Stocking, density and competition©

a quantitative measure of tree cover on an area, i.e., the amount of tree material per unit area or space.

Many foresters use the terms stand density and stocking synonymously. Conventionally, measures of stand density are accepted as being absolute and unaffected by management objectives. In contrast, stocking historically involves comparison of a given stand with some established norm, e.g., one established with a particular purpose of management in mind. Thus, stands are described as overstocked, 50% stocked, understocked, etc.

Because they are absolute, measures of stand density are more precise and more useful in analysis and estimation of forest growth and yield than stocking. Stand density is important in forestry because, within limits, the more growing space made available to a tree, the less competition it will face and the faster it will grow. Thus, an important role of the forester is to regulate stand density through initial planting spacing, thinning and other silvicultural practices.

Estimates of stand density are made to express the degree to which the growing space available for tree growth is utilised. Thus, stand density is a function of three elements:

1. Number of trees - which is readily determined by counting.

2. Tree size - which involves a number of factors, e.g.:-
   • Stem - characterised by diameter, height and taper
   • Crown - characterised by spread and depth
   • Root - characterised by spread and depth (both difficult to measure).

3. Spatial distribution on the ground - which is not readily determined. Generally, a square or triangular spacing is assumed.

Drew and Flewelling (1977, 1979 - For. Sci. 23 and 25) define maximum density:

as the density at which a stand undergoes substantial and continuing mortality induced by competition.

Changes in density may affect both the timber yield from a site and the sizes of the individual trees on it. The effects can be measured in either absolute or relative terms. Because efficient management of a forest necessitates careful regulation of stand density, there is a need to describe it quantitatively. This is done by the use of what are termed stand density indices.

Stand Density Index

• The variable used as the index should be simple and easily measured and applied in practice.

• The index should imply the same thing to all people, and the different amounts of tree material they are variously interested in (tree biomass, foliage weight, sawlog content, etc.) should all be derivable from the index.

• The index should be independent of age and site. Stratification of stands based on density as well as age and site will not improve volume estimates if the index of density is correlated with age and site.

• Variation in the index of density of a stand should be reflected in a difference in growth behaviour. It should also reflect differences in growth behaviour between stands.

• The index should be a variable which lends itself to forward projection, e.g. future yield is likely to be affected by the density at a future time which will be a reflection of the present density.

• Ideally, the index should be applicable to any kind of stand, even-aged or uneven-aged, single or mixed species.

The measures of stand density fall into two classes - biological and practical.

• Biological measures: These aim to describe the stand and reflect its growth behaviour.

• Practical measures: These are those used as a basis of for regulating stand density, e.g. indices derived essentially for the practical purpose of implementing a thinning schedule.

Indices

• Number of trees;
• Number of trees and dbhob;
• Number of trees and height;
• Number of trees, dbhob and height.

Number of trees

Stocking is a practical index of density for regulating stands of a specified species, age and site where the desirable number of trees per unit area at a given stage of development is known from past experience or research. Generally, however, number of trees must be combined with tree size to be a satisfactory measure of density.

Number of trees and dbhob

Stand basal area is another index incorporating number of trees and dbhob. The basal area of a stand of a given age varies with species for a given site and with site for a given species. However, for certain species, the basal area of stands on particular sites may be reasonably constant over a considerable period of development of the stand particularly towards maturity. Under this condition, stand basal area is a good measure of the maximum occupancy of the site and thus of stand density.

Stand basal area is widely used in the management of even-aged stands for a number of reasons, viz. it is a practical index of stand density; it is easily measured; it is the natural base for deriving stand volume; and volume increment and basal area increment are usually well correlated. Another index in this category is the crown competition factor (CCF). Leech (1984) demonstrated that crown width (CW) in open grown P. radiata in South Australia is linearly related to tree dbhob (d) viz.,

CW  =  0.7544  +  0.2073 d
      (0.0848)   (0.0032)

Leech used this model to calculate the CCF of P. radiata stands. Given an area of A hectares with a total stocking of N trees:

 CCF = 1/A [ 0.004 470N + 0.002 456 Sum(d) + 0.000 337 5 Sum(d^2) ] 

Leech suggests that the CCF should be a useful variable in growth and yield studies of radiata pine for it is independent of age and site.

Note that number of trees in relation to mean tree dbhob has often been used as a 'rule of thumb' method of thinning, e.g.,

Required spacing between trees (m) = 0.1 d (cm) +/- k.

Crown cover is another index incorporating number of trees and dbhob (through the crown diameter/dbhob relationship). The vigour of tree crowns is partly related to aerial growing space so crowns might be expected to reflect the density of a stand. Another is crown closure (also termed canopy closure), which is the ratio of the projected horizontal crown area to the total horizontal ground area, is used as an independent variable in aerial stand volume tables. Strictly speaking, it is an index of 'area occupation' rather than stand density.

In even-aged stands, crown closure may be proportional to basal area/ha. This relationship has led to the development of indices between estimates of crown closure obtained from aerial photographs and basal area. The value of crown closure as a variable depends on how well variation in stand volume is correlated with it: root space may be more important than crown space in determining stand growth!

Number of trees and height (Hart's Index)

HSR  =  H/S, thus S = H/HSR                                         
where	HSR is the height/spacing ratio;
	H is some index of stand height (mean height, predominant height, top height, 	etc.);
and	S is the average spacing between trees. 

It incorporates the number of trees per unit area and may be based on a triangular spacing (Holland) or square spacing (UK).

H should effectively reflect the site/age relationship because as site quality and age increase, spacing should increase. For this reason, predominant height (or top height) is the commonly used stand height index.

Number of trees, dbhob and height

Stand Bole Area:

The total bole area for all trees in a stand represents the base for potential increase in stand volume, therefore tree and stand bole areas should be variables of particular interest to foresters. Surprisingly, little attention has been given to them.

Most work on bole area has been done by Lexen (J. For. 41:883-5, 1943). Lexen's argument is that stand volume only provides a measure of wood capital and not of the potential of the stand to grow. He suggested that estimates of stand volume should be supplemented by estimates of stand bole area.

For the individual tree, bole area can be estimated by substituting girth for sectional area in Huber's or Smalian's formulae, or plotting girth against height on rectangular co-ordinate paper, and square counting. Lexen compiled bole area tables for P. ponderosa based on dbhob and height. He found that bole area of the individual stem could be approximated by applying the formula:

B = k dh
where   d is dbhob(ins)
h is total height (ft)
and k = 1/7 or 0.143 (= 0.0172 metric.  Metric = Imperial x 12/100).

SBo.A (m2) = Stand mean d (cm) x Stand mean h (m) x No. of trees x 0.0172

Stand Volume:

Other Measures of Stand Density

In recent years many attempts have been made to describe such relationships by equations. Many indices of density have been tested in these equations, the efficiency of a variable as a measure of density being judged mathematically by its contribution to the correlation. Almost invariably, basal area (G) has emerged as the most satisfactory variable. West (1983), in a detailed study of 17 measures of stand density in even-aged regrowth eucalypt forest in southern Tasmania, concluded that the more complex measures were no better than the simpler ones, e.g., G.

Point Density

The 'angle summation method' of Spurr (For. Sci. 8: 85-96, 1962) is an example of one technique giving a measure of point density. The method involves choosing a point or tree upon which we wish to determine the degree of competition from surrounding trees. Using the basic theory of Bitterlich (angle count sampling) each competing tree is imagined to be 'borderline' from the chosen point or tree and, thus, to have a specific basal area factor. The point density measure is obtained by appropriately summing a series of basal area per hectare estimates made using these trees.

Formula:

Point density (m2/ha) = [0.25(0.5(d1/l1)2 + 1.5((d2/l2)2  + .. +(n-0.5)(dn/ln)2 )]/n    

where: 	di is diameter in cm of tree i; (i = 1, ...., n).
	li is the distance in metres of tree i from the sample point or subject tree;
	n  is the number of competing trees measured.

References

Leech, J.W. 1984. Estimating crown width from diameter for open grown radiata pine trees. Aust. For. Res. 14: 333-337.

Nishizawa, M. 1968. "Measures of competition and stand density for individual trees of P. radiata". F.R.I. Management Report No. 14, N.Z. For. Service.

Spurr, S.H. 1952. "Forest Inventory", Chp. 19. West, P.W. 1983. "Comparison of stand density measures in even-aged regrowth eucalypt forest of southern Tasmania". Canad. J. For. Res. 13(1):22-31. (This is an excellent article on the subject).

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