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Gamma Theory

Modern Wild Faunal Resource Management

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Cross Current: Curve Fitting vs. Theory Building

For years I was a curve fitter. I collected data and fed it to a computer and got equations and used the equations to improve management and to explain my observations. I taught that if I had a strong relationship, typically an equation with a large R², then I should use it, then apply feedback to improve it. This was a black-box approach to the natural world. It was cost effective and admitted that I would never have enough time or resources to understand the many complex systems that were my responsibility. Egocentric, I failed to notice that there were at least 1000 other biologists/ managers out there doing the same thing and that if we each worked together and cooperated we might be able to develop fundamental knowledge about systems, not just a set of regression equations. The curve-fitting may help develop theory but perhaps it is best to start with theory, then see if the data ans related equations support it.

For example, perhaps animals respond to the volume in the vicinity of field/forest edges. If that is the case, volumetric (cubic) relations are more likely to pay off in strong relations and exxplanations than things that are linear.

If an expotential relationship shows up as the exponent 1.5, there may be a likelihood that this could have been 3/2 and this could be seen as plant volume relations per unit area (a square function).

In biological systems, when there are no resources (e.g., water) then there is no life. Most biological equations just have to be forced through the zero of the graph...the intercept must be zero for the equation to be realistic. Once that is done, then there must usually be some maximum or minimum condition with which every observer would agree. When stated, then the real relations among veraibles can be seen. If some regression analysis suggests to me that the coefficient of a logarithmto the base 10 is 1.85, I am going to ponder whether it might be 2.0 and thus the relationship is a square function. I got 1.85 because of the nature of the sample, measurement error, etc., and the fundamental relation will most likely be best expressed over the long run as the square of the number. I start with the premise that nature follows small, stepwise, simple rules. Most things in nature are curvilinear. Most things in nature have real limits and thresholds. Most things in nature are related to area (square functions) or volumes (cubic functions). Most things in nature are energy related and thus surface-area related as in the metabolic relations of mammals (approximately 0.75 or approximately 3/4 (3 being the cubic relation and 4 being the area relatiuonship)).

Curve-fitting may be the best that the practical manager can do, but over the long run, theory building and cooperative work will be more cost effective and advance the field of faunal resource emanagement faster than developing more site-specific equations, curves that fit the data but give little knowledge to others (and are wrong when extrapolated past the data).

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Last revision January 17, 2000.