Yield Tables Empirical Forestry Models

Throughout Europe in medieval times there was a substantial clearing of forests followed by even more extensive deforestation regionally. With the progressive reduction of forests, class conflicts over the products of forests intensified and this manifested itself in laws against poaching of animals, thieving of wood, and proscriptions against public use of forests, in general. In the mid-eighteenth century, a forest management concept called 'Nachhalttigkeit' or sustainability was developed by the Germans. From about 1800, this new forestry practice spread over Europe, particularly Northern Europe. This was essentially a transition from the earlier, exploitive extraction of materials from forests to a more 'trees as a crop' agricultural management of forest tracts. Nachhaltigkeit involved detailed determination of how to best manage forests to produce wood and other goods. Essential to this objective was manipulating density by spacing trees on a given site, either by planting trees or by thinning a naturally regenerated stand oftrees following a timber harvest or a natural disturbance. Additionally, one needed to determine how long one should wait before harvesting a stand of trees and then planting a new stand. This spacing/length-of-rotation problem had long been solved for crop plants through experimentation and observation. To produce trees as long-lived crops, elaborate long-term data collection started on the height; size in diameter; amount of wood; and size of crowns in forest stands of different densities at sites with different environmental conditions. Eventually, a forest modeling concept called the 'yield table' approach developed and became the signature of modern forestry (see Figure 1).

Nowadays, some of the historical forest data sets used in yield tables have grown to 250+ years of continual record. It was found that on a given kind of site (same soils, same rainfall, etc.) trees grew to the same height at a given age, regardless of density of trees. At low densities, one might find trees with large diameters and crowns and on an equivalent high-density location the trees would have small diameters and crowns - but the heights of the trees would be the same in both cases. In a yield table, decades and sometimes centuries of forest stand data are arranged by the height the trees at a given location reach at a given age, usually the typical age of tree harvest. The tree height at this standard age is called a 'site index' and is used to signify the overall quality of a location for growing trees. Site index is clearly defined in terms of the basic data that goes into a yield table and it can be directly determined by measuring the heights of trees on even-aged stands at the reference age.

Associating site index with actual plots of land is a learned skill and an art at the same time. A capable site surveyor can judge site index by reconnaissance of land in a particular region and can make a good wage practicing this trade. Along with such arcane practices as axe-throwing, log-rolling, and tree-felling, forestry schools have regular intercollegiate competitions of judging site indices among their students as part of 'Forestry Field Day' celebrations. At the edge of virtually all universities with a college of forestry, one will find plat of trees planted at different densities for field teaching on the calibration of yield tables. The yield table concept is the quantitative basis of modern forestry.

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Volume of wood (m3) per hectare for locations with different site indices

Number of trees per hectare for locations with different site indices

Volume of wood (m3) per hectare for locations with different site indices

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Number of trees per hectare for locations with different site indices

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Figure 1 Sections of stand yield tables for Switzerland. The site index is the height of the dominant trees in even-aged stands of spruce (Picea abies) at an age of 50 years. Note that this data set covers 120 years of measurement. The amount of wood (a) in a forests increases with age and slows in its rate of increase over time. Sites with higher site indices have more wood at any given time. The thinning of trees (due to suppressed trees being eliminated by more vigorously growing taller trees) slows over time (b) but is stronger in locations with higher site indices. Reproduced from Erragstafeln: Fichte. Eidgenössische Anstalt fur das forstliche Versuchswesen. Birmensdorf ZH, with permission from Swiss National Forest Inventory.

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