Modern Wild Faunal Resource System Management
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This is a long unit. It relates to many aspects of the course. Make notes for such a list of relations before you continue. This unit should be studied in several 'sittings.' Tap the OK button to begin.
Eventually the wildland or rural land manager has to transform the concept connoted by the word-symbol "risk" into a practical reality in his or her mind. Its meaning seems so intuitively evident that few people will spend any time thinking about it.
I am of the opinion that there are several kinds of risks that some day may be teased apart. At least there are qualitative differences among:
A vast literature has grown about risk in the past 20 years, ranging in topics among meanings, mathematical treatments, and metaphysics. Early work on the topic appeared in the mid 1700's. This literature has had little effect upon how the wildlands of the world are managed. It probably could have, and I think it should have. I believe there is a related-concept that every wildland manager should know and actively use. Not using it is tantamount to malpractice; I acknowledge the possibility of ignorance and accept the high likelihood that teachers have been tardy in presenting it within university wildland programs.
At an elementary level, fat reserves in animals can be considered as a means for them to reduce risks, that is of living within an uncertain environment.
I am attempting to develop a comprehensive treatment of how to conceive of and work with environmental- and natural-resource-related risk and its assessment. I know I shall fail, but I suspect there is no standard for comprehensive so I shall argue my cause with critics using: "as compared to what...?" My work follows on the work of (Giles et al. 1995) and is part of the rationally robust paradigm argued by them. Other work is underway.
Educated and having grown up in a conservative professional culture, one with unclear objectives, vast areas, long time horizons, and great flexibility, it has finally dawned on me that I work in a high-risk enterprise. Jensen (1978) observed that agriculture is a high-risk enterprise; so is wildland management. The game within which wildland managers work is full of uncertainties, dangers, and the costs of mistakes. The operation of the wildland system is very much a function of human greed, public demand, change in preference and behavior, inventions and style shifts, human population pressure, changing ecological systems and discoveries of adverse topography, shifts in climate, changes in regulations, and competition from neighbors of all types. All at once, in almost every major decision, the manager must deal with ecological as well as economic realities, both of which are dynamic, anticipate esthetic and cultural change, and predict a future with major differences in fossil energy availability.
Wildland managers readily realize that they are often in situations in which the following types of questions are realistic. These all have a major component recognized as risk. The typical questions: Is the wildland manager who is pointing out threats and problems running the chance of stifling growth and opportunities? Should some project be opposed? Should this project or that one be given limited legal and other resources? Will the outbreak subside or sweep the region? Should we act now or later? Is forest health in jeopardy?
I wish to argue that risk management can be replaced by a concept of the cost-effective expansion of reasonable certainty space, zeta for short, which I shall explain. I also argue that the rational manager needs to use it in decision-making. In fact, since wildland and related resource management is primarily (at least initially) decision-making, (Giles 1978), then zeta is a pillar to its structure and function. Zeta, perceived net benefits, and a perception of people affected by a decision are necessary ingredients for a rational, robust approach to maximizing utility in a world of uncertainty.
The Zeta Hyperspace
I wish to begin an exploration and explanation of this concept of zeta with the last word, space, the entity determined by 3 or more dimensions. A box has three dimensions. When there are more than 3, then we have a hyperspace. I want to show you that risk, a brief word, is not a brief concept. It is multidimensional, and results in zeta being a conceptual hyperspace. I would like to rush ahead with this idea but my teaching experience over 30 years suggests that few people have or quickly grasp the idea of hyperspace. It is not difficult; it sounds imposing and beyond reach. Let me attempt, briefly, to sketch one means to relate to the idea. We take one factor, one "dimension", say tree species richness or number of species, x. The second example is latitude. We take another, it is longitude. Together they are 3 dimensions and, related, can be used in mapping location of trees. I can add time and print a series of "cover maps" as tree area changes over time, displaying some idea of vegetative history as a series of pictures. The results can be shown as a moving picture, the frames being maps. The "greens" on the maps of species x contract and expand as the movie reel turns. Showing map changes -- species area changes per unit of time -- four dimensions. This is equivalent to flipping though a "Big-Little" book. When we include tree height, a fifth dimension, we can display on our movie or TV a shrinking and swelling volume in a particular place over time. If mapped area is included with elevation, the resulting vegetative shrinking-swelling volume can be viewed as if it were sitting on a topographic volume, a 3-D landscape, changing over time, all together a total of 6 dimensions. I can add others but the work becomes tedious, boring, and not especially useful. The point of emphasis is, folk-claims to the contrary, that almost everyone can "think beyond three dimensions." They can deal with hyperspace.
The risk-related hyperspace for the wildland2 manager has at least 30 major dimensions. Recognizing all of these dimensions is a major accomplishment.
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| Fig. 1. The concept of a reasonable certainty space can be readily shown for three dimensions. The management of that space is a task of the wildland manager. It is a concept that is an alternative of the many definitions and mixed concepts od "risk management." |
Minimizing Risk as an Objectives
There are seven types of objectives. Realizing this is the clue needed to get through the goals/objectives entanglements of the maze of the "future-committee." Type 3 is the "Success Criterion." It is no more than an answer to "what is your fundamental solution algorithm?", a question few will understand and fewer still answer. The answer might be "my objective is to maximize benefits" or "minimize costs" or "maximize risks." Once that is decided, a framework is set in which other types of objectives can be meaningfully set and phrased because each type-3 objective requires different answers, measures, and expressions of confidence and accuracy. It may be that "to minimize risks" is a good Type 3 objective. It is probably limited and should be replaced with "to maximize utility." Carl Walters (1986:13) suggested that when the objectives are unclear, then people tend to express implied ones as risk-averse behavior and resistance to change in general.
Most natural resource management decisions are based on a utility function. This is an estimate of the outcome and the probability, the product of which is the utility. We maximize utility, we go for "utilities." Part of our difficulty is in estimating outcomes (how many deer? how many cunits?) but also the odds. The latter item, the odds, is a serious problems, because we don't know whose odds to use -- the biologists, the Supervisor's, or the public jury. Different groups (or individuals) have very different risk levels. Some are averse to risk (e.g., young, married, mortgaged). Imagine the difference in a conservative no-change deer harvest season and one that is daring, experimental, leading-edge. You know well what people are risk-averse. (Notes on season setting.)
If a constant season will continue to produce 100 net units at high probability (say 95%) then the utility is
U = 100 x 0.95 = 95
If the new season will yield 200 units, the odds being 0.75, but it could yield only 50 units (the chances are about 25%) then the utility of the new season is
U = (200) (0.75) + (50) (0.25) = 163
Assuming mere harvest is desired, then the innovative season should be set because rational managers tend to maximize utility. For the risk averse manager, (or certain publics) the probabilities are suspect. They weight heavily the lowest probabilities.
Fig. 1. The concept of a reasonable certainty space can be readily shown for 3 dimensions. The management of that space is a task of the wildland manager. It is a concept that is an alternative of the many definitions and mixed concepts of "risk management."
Existence
I advance on the idea of zeta. One of its dimensions is existence. These are conceptual or nameable dimensions, largely unseen. They are not like the visible 3 of the Sunday-TV time-lapse photo of a growing plant, a 4-D presentation. They are more like time as a dimension. A rangeland manager who just slipped and fell into a creek and has a bloody shin knows about the existence of a rock. It is there! That rock! The abnormal skeptic (as some opposition attorney) might ask: are you sure; perhaps the other rock; perhaps both; perhaps a stick that floated away; perhaps a water monster, perhaps ... enough! I am sure! That rock! Now get a bandage.
This example is trivial, but it expresses the observable existence of rocks and for all reasonable purposes there is sufficient evidence and assertion, insufficient time, and it is clear silliness to explore other alternatives. The key ingredients of the situation are:
I do not need to examine or evaluate the bloody example above any more. I can try to clarify and explore the elements, perhaps find others, in similar examples. Note here, merely, that there is reasonable certainty of the existence of a rock. I shall not argue the existence of Bigfoot or Sasquatch, the legendary human-shaped creature of large size of the U.S. northwest (and elsewhere). It may exist, but I am skeptical. There are other more pressing, more meaningful, topics of existence (as it relates to risk) that need attention. One, for example, is the existence of cougars (Felis concolor) in Virginia. Publications say it has been eliminated. Some people in "environmental" groups want it re-introduced. Others claim they have seen it, which if true, nullifies the chance of re-introduction, since they are already here. If it is here, then we can tally one more species for our biodiversity count, tally one more opposing force against sheep raising, and list another piece of evidence against large predators regulating deer numbers (deer have increased rapidly in Virginia in the past decade).
They are here! say many people who have seen them. There are some photographs of the rear ends of large tawny animals in the brush. A member of the U.S. Fish and Wildlife Service searched for several years for them, for tracks, for any strong evidence, and found none. They are not here! ... But they could be! They are hiding; they are just passing through [from where to where?]; they are zoo escapes, etc., etc. This may be an nearly perfect situation or example to help explain or verify the truism: you cannot prove a negative [including this one]. You can prove cougars have recently been in the state if you have evidence, capture one, have several reputable observers see one simultaneously, etc. You cannot prove they are not here (since they may be hiding, etc.).
Given realistic, dedicated, formal effort to find something of known characteristics and given the ease with which we discredit singular filed observations (hoaxes, humorous big-fish-story tendencies, desire to see the "first", sensory aberrations in the field due to lighting etc.) and the lack of physical evidence (tracks, dens, road-kills, hunter kills, large livestock predation), I think the cougar does not exist in Virginia. It might; I cannot prove otherwise, but we will not invest time or money (or encourage others to do so) to prove otherwise. As I see it within our present human value system, it is reasonable to act and operate as if there were no cougars. This is a reasonable certainty. We risk little if we draw that conclusion. If we believed otherwise, we would stay out of forested mountainous areas or always go only with a companion and protective weapons. I shall not think ill of grandfathers who would gather up a force to finish what the rural settlers of the state did not do until 1911 (Handley and Patton 1947), the date the last one is said to have been seen.
I never use certain except in a metaphysical or theological sense. I suspect with some high probability, we cannot be certain about anything. I recommend using "certainty" as "the probability of not being in error, of making a false observation, or drawing a wrong conclusion." It is a long phrase with many connotations as discussed above. Certainty is an important symbol, a prose model for a large and somewhat difficult idea.
No one can be certain about anything non-religious, thus I use the phrase reasonable certainty. Always discussing uncertainty, always discussing negatives, null hypotheses, and improbability sounds silly, is not convincing to most people (even scientist). Dealing with uncertainty is clearly not profitable in creative work, and it otherwise provides no human satisfaction of closure. The practicing land manager operates with experience and logic, in that order. Certainty and things known are experiential.
I studied the life forms in a 40-acre Ohio forest intensively for 2 years. After an insecticide spray of the area, I found new species of insects on sampling catch trays laid out throughout the forest. These were new to the area, new to science! There are still new, never-seen things out there. There are areas of the world yet unexplored for their biological resources. It is as if something does not exist until it is properly named. [The unnamed insects yet await re-discovery in an Ohio museum collection.] A taxonomist recently lamented that in tropical areas you can catch so many insects in one sampling effort that they all cannot be processed (sorted, mounted, preserved, identified, etc.) in any reasonable period.
I do not know how to tell when a species "goes extinct" or no longer exists. People thought the ivory-billed woodpecker was gone, but there are reports of sightings south of the U.S. Maybe it was just not politically correct to exist. Maybe boundaries are a part of existence. Nevertheless, I do not believe a species needs to be taken to the zero level to be extinct. The first reason emerges from the above. You can never prove it does not exist, that it is zero. The second is rooted in wildland managers, understanding of extinction phenomena. We are all on the way out, sooner or later, as conditions change. Perhaps something has passed the extinction threshold; only 5 are in existence. Does the species exist? The answer depends on our observations as well as our definition. Let us start with the idea of a perceived nominal entity, some "thing" of interest.
Things That Cause Losses: The Risk Roots
Does something that exists have any potential for causing injury, death, disease, economic loss, or loss in quality of life? Is something a perceived threat? The answer to that broad question is likely to be, broadly, "yes." People die from stumbling on a marble, drown in their bath tubs. Almost everything can cause life difficulties or death. Some groups discuss these as perils; I'll call the list "trouble" from here in, mostly for brevity.
The above seems obvious and a needless discussion, but the discussion is much needed because wildland managers must know that there are types of things that have in the past, do now, or may cause trouble, and each has a different analysis. A reasonable person will respond to the answers from an analysis differently. Intelligence is defined by some as the "ability to discriminate." I am working for new discriminatory power for the land manager.
In the woods, under a tree, any limb may fall and kill a manager. Perhaps all tree limbs are hazards. In campgrounds and ORV parks, large overhanging limbs are viewed as hazards and often removed (e.g., Paine 1966). When is a limb a hazard? Always. When it exists and is a potential source of loss, cost, or injury. When is a limb hazardous? Is that limb [pointing to it] hazardous? Probably not, since there is judged to be a low probability (lower than some stated amount) of that particular limb causing trouble. Another limb nearby with different location, size, and characteristic may be more hazardous. Both limbs are hazards.
Okrent (1980), by example, distinguished between "hazard" and "risks." Using the above example, three people in a recreational vehicle (ORV) parked under a large tree have a risk of dying if a branch falls. A bus load of people can careen to their death if a driver swerves to miss a falling branch. Both groups face tree-branch-related death. The maximum societal hazard is 30 for the bus, 3 in the ORV. The risk of death to each person is given by the probability of the occurrence of a finely timed branch-fall. The utility to society is given by the number of people or their valued possessions multiplied by 1.0 minus the probability of the hazard.
A marsh exists. It can be viewed as a hazard. We make it hazardous if we try to cross it. If we try to walk across it, it is much more hazardous than if we try to cross using an airboat. Risk, at least in this paper, is always from a human perspective. A human incurs risk if he or she tries to cross the marsh. Everything is a hazard (it seems); things become hazardous depending on the types and levels of use, contact, approach, proximity, etc.-- all in the hands of humans. "Amount of risk" is a robust expression of how hazardous an item or act is to people under these uses or conditions. A marsh is a hazard; crossing the marsh is hazardous; the method of crossing determines how hazardous.
There are parallels with toxic substances. Pure water is a toxic substance if taken in excess, injected, etc. A substance is toxic or not depending on the environment, the actual or intended use, the condition of the population actually or potentially affected, the previous treatment or encounters with it or other substances, and many other factors. Toxic is another word for the potential to cause trouble. A substance may be called toxic to insects, hazardous to people. The meaning depends upon the objectives for which a thing is intended or may be used.
"How hazardous", hereinafter hazard level, may be influenced by controls, safeguards, and buffers. Some people formulate types of risk related to hazard as natural, latent, basic, or as risk roots. The hazard level of a trip in an average forest truck is reduced by using sound tires and a seat belt. Safe means a reasonable level of no harm, a condition in which risks are judged acceptably low, only slightly hazardous. If risk is the probability of trouble, of harm, injury, loss, or premature loss of life, then "safe" exists when risk is low, as in :
Safe = (1.0-Risk)
Type A hazards are things over which people probably have little control such as lightning strikes, death in a tornado, and poisonous snake bites. These things - lightning, tornadoes, poisonous snakes - are hazards. They are risk roots clearly agreed upon by a majority that they are evident potential sources of trouble.
A hand-held power saw is a hazard, but in the hands of a trained, experienced, safety- equipment-equipped person, its hazard level is low when it is in standard, conventional use for the designed purpose. Even on the shelf it is a hazard (cuts, falls, etc.). I am beginning to approach the concept of reasonable. (I shall not discuss it, only begin the sketch of meaning.) Type B things have potential for causing trouble but are controllable.
Perhapsequipped"y of Type B is needed for the tower of the high-diver, the sheer cliff with overhang for the climber, the space for the sky diver. The potential for trouble is very great; the controls minimal; "expertise" and "well equipped7quot; are expressions of "ability to control." Staying off the tower or mountain and out of the diving door seem reasonable ultimate control for such acts.
Type C things are controllable, but can escape control. They have an uncertain period of occurrence. Disease outbreaks may be an example. Many people think of cycles in natural events and Type C things, but they rarely occur because there is inadequate data to prove them, have slightly different periods (3, 4, or 5 year peaks), and very different peaks and troughs (the amplitude). You just cannot tell when another natural event of the same type will really occur. The unit "multimort" (1 chance in 1000 of death) has been used by some to describe some of these conditions.
The Probability
What is the risk of losing the contract on the timber sale? The answer may come as an amount or as a probability, for example $15,000 or 0.20. If you do not get the contract you lose many thousand dollars. Another expression is that the chances are about 1 in 5 of losing it to someone else's low bid. The terms risk, chances, odds, and probability are all used, often interchangeably. We'll use probability. "Possibility" is occasionally thrown into the mix of terms. It is a yes-or-no condition. A possibility means any probability other than zero. If there is absolutely no possibility of an event or a thing existing, then there is zero probability of it. If there is any non-zero probability, then there is a possibility of it (whatever it is) occurring. Since existence is so difficult to deal with and since it is so difficult to prove something does not exist, people usually adopt the notion that everything is possible and immediately shift to discussing probabilities, no matter how small they may be. The example from philosophy classes may be helpful: Is there a possibility the sun will not rise tomorrow? Yes, but it cannot be proven, so we can discuss the low probability of such an event.
What is the probability of a storm (A) occurring and a forest fire (B) at the same time. The probability follows the product rule (the clue is in the word and):
P(AB) = p(A) x p(B).
If the probability of a storm is 0.02 and the probability of a fire is 0.001, then the joint probability (P(AB)) is 0.00002, fairly low, as would be expected. The probability of one or the other (notice or) independent events occurring is the sum of the two, minus the product, i.e.,
P(A+B) - P(AB) = 0.00208.
The source of these probabilities is often in question. They are difficult to obtain for many situations. The chances of getting different estimates of probabilities of events are very high. The results depend very sensitively upon the definitions used and the assumptions made. The experience of coin-tossing suggests heads will come up about half of the time (i.e., the probability of heads is 0.5 but actual experiments suggest that you have to flip coins thousands of times to get this result.) Improbable events, however, seem to occur more often than our knowledge of probability suggests.
What is the probability of being bitten by your pet dog or snake? You've picked it up hundreds times. Is there no probability? Enough horror stories are told, with that incredulous look, suggesting these impossible events occur fairly frequently, with low probability but one not approaching zero (as for the sun not rising.)
Okrent (1980) said
"Decisions still have to be made, and they are likely to be better if they are made with the benefit of more complete information - - keeping in mind the need for judgment as to when the inability to completely quantify may lead to unwarranted dependance on estimates."
In no way am I suggesting that risk can be easily understood, that it is simple, or merely has been overlooked. As an example of the complexity, we may consider what are the health risks of a wildland manager "being fat." Obesity is a recognized health problem but in 1981 (Lewin 1981) it was noted that standard weight charts may be wrong. Maybe fat is ok, maybe the charts are based on doctors records (sick people come to see doctors), maybe people who die tend to weigh less than average people. Maybe extra weights it not the risk once thought!? What constitutes a risk? What constitutes "extra"? Maybe excessive weight (however it may be measured) is only a problem (reduces life expectancy) if accompanied by hypertension. Maybe the weight problem is a quibble among statisticians in the medical field. Even a topic in which many are interested and about which they have personal contacts or experience may not have answers that are intuitive or easily gained.
Numbers of people and proportions of events are used as probabilities. If only 9 percent of citizens are hunters, then the probability that a person selected at random will be a hunter is only 0.09. Interview people on the sidewalk and 27 out of 100 will be hunters. Yes, it depends on whether you're standing outside a sporting goods store for your interview. The condition assumed was "at random" and that is as hard to find or to arrange as finding a fair (unbiased) coin or flipping one in a consistently unbiased way.
Statistical tests are often done using the 95% level of confidence or alpha = 0.05. This implies that the user of the test is willing to say that there is no real difference between two average values gotten from the woods or a stream. It also implies that he or she is willing to be wrong about 5% of the time but no more than that. Managers could say there's no difference (say in number of salamanders upstream of a limestone ledge and the count below the ledge) when, in fact, there is. Maybe there is a difference and just due to the day, the technique, the temperature, the size, etc., etc. the averages came out about equal. The wildland manager takes a risk in making even simple decisions. Test statistics can help clarify the risks and bring them into use.
If 1000 experiments or comparisons (similar to the above comparison of averages) are made and the 95% level of confidence is used, then 50 of these are very likely to be wrong. There are not merely thousands but millions of such tests now done each year. The pressure is on researchers to find something different. The chances are that 50 is not the proper number. It is less. I do not see evidence for 50 erroneous decisions being made! There is intrinsic to our experiments, to our selections, to design, and to the flexibility and resilience of agricultural and wildland systems that suggests a lower standard than 0.05 can serve us well, perhaps alpha of 0.10 or 0.15 (i.e., 90%, 85%, or 67% level of confidence). The harsh criterion of alpha being 0.05 results in massive over investment in research samples, time, labor, processing, data storage, and analyses. A better investment (since a shift from 0.05 to 0.15 can cut by more than half the cost of a sampling program) would be to repeat the experiment elsewhere or later using the results from the first study in the second.
As we try to understand the meaning of the alpha level, we find 0.001 means 1 in 10,000 so when 1,500,000 people are given a drug there is a good chance that 1500 will show death or ill effects.
For a toxic substance, the risk and hazard questions include (based on Talcott 1992):
Talcott (1992) observed that
"To date, only a few studies have carefully integrated the uncertainty associated with individual elements of a risk estimation [at least the elements listed above] into an overall estimate of risk and its overall uncertainty."
The individual estimates are difficult to obtain but the results are generally unwanted because they are difficult to bear. This results tend to be vast uncertainty: even in well known systems. Take, for illustration, a 7-component system; 7 questions like the above with a probability of certainty of 0.90 for an answer to each one [recognizing this is an absurdly high confidence]. The overall certainty in such a situation is 0.48, the uncertainty or risk, 0.52. At this level of certainty we are within the scope of coin tossing to make a decision. When we are only 51% sure of each of the seven answers in the situation , the risk in the total situation becomes 0.99.
Because of the working of the "product rule" of probability, we can be very certain of 5 to 6 of the elements (say 0.95) in a 7 element system then express great uncertainty about 1 (say 0.10) and get risk levels (in the above situation) of 0.93. The manager's frustration is that there are rarely only 7, but many more elements in typical decision situations, thus the estimated risk level tends to increase.
Suppose the death rate for U.S. males, age 25 to 34, was 1 in 692. Now suppose by some new finding, some great scientific advance, we reduced the risk in the age class by 1 in 10,000 (an impressive amount). The overall risk for the future in the young age class would be 1 in 692 (which is 0.001445) minus (0.001 x 1/692) or 0.0014436 which results in a new annual death rate of 1 in 693. If you are the extra person, then the results have meaning, but most people, even when dealing with human life, potentially their own, would conclude that there was "no significant difference."
If a change of 1 human life saved out of 692 is not "significant" then what is? What are the mental calculations that people use to arrive at a decision of "no differences"? I tend to think this observation supports my previous comments about the need to reduce an alpha level say to 0.10, 0.20, or 0.33 as the criterion for wildland management decisions.
I am concerned here about how these numbers are translated into action. I am genuinely concerned about how the numbers can gain meaning. Taxes spent on low-probability research or on low-change research (say 1 in 100,000) may not be in the best interest of the wildland manager, or the wildlands, or the people dependent upon them.
If wildland managers insist that every benefit that they produce be accompanied by an expression of expected cost or loss (a net idea), then using statistics for such conclusions about benefits and costs is similar to that of "forestry" always including "replant" with "harvest." "No real difference" will take on new meaning. If there is no difference then no money can be afforded. The chances of failure are too high; the intense claim of "waste" to bright to ignore.
The probability of making an error in judgment is an expression of risk. From statistics we are provided tools for analyzing risk. We state an hypothesis: There is no difference between samples from A and samples from B. We compute a test statistic (e.g., t), then we decide: What are the chances of being wrong more than 1 time in 10. We say that alpha is 0.10 and use the available statistical tables. For example, if the calculated value of t exceeds the table value, we conclude that there is a real difference, one that is not due to chance. We, nevertheless, can make a bad decision. There may really be no difference! Every decision is risky. By using statistics we get an idea of how risky.
Less formal than the above, I see in the daily use of wildland managers various work combinations expressive of different certainty. I have no studies to prove these categories but they are consistent with my life observations and, besides, the risk of being wrong is very small:
Occurrence in Time
The head of a geology department said as we looked out of a restaurant window, "That water tank will fall." He explained its position on cotoctin sandstone, layers that slide when wetted. It seemed improbable, but I believed him. "It will surely fall ..., but I cannot tell you when", he said.
Occurrence is one of the dimensions of the reasonable certainty space. If a thing exists or may exist (like a tornado) at some reasonable level of certainty, then it must also occur (1) always, (2) with some reasonable frequency (3) within a reasonably short period, or (4) eventually. Knowing a comet may pass near Earth in 1 million years is interesting, of concern to some people, but the period of the event is not reasonably short. The frequency, the shortness, or both, must be decided for the dimension to have meaning or to be useful in making wildland decisions.
Occurrence phenomena include a break in a supply that is essential. Failures in hospital life-support systems are evident examples but failure to sustain funding of projects can cause unemployment and loss of massive investments in natural resource projects such as data-base building, modeling, and long-term basic ecological research.
Projects that depend on an instrument or part from an insecure supplier (a rumor of bankruptcy) realize the condition of risk, and are greater than that when parts are purchased from an old-line company.
If an event occurs at regular intervals, but these are very long (say a 200-year timber rotation), then the "reasonable period" may be related to difference in time now and the time of starting or ending the cycles.
"Prediction" is a word that has a time dimension. It is different, by that dimension, from simple estimation. It is always for the future. Things may be predicted. Occurrence may be predicted. Time of occurrence may be predicted (in some cases very precisely, like an eclipse of the sun). All are part of the idea of certainty space. The reasonableness must be decided in each situation along this dimension of occurrence.
Sequence is a major aspect of occurrence. A seed rain before a ground fire will result in a different environment than one occurring after a fire. Fungi spores before or after winds and leaf-wetting result in very different plant disease symptoms. A predator attack on an animal starved for 3 days or suffering from ingested toxicants has different results than the same attack on the same animal 3 days prior. Equifinality, however, reduces some types of events, assures others.
One aspect of risk is the time of failure. Not simply failure but an expression of when an event will occur is of unheralded importance in considering and computing risk.
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| Fig. 2. The probability (P) of or risk of failure for equipment changes over time. For a manager arriving on a refuge or forest, failures may occur a few days after equipment delivery, but for the manager arriving later (B), the equipment has aged. been used, and failure distribution shifts. |
Few wildland managers will face the realities of the sequences in the outdoors. Potential sequences are expressed i the high school algebra of permutations (N!). The permutations or possible sequences of 4 things is 4 x 3 x 2 x 1 = 24. The permutations of 10 things is 3,628,800 different sequences. The manager must select from among them the best sequence or the one that explains the observed conditions. The chances are small; the risks of being wrong may be great.
There is a need to study changing conditions and to express them in models that relate to decisions. The same things measured do not have the same relations if they act in different sequences. Why effects of permutations are not emphasized more in wildland studies, I do not know. Weisburger and Williams (1981) stated the need for sequential tests and studies. There are nearly infinite numbers of such tests to conduct but some resolution can be achieved if there are key decision points (e.g., exposure, duration, notable change).
Dynamics
Within the business community (and, strangely, all wildland managers are there but few realize it or admit it) risk is seen in many ways, but one is related to occurrence of events as related to their view of past events. People invest in stock on the basis of how the price of the stock fluctuates. It makes sense: the more it fluctuates the greater the risk. This measure, too, has difficulties because fluctuations over 5 years may not equal those over 50 years. There is a changing time dimension. Baumgartner and Hyldahl (1991) recommended using price data as a basis for studying risk in forestry. I think game harvests, recreation use, and other wildland "price-correlates" can similarly be used. The idea, similar to "beta" of the stock broker, is to study the fluctuation in price expressed by
Risk Index = (standard deviation/mean) x 100.
The standard deviation (merely the square root of the variance) is expressed in this index as a percentage of the mean and is the same as the coefficient of variation of statistics...but why not call it beta in a fancier field. The higher the risk index, the greater the risk of investment...or of any activity. The higher the index when temperatures are used, the greater the risk that some plant will be frozen or "cooked." The list can be easily expanded. Some observers, other than Hyldahl and Baumgartner (1991), have observed that the standard deviation, itself, is highly correlated with risk. (The higher the deviations, the lower the chance of picking the exact mean value in one observation ... not very astute.)
| Table 1. The geometric standard deviation as a means of interpreting uncertainty and variability in a data set. Generally, the higher the deviation, the greater are risks in decisions about environmental conditions or actions (From Talcott 1992:11). Risk01, a Basic computer program available from the author, supports such analyses. | ||
|---|---|---|
|
Geometric standard deviation |
Descriptive Term |
Examples of interpretive phrases |
| More that 10.0 |
||
| Extremely uncertain Extremely variable |
||
| 10.0 | There is a 2.5 percent chance that the actual value 10.0 may be higher than the median by more than a factor of 100 and a 2.5 percent chance it will be lower by a factor of 0.01 or less. | |
| Highly uncertain Highly variable |
||
| 5.0 | The value at the upper end of the 95 percent confidence interval is about 625 times larger than the value at the lower end. | |
| Fairly uncertain Fairly variable |
||
| The value of the 95th percentile is about 10 the value of the median and 100 times the value at the 5th percentile | ||
| Moderately uncertain Moderately variable |
||
| 2.0 | It is 95 percent sure that the value is not less than one-quarter of the value of the median, and not more than 4 times the value of the median. | |
| Moderately certain Moderately invariable |
||
| 1.50 | There is only 1 chance in 40 that the actual value may be greater than twice the median, and the same chance that it may be less than half the median. | |
| Fairly certain Fairly invariable |
||
| There is a 5 percent chance that the actual value may be as much as 50 percent higher or lower than the value of the median. | ||
| Highly certain Highly invariable |
||
| 1.05 | It is 95 percent sure that the actual value is within plus or minus 10 percent of the value of the median | |
| Extremely certain Extremely invariable |
||
| 1.00 | There is absolute certainty. | |
Talcott (1992) presented Table 1, a modification of the same idea. In security analysis, deviation in a stock of more than 2% per 1% change in the market is considered a high risk (Baumgartner and Hyldahl 1991). In Table 1, the index suggested is the geometric standard deviation (G). It is shown ranging from 1 to 10. When a median (M) is computed and where uncertainty is approximated by a log normal distribution, then the uncertainty or expected value (i.e., 1.0 minus the probable uncertainty) lies between
M/G < R < MG
The manager will be correct about 67% of the time when decisions are made based on this knowledge. To be correct more often, say 95% of the time,
M/(GG2) < R < M(G2)
For example, from the numbers in Table 2, it can be observed that the
| Table 2. Hypothetical observations, of wildland benefits, payoffs, or prices. See text for analyses. |
|
|---|---|
| 11 | 32 |
| 16 | 37 |
| 19 | 41 |
| 28 | 64 |
| 32 | 82 |
geometric mean (approximating the median) is 30.78, the geometric standard deviation is 1.84. By contrast, the arithmetic mean is 36.2. It can be said that with 66% confidence that the real central value lies between 16.73 and 56.62 but to be more sure (95%), it surely lies between 9.09 and 104.16.
The statistical geometric coefficient of variation is an important index to risk. It is an expression of the deviations or variations about the geometric mean and like the Risk Index above. It is
X = (G/M) x 100
and, from the data in Table 2, X is 5.98 percent. There is an average deviation close to the median of about 6%. The larger, the more variable, and probably the more risky decisions will appear to be. Trying to understand the phenomena that influence X, whether they be markets, behavior, or biophysical phenomena can probably reduce the uncertainty and allow increased confidence in the future. The arithmetic coefficient of variation, much as above, i.e., the standard deviation compared to the arithmetic mean, is usually not as useful in such analyses because of the high variation in much wildland work. In the above example, that comparison resulted in a coefficient of 60.63 percent.
For years, foresters have used the financial discount rate as a means to integrate concepts of risk into their decisions. If the bank saving rate (or some insured minimum) is 0.04 or 4%, then foresters would add percentage points into their equations depending on the hazards and risks they say for each trait, forest, or investment. In order to be sure that they would make the same amount of money as from a bank saving account over 50 years in the face of poachers, vandals, forest fire, insects, and disease, they would use 0.09 or 0.10 as the rate of investment. The more risky, the larger the rate used.
The present value (discounted value) of an expected timber harvest value of $50,000 at relatively secure 4%, after 50 years, is $7035.63. At 0.17, risks included, the present value is $19.48. The difference in magnitude is impressive and it occurs because of perceived risk and using a higher hypothesized, risk-related rate. In a related expression, $19.48 invested at 4% for 50 years would not yield $50,000 but only $138.44.
In Table 3 can be seen a set of Present and Terminal values. These are well-known relations. Approximately equally present values, say of 37, can produce very different results when different interest rates are involved.
Assumptions can be made about forests, say when $10,000 is invested at 5% over 40 years and is expected to result in a future value of $70,400. When that rate is inflated merely 2 percent to 7% the future value increases 2.56 times. Small changes in estimated rates drastically affect forestry decisions, probably incurring normally unacceptable risks. Studies show that the discount rate decreases as the planning - or investment-period increases. There is a tendency to view the time between today and 50 years from today as shorter than the time between 50 years from today and 100 years from today. Overton and Hunt (1974 ) suggested an alternative discounting procedure for wilderness investment. It has, in fact, a shifting rate of inflation, p, and value of the commodity.
N0 = Nt / ((1.0 + R)/ (1.0 + p) (1 + k))t
Table 4 shows a comparison of conventional discounting and the above procedure.
The estimate of the interest or investment rate was tricky, but not much more so than the difficulties and imponderables in other estimation procedures. The feeling I hope to leave is that risk estimation is complex, it has been done, it can be done better; there are aids and techniques for estimating it, and there are preferred ways to express it, at least among people who use risk in formal decision situations (e.g., approving a dam or licensing a product or practice as "safe").
In forestry, in getting the wood out and the profit in, the conventional investment decision has been plagued with analytical problems (Baumgartner and Hyldahl 1991) of :
Table 3. Present values and terminal (or future) values from investments at the designated rate. The discount rate may be viewed as an index to risk-taking for investors.
| Terminal Value | Discount Rate | Present Value |
| $10,000 | 0.03 | $3,065.57 |
| 5,000 | 0.03 | 1,532.78 |
| 3,333 | 0.03 | $1,021.86 |
| 2,500 | 0.03 | 766.39 |
| 2,000 |
0.03 |
613.11 |
| 10,000 | 0.05 | 1,420.46 |
| 5,000 | 0.05 | 710.23 |
| 3,333 | 0.05 | 473.49 |
| 2,500 |
0.05 |
355.12 |
| 2,000 | 0.05 | 284.09 |
| 10,000 | 0.07 | 667.81 |
| 5,000 | 0.07 | 333.90 |
| 3,333 | 0.07 | 222.60 |
| 2,500 | 0.07 | 166.95 |
| 2,000 | 0.07 | 133.56 |
| 10,000 | 0.09 | 318.38 |
| 5,000 | 0.09 | 159.19 |
| 3,333 | 0.09 | 106.13 |
| 2,500 | 0.09 | 79.59 |
| 2,000 | 0.09 | 63.68 |
| 10,000 | 0.11 | 153.84 |
| 5,000 | 0.11 | 76.92 |
| 3,333 | 0.11 | 51.28 |
| 2,500 | 0.11 | 38.46 |
| 2,000 | 0.11 | 30.77 |
| 10,000 | 0.13 | 75.31 |
| 5,000 | 0.13 | 37.66 |
| 3,333 | 0.13 | 25.10 |
| 2,500 | 0.13 | 18.83 |
| 2,000 | 0.13 | 15.06 |
| 10,000 | 0.15 | 37.33 |
| 5,000 | 0.15 | 18.67 |
| 3,333 | 0.15 | 12.44 |
| 2,500 | 0.15 | 9.33 |
| 2,000 | 0.15 | 7.47 |
| 10,000 | 0.17 | 18.73 |
| 5,000 | 0.17 | 9.37 |
| 3,333 | 0.17 | 6.24 |
| 2,500 | 0.17 | 4.68 |
| 2,000 | 0.17 | 3.75 |
| Standard Interest Rate |
Years | Conventional Present Value |
Overton and Hunt Modified Present Value |
0.03 25 477.61 2,311.10 0.03 50 228.11 5,501.41 0.03 75 108.95 13,095.72 0.03 100 52.03 31,173.46 0.03 125 24.85 74,206.25 0.03 150 11.87 176,642.80 0.03 175 5.67 420,486.10 0.03 200 2.71 1,000,938.00 0.04 25 375.12 2,288.88 0.04 50 140.71 5,448.51 0.04 75 52.78 12,969.80 0.04 100 19.80 30,873.71 0.04 125 7.43 73,492.73 0.04 150 2.79 174,944.40 0.04 175 1.05 416,442.90 0.04 200 0.39 991,313.50 0.05 25 295.30 2,267.08 0.05 50 87.20 5,396.62 0.05 75 25.75 12,846.28 0.05 100 7.60 30,579.68 0.05 125 2.25 72,792.80 0.05 150 0.66 173,278.20 0.05 175 0.20 412,476.80 0.05 200 0.06 981,872.30 0.06 25 233.00 2,245.69 0.06 50 54.29 5,345.71 0.06 75 12.65 12,725.09 0.06 100 2.95 30,291.19 0.06 125 0.69 72,106.07 0.06 150 0.16 171,643.50 0.06 175 0.04 408,585.50 0.06 200 0.01 972,609.40
The Place
Place of failure influences the willingness of people to accept it and their interest in it. In some ways the closer the event, the less risk a person is willing to accept. Thus, there is a continuous declining function. There is also a discrete function. Nearby, there is risk; far away it is irrelevant. There is a yes-no condition. The boundary may be fuzzy. Risk levels undoubtedly have a distribution with distance for a population of people.
The Personhood of Risk
Failures of any system for friends or families are of greater importance or intensity than for unknown or unliked people. Prized members of society (e.g., leaders, artists, inventors) also elicit different responses to risk than do average people. As described above, hazards are usually the same for individuals; risks have multiple dimensions, not just number of people but their loses as well ... and society's perceived loss due to greatness or role that is lost.
Payoff
I do not play in high-stake games of chance. I do, however, play the life game, but differently on different days. The day after recovering from the flu, I play at almost nothing. I take no risk. On other days, I may ride a motorcycle, walk against the light, not buckle my seat belt, or "study" a poisonous snake longer than is necessary. There is something unusual going on in human behavior and that of other animals that allows us different kinds of behavior in the face of risks. I've already discussed the "odds" or the numerical risk. Here, let me return to the payoff, the utility I seek to maximize.
I do not play the lottery when the chances are 1 in 20 million of making a million dollars, but when the "pot" gets to 10 million, I cannot resist. The chances remain the same, but my behavior differs because of the payoff. Even if the odds change, (become less), I'll probably play because of the outcome. The decision variable is the product:
Utility = (1.0 - Risk) x Payoff
but if my willingness to take risk changes with the payoff then I must weight risk and
w = f (Payoff)
so
Utility = (1.0 - WRisk) x Payoff
I shall return to W later.
Many statutes implicitly call for balancing risks (defined as "magnitude of expected loss" but not always) against benefits to get a ratio or net value and some require it (such as the Toxic Substances Control Act, the Pesticide Act, and the Consumer Product Safety Act). Acknowledging crude order-of-magnitude risks can be estimated, others claim that "benefits" (those from wilderness beauty, endangered species, or human life) cannot be so easily or (as if "costs" or "losses" was easily done) precisely estimated. Efforts to make benefit estimates have been called a primitive art form. They have engaged such important areas of decision making as accident and disease prevention, mountain rescue, and agricultural regulation and safety. The estimation has rarely been satisfactory because the analyses are very time consuming (with results not being produced in time for decisions), they may not reflect well the public values (or power groups), and the benefits are excessively difficult to quantify in a widely acceptable form.
The other side of the payoff coin is loss, with individual loss-of-life or group annihilation at one extreme end. Animals probably cannot see the end of life and probably do not "fear death" (contra "unwilling to risk losing life"). Humans (however, only some) can conceive of the future and can conceive of the future conditions for them and their families or others. A genetic code that resists life-threatening behavior may be a great asset to insects and other animals. People seem to have it in short supply. Such behavior seems to be left to the human thought processes, and I've noted a few limitations, especially for the long term. For the short term, however, the description is as above. The payoff for reasonable behavior is not dying; not losing a contract; not losing a friend, a marriage, or a sale. These are all negative expressions and part of the mixed meanings of risk. The idea is to play so as not to lose but to win. The term turns and now we can speak again of expected payoffs. The "expected" part of the expression is merely [1.0-Risk]. If the chance of losing is 1 in 10, then the chance of not losing (usually winning) (and we cannot be certain) is 9 in 10 or 90% [i.e., 1.0 - 1/10 = 0.90]. A reasonable wildland manager will try to make decisions so that his or her decision has a high expected payoff. "How large?" is a decision, too. There is a threshold--cultural, budgetary, sociological, or psychologic (as in "she did it; she just didn't seem to care!") and the judgement is usually made when the payoff exceeds a certain amount.
The reason this expected reasonable payoff relationship is so obscure is that
| Table 5. The relationship of the magnitude willingness to risk in relation to perceived benefits. A cubic relation seems to exist (Starr 1980). |
Benefits Tolerable Risks
0 0.00
10,000 21.54
20,000 27.14
30,000 31.06
40,000 34.19
50,000 36.83
60,000 39.13
70,000 41.20
80,000 43.07
90,000 44.80
100,000 46.40
200,000 58.46
300,000 66.92
400,000 73.65
500,000 79.34
600,000 84.31
700,000 88.75
800,000 92.79
900,000 96.50
1,000,000 99.95
|
In summary, the payoff dimension is itself complex. It is the probable gains minus the probable losses, all over time (often cumulative as in tree growth or total annual harvests of ruffed grouse over 10 years), all beyond the appropriate thresholds or constraints, the essence of "reasonable." Thus, it is expected reasonable perceived discounted net payoff to significant people that is our decision criterion.
Equity
High sure payoffs, high expected values are all desirable, but one emphasis made by students of risk and people of conscience is that one person's increase in expected gains should not be at the expense or loss to others. For example, reduced risk of flooding for a few may come at high cost, even increased risk to those influenced by a water control structure.
C.L. Comar observed in 1979
The unfortunate, overtaken by a one-in-a-million catastrophe, have a 100 percent chance of harm. The hard fact is that attempts to eliminate risks for the unfortunate few tend to markedly increase them for the rest of a large population. This idea is most difficult to defend politically, especially when the unfortunate few are known and the unfortunate many are nameless. In addition, it is necessary to take into account such matters as validity and uncertainty in risk expiates, nonlethal and esthetic effects, voluntary versus involuntary risks, societal abhorrences, and the strange versus the familiar.Hurricanes can cause billions of dollars of losses. It now seems feasible to reduce the destructive force by seeding with silver iodide crystals. What if you seeded and the storm caused damage (as likely); would you be liable for the storm damage that was not prevented by your work? What if it was unusually large, 20% of the normal loss was reduced, but effect was greater than ever seen before?Nevertheless, other than depriving the news media of a ready source of attention-grabbing items, the pragmatic de minimis approach should serve to promote understanding about how to deal with risk in the real world: encourage identifiers of risk to provide risk estimates; focus attention on actions that can effectively improve health and welfare and at the same time avoid squandering resources in attempts to reduce small risks while leaving larger ones unattended; and prevent anxiety, apathy, or decision as a response to the increasing recognition that we apparently live in a sea of carcinogens [and other threats].
Howard et al. (1972: 1201) said:
The decision to seed a hurricane imposes a great responsibility on public officials [read: they must take a great risk with high expected value of the outcome]. This decision cannot be avoided because inaction is equivalent to a decision not to permit seeding. Either the government must accept the responsibility of a seeding that maybe perceived by the public as deleterious, or it must accept the responsibility for not seeding and thereby exposing the public to higher probabilities of severe storm damage.He also said:
Nearly all the government hurricane meteorologists that we questions said they would seed a hurricane threatening their homes and families---if they could be freed from professional liability (Howard 1972: 1191).
Okrent (1980) described the equity criteria as one in which a decision resulted in no gross inequities and that no individual is knowingly left exposed to a risk significantly greater than some acceptable upper limit.
The reasonable, net, expected, present-discounted utility of a wildland decision alternative is Uj. It should be compared to other alternatives and the maximum selected. The formulation at present seems to be
U = zeta1 [
pP /(1.0 + r)t ] [k N1] x zeta2 -
zeta2 [c/(1.0 + r)t ] [k N2]
where
N
zeta1 is 
1.0- _ wiR
zeta2 = same for costs or losses
zeta2 is similarly 1.0 minus the probability of loss of control over an object, event, or condition, one otherwise safe.
R is the estimated risk
and
Wi (within zeta) is estimates of all weights as described above and include other weights related to existence; suitable time of occurrence; desirable frequency of occurrence; sequence of occurrence; desirable place; similar resources available (perceived substitutability)
P is the final value of payoff; p its probability of being a correct estimate or 100-Risk Index
t is time, such as 50 years in a planning period
r is a discount rate
k is the perceived importance of groups of people or the equity issue
and N1 symbolizes the people ("publics") likely to be benefitted.
zeta2 = similarly
C is the total costs and losses; c is the probability it is correctly perceived
N2 the people likely to be affected adversely.
A set of constraints is usually stated such as a budget limit, area limit; requirement for a decision (not to abstain); limits on people to be included and time within which a decision must be made. Absolute values are not important, only a consistent means for computing the relative values of alternatives.
The wildland manager needs to come to grips with, to realize fully, that most wildland decisions commonly have great risks attached. There are physical, biological, and political phenomena interacting in non-linear ways, often some having thresholds of change. Nevertheless, the manager can use the information on risks that is available. He or she needs to be on guard that risk analysis it does not cost more than it is worth. [A facility appraisal or research study may cost $5000. You can buy a lot of insurance for $5000!] He or she may suggest that comparisons be made in orders of magnitude. He or she may present the risk information that is available in a clear way so others will see an analysis as you do and show the conservative answer. We have done elementary computer simulations that suggest a range of risk estimates can be used within a model and many of the same decisions would be made. Where the changes occur can be presented. This is a type of sensitivity analysis, a look at how sensitive the system is to the range of risks as compared to changes in other variables. The system performance measure should never be risk itself but utility. Rational, robust, improving, adaptable, socially-relevant risk is needed to estimate that utility.
Toward Being Certain of Risk
I am of the view that an expert system can be devised that incorporates into a singular expression an answer to whether a project or technology is safe. I expand our previously brief definition of "safe" to mean: has an acceptably-high reasonable net social expected value for at least 50 years. I think this is relevant to wildland management.
The system has many major components with many associated criteria
Literature Cited
Baumgartner, D. and C. Hyldahl. 1991. Using price data to consider risk in the evaluation of forest management investments. USDA For. Serv., Gen. Tech. Report NC-144, N. Central For. Expt. Sta., St. Paul, MN. 8 pp.
Cropper, M. L. and P. R. Portney. 1992. Discounting human lives. Resources (Resources for the Future) No. 109, Summer, p. 1-4.
Englehard, R. J. and W. C. Anderson. 1983. A method of assessing risk in forestry investment. USDA For. Serv. Southern For. Exp. Sta., Res. Paper SO-189, New Orleans, LA. 13 pp.
Fischhoff, B. P. Slovic, and S. Lichtenstein. 1979. Weighing the risks. Environment 21(4):17-38.
Halliday, I., A. T. Blackwell, and A. A. Grifin. 1984. The frequency of meteorite falls on the Earth. Science 223:1405-1407.
Howard, R. A., J. E. Matheson, and D. W. North. 1972. The decision to seed hurricanes. Science 176(4040):1191-1202.
Hyldahl, C. A. and D. C. Baumgartner. 1991. Risk analysis and timber investments: a bibliography of theory and applications. USDA For. Serv. Gen. Tech. Rpt. NC-143, N. Central For. Exp. Sta., St. Paul, MN. 29 pp.
Jensen, N. F. 1978. Limits to growth in world food production. Science 201:317-320.
Kaplan, S. and J. Garrick. 1981. On the quantitative definition of risk. Risk analysis: An International Journal 1(1):
Kogan, N. and M. A. Wallach. 1964. Risk taking: a study in cognition and personality. Holt, Rinehart, and Winston. New York. x + 278 p.
Okrent, D. 1980. Comment on societal risk. Science 208:372-375.
Overton, W.S. and L.M. Hunt. 1974. A view of current forest policy, with questions regarding the state of forests and criteria of management. Trans. N. America Wildlife and National Resource Conference. 39: 334-353.
Paine, L. A. 1966. Tree hazard control on recreation sites ... estimating local budgets. USDA For. Serv., Pacific SW For. Exp. Sta., Berkeley, CA. PSW160. 5 pp.
Starr, C. and C. Whipple. 1980. Risks of risk decisions. Science 208:1114-1119.
Talcott, F. W. 1992. How certain is that environmental risk estimate? Resources (Resources for the Future) Washington, D.C., Spring, No. 107. p. 10-15.
Weisburger, J. H. and G. M. Williams. 1981. Carcinogen testing: current problems and new approaches. Science 214:401-407.
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