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Homework answers / question archive / BIOL-213, INTRODUCTION TO ECOLOGY, FALL 2022 COMMUNITY STRUCTURE QUANTIFYING A WOODLAND TREE COMMUNITY, MILLS RESERVATION, USING A PLOTLESS SAMPLING TECHNIQUE: THE POINT QUARTER METHOD Exercise adapted from Cox (1980:46-49, Laboratory manual of general ecology, fourth edition, W








Exercise adapted from Cox (1980:46-49, Laboratory manual of general ecology, fourth edition, W. C. Brown Co., Dubuque, Iowa).


Adapted by J. A. Smallwood.


Natural communities frequently are described in terms of the species which have the greatest biomass, usually the dominant plants.  The importance of each species may be expressed as a combination of its density, distribution, and average size.  Because it is impractical to measure every individual organism in the community of interest, some method of representational sampling is employed.  A number of vegetation sampling techniques utilize measurements of distances between plants or from randomly chosen points to the nearest plants.  One of the most widely used of these is the point-centered quarter or point-quarter technique.  This technique is best adapted for sampling communities in which the individual plants are widely spaced or in which the dominant plants consist of woody plants shrub size or larger.  However, the technique may be adapted to sampling other types of plant or animal populations, such as animal nests (wood rats, etc.) or holes (anthills, fiddler crab burrows, etc.) or sessile or sedentary animals (barnacles, scale insects, etc.).





The objectives of this exercise are (1) to appreciate the utility of sampling in order to obtain representational data, (2) to understand the point-quarter sampling technique through an actual field application, (3) to determine the dominant tree species present at Mills Reservation, and (4) to illustrate the relationship between sampling effort and estimated community richness.





The class will form five teams, one team for each sampling transect.  Team members will share responsibility for orienting the transect properly, pacing the distances to each sampling point, identifying tree species, and recording data.


A total of 120 trees will be sampled by the following procedure.  A baseline (an imaginary line running through the woods) will be established at the study site.  Five parallel sampling transects, A-E, beginning at the baseline and extending in a direction perpendicular to it, will be spaced 50 paces apart from each other.  Six sampling points will be located along each sampling transect at random distances from the baseline (these distances will be provided for you).  This design is an example of "stratified random sampling."


Each sampling point will be marked with a flag.  The area surrounding each point will be divided into four quadrants, delineated by the intersection of the sampling transect and an imaginary line running perpendicularly through that point.  In each quadrant, the tree (with a diameter ?10 cm) nearest the point will be identified.  For each tree the team will record the species, the point-to-plant distance, and tree size.  Point-to-plant distance should be measured in meters (to two decimal places) to the estimated center of the trunk, not to the surface facing the point.  Tree size will be characterized by trunk DBH (diameter, breast height, in cm).


The data will be compiled for you, and the summary will be provided at our next class meeting.





Density.?Total density of all trees (?10-cm diameter DBH) is calculated by computing the mean point-to-plant distance for all 120 trees, squaring that mean, and taking the reciprocal:


                                Total density of all species = 1 / (mean point-to-plant distance)2.


In other words, each plant, on average, occupies a square area that is the mean point-to-plant distance wide by the mean point-to-plant distance long.  This value will be in trees per m2.  Convert this value to the number of trees per hectare; since a square that is 100 m on each side has an area exactly 1 ha, multiply your calculated density value by the fraction 10,000 m2 / 1 ha.


Relative density is calculated for each species:


                                Relative density of species i = individuals of species i / total of all individuals, i.e.,

                                Relative density of species i = individuals of species i / 120.


Note that the relative densities for all species will sum to 1.


                                Density of species i = relative density of species i × total density of all species.


Frequency.?Frequency is a measure of how evenly distributed each species is.  For this we will tally the number of sampling points at which each species occurs; a species scores a 0 if it does not occur at the point, and a 1 if there are either 1, 2, 3, or 4 individuals at that point.


                                Frequency of species i = number of points where species i occurs.


                                Relative frequency of species i = frequency for species i / sum of frequencies for all species.


Note that frequency ranges from 1 to 30, and the relative frequencies for all species will sum to 1.


Dominance.?Dominance is a measure of tree size.  For this we will calculate basal area, that is, the area in cm2 of the trunk at breast height.  Recall that the area of a circle is, by definition, πr2, and that r, the radius, is one-half the diameter.  Since we will be measuring tree circumference rather than diameter, remember to make the appropriate conversion.  Note that basal area must be calculated separately for each tree, not from the mean circumference of all trees; mean basal area does NOT equal π(mean r)2.


                                Dominance of species i = mean basal area for species i ? density of species i.


The calculated dominance will be in cm2/ha.  Convert these values to m2/ha.  Note that there are 10,000 (not 100) cm2 per m2.


                                Relative dominance of species i = dominance for species i / total dominance for all species.


Note that the relative dominances for all species will sum to 1.


Importance Value.?The "importance" of each species is some combination of relative density, relative frequency, and relative dominance.  For this exercise we will weight these three measures equally; the importance value will simply be the sum of the three relative measures.  Note, then, that the importance values for all species will sum to 3.  The tree species that have the greatest importance values are referred to as the "dominant" tree species in that community (an unfortunate choice of terms, since we already are using "dominance" to mean something else!).  For example, in a beech-maple forest in southwestern Ohio, one would expect beech and maple to have the highest importance values.  Also note that the determination of which species are dominants and which are not is based ONLY on the importance value, not on comparisons of density, frequency, or tree size.





You will be provided a list of each tree, identified by species, included in our sample.  The sequence will be randomized by machine.  From the resulting sequence you will generate a graph that illustrates the relationship of sample size with estimates of species richness.  The y-axis will be the proportion of species detected (0-1), and the x-axis will be number of trees sampled (0-120).  For example, suppose a total of eight species were represented in our sample of 120 trees.  When the sample size is one, the proportion of species detected is 0.125 (one-eighth, the first of eight species).  If the next tree in the sequence is a different species, the proportion of species detected at n = 2 would be 0.25 (two-eighths).  Perhaps the next three trees in the sequence belong to the two species already sampled.  On the sixth sampling point we find a third species (proportion = 0.375, or three-eighths), and so on.  The curve will rise monotonically until it reaches 1, either at or (more likely) before n = 120.  The shape of the resulting curve will reveal something about how to allocate sampling effort in a field study.





As always, use an Excel spreadsheet to do all your calculations.  The only values you will enter are the raw data.  Every other value in the spreadsheet will be based on cell addresses and the appropriate formulas.  To avoid compounded rounding errors, NEVER enter a calculated value into a cell by hand.  To get any credit, your calculated values must be exactly correct.


use formulas with addresses pointing back to


The lab report will consist of four parts.


1.            Table 1 will show the community structure analysis.  A blank form has been provided for you.  Using the values calculated in your Excel spreadsheet, fill in the form by hand and include a descriptive (what, where, when) title at the top.  Fill in the units of measure within the parentheses at the top of selected columns (e.g., density should be trees/ha).  Be consistent within each column in regard to the number of decimal places displayed (the decimal points must be aligned, and values less than one must begin with zero; e.g., 0.123, not .123).  Use your judgment here; display your numbers to just enough decimal places so that differences within a given column are apparent.  The species MUST BE IN RANK ORDER, those with the highest importance values at the top of the table.


2.            In one succinct paragraph, (a) identify all the dominant tree species, and (b) explain how you decided which species were dominant (vis-a-vis which were not; state the exact decision rule you employed, which should be one that would reasonably apply to other sets of data).  Note that when you report results in a scientific paper, you are relating things that have already happened; thus, you should use past tense.  Please be as succinct as possible, omitting any word or phrase that does not convey essential information.  For example, never introduce a statement with an expendable phrase such as "From the data in Figure 1 it can be seen that..."  As an incentive toward developing effective writing skills, ONLY THE FIRST 6 LINES OF TEXT WILL BE READ AND GRADED.


3.            Figure 1 will demonstrate the relationship of sample size and estimated richness, and should be generated according to the directions above.  Be sure to label your axes and provide a descriptive title.  The entire figure, including titles, labels, and tick marks, must be generated by Excel; do not annotate by hand.  The height of the y-axis should be between 67% and 75% of the length of the x-axis.  Import Figure 1 from Excel to a single page in your lab report, which will be in Word.  The figure should be in portrait mode.


4.            In a second succinct paragraph, interpret Figure 1.  What does this curve tell you about sampling effort and estimating species richness, i.e., was the sample size adequate, and how do you know?  For this paragraph, ONLY THE FIRST 6 LINES OF TEXT WILL BE READ AND GRADED.


Use MS Word to produce the lab report (except for filling in Table 1).  Use a simple typeface, such as Times New Roman or Arial (block letters), with a 10-12 point size, and use the same font throughout the paper (including the cover page).  The report must be on 8½ × 11-inch paper, one side only, with one-inch margins all around.  Double-space all text.  The text in Figure 1 also should conform to the 10-12 point size limits.  Do not use color or additional graphic images, unless they contribute substantively to understanding the information being conveyed.  Begin with a cover page containing ONLY a descriptive title of the paper, your name, our class name (BIOL-213, Introduction to Ecology, Fall 2021), and the date of submission.


Assemble the report in this sequence: cover page, Table 1 (filled in by hand and the only page in landscape mode), paragraph 1, Table 1, and paragraph 2.  You probably can fit paragraph 1, Table 1, and paragraph 2 on a single page.  Bind the lab report ONLY with one staple in the upper left-hand corner.  Proofread your paper very carefully.  FOLLOW ALL DIRECTIONS WORD-FOR-WORD.


Submit the printed copy of your Word document and upload to Canvas BOTH the original Excel file and the original Word file you used to generate the printed copy.  As always, both are due no later than the beginning of the next lab meeting.

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