Using seasonal succession in Lake Plankton to illustrate concepts of community structure & species diversity.
Biological diversity (Research)
Ecological succession (Research)
|Author:||Hooker, Laura J.|
|Publication:||Name: The American Biology Teacher Publisher: National Association of Biology Teachers Audience: Academic; Professional Format: Magazine/Journal Subject: Biological sciences; Education Copyright: COPYRIGHT 2009 National Association of Biology Teachers ISSN: 0002-7685|
|Issue:||Date: Oct, 2009 Source Volume: 71 Source Issue: 8|
|Topic:||Event Code: 310 Science & research|
|Geographic:||Geographic Scope: Canada Geographic Code: 1CANA Canada|
Biological communities are of interest to people for a wide range of reasons. For example, people may want to know the reason for blooms of noxious algae in the lake where they possess recreational property, or whether the creek that borders the backyard of their house can support fish, or they may simply appreciate the diversity of organisms found on a patch of forest where they hike. Ecologists and environmental scientists frequently need to describe biological communities as part of research programs that attempt to explain how the natural world operates or to determine the effects of manmade or natural perturbations. Direct cause and effect is difficult to show. However, careful documentation of the structure of the community and how it is changing can provide a wealth of evidence that, in turn, can yield a persuasive argument.
There are a number of parameters that can be used to describe the biological structure of communities, for example: the taxonomic identity of organisms present, their trophic role, the number of different taxa present, and the relative abundance of each taxon. The latter two parameters are commonly distilled down to a single metric called species diversity, sometimes referred to as "community diversity" (Krebs, 2001; Smith & Smith, 2001).
The biological structure of different communities can be highly variable. For example, planktonic communities found in extremely saline environments may support only a few species that can physiologically withstand the high salinity, but the abundance of individuals of each species can be very high. Stream communities can be very diverse, but, unlike terrestrial systems, their trophic structures are largely based on detritivores feeding on leaf litter that has fallen into the stream, as opposed to autotrophic activity within the stream. In terrestrial communities, the growth forms of the plant species present can change the physical structure of the community. For example, long-lived trees in forests that persist through the seasons have a more profound effect on community structure than short-lived herbaceous species in grasslands that die back in winter.
Communities change overtime and, for many people, the usefulness of community parameters is best appreciated in this context rather than by comparing geographically distinct populations. Communities can change as part of natural long-term succession, in response to short-term disturbance events, or due to cyclical seasonal fluctuations. For educational purposes, seasonal changes are suitable because they can be studied over a short timespan. Seasonal succession in plankton communities is easier to study than in terrestrial communities. Analyses of terrestrial communities require data collection over a large spatial scale which can entail a considerable amount of time in the field, possibly under inclement weather conditions. In contrast, the microscopic scale of plankton communities allows for easy presepeation and transport of samples to the lab for data collection. Planktonic taxa can be more difficult for students to identify than macroscopic plants and animals, but fortunately, many parameters of community structure require merely that students discriminate between species and don't require actual identification.
This article presents a simple technique for easy viewing of lake plankton communities, a simple dichotomous key that will ease students into the identification process, and a suggestion for an exercise to demonstrate changes in community structure as a result of seasonal succession. I run this exercise as a lab for first-year university students in conjunction with lectures on community ecology. For the sake of completeness, this article also presents some background information about lake plankton and measurements of species diversity. The exercise can likely be modified for different levels of high school, perhaps as a more qualitative assessment. The degree of modification required is probably best determined by the teacher who knows the capabilities of his or her students. The exercise and the dichotomous key should work for most temperate lake ecosystems regardless of geographic locale.
After successfully performing the following exercise, the students will:
* know how ecologists and environmental scientists describe community structure and quantify species diversity.
* become familiar with some of the constituents of lake plankton communities.
* be able to list some of the factors that cause lake communities to change with the seasons.
Plankton are those organisms that live in the water and drift with the currents. Animals, such as adult fish, that are strong swimmers are not considered part of the plankton. In lakes, plankton comprise three groups of organisms which represent different trophic levels:
1. Phytoplankton consist of the cyanobacteria (also known as blue-green algae) and the eukaryotic algae. They are photosynthetic and are the primary producers of planktonic systems. A few taxa, such as some dinoflagellates, are also are able to uptake dissolved organic carbon directly and phagocytise small particles. This ability is called mixotrophy (Lampert & Sommer, 1997; Stoeker, 1999).
2. Zooplankton which feed primarily on phytoplankton are the primary consumers. A few types of zooplankton feed on other zooplankton and so are considered secondary consumers. Zooplankton can be animals or non-photosynthetic protists. The protists are primarily bacteriovores and, being very small, are often referred to as microzooplankton. Rotifers and small crustaceans are the most common components of the lake zooplankton.
3. Bacterioplankton are the bacteria exclusive of the cyanobacteria. Most of these bacteria are heterotrophs and are responsible for the breakdown of dead organic matter. They are exceedingly important for recycling nutrients in aquatic ecosystems but, because of their very small size, they cannot be collected and observed by the technique presented here.
Species Diversity Indices
The species diversity of a community is a combination of two factors: the number of different species present in a community, and the degree to which each species is represented in the community. The first factor is termed "species richness" and it is the oldest and simplest parameter of community structure. The second factor is termed "evenness" or "equitability" (Krebs, 1999; Smith & Smith, 2001). This measure of species diversity recognizes that a community of ten equally abundant species should be considered to be more diverse than another community also with ten species, but with one species that makes up 99% of the total individuals. Analysis of empirical data indicates that species richness and species evenness are separate factors contributing to species diversity since they are not consistently statistically correlated (Stifling & Wilsey, 2001).
Figure 1 illustrates how the two concepts of species diversity relate to community structure. Community A has the same number of species as Community B but the relative abundances are more even, so, by an evenness measure, A is more diverse than B. Community C has the same abundance pattern as B but has more species, so it is more diverse than B by virtue of a greater species richness value. A diversity index distils the effects of species richness and evenness into a single value. Because of this, it is possible for communities such as A and C to have equal diversity values by virtue of their high evenness and species richness respectively. Species richness, evenness, and diversity indices can be calculated as baselines against which changes in community structure can be measured or can be used to compare communities. A stand-alone value has little meaning because these indices are only useful as a measure when employed for making comparisons.
Two of the most well known diversity indices are the Simpson index and the Shannon-Wiener index. The Shannon-Wiener index is sometimes incorrectly referred to as the Shannon-Weaver index (Krebs, 1999; Spellerberg & Fedor, 2003), possibly because it was popularized in a publication by Shannon and Weaver (1945).
[FIGURE 1 OMITTED]
The theoretical underpinnings of the Shannon-Wiener index (H') lie in information theory; it describes how difficult it is to predict correctly the species of the next individual collected (Krebs, 1999). H' was originally measured by the following function:
H' = -[summation][p.sub.i] [log.sub.2] [p.sub.i]
where [p.sub.i] is the proportion of the total sample belonging to the ith species (Krebs, 1999; Smith & Smith, 2001). Currently, H' is more commonly expressed using natural logs or common logs. H' represents the uncertainty of predicting the next "bit" of information. As a unit, bit is not very intuitive, therefore the Shannon-Wiener index is sometimes expressed as (when H' is calculated from log base 2):
[N.sub.i] = [2.sup.H']
where [N.sub.i] represents the number of equally abundant species that would be needed to produce the same diversity as the calculated H'. In this case, the unit of the exponential form of the Shannon-Wiener index is "species."
Simpson's index is derived from the assumption that diversity is related to the probability that two individuals picked at random from a community will belong to the same species. Most people use the reciprocal form of the index (1/D):
1/D = 1/[summation] [p.sup.2.sub.i]
Similar to the exponential from of the Shannon-Wiener index, Simpson's reciprocal index can be most easily interpreted as the number of equally abundant species required to generate the calculated D of the sample. Therefore the unit of Simpson's reciprocal index is also "species" (Krebs, 1999). The values for these two indices range from 1 to the value that represents the number of species in the community.
Evenness is commonly expressed by scaling one of the diversity measures against its maximum value. For example:
[E.sub.1/D] = 1/D/1/[D.sub.max] - or [E.sub.H'] = H'/[H'.sub.max]
The maximum value of '1' occurs when the abundances of all species in the community are equal. There are independent methods for the determination of evenness, such as Smith and Wilson's (1996) index of evenness but they require computer programs to calculate.
The Shannon-Wiener index tends to emphasire the rarer species whereas the Simpson's reciprocal index emphasizes the common species (Krebs, 1999; Lampert & Sommer, 1997). As such, the choice of using one index over the other depends on what needs to be emphasized. If you are interested in assessing the recovery of a lake after a catastrophic event, the Shannon-Weiner index might be most useful because it is more sensitive to the return of initially rare species. Under another circumstance, evaluation of species that are relatively abundant and, therefore more important as a significant source of food for fish, might be of more interest. In this case, Simpson's reciprocal index would be more suitable.
Providing sample calculations is essential for many students. I use data from a terrestrial environment so that students can see that these parameters are useful for any biological community and are not specific to plankton communities. Sample data can be set up as in Table 1 so that students have a clear idea of how to organize their data to more easily calculate the indices. Table 1 also shows step-by-step calculations for the exponential form of the Shannon-Wiener index and Simpson's reciprocal index. The column of proportional representation (p,) can be used to construct histograms such as those shown in Figure 1. The evenness measures require the determination of maximum values. For the Simpson's reciprocal index and the exponential form of the Shannon-Wiener index, it follows that the number of species present in the sample is the maximum value (Krebs, 1999). Therefore, for the data in Table 1, [E.sub.1/D] = 3.13/11 = 0.28 and [E.sub.H'] = 2.03/11 = 0.18.
Using the data they have collected, students should be able to estimate the species richness of their samples, calculate the proportional abundance of each type of organism, create histograms like Figure 1, and calculate Simpson's reciprocal index, the exponential form of the Shannon-Wiener index, and evenness.
* Plankton Sampling & Specimen Preparation
Plankton are most easily collected using a zooplankton net with a mesh size of approximately 100 [micro]m. A smaller mesh size allows you to retain smaller plankton but it will also clog more easily. Simple plankton nets can be obtained from most biological supply companies. The net is designed so that the plankton collect into the far end of the net, which is usually a rigid container that can be released from the net, and the concentrated sample transferred to a jar. The net can be dragged vertically or horizontally through the water column. For a horizontal tow, drag the net just below the surface of the water. A tow using a net diameter of 30 cm for a total length of 25 m is usually sufficient in moderately-productive lakes. For a lab of 20 students, you will need about 35 mL of concentrated sample.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Selection of the site for sampling can be important; plankton should be sampled as far away from the influence of the shore and the inflow of creeks as possible, and in water deep enough to accommodate the zooplankton net. In addition, zooplankton tend to avoid brightly-lit water, so shallow areas with lightly-colored substrate should be avoided. Shallow waters may also contain more suspended particles, making it harder to see the actual organisms. Ira boat is not available, then dragging the net off the end of a dock is a good alternative. Try to sample from the same location each season.
Once collected, the sample can be transported back to the lab alive or preserved. Samples will remain living for at least a week providing that they are aerated and kept reasonably cool. Preserve with 90% ethanol diluted with sample to form a 70% solution. For my course, I sample in late August while the lake is thermally stratified and preserve the sample for later use. I then sample the lake again during March while the lake is not thermally stratified and transport that sample back to the lab alive. Here I split the sample in two, preserving one half while leaving the other half alive. Identification and counts should be performed on the preserved sample. Use the living sample to allow the students to observe the natural coloration of the organisms and their forms of locomotion.
In the lab, fill 15 mL plastic centrifuge tubes with well-mixed preserved sample, and cap. For a lab section of 20 students, I fill ten tubes for each of the seasons sampled. Let the samples settle overnight. After settling, draw down the supernatant to 1.5 mL, which happens to be where the tube starts to narrow to the conical point. Students can then use a Pasteur pipet to re-suspend the sample and then to dispense a drop into a dimple slide. The dimple of the slide needs to be completely filled with sample in order to avoid bubbles when a cover slip is placed on top. Ethanol evaporates quickly so the cover slip is needed to retard evaporation long enough for observations and counts to be made.
In order to obtain an overview of the plankton community, students should look first at the living sample, which tends to be more interesting because the specimens are alive and are not distorted by the preservative. Also, many dichotomous keys are easier to use on fresh specimens because natural colors can be observed. On the other hand, the preserved samples should be used for counting because the specimens are stationary. Figure 2 is a photograph of a preserved and concentrated sample. Note that there is considerable detritus. It is useful to tell students that non-symmetrical particles or ones with ill-defined edges are usually inorganic or dead, and thus not to be considered.
Each student should obtain a clean slide and place a drop of living sample into the dimple. Have them use the 10X objective lens to scan around the slide and then use the 20X or 40X objective lens to look closer at the organisms as needed. This shows the students the size range of plankton. It is important that the iris diaphragm of the microscope be closed, otherwise the image will appear too washed out. Have the students try to identify organisms using the dichotomous key. A dichotomous key asks the user to choose which of two descriptions (a couplet) best characterizes a specimen and, then, based on that decision, directs the reader to another couplet, eventually leading to the identification of the specimen. Many taxonomic keys use specialized terms and require considerable knowledge prior to using them; the key provided with this exercise does not. As such, I have found that most college level students easily grasp the idea and, with only a little guidance, can begin working with the key right away. For less academically mature students, working with this key, and possibly others, could be incorporated as a preliminary exercise to the one presented here. Perhaps work through a couple of examples with the key, provide some specimens that the students then have to identify using a key, provide four objects (such as a glass beaker, glass Pasteur pipet, metal spatula, and metal dissection probe), and have the students construct a dichotomous key to the [our objects. Published keys for the invertebrates can be found in Thorpe and Covich (1991), for the algae in Wehr and Sheath (2003), and for the protozoa in Patterson and Hedley (1992). Pennak (1989) provides keys for protozoa and some invertebrates.
With the preserved samples, students should work in pairs to collect data from both seasons. Each student in the pair should be responsible for a different season, but should look at the other's samples to observe the different types of organisms present in the two communities.
After becoming oriented to their samples with the 10X objective, have the students switch to the 20X or 40X objective lens and randomly choose a spot on the slide that contains some organisms, but not a spot so concentrated that the organisms are lying on top of each other. From what can be seen in the field of view, have them make little sketches of the different types of organisms that are present. These do not have to be Rembrandt quality, just sketches so that each type of organism can be recognized again if encountered in a subsequent field of view'. The name of the organism is not important for calculating the indices or richness. It can be called Bob, Alice, Fred, etc., as long as it is remembered what Bob, Alice, and Fred look like. Some students find that adding a few descriptive notes helps to remember the organisms, and some students will actually want to use the key to provide proper names. It is useful to remind students that organisms may look different when viewed from different angles
Have the students count the number of individuals of each type of organism in the field of view. Individuals are the units of reproduction, so it is like counting the number of deer and the number of pine trees in a hectare. Each animal is a multicellular individual, but the microzooplankton and planktonic algae (even the filamentous and colonial forms) are unicellular individuals. Students may have to look carefully for cell walls to see where one individual ends and the other begins, and in many cases students will have to estimate the number of cells in a filament or in a clump of algae.
The students then move to a second field of view. If the same types of organisms are encountered as were seen in the first location, then the number of individuals are tallied to the first count. If new types organisms are encountered, they are added to the list.
Enumerate as many fields of view as needed to get a good representation of the sample. A good initial scan of the sample is needed in order to determine whether or not what has been tallied is representative. There is no set number of fields: it depends on how dense the samples are. I often find that five to ten fields are sufficient, and my students usually collect enough data for analysis after an hour of identification and counting. Diligence affects the magnitude of the indices because examining more of the sample will increase the likelihood of encountering rare species. At the end, each student should have a tally sheet that resembles Figure 3.
* Discussion & Interpretation of Comparative Lake Data
Students should hand m their data tables and calculations so that an average value for species richness, diversity, and evenness for each season can be calculated and used for class discussion or an assignment. The list of species observed can also be recorded.
Comparison of the results from pairs of students to class averages allows for a discussion of the concept of sampling error. However, it is better to use average values and common observances of species presence/absence to discuss how seasonal changes in the lake affect the structure of the plankton community. Using the average values helps to buffer against sampling error as well as the effects of less than enthusiastic students.
I sample a lake in southwestern Canada with a volume of 0.2 [km.sup.3] and a surface area of 9 [km.sup.2]. It has intermediate levels of nutrients and seldom freezes during the winter. My students typically find a greater species richness and species diversity in the late summer when the lake has been thermally stratified for a number of months than in the winter when the lake is mixing. The students see that the organisms that make up the communities differ as well. During the summer many species of cyanobacteria, diatoms such as Asterionella and Fragellaria, dinoflagellates, desmids, calanoid copepods, and cladocerans are present whereas in the winter there are centric diatoms, calanoid copepods, the cyanobacterium Anabacna, and small flagellated algae. We discuss the relative influence of:
* less abundant nutrients, and thus greater competition for those nutrients during periods of summer stratification compared to winter.
* greater amounts of light and warmth for photosynthesis during the summer compared to winter.
* a greater potential risk of predation in the summer compared to the winter.
The physiological tolerances of these organisms can be discussed and the concepts of fundamental and realized niche introduced. For those people wanting very detailed information, R.G. Wetzel (2001) provides a thorough discussion of factors affecting seasonal succession of plankton in different categories of lakes; otherwise, most introductory limnology textbooks (e.g., Cole, 1994; Kalff, 2001; Lampert & Sommer, 1997) will provide sufficient information to interpret the data.
Over the years, I have found that most students enjoy this exercise. If the instructor is enthusiastic, and does not get hung up on the details of counting or identification, then the students learn that biological communities have structure, they learn something about seasonal lake dynamics and, at the very least, they obtain an appreciation for some of the beautiful organisms that make up a community that many did not know existed.
Thanks to Dr. Bob Lalonde, Blythe Nilson, and anonymous reviewers for editing and general advice on the manuscript. Also to Val Ward for help with the Nikon photographic system used to obtain Figure 2.
Cole, G.A. (1994). Textbook of Limnology, 4th Ed. Prospect Heights, IL: Waveland Press, Inc.
Kalff, J. (2001). Limnology. Prentice Hall.
Krebs, C.J. (1999). Ecological Methodology, 2nd Ed. Menlo Park, CA: Benjamin Cummings.
Krebs, C.J. (2001). Ecology, 5th Ed. Menlo Park, CA: Benjamin Cummings. Lampert, W. & Sommer, U. (1997). Limnoecology: The Ecology of Lakes and Streams. Oxford University Press.
Patterson, DJ. & Hedley, S. (1992). Free-Living Freshwater Protozoa: A Colour Guide. Aylesbury, England: Wolf Publishing.
Pennak, R.W. (1989). Freshwater Invertebrates of the United States: Protozoa to Mollusca. John Wiley and Sons.
Shannon, C.E.& Weaver, W. (1949). The Mathematical Theory of Communication. Urbana, IL: University of Illinois Press.
Smith, R.L. & Smith, T.M. (2001). Ecology and Field Biology, 6th Ed. Menlo Park, CA: Benjamin Cummings.
Smith, B. & Wilson, J.B+ (1996). A consumer's guide to evenness indices. Oikos, 76 (1), 70-82.
Spellerberg, I.F. & Fedor, P.J. (2003). A tribute to Claude Shannon (1916-2001) and a plea for more rigorous use of species richness, species diversity and the "Shannon-Wiener" index, Global Ecology and Biogeography, 12, 177-179.
Stirling, G. & Wilsey, B. (2001). Empirical relationships between species richness, evenness, and proportional diversity, American Naturalist, 158(3), 286-299.
Stoeker, D.K. (1999). Mixotrophy among dinoflagellates. Journal Eukaryotic Microbiology, 46, 397-401.
Thorpe, J.H. & Covich, A.P. (1991). Ecology and Classification of North American Freshwater Invertebrates. San Diego, CA: Academic Press Inc.
Wetzel, R.G. (2001). Limnology: Lake and Bluer Ecosystems, 3rd Ed. San Diego, CA: Academic Press.
Wehr, J.D. & Sheath, R.G. (2003). Freshwater Algae of North America: Ecology and Classification. San Diego, CA: Academic Press.
LAURA J. HOOKER is Associate Professor in the Department of Biology and Physical Geography at the University of British Columbia Okanagan, Kelowna, B.C. V1V 1V7; e-mail: firstname.lastname@example.org.
Figure 4. Dichotomous Key for the Identification of Lake Plankton Preserved in Ethanol. (This key is generic; it would be most effective when illustrated with local examples). 1a) Form is either hair-like (filamentous), colonial, or is less than about 0.04 mm in length (diameter of field at 400X total magnification) ... Go to #2. 1b) Form is not hair-like and is about .04 mm in length or greater ... Go to #11. 2a) Cells possess cilia or pseudopodia ... microzooplankton. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 2b) Cells lack cilia or pseudopodia ... Go to #3. 3a) Cells possess flagella and lack pigmentation ... microzooplankton. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 3b) Cells lack flagella, or if they possess flagella they also possess pigmentation ... Go to #4. 4a) Cell size generally less than 0.005 mm; if pigmentation can be determined, it will be bluish-green ... cyanobacteria. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 4b) Cell size generally greater than 0.005 mm ... Go to #5. 5a) Cells possess flagella ... Go to #6. 5b) Cells lack flagella ... Go to #8. 6a) Equatorial groove present; if pigmentation can be determined, it will be brown ... dinoflagellates. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 6b) Equatorial groove absent ... Go to #7. 7a) Cell covered in scales with long spines or inside a casing arranged in a branching treelike structure; if pigmentation can be determined, it will be golden-brown ... golden-brown algae. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 7b) Gullet groove often present, chloroplasts often conspicuous.., small motile algae. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 8a) Cell walls are glassy in appearance and frequently ornamented with bumps, small holes, and lines; if pigmentation can be determined, it will be golden-brown ... diatoms. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 8b) Cell walls not glassy in appearance ... Go to #9. 9a) Cell looks like two mirror images divided by a central constriction: if pigmentation can be determined, it will be grass-green ... desmids. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 9b) Cell is not mirror image ... Go to #10. 10a) Cells arranged in long, sometimes branching filaments. Chloroplasts are conspicuous; if pigmentation can be determined, it will be grass-green ... filamentous green algae. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 10b) Cells not arranged as filaments, chloroplasts conspicuous: if pigmentation can be determined, it will be grass-green ...other green algae. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 11a) Body segmentation absent: if present, body is terminated in one or two ciliated rings ... rotifers. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 11b) Body segmentation present and no ciliated rings ... Go to #12. 12a) Jointed appendages absent, body slender, head capsule with eyes and antennae present ... insect larvae. [ILLUSTRATION OMITTED] 12b) Jointed appendages present ... Go to #13. 13a) Body laterally flattened and mostly enclosed in transparent paired valves (like a clam shell) ... cladocerans. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED] 13b) Body dorsoventrally flattened and not mostly enclosed in paired valves ... copepods. [ILLUSTRATION OMITTED] [ILLUSTRATION OMITTED]
Table 1. Sample data for trees and shrubs in a western North American forest. Used to show students the format for the data table and sample calculations. This example shows the Shannon- Wiener index calculated from log base 2, but it can be even more easily calculated from common logs or natural logs. Tree species # of individuals [p.sub.i] Douglas Fir 1923 1923/4828=0.398 Salal 1840 0.381 Western Red Cedar 534 0.111 Big Leaf Maple 189 0.039 Western Hemlock 95 0.020 Snowberry 93 0.019 Red Huckleberry 85 0.018 Red Alder 43 0.009 Vine Maple 15 0.003 Pacific Dogwood 7 0.001 Grand Fir 4 0.001 SUM 4828 1.000 [p.sub.i] [log.sub.2] Tree species [p.sub.i] [p.sub.2.sup.i] Douglas Fir 0.398(-1.33)=-0.529 0.398(0.398)=1.59E-01 Salal -0.530 1.45E-01 Western Red Cedar -0.351 1.22E-02 Big Leaf Maple -0.183 1.53E-03 Western Hemlock -0.112 3.87E-04 Snowberry -0.110 3.71E-04 Red Huckleberry -0.103 3.10E-04 Red Alder -0.061 7.93E-05 Vine Maple -0.026 9.65E-06 Pacific Dogwood -0.014 2.10E-06 Grand Fir -0.008 6.86E-07 SUM -2.027 0.318815 H'= -1(-2.027 )=2.03 [N.sub.i]=[2.sup.H']=4.08 1/D=1/0.319 =3.13
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