Rural System's

Modern Wild Faunal Resource System Management

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Performance Measures and Magic Numbers

"And how do you know when you are managing a wild animal population?"

Leading question! First, we may not be managing an animal population. We may not need to. We are managing a resource, the wild animal resource. Some will say, "Because I say that I am!", (not very satisfactory). Others take the negative: It is the difference between what agencies do when they have wilderness and park-like areas...and other areas.

But how do you know when you are managing (ignoring for the time whether you are doing it well or not)? There are many ways to know things (epistemology), but perhaps there ought to be some agreeable way to know about wildlife resource management. You can say what you do, as in the definition, but what should we expect to see? What evidence would be acceptable? In the public agency, what is the contract with the public? What should they expect as proof of a manager having "managed"?

Wildlife managers manage whole systems, at least viewed as one resource-system for a region and a period. The above questions are about the system performance, and by inference, the performance of the manager of that system. A manager can list many activities, things that they do, but the question usually dodged is that of the performance measure. The field person often gets the question of "how are things?" and rarely knows how to answer and quickly turns attention to the weather. The question is about the performance measure, but it is unclear just what that really is.

Typical wildlife agency performance measures are hunters buying licenses and county-level or statewide game harvests. They may suffice for some managers but increasingly they become estimates of thousand hours of quality-weighted hours spent in animal-related activity.

Managers produce annual reports, usually usually about their miles of roads built, meters of waterfowl dikes replenished, acres fertilized and limed, feeding areas constructed, nest boxes placed, miles of boundary marked, arrests made for poaching, trees girdled to open the understory, acres flooded for waterfowl, and survey-routes run. These are all actions, processes within the system. Presumably they were done for a reason and the question is: what is that reason...and were you successful? The answer is: all of these things, some together (and only sensible if done together), were done to achieve a set of objectives. These are system processes, not outcomes.

The objectives are many and complex and some are difficult or expensive to measure, and so managers have picked one or two things that suggests how well we are achieving all of them. We use system performance measures.We may plot the reported annual harvest of wild turkeys. We know this is limited because the reports may be limited and law-violations are well-known (but there have been few studies of the magnitude). We report the annual harvest but we realize that the population this year was very much a function of the populations present over at least the past 2 years. We are unclear about the sex or ages of the birds taken. We study the turkeys because their habitat (read "faunal space") requirements range from grassy areas to mature forests so if the turkeys are doing well (that is, a population is doing well enough to stabilize or increase even under fairly presumed-constant hunting pressure), then animals that depend on small units of this range of young-to-old habitats are probably doing well. The wild turkey harvest is a system performance measure. Of course it is flawed! It is a performance measure, not the performance itself, but since we cannot or do not know how to communicate that, we use a "measure." There may be several measures. Too many confuse the users. A measure, by nature, is a simplification. It is the same type measure used to express the national economy (e.g.,the Dow-Jones), the state of the nation (the gross national product), or the status of an industry (e.g., the cars leaving the line)...but all of these are flawed...but decision makers, knowing they are flawed, still use them.

Use is the argument of the pragmatists. Good? Used well? Over-inflated? Use is a poor argument and begs for an alternative.

Reported harvest (H) is interesting but harvest per hunter (h) may be a better statistic to use as a performance measure. Harvest per hour spent (S) (averages obtained from hunter interviews) may be an improvement. Area of habitat (A) can be grossly mapped and included. Thus an index (K) can be devised that might allow in a word the question of "how are things?" to be answered:

K = H h S

For example on a 30,300-acre managed area, where 90 birds are taken and the average hours spent in a season is 15.6 per bird taken,and there are 777 hunters, the unsuccessful ones spending 19.4 hours, then

K = (90 x 15.6) + ((777-90) x 19.4)

K = 14,732

K expresses the hours of turkey hunting provided by the management area. Other performance measures could have been the kill per hunter (0.0116), the harvest per 1000 acres (2.7), or the hours produced per acre (0.486). The index can become very complicated but computer assistance is readily available. Not so readily available is the answer to questions such as what are we trying to show? Are we producing animals or hours of hunting experience? What happens to the index if the hunters decrease (maybe the kill per hunter will increase!) What happens to the index if the hunters become more efficient? What happens if there is a forest fire and the area of habitat increases one year, declines the next? Besides, perhaps the objective was preserving an endangered ecological community. Turkey harvest may be irrelevant. Even complicated performance indices may fail to capture the essence of why the managers are at work. I call the complicated indices "magic numbers" because few people will ask about their derivation (or understand the answers). It is possible to get indicators of how well a system is performing and to take out some of the annual variability out of them due to rules, regulations, gas prices, land use changes, and local population fluctuations. Kill per hunter per 100 acres per day of the season is an example. The per...per...per gives it away. One systems person joked that if you give any biologist a columns of numbers, he or she will divide one by the other. The modern wildlifer wont, and will realize that a complex performance measure, an index, can be very dangerous. Very different states of a system can produce the same index (e.g., K = 3 / 10 vs K = 0.891 / 2.93).

There has to be a way out of this mess. There is. First, system performance indicators are designed to reflect how systems are performing. As compared to what? Hopefully, to objectives. Thus, as will be said and will be evident soon... as compared to objectives. Few wildlife managers (or their agencies or companies) have clear objectives, thus "as compared to what?" has little meaning. The objectives are essential for clarifying what the system should be doing, then a measure, some estimate, something that reflects the major aspects of those objectives, can be devised.

When it comes right down to the wire and a decision is needed, a magic number can be used. A magic number is an index, a practical number resulting from at least one operation (like multiplication or taking a square root). Anexample is 0.0000033 which is the proportion of hunters successful per day per square mile of deer range in a hunting zone. People in a state with 100 counties with open seasons may want to know which is the "best" county or "most productive." This question bears a lot of scrutiny. (What is the real question?) There is an underlying concept of a system performance measure at work here. The number is magic because no one will listen to the "...per...per...per list" list of words used to explain them. They are used to determine relative conditions or trends and when a number is "high," the situation is "good;" when "low," then it is "bad." They are practical, functional, useful. Following the deer harvest example, there may be 100 counties with reported harvest. Imagine County A having a reported harvest of 2000 animals, County B, 1000 animals.Which is best? Well A of course! But the skeptic says:How big is County A relative to B? Now we begin creating the magic number because County A has 200,000 ha, County B, 130,000. Thus, the harvest per 1000 ha is 5.0 for A and 7.7 for B. Now B appears better. "How many of these hectares are in habitat?" is the follow-up question. A has 50 percent,B has 30 percent. We operate again [2000/(200 x 0.50)] vs [1000/(130 x 0.30)] or 20 versus 25.6. Still County B is better. But how many hunters were there for each 100 acres? As it turned out County A did not have enough to harvest the calculated surplus. The magic number, Q, finally, was "male antlered deer reported harvested per 1000 hectares of deer habitat per 1000 male hunters over the age of 16 and using rifles." The number became the basis for sorting, looking at regions and groupings, allocating funds, and checking for anomalies and research needs. The final numbers were operated on at least 6 times to gain an index somewhat expressive of harvest with all responsible, appropriate adjustments made with readily-available data. Pikul (1974) listed many indexes that have been used. Typical magic numbers are (Q2) = hunter success = f(hectares, edge, time, brush piles, week of year, number of days, quality of days) and (Q3) = fire index = f (rainfall, area, time, temperature, days since rain, litter volume). Another example of a magic number for an area is Xi (or some known symbol and easily spoken word) and it might express quality of the deer herd and hunter experience. Few people will listen very long but the faunal resource manager may explain "improvements in the Xi index "for the herd or the area which might be computed as: Xi = (doe harvest/500 acres/quality-weighted 10-hour units spent by all hunters) - (count of hunting accidents reported) The dimensions are many and the computed results may have many uses. In general, and until more precise numbers become available (which may not be useful with the public), the magic number may be sufficient. The "gross-national product" or GNP is a magic number just as are many other indexes. Many include weights and adjustments. The skeptic may wish to press for the dimensions and analyze the index. The manager or decision maker, however, is usually grasping for an aid for making a decision. The magic number may suffice. The systems person will insist on: Making these as easily calculated as possible and providing computer aids for doing so. Storing and retrieving data so they are readily used within such an index. Formulating proper procedures and weights, and Encouraging alternative methods (such as multiple regression and factor analyses) because the magic number is limited, hides things usefully displayed, and may result in poor decisions. It is fast and better used than not using the available data. One of the limitations in some applications is that equifinality may easily occur. A county with a harvest of 500 in 100 units by 5000 people will get the same number as one with a harvest of 5000 in 50 units by 10,000 people. There is no way to separate causative forces, e.g., habitat or people and a test for the significance of any component is impossible. Green (1979:95) was very positive in his disdain for magic numbers or "derived variables." He said, "Unfortunately, environmental biologists often formulate and use index variables intuitively, thereby avoiding clear thinking about hypotheses and intervariable relationships." Magic numbers are not a bad idea until timely, robust models are created for companies and agencies. This is no longer difficult. Green (1979:95) recommended using linear models, especially with logarithmic transformations of the variables. The signs (+ or -) of the coefficients for each variable then became very instructive to the decision maker.

A conclusion, use them only if you must, but otherwise do not use magic number indices for the above reasons. There can be equifinality; the different conditions can produce the same result.

Do use regression. Once the performance measure (e.g., cars passing an entrance point) is selected, then call it the "dependent variable" and develop regression equations (at least simple linear ones; later get help with developing multiple regression and logistic regression procedures that estimate the probability of an event).

It is likely that a simple objective can or will be stated. There will probably be a set developed (Probably one for each major game animal, others for diversity, land preservation, employee morale, citizen interaction, etc.).It will usually be possible to assign weights of relative importance to each of these objectives within the set. A panel of citizens and/or staff can estimate grossly how well each has been achieved (say on a scale of to 10). Weight each score by its importance and add them up or get a weighted percentage. Call this B (for "benefits" or probable achievement of desired structures, services, dynamics, and relations), a system performance measure for the present or recent-past conditions. Perhaps the weighted percentage is, for example, 76. Understandably, the score is not bad and the managers are trying to move it to the desired condition of 100. This estimate of B does not include costs and the treatment of each objective is done in haste by people with diverse backgrounds and interests. It suffers some of the same limitations as above but it is a performance measure, emphasizes objectives, discourages using one-species data sets, and is a fairly inexpensive procedure to obtain an estimate, a group perception, of how well the system is performing. We'll discuss objectives, especially costs in other units, and how to move R, a system performance measure, to R*.

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Last revision February 17, 2005.