| A unit of Lasting Forests
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A Total Forest Management Plan
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Rural System staff have analyzed the concepts of stem counts, stand density, and stocking rates and have arrived at a useful, practical way to understand these dimemsions for the forest. They are complex and full of the stresses of conflicting data, unusual analyses, challenging theories of plant competition and thinning, confounding effects of soil type, precipitation, depth to bedrock, and topography (slope, aspect, and relief), and unclear objectives. Efforts to be very precise have required phrases that have not helped field people to understand the problem or how to use the results of finding answers.
Being systems oriented, we start with objectives. How do you know what is good stocking? A good density of trees per acre? The problems of what is good is as profound here as in philosophy debates. We hold that to decide on what is good, the observer must have a set of criteria. There must be criteria or, we prefer, objectives. How do you know when good occurs? The answer: When the conditions allow the objectives to be met!
As described may times and places, the forests of the area must be managed to produce many benefits. Growing maximum amounts of wood may be one benefit or major objective, but maximum profits over 50 years may be another, and thus there is no guarantee that the same forest will achieve both objectives. More profits may be made from a combination of wildlife and tree sales than from simply logging at a set rotation. Different stocking levels result in different tree growth but also in different tree disease, different deer forage, different groundwater recharge and different reforestation costs. What do we really want? is a very difficult question. Only when it is answered well can we begin to decide upon the desired stocking level or resulting stem density.
For tree wood value estimates (given other measures for other benefits being produced), we estimate the sawn volume change and the pulp chip volume (minus bark) over time in the 1 foot to 9-foot bole.
Trees in stands compete with each other. Here we ignore the debates about whether plants really compete and "want to win-out" over nearby plants. There is limited energy, water, and nutrients in a system. Plants (trees) use all of those that they can process. Trees use these resources within the spatial limits of the canopy or the roots. Plants compete with nearby plants within the area or "volume of influence". In the past this has been based on a circle of fixed radius but we use a hexagon, imagining trees may fit into an area as if in a honeycomb of hexagons of average size.
The well-known relations of hexagons are (where S = area and S = 3ar; a = length of one side; R = radius of circumscribed circle (the distance to the vertices); r = radius of inscribed circle (the distance to the midpoint of the side):
| Relations | Hexagon Coefficients |
|---|---|
| s/a2 | 2.5981 |
| S/R2 | 2.5981 |
| S/r2 | 3.4641 |
| R/a | 1.0000 |
| R/r | 1.1547 |
| a/R | 1.0000 |
| a/r | 1.1547 |
| r/R | 0.8660 |
| r/a | 0.8660 |
The area of influence is the combined crown, stem, and roots in which a tree can effectively acquire resources. The area is no circle since plants compete differently in different directions and the overlap or empty space among mapped circles is confounding to any analysis or theory building. Trees are often asymetrical in canopy and root, responding differently to light, shading from nearby plants, soil rockiness and depth, and phytotoxins. Of course each plant has initial conditions that may vary (genetics, time of seeding, time of germination, etc.). Regular distributions of trees in any stands seem very unlikely.
Where the area of influence(or volume) of a tree is a and the total surface area for all trees is A, then the maximum number of trees for the area (the density) is A/a. The actual number will be less because trees die, competition is not equal; qualities of each plant vary. It seems unlikely that there is a thinning rule (Weller 1991) but changes over time are evident. We propose to work out the estimated biomass per unit volume (the average hexagonal "column") as the basis for explaining tree size and space relations. Specific gravity of the woods will play an easily-added role in our analyses as we shift from the area occupied by plants (an analysis of packing geometry) to an analysis of the factors that produce biomass in an alpha unit. It seems likely that when the biomass of the stand volume reaches a maximum, then trees die, all at once if they are identical, otherwise slowly, inversely to their competitive ability thereafter.
The quadratic mean diameter may be used as a surrogate for tree weight or biomass. The quadratic mean diameter is the diameter of a tree having the average basal area.
Post et al. (1998) found that percent runoff (R) was related as:
Rold growth = - 0.318 + 58.41
Rregrowth = - 0.048 Stocking + 54.22
Tenative use in The Trevey is for a relationship of
RTrevey = - 0.1 Stocking + 55
to approximate the response of ungauged watersheds or catchments.
where stocking density (Stocking) is trees per hectare.
Other relations of stocking density are being explored.
References
Brisson, J. and J.F. Reynolds. 1997. Effects of compensatory growth on population processes: a simulation study. Ecology 78(8): 2378-2384.
Post, D.A., J.A. Jones, and G.E. Grant 1998. An improved methodology for predicting the daily hydrologic response of ungauged catchments. Env. Modeling and Software 13: 395-403
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Last revision January 17, 2000.