| A unit of Lasting Forests
evolving since March 30, 1999 |
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A Total Forest Management Plan
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Because different species of plants and animals utilize different stages of biological community succession, then if area managers will maximize the number of successional stages (age groups), then they can increase the number of species within a given tract of land. Any habitat manipulation involves a trade-off between species that benefit from the change and those that do not. Whether this increase in local species richness represents an increase in overall biological diversity is, in part, a question of geographic scale. Understanding the importance of scale is critical to assessing accurately the impacts of various activities on biological diversity. If the species that are harmed by a given management action are rare or more imperiled than the ones that benefit; or if the manipulation eliminates on of the few occurrences of a species, community, or process; then biological diversity is reduced. If the land area manipulation eliminates an element that is common elsewhere in the landscape and provides an opportunity for an imperiled element in the landscape to increase, then biological diversity is more secure. Perhaps such change is not desired; much careful discussion, precise writing, some research , and difficult decisions are needed.
The above topics indicate that biological diversity is extraordinarily complex, that much of it is hidden from easy view, and that diversity itself, by several definitions, is likely to be changing over time and across geographic scales. It may change due to human decisions and actions as well as due to natural forces such as hurricanes. It is essential to have a measure or estimate of it as required by law and for possible use. How will we know when we are conserving biological diversity and when we are not? How will we know when the objectives are implicit within the word being achieved? We need a system performance measure that synthesizes the many aspects of biological diversity. The performance measure can guide the forest teams and citizens in formulating and implementing strategies, plans, programs, and projects. A biodiversity performance measure may express the status and achievment of one objective that has been decided upon for a Forest District or Forest. There are many other objectives, and among them there are great differences in relative importance or weights.
The Trevey staff are convinced that "biodiversity" has many meanings, too many to assure consistent agreement on use or on observed performance. As a result, using the word, due to the laws of chance alone, is likely to produce disagreement thus conflict or at least frustration. For example, we have found that in public meetings, people disagree on the meaning of diversity when discussing whether the black and red squares of a standard chess board are more diverse than if the same board had black squares distributed at random? Land managers also disagree among themselves. They similarly disagree that a "high" index of diversity should reflect that all species have the same number (i.e., be completely even in distribution). We no longer believe that these disagreements can be considered minor or that they will be self-correcting. These cannot be brought to a singular meaning within the present social or scientific atmosphere. The biological rules of prior usage have little utility in helping us select the right word for a desired functional relationship for understanding, explanation, or prediction. Published statistical indices are often reciprocals or inverses of each other. Some definitions are single-component (richness = diversity = count of taxa) while others combine taxa counts and abundance or some other expression of dominance or ecological significance of each taxon. Our view is that people want to know something (e.g., the probable growth rate of a forest stand (r)) and they want an index to that, some low-cost means to get an estimate. They may only want to know limits, that the rate, r, is not declining (due to pollution, etc.) The assumption then, is that if there is a good measure of biodiversity, D, then r, this topic of interest can be modelled as
r = a + bD
where a and b are derived coefficients based on observations or experts. The concept, briefly, is that if D is stable, then the rate of forest growth (r) is stable. The model may be made much more complex as time and space variables are included. The point, here, must be clear. The reason for estimating diversity for the practicing land manager or for his or her advisor, is to be able to estimate well the value of r (whatever it may be -- health, abundance of species x, or probability of occurrence of species y. Eventually, when the condition r has been decided as optimum (based on the complexities of total forest system benefit production -- energetics, esthetics, ecology, and economics), then an optimum richness can be determined. No one yet knows (or has decided) whether a maximum number of species is desirable or a maximum number of individuals is desirable (beetles? deer?) or whether equal numbers of each is desirable (condors and catbirds?).
Few people appreciate a major mathematical difficulty that is very likely to occur in creating and calculating and using many of the biodiversity indices. It is the problem of equifinality, namely that an equal value for one index can result from very different conditions in the field. For example, 2 + 46 = 48 as does 24 + 24. Trivial, at first glance, the difference can (1) explain why something does occur in very different conditions but (2) it can prevent proper statistical conclusions because of the extremes in squared differences, and (3) an identical index may mask the real differences that do trigger differences in the variable being estimated.We need to separate the variables, leaving them as in a multiple-regression equation rather than having the separate variance of each variable hidden or aggregated within an index.
We now believe that when anyone asserts the need for biodiversity, the reply should not be an answer but a question about the use to which an estimate will be put. Under pressure, advocates will claim that they need to know r, perhaps r1... rn. Once that is expressed, a model can be created
r = f (Di).
Di is one of n types of biodiversity estimators. We have identified 21 types.
We recommend that they be used separately, each for a specific purpose, each selected as appropriate to meet stated objectives in each situation (most of which we believe are unique).
Suspecting that this recommendation will not be taken, we suggest a composite score for managers. The score is an answer to "how well are you doing in achieving desired biodiversity?" With little guidance and 21 types of biodiversity it is evident why managers are reluctant to select one type. The odds of being right are merely 1 in 21 or 0.048. Realizing there is some good in most of the type expressions, it is possible to assign to each a weight of relative importance or goodness among the scores, then to get a weighted grand score. We have provided a program to aid managers in this computation. For example, having selected 3 type scores, assigning others values of importance relative to the top-most important type, the results are as follows:
| Score | Weight | |
|---|---|---|
| D14 | 90 | 6 |
| D20 | 62 | 9 |
| D17 | 81 | 10 |
The final score is 76, i.e.((540 + 558 + 810)/25). This is a managerial score, a composite of three selected types of biodiversity, and should not be used as an independent variable or to suggest ecological trends. It is simply a means for a manager to express better than by means of a total or average... how well work to achieve biodiversity is being done. Perhaps plotting this score over several years can be used to suggest managerial progress or trends.
The types of expressions of biodiversity are as follows. They are classical, traditional concepts of biodiversity used by some scientists, students of diversity, or managers. There are many such concepts. This large number is part of the problem of attempting to achieve it. "Biodiversity" means at least 21 different things. It means several things to the same person. This analysis and the program that supports it has been created in response to genuine desires and the real objective of many people. The programs merely attempt to approximate (not measure precisely) that interest and concern as it may be achieved on a District or Forest.
Type 1 - Total Faunal Richness
In most discussions of biodiversity, the desire for abundant species is implied. This is called richness and where S is the number of species, then richness can be computed after R has been evaluated and decided as the standard or baseline condition.
We suggest 10 separate analyses, one for each major animal group, one for all animals, and several for vascular plants. We hasten to add that we have not included insects, crustaceans, mollusks, mosses, mushrooms, lichen, and several other forms, and these need to be added to the analyses as expertise and funds become available. It is regrettable that we (as a society, agency, public, and science-teams) seek to comprehend, discuss, and manage whole ecosystems and cannot even list all of the parts of the ecosystem comprising one major area of any District. The demands for analyses of biodiversity have exceeded the demands for collecting the data and completing the taxonomy and museum work.
The size of S may increase or decrease due to study. Similarly, study can reveal misidentification. We assume here that a positive increase in the number, S, will be viewed as good. A conventional rate of change between periods or as compared to a baseline can be computed (see the BASIC program BIODIV.BAS).
For example, where there are 205 species present and 2 are added (discovered) due to field studies in an area. Then where R, the area standard, is 210, the note improvement between the two years is 0.01 and the score, relative to the standard or baseline is 99. There may be years when no changes are made. The value of S is always taken at some stated standard time. It should only be taken when a good comprehensive analysis has been made since a limited survey could result in a very small score and influence future scores. The computation of D1 is for all animals, then each faunal category is analyzed, i.e., D2 - Birds; D3 - Mammals; D4 - Fish; D5 - Salamanders; D6 - Toads and frogs; D7 - Turtles; D8 - Lizards; and D9 - Snakes.
Type 10 - Plant Richness Total plant species (including trees) are treated as above.
Type 11 - Tree Species Richness A subset of Type 10.
Type 12 - Shrub Species Richness A subset of Type 10.
Type 13 - Forb and Grass Richness A subset of Type 10.
Type 14 - Threatened, Endangered, and Rare Species (both plants and animals)
The list of threatened and endangered species of an area, District, or Forest should not increase and perhaps can decrease. These species are included within the count for D1. The scoring mechanism for this condition in which no rare species are desired and management is presumed to attempt to remove them from this condition is:
D14 = [1.0 - ((n1 - n)/n] x 100
Where n is the number of threatened and endangered species at the standard year and n1 is the count as some specified future date.
For example, if the number was 5 in 1992 and it is now 6, then the score would be
D14 = [1.0 - ((6-5)/5] x 100 = 80.
No change results in a score of 100. When species are removed from the list (for whatever reason), the score remains at 100.
Type 15 - The Restoration Index
A statement might be made: "There appear to have been - species lost within this area during the regional settlement period beginning 384 years bp)." Perhaps they can be restored. The restoration index is
D15 = [1.0 - ((X-n)/X]x 100
where X is the number of species lost and n is the number of species restored.
For example, where there have been 6 species lost (e.g., the woodland buffalo, passenger pigeon, wolf, mountain lion, etc.), and then was one (n = 1) restored, then
D15 = [1.0 - ((6-1)/6] x 100 = 17.
Recall that a goal of biodiversity has been said to be restoration.
Type 16 - The Stand-Type Index - I - Forest Base
Maximum diversity would imply that every stand in an area was of a different forest type. A forest "type" (a characteristic group of trees dominated by one or two species.) For example, there are 33 types that occur within the Jefferson National Forest.
Because of limited size of most areas and Districts, and limited ecological conditions, only a few of these types are likely to be present. A percentage of these types is thus considered, thus the Forest-base index to type diversity is
D16 = (t/T) x 100
where t is the number of types in the area or District and T is the total number of types that occur on the Forest.
When there are 36 types on the Forest and 30 in an area then
D16 = (30/36) x 100 = 83.
Component 17 - The Stand-Type Index - II - Area Base
An index of the proportion of "area" in each type is computed using the modified Simpson index (Odum 1971): converted to score relative to a maximum which occurs when all areas are equal in each type.
Component 18 - The Stand-Type Index - III - Stand Base
An index to type dominance is used. If all stands are of one type, the index is 0. This is an index grounded in the Simpson index (1949) as above, and is here
D18 = [1.0 - Sn t = 1 (Pt)2] x 100
where there are n types, Pt is the proportion of the stands in each type.
If there were 3 types:
| Stand Types | Proportion | Pt2 |
|---|---|---|
| 1 | 0.36 | 0.129 |
| 2 | 0.24 | 0.058 |
| 3 | 0.40 | 0.160 |
| Sum = 0.347 |
Thus,
d = (1.0 - 0.347) x 100 = 65.3
and compared to the maximum value which occurs when there is complete evenness, the score, is D18, (65.3/66.7) or 97.9.
Component 19 - The Stand Size Index
Stands, the smallest similar unit of land, all of one type, and usually treated similarly, vary from large to small throughout the District. They should vary in size to provide the diversity of conditions suitable for many animals and plants. Opportunity Areas are too small for an index to be of great value but they may be of use in some analyses. herein,trhe distribution desired is said to be Poissonal (i.e., the mean of the sizes should approximate the variance and many observers say "randomly distributed".) The scoring device is
D19 = [1.0 - ABS ((variance - mean)/mean] x 100
where ABS mean "absolute value." If there is no difference in the mean and variance, then D19 = 100.
Type 20 - The Older-Stand Age - Index
Different life forms are associated with ages of forest stands. Many are strongly related to stands with a predominance of old (60+) trees. In mixed-age hardwood stands influenced by previous harvests, fires, and storms, the predominant age is difficult to determine. Stands with a low stem count and high basal area are typically old-age stands.
The age index analysis for older-aged stands, is based on 1/3 of a forest area being in older-age growth.
D21 = 1.0 - ABS (total area in older-age stands - (0.33 x Total Stand Area)) x 100
The younger-age stands are assumed to be distributed as the negative log or the reversed-J distribution widely recognized within forestry. The analysis is based on area of all stands of less than 60 years. To extent that the actual distribution fits (R2 analyses) the reversed-J distribution, a score for D23 of 0 to 100 is assigned.
D22= 1.0 - (Actual Distribution - Hypothesized Distribution) x 100 Hypothesized Distribution
These scores are weighted, added, and averaged to produce the Composite Biodiversity Index, D-star (D*). It is computed as described previously and as:
n n D* = (S Di Wi) / S Wi) i = 1 i = 1
where n represents the 22 components of the concept of biodiversity.
The Trevey staff has developed the above approach: (1) to be inclusive; (2) to allow expert knowledge about the goodness or relevance of each index to be expressed; (3) and to provide a means to evaluate past or proposed changes on the land.
It is tedious for anyone to use, but a computer aid is available. If biodiversity is as important as many thoughtful people believe, then it deserves at least the effort needed to synthesize these observations. The need is for a value, one among literally hundreds that go into improved decisions for managing areas, Districts, and Forests.
By studying alternative actions or before-and-after situations, differences in biodiversity may be observed. An action that lower the biodiversity score may not be bad if many other weighted objectives are achieved simultaneously. Similarly, a score may be lowered on one Area, and increased on another Area to result in an improved District biodiversity score. The score will change over the years even if no other forces are at work due to changes in the age and composition of forest stands. These are all dimensions of the Composite Biodiversity Index that need to be in the mind of the people who actually use the index.
We are aware that people do not want to lose any species. Retaining species is the same as not allowing richness to decline. Beyond that wish (and the numbers that support it) the desire for biodiversity is not at all clear. Some answers may be found by research but we believe most will be found in logical scholarly work, and then decisions have risks, but they must be taken. Risks within the "undecided" condition seem clear… and great.
Odum, E.P. 1971. Fundamentals of ecology, 3rd ed., W.B. Saunders, Co., Philadelphia, PA. xiv +574p.
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Last revision January 17, 2000.