data Steps 1. Work in groups and collect four datasets (one for each group member to publish). 2. Collect two datasets in a woodlot and two in grassland. 3. Grassland, dataset 1: Use quadrats placed in the grassland to record this dataset: total abundance of plants (try doing a very, very quick count of every individual), total number of different plant species, total cover of all vegetation within plots, and total cover of grasses (n = 25 quadrats randomly placed). 4. Grassland, dataset 2: Use transects within the grassland to collect this dataset: randomly place transect tape, walk along it, and select a visible plant species that is easy to identify and spot quickly. Every time you spot your target plant species, record the distance on the transect you found it, measure its height, number of leaves, number of flowers, and whether it was in a crowded patch of other plants (0 = open, 1 = some plants nearby, 2 = quite a few plants, 3 = very crowded bunch of plants within 50 cm). Sample at least 50 individuals. If you need to run out another transect to capture 25 plants of your species, use random number table and move it your tape over and repeat. 5. Woodlot, dataset 3: Use transect measuring tapes and record the following: walk a straight line from edge of woodlot to centre of woodlot, every instance you encounter an adult tree (i.e. make a rule such as twice your eight), record the distance from this tree to the next and record the diameter at breast height (dbh) of every tree, and its condition (0 = dead, 1 = living, and 2 = huge green canopy). Ensure you have at least 10 pairs of trees. 6 Woodlot, dataset 4: Use transects measuring tapes and record the following: the dbh of 10 randomly selected adult trees (same species), estimate extent of canopy coverage (make a square with fingers and hold up and estimate how might sky you can see), and record distance to nearest sapling of same species. When you find the sapling, measure its dbh too. 7. Take notes on what you as a group did for your particular dataset (i.e. what, when, who, where and how you recorded it). Describe the study site. 8. Publish your dataset on figshare within 1 week of your lab date. Ensure you use the following tags: York University, BIOL2050, Lortie, techniques lab plants, and ecology. You must also use additional tags for your specific dataset as well such as grassland or woodlot, campus, plant traits, density, cover, abundance, quadrat, transect, etc. Paste your methods into the description box and ensure that you had both the ‘data’ sheet within the excel file you uploaded and the ‘meta-data’ sheet too. The teaching assistant will assign grades using all four elements within your submission: the data sheet, the meta-data sheet, the tags, and the description.
  11. 11. 11 Techniques & data: resources for field sampling (read if you need)
  12. 12. 12 Here is a short list of the common species that you will see on campus and a dichotomous tree guide is also included. These lists are based on the plants spotted lurking on campus in the past few years however there will be many, many more.
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  16. 16. 16 Tree leaf key. Coniferous trees (leaves needle-like) 1. (a) Leaves (needles) singly placed, no clusters – go to 2 (b) Leaves (needles) in clusters – go to 3 (c) Leaves not needles but flat, horizontal scales in 4 rows. Shoots flattened and complex, and yellowish green… eastern white cedar (Thuja occidentalis) 2. (a) Leaves (needles) flat, blunt tipped, short stalked, 8-15mm in length, 2 white bands on undersurface of leaf; slender twigs; seed cones avoid 12-20mm in length…eastern hemlock (Tsuga canadensis)(KM, VC). (b) Leaves (needles) flat; blunt tipped, stalkless, 15-25mm in length, 2 white bands on undersurface of leaf; strong balsam odour when crushed; stout twigs; seed cones erect, barrel shaped, 4-10cm in length… balsam fir (Abies balsamea) (VC) (c) Leaves (needles) not flat, four-sided, pointed tip. White spruce (Picea glauca)(KM). 3. (a) 5 leaves per cluster, leaves flexible (do not snap when bent); seed cones cylindrical, 8- 20cm in length… eastern white pine (Pinus strobus)(KM,VC) (b) 2 leaves per cluster, leaves brittle (break when bent); seed cones ovoid, 4-7cm in length… red pine (Pinus resinosa)(VC) (c) 15-60 needles per cluster or tuft… Tamarack or larch (Larix laricina) Note: this may be European Larch Deciduous trees 1. (a) Leaves compound (i.e. the blade is divided into separate parts or leaflets. If you are not sure what a compound leaf looks like, check the diagrams; the leaflets will be attached to a green midrib, not a woody stem) – go to 2 (b) Leaves simple (i.e. the blade not divided into separate leaflets) – go to 6 2. (a) Leaves (not leaflets) are opposite – go to 3 (b) Leaves (not leaflets) are alternate – go to 5 3. (a) Leaflets oval to lanceolate, 7-12mm long, 2.5-7.5cm wide, 5-11 leaflets per leaf… ash – go to 4 (b) 3-9 leaflets, irregularly toothed or lobed, often asymmetrical, underside of leaf grey-green; twigs covered with waxy whitish bloom (powder) that can be rubbed off … Manitoba maple (Acer negundo)(VC) 4 (a) Leaflets hairless, except along the veins, leaflets have long stalks; twigs smooth and shiny; bark ridged, ridges forming a diamond-like surface pattern, particularly at the base of the trunk … white ash (Fraxinus americana)(KM, VC) (b) Underside of leaf and twigs densely hairy, leaflets had short stalks; bark ridged, ridges forming a diamond-like surface pattern, particularly at the base of the trunk… red ash (Fraxinus pennsylvanica)(KM, VC)
  17. 17. 17 5 (a) Leaflets are narrow and pointed, sharply toothed. 11 to 31 leafltes per leaf, almost stalkless; twigs and underside of leaves very hairy; shurb or very small tree, fruit and fall leaves are crimson… staghorn sumac (Rhus typhina)(KM) (b) Leaflets are narrow, long-pointed and get bigger towards the leaf tip. 7-11 leaflets. Twig bud is sulphur yellow… Bitternut hickory (Carya cordiformis) 6 (a) Leaves with lateral veins curving forward and following the margin to the leaf tip – go to 7 (b) Leaves with lateral veins extending directly towards the leaf margin or slightly curving forward, but to not follow the margin or reach the leaf tip – go to 8 7 (a) Leaves sub-opposite (opposite but not quite aligned), ovate, finely toothed, 3-5 veins per side, some dwarf shoots end in a thorn … European buckthorn (Rhamnus cathartica)(VC) (b) Leaves alternate (only one leaf per node), ovate, smooth margin, slightly pubescent underneath, 8 or 9 pairs of veins … glossy buckthorn (Rhamnus frangula)(VC) (c) Leaves alternate with slightly wavy margins. Leaves may appear opposite or whorled on short twigs. Terminal bud very small. Twigs shiny reddish… Alternate leaved dogwood (Cornus alternifolia) (If you are unsure of leaf arrangement, look at the leaves that are closest to the tip of the twig, if it is still unclear, check the bud arrangement.) 8. (a) Leaves opposite (leaves occurring in pairs at node) – go to 9 (b) Leaves alternate (only one leaf per node) – go to 11 (If you are unsure of leaf arrangement, look at the leaves that are closest to the tip of the twig, if it is still unclear, check the bud arrangement.) 9. Leaves with 3 to 5 lobes; twigs smooth (no thorns); leaves long stalked; fruits, winged seeds … maples – go to 10 10. (a) Leaves 3-lobed, teeth fine and regular; bark green with conspicuous vertical white stripes…striped maple (Acer pensylvanicum)(KM,VC) (b) Leaves with 3 or 5 lobes with Sharp irregular teeth, V-shaped notches between lobes; bark grey-brown separated into scaly ridges which may be loose at edges … red maple (Acer rubrum)(KM,VC) (c) 5 lobes, with long blunt-pointed tips and a few irregular wavy teeth, U-shaped notches between lobes; bark may be fissured into long, thick irregular strips that appear to break outward along one side … sugar maple (Acer saccharum)(KM,VC) (d) 5-7 lobes with coarse, sharp, irregular teeth. Leaves silvery-white beneath… silver maple (Acer saccharinum) 11. (a) Leaves lobed… oaks – go to 12 (b) Leaves with a smooth or toothed margin, not lobed – go to 13 12. (a) Lobes pointed at ends, separated by rounded notches… red oak (Quercus
  18. 18. 18 rubra)(KM,VC) (b) Lobes rounded at ends, separated by deeply cut rounded notches … white oak (Quercus alba)(KM) (c) Leaves broader at end with large terminal lobe, hairy underneath…. Bur oak (Quercus macrocarpa) 13. (a) Base of leaf very asymmetrical – go to 14 (b) Base of leaf symmetrical – go to 16 14. (a) Leaf heart-shaped, sharp toothed, 12-15cm long and almost twice as wide, tufts of hair in the axils of the veins; twigs hairless … basswood (Tilia americana) (KM,VC) (b) Leaves not heart-shaped …elms – go to 15 15 (a) Lenticels prominent on twigs; leaves fragrant, several forked veins per leaf; twigs hairy… slippery elm (Ulmus rubra)(VC) (b) Lenticels inconspicuous, twigs hairless or slightly hairy; 15-20 veins per side, no more than 2 or 3 of which are forked… American elm (Ulmus americana)(KM,VC) 16. (a) Length of leaf stalk greater than half the length of the leaf blade – go to 17 (b) Length of leaf stalk less than half the length of the leaf blade – go to 18 17. (a) Leaves vary from egg-shaped with a short tip to oval, with blunt tip, large uneven teeth that curve inwards, stalk flattened, shorter than the length of the leaf blade; twigs are moderately stout, dull, may be hairy with orange lenticels (markings) … bigtooth aspen (Populus grandidentata)(VC) (b) Leaves egg-shaped tapering to a long sharp tip; leaf stalk about half the length of the leaf and round in cross section (roll between thumb and forefinger to check this); warty glands may be present at leaf base; twigs stout and smooth… balsam poplar (Populus balsamifera) (VC) (c) Leaves nearly heart-shaped with short sharp tip, short sharp irregular teeth rounded base; hairless flattened stalk usually longer that the leaf blade; twigs slender, shiny, round in cross-section; lenticels oval …trembling aspen (Populus tremuloides)(VC) 18. (a) Lateral veins do not extend to leaf margin – go to 19 (b) Lateral veins do extend to leaf margin – go to 24 (If you are unsure whether or not the lateral veins extend to the leaf margin, then assume that they do not) 19. (a) Glands at base of leaf … cherries – go to 20 (b) No glands at base of leaf – go to 21
  19. 19. 19 20. (a) Leaves lanceolate, gradually tapering to both ends, sharp-pointed, upper surface of leaf shiny, bright green, teeth sharp incurved, undersurface of leaf hairy on both sides of midvein… black cherry (Prunus serotina)(VC) (b) Broadly oval to widest above the middles of the leaf, tapers abruptly to both ends, upper surface a leaf dull green, sharp-toothed, 4-5 teeth per vein, lower surface hairless, except for occasional tufts of hair at the vein junctions… choke cherry (Prunus virginiana)(VC) 21. (a) No stipules at base of stalk – go to 22 (b) Bearing stipules at base of stalk…willows – go to 23 22. Leaves oval to round, finely and regularly toothed, usually less than 8cm long, veins straight and parallel; bark conspicuously marked by a network of twisted vertical lines; shrub or small tree; berries fleshy and purplish… serviceberry (Amelanchier spp.)(KM) 23. (a) Leaves narrow elliptical, tapering to both ends, smooth or wavy margin, upper surface of leaf dull green and wrinkled, undersurface covered with white hairs… bebb willow (Salix bebbiana)(VC) (b) Leaves oval, rounded base, short teeth, uppersurface dark green; odour of balsam from bruised leaves and twigs… balsam willow (Salix pyrifolia)(VC) 24. (a) One tooth per vein, straight-veined, 9-14 veins per side, leaves narrowly oval with a leathery texture, upper surface dark bluish-green. Beech(Fagus grandifolia)(KM,VC) (b) Several teeth between the veins – go to 25 25. (a) Bark paper-like, with conspicuous horizontal markings… birch -go to 26 (b) Bark not paper-like, may be smooth, shaggy, ridged or scaly – go to 27 26. (a) Leaves triangular or ovate; base of leaf tootheless for 1 cm on either side of stalk; double-toothed, 9 veins or fewer per side, each ending in a large tooth; smooth thin reddish-brown on young stems, becoming creamy white with maturity, conspicuous horizontal lenticels on young bark… white birch (Betula papyrifera)(KM, VC) (b) Leaves triangular or ovate; base of leaf toothless for 1cm on either side of stalk; double-toothed, 9 veins or fewer per side, each ending in a large tooth; smooth thin reddish-brown when you, becoming yellowish-grey or bronze with maturity … yellow birch (Betula alleghaniensis)(KM, VC) (If you are confused, look at the upper part of the tree; if it is white, or white with grey, call it white birch) 27. If tree has thorns go to 28, otherwise (a) Leaves oval, thick textured, veins deeply impressed above, with veinlets forming a ladder-like pattern; smooth reddish-brown bark with conspicuous orange horizontal markings; usually a coarse shrub with crooked trunks, but may be a small crooked tree … speckled alder (Alnus incana ssp. Rugosa)(VC) (b) Leaves elongate with rounded base, smooth texture, soft and fragile; bark shaggy breaks up into narrow vertical strips that are loose at both ends and can be easily removed… ironwood (Ostrya virginiana) (KM, VC)
  20. 20. 20 (c) Twigs smooth, greenish, 4-sided. Leaves oval, 5-12 cm long, pointed, finely toothed… spindle tree (Euonymous SP.) 28. Small tree with long, sharp thorns… hawthorns (Crataegus spp.)
  21. 21. 21 Common plant species lists in meadows and old fields. Trees and shrubs Russian-Olive (Elaeagnus angustifolia) ( ornamental tree) Trembling Aspen (Populus tremuloides) Willow (Salix spp.) Eastern Red Cedar (Juniperus virginiana) Herbaceous species Aster (Aster spp.) Goldenrod (Solidago spp.) Graminoids (grasses) Common Milkweed (Asclepias syrica) Queen Anne's Lace (Daucus carota) Toadflax (Linaria vulgaris) Thistle (Sonchus spp. or Cirsium spp.) Sweet White Clover ( Melilotus alba) Common Plantain (Plantago major) Vetch (Vicia spp.) Raspberry (Rubus spp.) Common St. John’s Wort (Hypericum perforatum) Horsetail (Equisetum arvense) Hawkweed (Hieracium spp.) Wild Strawberry (Fragaria virginiana) Common Mullein ( Verbascum thapsus) Black Eyed Susan (Rudbeckia hirta) Aven (Geum spp.) Jewelweed (Impatiens pallida) Woodlots Trees and shrubs Alternate-leaf Dogwood (Cornus alternifolia) American Elm (Ulmus americana) Balsam Fir (Abies balsamea) Balsam Poplar (Populus balsamifera) Balsam Willow (Salix pyrifolia ) Basswood (Tilia americana) Bebb Willow (Salix bebbiana) Beech (Fagus grandifolia) Bigtooth Aspen (Populus grandidentata) Black Cherry (Prunus serotina) Bur Oak (Quercus macrocarpa) Chokecherry (Prunus virginiana) Eastern Hemlock (Tsuga canadensis) European Buckthorn (Rhamnus cathartica) Glossy Buckthorn (Rhamnus frangula) Ironwood (Ostrya virginiana) Larch (Larix laricina) Manitoba Maple (Acer negundo) Red Ash (Fraxinus pennsylvanica) Red Maple (Acer rubrum) Red Oak (Quercus rubra) Red Pine (Pinus resinosa) Serviceberry (Amelanchier spp.) Silver Maple (Acer saccharinum) Slippery Elm (Ulmus rubra) Speckled Alder (Alnus incana ssp. Rugosa)
  22. 22. 22 Spindle-tree (Euonymus spp.) (not in key) Staghorn Sumac (Rhus typhina) Sugar Maple (Acer saccharum) Trembling Aspen (Populus tremuloides) White Ash (Fraxinus americana) White Birch (Betula papyrifera) White Cedar (Thuja occidentalis) White Oak (Quercus alba) White Pine (Pinus strobus) White Spruce (Picea glauca) Yellow Birch (Betula alleghaniensis) Herbaceous species Bramble (Rubus spp.) Canada Goldenrod (Solidago canadensis) Clearweed (Pilea pumila) Enchanter's Nightshade(Circaea quadrisulcata) Garlic Mustard (Alliaria petiolata) Graminoids (grasses) Grapevine (Vitis spp.) Herb Robert (Geranium robertianum) Jewelweed (Impatiens pallida) Mayapple (Podophyllum peltatum) Nettle (Urtica spp.) New England Aster (Aster novae-angliae) Poison Ivy (Rhus radicans) Rough Avens (Geum virginianum) Sedge (Carex spp.) Solomon's Seal (Polygonatum biflorum) Violet (Viola spp.) Virginia Creeper (Parthenocissus quinquefolia) Wild Geranium (Geranium maculatum)
  23. 23. 23 Sampling Sampling elements are important in all ecological and environmental sciences. The scale, representativeness, and reliability of the of the sampling are critical concerns that require a well-developed skill set in designing effective surveys and manipulative experiments. The terms you will encounter are summarized herein in a schematic from Albert et al. 2008 (Ecography). In deciding where and how to place your quadrats and transects, in the lab this week in next and in designing your experiments, there a several pitfalls to avoid. Truncated gradients (sampling only a part of gradient such as disturbance), indirect gradients (i.e. you assume a gradient has the same effect everywhere or that the factor you are sampling on is the direct driver of change and it is not), scale (you sample/test an area that matches the scale of the ecological process in question), sampling design (quadrats, transects, or other tools match the process), and knowledge of the system (you walked around and did some observations to ensure you selected a representative location or set of locations/individuals (Albert et al. 2008). There are numerous ways to sample including simple random, following pathways/roads/rivers (major gradients), systematic (i.e. every 1m or 25 steps in a straight line), model-based (using previous data to model where to sample), or hybrid sampling designs such random-stratified (i.e. you use a random number table to select where to sample or do your experiment within a strata or level/block). Simple random sampling within the appropriate area at the right scale is often the best decision to capture natural patterns via surveys particularly when the study area is relatively uniform (in terms of coarse-scale environmental heterogeneity or distribution of your target taxa). For many manipulative experiments, random-stratified is the best, i.e. we placed our removal plots randomly with each of the forest strata (within each part of the woodlot such as north, south, east, west edges and centre, we then walked x random steps on a grid and selected plots). Random-stratified is useful to ensure you sample/use all major habitats within your study area. The number of samples/plots you do generally increases the relative accuracy of your estimate of the ecological/environmental process in question. However, there can be diminishing returns in adding more of the sample samples versus sample additional study areas or in exploring other factors that can be important.
  24. 24. 24 Transect versus quadrat The quadrat is typically a square frame (bit can be circular or rectangular) made of pvc piping, metal or wood that is placed in vegetation or on the ground (or ocean floor) to record plant or slower moving animal abundance and diversity. It is excellent as a sampling tool if placement is free from bias and representative. It also ensures you sample well within the designated area as long as you apply rules for edge effects (i.e. plants rooted inside are counted or insects/animals within quadrat within the first 2 minutes of placement etc). The major limitation is however the amount of area you can sample in terms of an entire grassland or woodlot or system.
  25. 25. 25 There are two types of transects: line wherein all target organisms touching tape/rope are sampled or distance to line/tape is measured, and belt wherein the presence of organisms within a certain distance of the transect usually on either side of the line. Transects are excellent for covering more ground within a system and sampling a wider-range of conditions. They are also excellent for sampling animals that are more mobile, i.e. you walk a transect for a certain length of time and record distance from transect and frequency of occurrence/spotting of your target animal. Similar to the representativeness limitation of quadrat-based sampling, placement of transects is an important issue. The sampling regime selected for transects however is more dependent on the purpose and scope of the study. For instance, if you would like to sample bird frequency within a relatively small woodlot, it is reasonable to place transects systematically along the length of the woodlot. A design like this is entirely appropriate: we placed belt transects 25m apart for a total of 4 transects each 100m long and sampled the entire woodlot by walking and recording the frequency of birds spotted within 5m of either side of line whilst walking along each. However, if the scale is larger, randomly placed transects may be more important. Familiarity within the system and previous research in your field/system will help you decide what technique and sampling design is most appropriate. Note: the point-intercept method is also a very common sampling design in ecological research. It can be used with both gridded quadrats and transects and is simply recording the target taxa interception with your grid interstices or your gradations on your transects.
  26. 26. 26 Both quadrats and transects can be used to measure distances between individuals, abundance, and diversity.
  27. 27. 27 Density versus plant cover Density is the number of individuals per unit area (often synonymous with abundance if you use the same size quadrat for the entire study). Density is the best measure to use if you can accurately count individuals (i.e. in plants you can tell it is separate plant if it is not prostrate) and if the density is relatively low (you can count in a reasonable amount of time that balances precision versus getting all your quadrat completed for the region you will sample). Note: frequency is the proportion of quadrats/transects with your target species present and is not synonymous with density. Total cover is less accurate but much quicker. You estimate the total cover for your class such as the grasses within a plot. If you use this technique, it is good to either use the same person to estimate cover in all your sampling or calibrate each individual that will estimate cover to ensure you generate the same values. There are numerous other tools used for both density and cover estimates that facilitate reliable sampling and often these include grids within the quadrat or point-based assisted sampling.
  28. 28. 28 Random sampling and number tables Use of a random number table (generated in excel using the rand function is a very common tool used to avoid haphazard or biased sampling. Also, this site summarizes random number tool options more broadly ( Remember, random numbers do not ensure representativeness in that by chance you could end up sampling within a given part of the grassland/woodlot. Generally, the random number tool provides a list of numbers that you use as coordinates to determine where to sample within an area. You can use the random numbers to move/place your plots using steps or distances. Throwing your quadrat ‘randomly’ is not random but haphazard sampling. Truthfully, haphazard is not an uncommon approach but is a poor decision for so many reasons. You can also break your area to be sampled into a numbered grid and the random number table to determine the areas to sample within the region. ANOVA versus regression-based sampling There are also two major camps of environmental sampling regimes associated with the underlying statistics you prefer primarily those that prefer regression versus those that prefer ANOVA (Cottingham et al. 2005). ANOVAs compare groups statistically using central tendency whilst regressions fit the response of your system to the factor (with a variety of levels). So, it is groups versus levels. Or blocks versus variation. If you have really clearly groups within your system, i.e. in the forest or out of the forest, under versus open, high versus low, then designing your sampling around these natural blocks is appropriate. However, if there is variation around your categories, there is no high versus low just a hill or mountain, or you suspect the variation acts in different and non-linear ways when you observe your system, then you should consider sampling a variety of levels. The sampling decision here is whether you ‘block’ the environment into simple groups you define or whether you sample more of the environment an seek to estimate the extent that variation in the environment or system is important. Like all sampling decisions, the scope of the question and purpose also determine the decision to block or walk. If you want to know whether vegetation or insects are different at the top of the mountain relative to
  29. 29. 29 the bottom, then ANOVA-blocked design is likely a viable and simpler/quicker design that will satisfy the study. If you want to know how elevation effects plant or insect diversity in the alpine, then sampling a range of different elevations (at least 5 of them) ranging from your previous low to high categories is more effective. Sampling a range of locations can be more time consuming and Cottingham et al. (2005) proposed replicated-regression as a good hybrid. Instead of doing half of all your reps in one spot then another, 5 in high and 5 in low, do 2 replicates at each of your five locations. Cottingham et al 2005. versus
  30. 30. 30 WK4. Techniques & data: field sample training with animals (pans, pitfalls, sweeps, and distances) Location: York University grasslands and woodlots. Tasks: Collect 4 datasets as groups to familiarize with sampling tools, publish dataset individually Products: Individual dataset worth 5%. Skills Use pans, pitfall traps, sweep nets, and distance-based techniques to estimate animal abundances Collect field data Write meta-data and methods description Publish data Steps 1. Work in groups and collect four datasets (one for each group member to publish). Think about important factors that can relate to the capture/estimation rates for your target taxa. 2. Pitfall trap dataset: at the start of lab, bury 10 plastic cups in a highly disturbed grassland area and 10 in a woodlot. You decide on design type (i.e. disturbance, light, cover and as blocked or regression based). Return at the end of lab and count number of insects captured in each cup and release the insects. Record the number of different recognizable taxonomic units (rtus) per sample as well (i.e. flies, bees, spiders, etc.). 3. Pan trap dataset: place 10 solo bowls filled with soapy water in the grassland and 10 in the woodlot at the start of the lab. Return at the end of lab and count number in of insects captured in each bowl (do this by pouring out through a sieve preferably) and the number of different rtus. If different colored bowls are available, decide how you place and arrange them and also specifically where/how to structure sampling within each habitat type. 4. Sweep net dataset: Use sweep nets and transects. Walk transects (you determine distance) in the grasslands for a specified length of time and record both total number of insects captured and total number of unique rtus. Repeat 10 times. 5. Distance-based dataset: Use belt transects and record the frequency of sightings within the specified area of the grassland and woodlot. Record both frequency and species/family of bird species. Do at least 5 transects in each habitat type. Record wind speed using Beaufort scale and estimate distance from transect to bird for each spotting event as well. 6. Publish your dataset on figshare within 1 week of your lab date. Ensure you use the following tags: York University, BIOL2050, Lortie, techniques lab animals, and ecology. Use additional tags to summarize your specific dataset such as campus, sweep or pitfall or pan trap, insects, birds, random design or systematic etc. Paste your methods into the description box and ensure that you had both the ‘data’ sheet within the excel file you uploaded and the ‘meta-data’ sheet too. The teaching assistant will assign grades using all four elements within your submission: the data sheet, the meta-data sheet, the tags, and the description.
  31. 31. 31 Techniques & data: resources for field sampling (read if you need) Pitfall traps Pitfall traps are amazing. However, no one technique can capture or estimate your population perfectly. The best approach is to use more than one sampling approach. The advantages and disadvantages of pitfall traps have been discussed at length in the ecological literature. One more favourites is the ‘The pitfalls of pitfall traps’ by Enge in 2001. Limitations include number of openings, whether the pitfall trap has a room, presence of litter nearby, habitat structure, and variation in size of individuals and their relative likelihood of both falling in and also of escaping. Placement of pitfall traps is a critical issue. Think of them as the quadrats of the plant world. The basics of a pitfall trap. The layout of a pitfall.
  32. 32. 32 From Greenslade 1964 in Journal of Animal Ecology. An example of a factor to consider in pan trapping. From Greenslade 1964 in Journal of Animal Ecology.
  33. 33. 33 From Melbourne 1999 in Australian Journal of Ecology Pan traps Pan traps are an excellent means to estimate the abundance and diversity of flying insects. Pan traps are often blue, yellow, and white to attract different sets of insects. Pollinators are often captured using this approach. Similar limitations to quadrats and pitfall traps apply to this design. A detailed sampling design including handy bee key is provided on the CANPOLIN (Canadian Pollinator Initiative) website:
  34. 34. 34 From Leong & Thorp 1999 in Ecological Entomology. Sweep nets Sweep nets are also a very common sampling technique for capturing pollinators. This approach is the analog for transect-based sampling in plants. Usually a belt transect approach is used and all insects are swept within a certain area along a transect within your habitat. The total time spent sampling is a key variable to record as the longer you sweep, the more you catch in many systems. Sweeps and pans often catch different insects. Hence, these can introduce different biases of your estimate of the larger community of insects or pollinators. Ideally, you test both in your pollinator system.
  35. 35. 35 From Spafford and Lortie 2013. Distance-based sampling Everything you want to know about distance-based sampling for animals in the classic paper by Burnham et al. (1980) in Wildlife Monographs. It is a fascinating read. As described previously for transects, there are many ways to use transects to sample your plants and animals. Line and belt transects are usually used to facilitate this sampling approach. This class of sampling is called distance-based the population of interest is usually mobile and is always is a set of
  36. 36. 36 distances away from the observer. Organisms located at smaller distances are also more detectable than those farther away and distance is thus always a factor. Distance Belt Layout is an important design decisions when using distance-based sampling.
  37. 37. 37 Sighting angle is also an important feature of this sampling approach because as the angle changes our capacity to detect/spot organisms also changes.
  38. 38. 38 Wind for bird sampling
  39. 39. 39 Common bird species in Toronto Warbler species Yellow Common Yellowthroat Tennessee Chestnut sided Nashville Magnolia Blackburnian Bay breasted Blackpoll Black and white Connecticut Cape May Black throated Blue Yellow rumped Black throated Green American Redstart Ovenbird List of common birds Cooper's Hawk Northern Mockingbird Baltimore Orioles American Goldfinch American Robins Sharp Shinned Hawks Swainson's Thrush Belted Kingfishers Warbling Red eyed Vireos Cedar Waxwings Black capped Chickadees Gray Catbird Ruby throated Hummingbirds Mourning Doves Blue Jays Northern Cardinals Downy Woodpecker Brown headed Cowbird Red breasted Nuthatch Blue Gray Gnatcatcher Purple Martin Tree Cliff & N. Rough Winged Swallows Chimney Swift Song Sparrow Black Crowned Night Heron Great Blue Heron House Sparrow Rock Pigeon Common Nighthawk Ring Billed Gull & Herring Gull Fly Catchers Olive sided Yellow bellied Willow/Alder Least Great Crested Eastern Wood Pewee Eastern Kingbird See field guides for pictures and detailed keys.
  40. 40. 40 Common invertebrate species in Toronto. Major groups Dragonflies and damselflies - Order Odonata - These insects are good indicators of healthy freshwater habitats as they will disappear when water becomes polluted. Adults eat mosquitoes and other insects. Mayflies - order Ephemeroptera - These are small insects that spend most of their lives in the water. Adults emerge in great numbers but live only for a day. Mayflies are an important food source for many fish. Grasshoppers, mantises and crickets - order Orthoptera. Many insects of this order produce sounds by rubbing body parts together. Bugs - order Hemiptera, suborder Homoptera - These are the true bugs; their lower lip is modified into a sucking tube that the insect inserts into plant or animal tissues in order to feed. Aphids and plant hoppers are bugs. Butterflies and moths - order Lepidoptera - These are the familiar beautiful insects that we readily welcome to our gardens. Besides being beautiful to look at, they are important pollinators. Beetles - order Coleoptera - This order includes the familiar June beetle, ladybird beetle and fireflies. Beetles are also pollinators but play an extremely important role in the recycling of animal dung and dead animals. Flies - order Diptera - True flies have a single pair of wings; their hind wings are reduced to stalked knobs called halteres that they use to keep their stability while flying. Flies are important pollinators and also feed on dead carcasses so that nutrients are recycled back into the environment. Ants, wasps and bees - order Hymenoptera - We are all familiar with these insects and often consider them to be a nuisance. However, they are important pollinators of many of our agricultural plants including apples, tomatoes, beans, peas, oilseed and fibre crops. Here are some fantastic digital insect keys. All free and online. So, collect samples then look up on laptops/smartphones/tablets. Key to the local insect orders. Hein Bijlmakers. 2012. When you want to identify an insect the first step is to find out in which Order it is classified. For this you can use a dichotomous key. A dichotomous key is a tool that uses paired statements or questions to guide you to the solution. To use the key it will be necessary to have a good hand lens and you should be familiar with the terminology used for the different parts of an insect body. If you don't know a word or term, please have a look in the glossary. To use the key, start at the top and compare statements 1a and 1b. Select the statement that describes your insect specimen and continue with the number indicated on the right (click the number to jump to the next statement). Identification keys are a good starting point, but you should realize that there are hundred thousands of insect species in this world and among them there is a lot of variation. The keys cannot cover all this variation. When you have reached a solution, always double check the result by reading a detailed description of the insect Order. 1a Insect with wings 2
  41. 41. 41 (but the forewings could be partly or entirely stiffened as 'wing-covers' or 'wing-cases' and are not used for flying) 1b Insect without wings 32 (but there could be remnants of wings resembling small scales or pads) 2a Insect with one pair of wings 3 2b Insect with two pairs of wings 9 3a The dorsal surface of the prothorax extends backwards over the abdomen; the hind-legs enlarged and modified for jumping; insect looks grasshopper-like in general appearance Orthoptera 3b Insect different 4 4a The wings are horny or leathery (stiff or rigid) and are not used for flying 5 4b The wings are membranous (flexible) and are used for flying 6 5a The wings overlap at least a little in the centre-line and with obvious veins present Phasmida 5b The wings (elytra) meet in the centre-line (sometimes they are fused together) and without veins (note that the elytra may have longitudinal grooves or striae but these should not be confused with veins) Coleoptera 6a The abdomen has one or more long terminal appendages 7 6b The abdomen is without terminal appendages 8 7a The wings have only one forked vein; antennae are relatively long; small insect usually less than 5 mm long Hemiptera 7b The wings have many veins; antennae are short; larger insect Ephemeroptera 8a The thorax has a pair of club-shaped structures (halteres) situated just in front of the wings Strepsiptera 8b The thorax has a pair of club-shaped structures (halteres) lying just behind the wings (these halteres may be hidden by body hairs and other structures) Diptera 9a The forewings are partly or entirely horny or leathery and form stiffened covers for the membranous hindwings 10 9b Both pairs of wings are membranous (flexible) and used for flying (sometimes the wings are feather-like rather than membranous or their membranous nature may be obscured by a covering of hairs, scales or waxy powder) 16
  42. 42. 42 10a The mouth-parts form a tube-like 'beak' (rostrum) which is used for piercing and sucking (this rostrum is usually folded backwards under the body when not in use) Hemiptera 10b The mouth-parts have jaws (mandibles) and are designed for biting and chewing 11 11a The forewings overlap at least a little in the centre-line and usually with many veins present 12 11b The forewings (elytra) meet in the centre-line and have no veins (note that the elytra may have longitudinal grooves or striae but these should not be confused with veins) 14 12a The hind-legs are enlarged and modified for jumping; insect looks like a grasshopper in general appearance Orthoptera 12b The hind-legs are not modified for jumping and are usually similar in thickness to the middle-legs; insect is not grasshopper-like 13 13a The prothorax is much larger than the head; cerci nearly always many-segmented and fairly prominent Dictyoptera 13b Prothorax and head are of similar size; cerci are not segmented and very short Phasmida 14a The forewings (elytra) are long and cover all or most of the abdomen Coleoptera 14b The forewings (elytra) are short and much of the abdomen remains exposed 15 15a The abdomen has a pair of terminal pincers or forceps Dermaptera 15b The abdomen has no terminal pincers Coleoptera 16a The wings are very narrow without veins and fringed with long hairs (feather-like); tarsi are 1- or 2- segmented; small slender insect often found in flowers Thysanoptera 16b The wings broader with veins present; if wings are fringed with long hairs then tarsi are comprised of more than 2 segments (the wing veins of some insects may be much reduced and hardly visible or partly obscured by hairs, scales or waxy powder) 17 17a The hindwings are clearly smaller than the forewings 18 17b Both pairs of wings are similar in size or hindwings larger than forewings 26 18a Wings and much of the body covered with white waxy powder; tiny insect usually less than 2-3 mm long 19 18b Without powdery covering 20
  43. 43. 43 19a When at rest the wings are held flat over the body; the mouth-parts form a tube-like 'beak' (rostrum) for piercing and sucking (this rostrum is usually folded backwards under the body when not in use) Hemiptera 19b When at rest the wings are held roof-wise over the body; the mouth-parts have jaws (mandibles) and are designed for biting Neuroptera 20a The wings are more or less covered with very small scales; the mouth-parts when present are forming a coiled proboscis or 'tongue' Lepidoptera 20b The wings are usually transparent (wings without scales but often hairy); the mouth-parts are not forming a coiled proboscis 21 21a The forewings have many cross-veins making a network pattern; the abdomen has 2 or 3 long thread-like terminal appendages Ephemeroptera 21b The forewings show relatively few cross-veins; the abdomen is usually without or with only very short terminal appendages (cerci) 22 22a The wings are noticeably covered with hairs; insect looks moth-like in general appearance Trichoptera 22b The wings are not noticeably hairy (but wings may be fringed with hairs or tiny surface hairs may be seen if wings are inspected under a microscope or strong hand-lens) 23 23a The mouth-parts form a tube-like 'beak' (rostrum) for piercing and sucking (usually the rostrum is folded backwards under the body when not in use; the abdomen sometimes has tubular outgrowths or cornicles near the hind end) Hemiptera 23b The mouth-parts has jaws (mandibles) and are designed for biting and chewing 24 24a The tarsi are 4- or 5-segmented; hard-bodied insects with the abdomen often constricted at its base into a petiole or narrow 'waist' Hymenoptera 24b The tarsi are 2- or 3-segmented; small soft-bodied insect 25 25a Antennae with at least 12 segments Psocoptera 25b Antennae with only 9 segments Zoraptera 26a The tarsi are 5-segmented 27 26b The tarsi are 3- or 4-segmented 29 27a The wings are noticeably covered with hairs; insect is moth-like in general appearance Trichoptera 27b The wings are not noticeably hairy (but tiny hairs may be seen if the wings are observed under a microscope or with a strong hand-lens) 28
  44. 44. 44 28a The front of the head is extended downwards to form a beak-like structure with jaws (mandibles) at its tip Mecoptera 28b Insect without such a beak-like extension of the head Neuroptera 29a The tarsi are 4-segmented Isoptera 29b The tarsi are 3-segmented 30 30a The wings are noticeably hairy; the front tarsi are with the first segment greatly swollen Embioptera 30b The wings are not noticeably hairy; the front tarsi are simple 31 31a The wings have many cross-veins, which makes a network pattern; wings are held away from the body at rest (either outstretched or folded vertically); the antennae are short and inconspicuous Odonata 31b The wings have relatively few cross-veins and are folded flat over the body when at rest; the antennae are long and slender (longer than the width of the head) Plecoptera 32a Small soft-bodied insect which lives on terrestrial plants with the body encased under a protective shield ('scale') or the body is partly covered with white waxy filaments or powder Hemiptera 32b Insect different 33 33a Thoracic legs are absent or enclosed in a membrane preventing any movement (Larvae and pupae of most Orders of Endopterygota) 33b Thoracic legs are present and fully functional 34 34a The abdomen has false-legs or prolegs (prolegs are fleshy leg-like structures that are different from and additional to the jointed legs of the thorax); the insect looks like a caterpillar in general appearance 35 34b The abdomen has no prolegs; the insect is not caterpillar-like in appearance 37 35a Abdomen with not more than 5 pairs of prolegs Larvae of Lepidoptera 35b Abdomen has at least 6 pairs of prolegs 36 36a The head has a single small eye (ocellus) on each side Larvae of Hymenoptera 36b The head has several small eyes (ocelli) on each side Larvae of Mecoptera 37a The insect lives in a terrestrial habitat or on the surface of water (not underwater) 38 37b The insect is truly aquatic (living underwater) 70 38a The abdomen has cerci or other terminal appendages (but be careful not to confuse terminal hairs or bristles with cerci) 39
  45. 45. 45 38b The abdomen does not have such terminal appendages (but it may have small appendages on proximal segments or a pair of tubular outgrowths or cornicles near the hind end) 56 39a The abdomen has 6 or fewer segments; usually the abdomen has a forked terminal appendage (springing organ) folded under the rear end when not in use Collembola 39b The abdomen has more than 6 segments (usually 8 or more are clearly visible); the terminal appendages are of a different form 40 40a The antennae are short and often inconspicuous (the same length as the head or shorter) 41 40b The antennae are long and conspicuous (usually they are much longer than the head) 42 41a The tarsi have at least 3 segments (usually they are 5-segmented) Phasmida 41b The tarsi have fewer than 3 segments (often they are reduced to single or paired claws on the end of each leg) Larvae of Coleoptera 42a The hind-legs are enlarged and modified for jumping; insect looks like a grasshopper in general appearance Orthoptera 42b The hind-legs are not modified for jumping; usually the hind-legs are similar in thickness to the middle-legs; insect does not look grasshopper-like 43 43a The terminal appendages of the abdomen form a pair of pincers or forceps 44 43b The terminal appendages of the abdomen are different 45 44a The tarsi are 3-segmented Dermaptera 44b The tarsi are 1-segmented Diplura 45a The terminal appendages of the abdomen are long (much more than half the length of the abdomen) 46 45b The terminal appendages of the abdomen are short (less than half the length of the abdomen) 48 46a The abdomen has 3 terminal appendages (these are a paired cerci and a median filament) Thysanura 46b The abdomen has only 2 terminal appendages (cerci) 47 47a The tarsi are 3-segmented; the terminal appendages of the abdomen (cerci) are unsegmented Dermaptera 47b The tarsi are 1-segmented; the terminal appendages of the abdomen (cerci) are many-segmented Diplura
  46. 46. 46 48a The tarsi are usually 5-segmented (but sometimes fewer on regenerated legs of Phasmida) 49 48b The tarsi have fewer than 5 segments on all legs 52 49a The front of the head is extended downwards to form a beak-like structure with jaws (mandibles) at its tip Mecoptera 49b Insect without such a beak-like extension of the head 50 50a The prothorax is much larger than the head Dictyoptera 50b The prothorax and head are of similar size (the prothorax is at most only a little bit larger than the head) 51 51a The cerci are 8-segmented and are moderately long Grylloblattodea 51b The cerci are unsegmented and are very short Phasmida 52a The tarsi are usually 4-segmented Isoptera 52b The tarsi have fewer than 4 segments 53 53a The tarsi are 1-segmented Diplura 53b The tarsi are 2- or 3-segmented 54 54a The tarsi are 2-segmented Zoraptera 54b The tarsi are 3-segmented 55 55a The front tarsi have a first segment which is greatly swollen; the cerci are 2-segmented Embioptera 55b The front tarsi are not swollen; the cerci are unsegmented Phasmida 56a The insect lives as a parasite on a warm-blooded animal or it is closely associated with such an animal (for example it lives on the body or in the nest or den of a bird or mammal) 57 56b The insect is not parasitic on a warm-blooded animal 61 57a The insect body is flattened from side to side; jumping insect Siphonaptera 57b The insect body is flattened from top to bottom 58 58a The head is partly withdrawn into the thorax 59 58b The head is not withdrawn into the thorax 60 59a The antennae are short and inconspicuous (they are much shorter than the head); legs with strong and distinctly hooked tarsal claws Diptera 59b The antennae are long and conspicuous (they are more than twice the length of the head); legs have small and only slightly curved tarsal claws Hemiptera 60a At least the prothorax is distinct from the other thoracic segments; the legs have small tarsal claws; the mouth-parts have jaws (mandibles) and are designed for biting Mallophaga
  47. 47. 47 60b All the thoracic segments are fused into a single unit; the legs have large tarsal claws which can close tightly against the legs; the mouth-parts form a tube-like proboscis for piercing and sucking (this proboscis is retracted within the head when not in use) Siphunculata 61a Insect without antennae (very small soil-living insects usually less than 2 mm long) Protura 61b Antennae are present 62 62a The abdomen is strongly constricted at its base into a narrow petiole or 'waist'; the antennae are often bent into an elbowed shape Hymenoptera 62b The abdomen is not constricted into a 'waist'; the antennae are more or less straight 63 63a The body is covered with dense scales and flattened hairs Lepidoptera 63b The body is bare or with sparse bristle-like hairs 64 64a The mouth-parts form a tube-like proboscis or rostrum for piercing and/or sucking (this proboscis is usually folded backwards under the head when not in use) 65 64b The mouth-parts are with jaws (mandibles) and designed for biting and/or chewing 67 65a The tarsi are usually 5-segmented Diptera 65b The tarsi have fewer than 5 segments 66 66a The proboscis is small and cone shaped (it is much shorter in length than the head) (small slender insect often found in flowers) Thysanoptera 66b The proboscis or rostrum is long and jointed (it is nearly always longer than the head) (abdomen sometimes with tubular outgrowths or cornicles near the hind end) Hemiptera 67a The antennae are short and often inconspicuous (length of the antennae is at most about the same length as the head) 68 67b The antennae are long and conspicuous (they are much longer than the head) 69 68a The abdomen has 6 or fewer segments Collembola 68b The abdomen has more than 6 segments (usually 8 or more segments are clearly visible) (Larvae of various Orders) 69a The head is narrower than the body; the mandibles are very long and protruding forward well in front of the head (the mandibles are clearly visible from above) Larvae of Neuroptera
  48. 48. 48 69b The head is as wide or nearly as wide as the body; the mandibles are small and not protruding in front of the head (they are not visible from above) Psocoptera 70a The mouth-parts with a tube-like 'beak' or with long stylets and are designed for piercing and sucking 71 70b The mouth-parts have jaws (mandibles) and are designed for biting and/or chewing 72 71a The mouth-parts form a robust tube-like 'beak' (rostrum) folded backwards under the body when not in use Hemiptera 71b The mouth-parts form a pair of long and slender stylets extending more or less straight forward in front of the head between the antennae and about as long or longer than the antennae Larvae of Neuroptera 72a Head has a hinged grasping organ (or 'mask') that can stick out; this organ bears large terminal claws (normally it is folded beneath the head when not in use) Nymphs of Odonata 72b No hinged grasping organ or 'mask' beneath the head 73 73a The abdomen has pairs of feather-like or flat plate-like lateral appendages on some segments (gill filaments) and 3 long terminal appendages (paired cerci and a median filament) Nymphs of Ephemeroptera 73b Insects without this combination of features 74 74a The abdomen is without lateral appendages but with 2 long terminal appendages (cerci); the antennae are long and slender (they are much longer than the head) Nymphs of Plecoptera 74b Insects without this combination of features 75 75a The abdomen has pairs of multi-jointed feather-like lateral appendages on some segments (gill filaments) and sometimes a single terminal appendage Larvae of Neuroptera 75b The abdomen is without lateral appendages (gill filaments) or if such appendages are present then they are always unjointed 76 76a The last abdominal segment has a pair of fleshy appendages each bearing a strong claw; the middle-and hind-legs are longer than the width of the thorax; the body is often enclosed in a tubular case made from small pebbles or other debris Larvae of Trichoptera 76b Insects without this combination of features Larvae of Coleoptera
  49. 49. 49 Detailed insect species list 7. Dragonflies and Damselflies Variable dancer (Argia fumipennis) Ebony Jewelwing (Calopteryx maculata) Eastern Forktail (Ischnura verticalis) Ruby Meadowhawk (Sympetrum rubicundulum) Meadowhawk sp. (Sympetrum sp.) Band-winged Meadowfly (Sympetrum semicinctum) Blue Dasher (Pachydiplax longipennis) Common Baskettail (Tetragoneuria cynosura) Common Green Darner (Anax junius) Calico Pennant (Celithemis elisa) Common Whitetail (Libellula lydia) Twelve-spotted Skimmer (Libellula pulchella) Eastern Pondhawk (Erythemis simplicicollis) 8. Spiders Garden Spider (Araneus diadematus) Three-spotted Jumping Spider (Phidippus audax) Zebra spider (Salticus scenicus) Black-footed Spider (Cheiracanthium mildei) 1. Bees and Wasps European Paper Wasp (Polistes dominulus) German Yellowjacket (Vespula germanica) Paper Wasp (Polistes sp.) Bald-faced Hornet (Vespula maculata) Large Carpenter Bee (Xylocopa virginica) Green Metallic Bee (Agapostemon virescens) 2. Beetles Pennsylvania Leather-wing (Chauliognathus pennsylvanicus) Blister Beetle (Meloe sp.) Milkweed Beetle (Tetraopes tetrophthalmus) Locust Borer (Megacyllene robiniae) 3. Grasshoppers, Crickets and Cicadas Carolina Grasshopper (Dissosteira carolina) Tree Cricket (Oecanthus sp.) Field Cricket (Gryllus pennsylvanicus) Dogday cicada (Tibicen canicularis) 4. True Bugs Small Eastern Milkweed Bug (Lygaens kalmis) Scarlet-and-green Leafhopper (Graphocephala coccinea) Meadow Spittlebug (Philaenus spumarius) 5. Flies Green Bottle Fly (Phaenicia spp.) Drone fly (Eristalis tenax) 6. Butterflies Mourning Cloak (Nymphalis antiopa) Comma (Polygonia comma) Compton Tortoiseshell (Nymphalis vaualbum) Red Admiral (Vanessa atalanta) White Admiral (Limenitis arthemis) Orange Sulphur (Colias eurytheme ) Common Sulphur (Colias philodice ) Cabbage White (Pieris rapae) Monarch (Danaus plexippus) Eastern Tailed-Blue (Everes comyntas) Pearly Eye (Enodia anthedon ) Large Wood Nymph (Cercyonis pegala) Acadian Hairstreak (Satyrium acadica) Least Skipper (Ancloxopha numitor)
  50. 50. 50 Experimental design module
  51. 51. 51 WK5. Experimental design: experimental design training & your own experiment Location: Lab. Tasks: Familiarize with experimental design principles, design experiment as group, submit the group directed acyclic graph (dag) in the lab, and begin your individual design document. Products: DAG worth 2% (group-level submission in lab period) & individual design worth 3% within 1 week. Skills Integrate sampling techniques to design a novel field experiment Draw a directed acyclic graph to summarize relationships between variables Write a clear hypothesis and supporting predictions Consolidate your methods description writing this week Steps 1. Attend tutorial by teaching assistant on principles of experimental design. 2. Brainstorm in groups on an experiment appropriate for York University campus that will be done with two lab sessions and your group members to explore an ecological topic of interest. Ensure that the experiment directly links to a major ecological theory or maxim we have discussed in the lecture or read about. 3. Present ideas from your group to the teaching assistant and then decide as a group on the final topic/hypothesis you will explore in the following weeks. 4. Draw dags individually, discuss within group, and select best one to submit for grading (2%). 5. Design experiment as group and take notes on decisions. Consider making an equipment list to ensure you have all the materials/equipment you need. Also, consider assigning task to each group member now to ensure that next week runs more smoothly. 6. Write up hypothesis, predictions, and methods to be submitted within 1 week of your lab to your teaching assistant (worth 3%). Remember, you will have to write individual lab reports on your group experiment and this preliminary document is the perfect opportunity to get direct feedback from your teaching assistant.
  52. 52. 52 Experimental design: resources (read if you need) Hypothesis and predictions Hypotheses and predictions are frequently mixed up. A hypothesis is a proposed explanation of how a system works. Hypotheses are tested in science via predictions. Predictions are statements of outcomes logically derived from the hypothesis. The hypothesis is the big picture and the predictions are the outcomes that if supported suggest that the hypothesis is a viable explanation for the phenomenon in question. Using we only the alternative hypothesis in modern ecology, an explanation and do not include the null hypothesis of no effect/relationship. Select a few ecology papers to get a sense for the variation in scale of hypotheses and predictions proposed. Here is a fun example. Hypothesis: Public transit is a less reliable form of public transit for students and employees to reach York University campus relative to those that drive personal vehicles. To explore this hypothesis, we will contrast punctuality of BIOL2050 students in arriving to the 830am lecture via the ttc and personal vehicles (note: we will exclude those that live on campus, carpool, and use the early morning arrival only to control for differences in time of day). Note – you can see right away that there are so many other interesting variables we cannot explore here in a simple experiment such as distance travelled, time of day, bus versus subway, etc, however we should try to capture some of these other variables in our survey and data collection of arrival times of students. Predictions: (1) If public transit is less reliable, students that use it will on average arrive late to lecture more frequently than those that drive (arrival time will be coded as on time and late only). (2) If public transit is less reliable, students that use it will have more variable arrival times relative to those that drive (actual arrival times recorded). We can stop there if we have limited resources or time to conduct this study. However, it would be ideal to add in another major variable that is
  53. 53. 53 also likely an important factor relating the variability of public transit such as distance travelled, time of day, number of changes, train versus subway, etc. If so, you would propose another prediction to explore this potential factor here. There is also another really interesting and simple experiment that could be done. Ignore car drivers and just survey public transit rider students very extensively and capture the process in great detail. This is appealing in that it is a much simpler experiment but the scope of inference is more limited. For instance, from an experimental science perspective and carbon footprint, it would be really useful to provide evidence for students to make a better decision on how to get to school. You may find that short distance commutes on the ttc with limited number of changes is more a reliable form of transit than driving in the morning because the dedicated bus lane protects the riders from heavy traffic more effectively. You may also find that driving longer distances is more reliable than shorter distances on average because you are in your one car with no changes, use more major arteries to get to campus that are less variable, and depart from your home earlier to arrive in time for the 830am lecture. Here is an ecological example from Lamarque et al. 2012 in Ecography done right here in Toronto with maple trees (and also with maples from Canada in France). “Here, biogeographical contrasts were applied using spatially-structured local density surveys and regional surveys for two maple tree species Acer negundo and Acer platanoides both of which are reciprocally native in one range and introduced into the range of the other where they are assumed invasive. This is a perfect opportunity to explore biogeography as it relates to invasion and extends the previous work of Reinhart and Callaway in 2004. The following three predictions were thus tested to examine the overarching general hypothesis that biogeographical contrasts are an effective means to describe invasiveness of a plant species: 1) if a species is invasive, the introduced populations occur at higher density and abundance relative to the native conspecifics, i.e. there are intraspecific inter-regional differences in density. 2) If a species is invasive, it must at some even minor level negatively impact the density of the native species due to interference or displacement/saturation. 3) If a species is to be considered invasive, the regional spread of the species in the novel region should be at least 10%, i.e. more than 1 in 10 communities surveyed should have the introduced species present at even low densities of juveniles or adult trees. We recognize there are limitations to or counter-arguments against these three predictions but nonetheless propose that taken together they definitely demonstrate that relative differences in the density and extent of presence within a novel region can be used to infer invasiveness.” Here is another set by Sotomayor et al. 2014 in Austral Ecology. “The purpose of this study was to determine the effects of nurse plants on seed biology and germination of understorey annual plant species relative to the same species growing in open micro-habitats. We hypothesized that facilitation by nurse-plants generates sufficiently different micro-environmental conditions that lead to consistent differences in seeds traits of understorey plants. We explored the following predictions to test this hypothesis: seeds collected from plants associated with the nurse-plant micro-habitat would (i) be larger due to more favourable growing conditions, (ii) have greater viability and germination rate (iii) have less variability in size and viability due to reduced environmental heterogeneity provided by nurses (buffering), and (iv) germinate faster due to potential apparent competition with other annuals.” Variation Design and number of replicates are two major sets of decisions that influence that capacity for your experiment (manipulative or mensurative survey) to effectively test your predictions and explore your hypothesis. We have discussed design briefly in that the technique and how you elect to block/spread our sampling dramatically impact the outcome of your experiment. However, considering the variation directly is also very important in the environmental sciences. Certainly, the mean effect is important but the variation associated with the mean of your process
  54. 54. 54 or pattern is interesting and ecologically informative in its own right. This paradigm shift happened over 20 years ago in ecology but the effects on sampling design are still percolating. From Benedetti-Cecchi (2003) in Ecology. This is similar to the ANOVA versus regression-based approaches to designing ecological experiments. If your design can estimate and describe the variance in your system, then the dataset and interpretation will be more useful and reusable for other scientists. There will always be variance in natural systems; the real trick is to design experiments with a mechanism to explain as much as the variation as possible. The way of the ecologist can help here. Observation of the system and creative exploration of the variables that can generate the patterns are invaluable tools in promoting effective design decisions. Consider the intensity of the process, the variation, and the spatial and temporal effects that may shape the process you are interested in examining.
  55. 55. 55 From Benedetti-Cecchi (2003) in Ecology. Sampling tip In designing your experiment, absolutely consider all the limitations and strengths associated with the techniques you elect to use. Also, consider the extent that you will be able to replicate and how to spread those replicates (i.e. in blocks are on a gradient of some sort). The final issue is to consider all the potential variables that might impact your outcomes or estimations of the process within the natural system. To do this, make a list as long as you like of all the factors that might influence the outcomes your proposed in your predictions. Then, sort them into biotic and abiotic ones and code them again to ones that you can measure or control for in your design. With that final list in hand, you are now ready to start designing your experiment and sampling. Causality
  56. 56. 56 Correlation is not causation (but almost always implies it). Spurious correlations are a major issue in the environmental sciences. It is all too easy to conclude that the variables we measured directly related to the outcomes observed. This is a less of an issue in well-executed manipulative experiments that considered many of the important factors that can relate to the outcome. Nonetheless, surveys are an important component of environmental science and ecology and natural systems are complex. The single best design tool at hand to help you ensure relatively sound interpretation are creative (pictures, the directed acyclic graphs described next). Conceptually however, there are least two forms of correlation to be aware of in your designs. Accidental ones and genuine ones.
  57. 57. 57 From Haig (2003) in Understanding Statistics. All forms illustrated above are present in ecology and the environmental sciences. Listing variables and sketching out potential relationships are best quick tools we have against incorrectly assuming relationships. There are more sophisticated options available as well including Bayesian statistics and models such as simulations of patterns. The same principles apply however in meditatively considering the system deeply and creatively exploring interactions.
  58. 58. 58 Directed acyclic graphs In ecology and the environmental sciences, directed acyclic graphs (dag) are applied to the design and interpretation of experiments and associated datasets. They are applied less formally (but not always) than in mathematics. A dag is a directed graph with no directed cycles. It is a visualization of a model of interactions both biotic and abiotic that relate to the outcome of our ecological predictions. Here is a collection of examples to give you a feel for them as tools to explore causality (and interactions more broadly) and experimental design.
  59. 59. 59 These are really simple but you get the point. Make your variables visible and illustrate your assumptions. Visual models of your system will help you design experiments by providing you with a tangible model that you can then use to highlight what you will test without forgetting about all the other variables that can also be important and may need to discussed in the final paper even if you could not explore them in your experiment. Statistics In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. The phrase ‘test of significance’, like so much in modern statistics, was coined by Ronald Fisher "Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first."[1] Statistical significance is different from the standard use of the term "significance," which suggests that something is important or meaningful. For example, a study that included tens of thousands of participants might be able to say with very great confidence that people of one race are more intelligent than people of another race by 1/20th of an IQ point. This result would be statistically significant, but the difference is so small as to be completely unimportant. Many researchers urge that tests of significance always be accompanied by effect size statistics, which approximate the size and practical importance of the difference.
  60. 60. 60 The amount of evidence required to accept that an event is unlikely to have arisen by chance is known as the significance level or critical p-value: in traditional frequentist statistical hypothesis testing, the p-value is the frequency or probability with which the observed event would occur, if the null hypothesis were true. If the obtained p-value is smaller than the significance level, then the null hypothesis is rejected. In simple cases, the significance level is defined as the probability that a decision to reject the null hypothesis will be made when it is in fact true and should not have been rejected: a "false positive" or Type I error. More typically, the significance level of a test is such that the probability of mistakenly rejecting the null hypothesis is no more than the stated probability. This allows for cases where the probability of deciding to reject may be much smaller than the significance level for some sets of assumptions encompassed within the null hypothesis. The significance level is usually denoted by the Greek symbol, α (alpha). Popular levels of significance are 5% (0.05), 1% (0.01) and 0.1% (0.001). If a test of significance gives a p-value lower than the α-level, the null hypothesis is rejected. Such results are informally referred to as 'statistically significant'. For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence," a 0.001 level of statistical significance is being implied. The lower the significance level, the stronger the evidence being required. Interpretations Statistical error: Type I and Type II Statisticians speak of two significant sorts of statistical error. The context is that there is a "null hypothesis" which corresponds to a presumed default "state of nature", e.g., that an individual is free of disease, that an accused is innocent, or that a potential login candidate is not authorized. Corresponding to the null hypothesis is an "alternative hypothesis" which corresponds to the opposite situation, that is, that the individual has the disease, that the accused is guilty, or that the login candidate is an authorized user. The goal is to determine accurately if the null hypothesis can be discarded in favor of the alternative. A test of some sort is conducted (a blood test, a legal trial, a login attempt), and data are obtained. The result of the test may be negative (that is, it does not indicate disease, guilt, or authorized identity). On the other hand, it may be positive (that is, it may indicate disease, guilt, or identity). If the result of the test does not correspond with the actual state of nature, then an error has occurred, but if the result of the test corresponds with the actual state of nature, then a correct decision has been made. There are two kinds of error, classified as "Type I error" and "Type II error," depending upon which hypothesis has incorrectly been identified as the true state of nature. Type I error Type I error, also known as an "error of the first kind", an α error, or a "false positive": the error of rejecting a null hypothesis when it is actually true. Plainly speaking, it occurs when we are observing a difference when in truth there is none. An example of this would be if a test shows that a woman is pregnant when in reality she is not. Type I error can be viewed as the error of excessive skepticism. Type II error Type II error, also known as an "error of the second kind", a β error, or a "false negative": the error of failing to reject a null hypothesis when it is in fact not true. In other words, this is the error of failing to observe a difference when in truth there is one. An example of this would be if a test shows that a woman is not pregnant when in reality she is. Type II error can be viewed as the error of excessive credulity. See Various proposals for further extension, below, for additional terminology.
  61. 61. 61 Understanding Type I and Type II errors When an observer makes a Type I error in evaluating a sample against its parent population, they are mistakenly thinking that a statistical difference exists when in truth there is no statistical difference (or, to put another way, the null hypothesis should not be rejected but was mistakenly rejected). For example, imagine that a pregnancy test has produced a "positive" result (indicating that the woman taking the test is pregnant); if the woman is actually not pregnant though, then we say the test produced a "false positive". A Type II error, or a "false negative", is the error of failing to reject a null hypothesis when the alternative hypothesis is the true state of nature. For example, a type II error occurs if a pregnancy test reports "negative" when the woman is, in fact, pregnant. From the Bayesian point of view, a type one error is one that looks at information that should not substantially change one's prior estimate of probability, but does. A type two error is that one looks at information that should change one's estimate, but does not. (Though the null hypothesis is not quite the same thing as one's prior estimate, rather it is one's pro forma prior estimate.) Common statistical tests in ecology Correlation In statistics, correlation (often measured as a correlation coefficient, ρ) indicates the strength and direction of a linear relationship between two random variables. That is in contrast with the usage of the term in colloquial speech, which denotes any relationship, not necessarily linear. In general statistical usage, correlation or co-relation refers to the departure of two random variables from independence. In this broad sense there are several coefficients, measuring the degree of correlation, adapted to the nature of the data. Several authors have offered guidelines for the interpretation of a correlation coefficient. Cohen (1988) has observed, however, that all such criteria are in some ways arbitrary and should not be observed too strictly. This is because the interpretation of a correlation coefficient depends on the context and purposes. A correlation of 0.9 may be very low if one is verifying a physical law using high-quality instruments, but may be regarded as very high in the social sciences where there may be a greater contribution from complicating factors. Along this vein, it is important to remember that "large" and "small" should not be taken as synonyms for "good" and "bad" in terms of determining that a correlation is of a certain size. For example, a correlation of 1.0 or −1.0 indicates that the two variables analyzed are equivalent modulo scaling. Scientifically, this more frequently indicates a trivial result than a profound one. For example, consider discovering a correlation of 1.0 between how many feet tall a group of people are and the number of inches from the bottom of their feet to the top of their heads. Correlation Negative Positive Small −0.3 to −0.1 0.1 to 0.3 Medium −0.5 to −0.3 0.3 to 0.5 Large −1.0 to −0.5 0.5 to 1.0 T-tests A t-test is any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is true. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistic (under certain conditions) follows a Student's t distribution. Among the most frequently used t-tests are: * A one-sample location test of whether the mean of a normally distributed population has a value specified in a null hypothesis.
  62. 62. 62 * A two sample location test of the null hypothesis that the means of two normally distributed populations are equal. All such tests are usually called Student's t-tests, though strictly speaking that name should only be used if the variances of the two populations are also assumed to be equal; the form of the test used when this assumption is dropped is sometimes called Welch's t-test. These tests are often referred to as "unpaired" or "independent samples" t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. * A test of the null hypothesis that the difference between two responses measured on the same statistical unit has a mean value of zero. For example, suppose we measure the size of a cancer patient's tumor before and after a treatment. If the treatment is effective, we expect the tumor size for many of the patients to be smaller following the treatment. This is often referred to as the "paired" or "repeated measures" t-test:[5][6] see paired difference test. * A test of whether the slope of a regression line differs significantly from 0. Two sample t-tests for a difference in mean can be either unpaired or paired. The unpaired, or "independent samples" t-test is used when two separate independent and identically distributed samples are obtained, one from each of the two populations being compared. For example, suppose we are evaluating the effect of a medical treatment, and we enroll 100 eligible subjects into our study, then randomize 50 subjects to the treatment group and 50 subjects to the control group. In this case, we have two independent samples and would use the unpaired form of the t-test. The randomization is not essential here — if we contacted 100 people by phone and obtained each person's age and gender, and then used a two-sample t-test to see whether the mean ages differ by gender, this would also be an independent samples t-test, even though the data are observational. Dependent samples (or "paired") t-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice (a "repeated measures" t-test). A typical example of the repeated measures t-test would be where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are tested again after treatment with a blood-pressure lowering medication. A dependent t-test based on a "matched-pairs sample" results from an unpaired sample that is subsequently used to form a paired sample, by using additional variables that were measured along with the variable of interest [8]. The matching is carried out by identifying pairs of values consisting of one observation from each of the two samples, where the pair is similar in terms of other measured variables. This approach is often used in observational studies to reduce or eliminate the effects of confounding factors. Suppose students in a particular school are given the opportunity to receive after-school mathematics tutoring. If only a fraction of the students complete the tutoring program, one might wish to evaluate the effectiveness of the program by comparing the students who did and who did not complete the program, using scores on a standardized test given after the program is finished. A difficulty is that the students who completed the tutoring program may already have differed in mathematical achievement before the tutoring program began. To reduce the confounding effect of baseline mathematical achievement, one can attempt to match each subject who completed the tutoring program to a subject who did not, matching on the students' mathematics grades from the previous semester. If we then compare the students within matched pairs using a paired t-test, baseline mathematical knowledge should have little effect on the results. Note that a paired data set can always be analyzed using the unpaired or paired versions of the t-test, but an unpaired dataset must be analyzed using the unpaired t-test unless some form of pairing can be defined. An ideal pairing takes the form of blocking. For example, when comparing pre-treatment and post-treatment blood pressure within individuals, characteristics such as age and gender which are unrelated to the treatment but that may affect blood pressure do not affect
  63. 63. 63 the results of the paired t-test. In this case, the paired t-test will have greater power than the unpaired test. A different situation arises when following the matched-pairs strategy, where the goal is to reduce confounding. The cost of matching to reduce confounding is usually a reduction in power. ANOVAs In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables. In its simplest form ANOVA gives a statistical test of whether the means of several groups are all equal, and therefore generalizes Student's two-sample t-test to more than two groups. In practice, there are several types of ANOVA depending on the number of treatments and the way they are applied to the subjects in the experiment: * One-way ANOVA is used to test for differences among two or more independent groups. Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a T-test (Gossett, 1908). When there are only two means to compare, the T-test and the F-test are equivalent; the relation between ANOVA and t is given by F = t2. * One-way ANOVA for repeated measures is used when the subjects are subjected to repeated measures; this means that the same subjects are used for each treatment. Note that this method can be subject to carryover effects. * Factorial ANOVA is used when the experimenter wants to study the effects of two or more treatment variables. The most commonly used type of factorial ANOVA is the 22 (read "two by two") design, where there are two independent variables and each variable has two levels or distinct values. However, such use of Anova for analysis of 2k factorial designs and fractional factorial designs is "confusing and makes little sense"; instead it is suggested to refer the value of the effect divided by its standard error to a T-table.[1] Factorial ANOVA can also be multi-level such as 33, etc. or higher order such as 2×2×2, etc. but analyses with higher numbers of factors are rarely done by hand because the calculations are lengthy. However, since the introduction of data analytic software, the utilization of higher order designs and analyses has become quite common. * Mixed-design ANOVA. When one wishes to test two or more independent groups subjecting the subjects to repeated measures, one may perform a factorial mixed-design ANOVA, in which one factor is a between-subjects variable and the other is within-subjects variable. This is a type of mixed-effect model. * Multivariate analysis of variance (MANOVA) is used when there is more than one dependent variable. Regression Regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function that can be described by a probability distribution.