A unit of Lasting Forests Sustained forests; sustained profits evolving since March 30, 1999

As a boy I was more interested in "skinned cats" than in the wisdom of my grandfather's oft-used "there's more than one way to skin a cat." I could not imagine why there were so many such events or that a saying would have emerged. Unquestioning, I waited, for I had heard the non-answer enough times: "you'll learn one of these days." I think I have learned and I want to share knowledge of equifinality because it has provided me many new insights and a pattern for some explanations.

Perhaps equifinality is only a word for some old ideas. I do not know where or when I first heard it but it has taken at least 20 years to grow from its seed bed. Ludwig Von Bertalanffy, though not the first, used it in General Systems Theory in 1968. It means, simply, that there can be several pathways to the same destination. Machines rarely exhibit equifinality. For them there is one pathway. There may be several end states from the machine; the good products and the rejects. Wild animal and other natural resource systems often exhibit equifinality.

Most regression models resulting from making field observations and relating a factor of interest to som likely causative factor are judged on the basis of the R-square value. The closer the R-square value to 1.0, presumably the better is the model of the relationship, for the higher the R, the greater the variability that is accounted. I have seen vast amounts of field data scrapped because it "didn't shown anything" (the R-square was too low). Not at all hostile to regression analysis, I find the concept of equifinality suggesting

1. enough samples (in each class, therefore in total) will rarely be available,
2. there are threshold and non-linear phenomena at work behind every stump,
3. a low R-square is a reasonable hypothesis in the woods, and
4. alternative managerial modeling approaches (e.g., expert systems) may be more useful than regression analysis.

Biodiversity lurks around every pillar in conference halls. I have a computer program with 18 ways to compute diversity (which I now call variety because of the diverse definitions of diversity). I can change numbers (e.g., simulate stocking 50 animals of a rare species) and see what happens to the index. Invariably, changing the animals causes 9 of the indexes to increase, 9 to decrease! The frequently-used Shannon-Weaver index is notable for its ability to produce the same index from very different numbers. A community with 55 animals in each of 10 species has a diversity index of 0.23... just as does a 3-species community with 50, 100, and 400 animals in each species. The index is descriptive of an end state. The details of estimating diversity are not at issue here. It can be comforting to know that there are several ways that it (whatever it is) can be achieved. It can be comforting to lawyers to know that the index sword has 2 edges that cut both ways. The sparkling edges, points of lights, will be of little comfort to those claiming in courts that diversity has not been achieved or maintained. There is a great amount of very difficult work ahead on the concept of diversity as a system performance measure and its estimation. I suspect there are several characteristics of the desired end state loosely and too hastily expressed by "diversity" and "biodiversity", words now in the law. The characteristics describing "the good" will be teased apart eventually, then systems for achieving them, many and varied, can be developed.

Figure 1. System performance is identical at A, B, C, etc. although quite different factors may have had these results.

Cyclic natural phenomena are obvious examples of the same recurring population or economic numbers. Presumably there is one system at work producing the undulations, but the alternative (and I believe more plausible) hypothesis is that there may be very different phenomena producing the "curve." The end state, at points A, B, and C in Figure 1 are identical. They are manifestations of system potentials over-riding constraints, and probably unique combinations of usually over 300 conspicuous, generalized working factors in an average forest or North American wildland. The potentials relations (R) among this n = 300 factor system is merely

R = n (n-1).

Ecologists are said to study relations. They may be irrational even to pretend to engage R relations (here only 89,700) as well as to work with n specialists.

Figure 2. Harvests in one year are likely related to those two years previously. Equifinality occurs at B, C, and D. The mean is shown at the center.

Infrequently seen is a graph such as the above Figure 2, a picture of deer harvest as related to the harvest two years previous (often a strong inverse relationship). Equifinality results in nearly identical harvests as a result of three very different harvests as at A, B, and C.

Figure 3. Information in Figures 1 and 2 can be considered in three dimensions. The central tendency is shown as the dotted core. The system may never occur in the central tendency, usually represented as an average statistic.

These ideas (shown as cyclic or irruptive populations or as the circular so-called" phase plane") (Figure 2) can be combined to produce a picture in 3 dimensions that can be very instructive (Figure 3). If not careful or resistent, an observer may relax with the conventional wisdom of two-dimensional blackboard images. As seen in Figure 3, there can be many states of systems that are working that produce the "coil". When managers quickly generalize about systems, they often use the central tendency. This shaded center-core (Figure 3) does not exist! No point on the curve showing final states of the system occurs along the shaded line at the center. Equifinality is descriptive of the ways that points on the curve are reached. It does not describe how the non-existent center is achieved. Forests and related natural resource systems are not 3 but n dimensional. Knowledge of the center space, the "central tendency" , is not likely to serve practical, responsible managers well in the future. What can serve is knowledge of the systems that produce measurable ends.

What comes next (or first, or simultaneously) is clear thinking and articulating the forest objectives -- the desired end state.

The climax forest is an example of equifinality. Several nearly identical forest stands may have achieved a similar condition in very different ways over different periods.

Trivial examples of equifinality are:

3 x 3 = 9

1 + 8 = 9

81^0.5 = 9

In habitat work, an example of equifinality is the observation that crop plants seem to trade off water and nutrients. The same production of forage in a year can result from different amounts of available water and a mixture of nutrients.

Implications

1. The manager needs to assume that equifinality may and does occur in all complex systems. The exception is notable.
2. It often occures in cyclic or periodic ecological phenomena.
3. Statistical tests of factors that affect some system output or end-state need to be carefully and reluctantly used. The Y variable (dependent) can result from many combinations of different X's. A low R2 is highly probable. Improved and reduced-cost sampling schemes can be devised.
4. All means to the same end, to some equifinal state, probably do not cost the same. Lowest-cost pathways need to be sought.
5. For analytical work, avoid using indexes! For example, 3/6 has the same numerical result as 3.5/(49 ^0.5) but only in one condition. The factors may not be linear. A change in one factor (either), or two, may produce identical results.
6. For managerial work, use indexes. The manager has more options available when he or she can manipulate simultaneously all factors to get a performance index to move over time as desired.

This Web site is maintained by R. H. Giles, Jr.
Last revision February 3, 2001.