Stand Structural Diversity
Objectives
- To define stand structural diversity
- To distinguish between vertical and horizontal structural patterns
- To introduce and evaluate methods of calculating structural diversity
- Concepts
Stand structure -- the arrangement (distribution pattern) of trees in space (horizontal and vertical components) within a stand
Stand structural diversity -- variability among trees vertically and horizontally within a stand.
- Vertical distribution patterns
a) Defining patterns
Single-storied/normal distribution - trees of medium size have the highest frequency
Multi-storied/inverse J distribution - the smaller trees have the higher frequency
Two-storied/bimodal distribution - frequency peaks at two size classes
Multi-storied/irregular distribution - frequency peaks at three or more size classes but not an inverse J distribution
b) Quantifying vertical structure
Two types of methods have been frequently used in literature to quantify stand vertical structure. One originates from the Shannon-Weiner index approach (Shannon and Weaver 1949). The other uses the concept of variability of tree size (height and/or DBH) (Zenner 2000; Staudhammer and LeMay 2001).
With the Shannon-Weiner index approach, tree size is classified into discrete classes. For example, DBH or height can be classified into 5-cm or 5-m classes. Stand structural diversity index (H') can be calculated as
(1)
where pi (i = 1, 2, 3,…n) is the proportion of individuals in the ith height or DBH class. The proportion of the height or DBH classes has been based on a variety of variables including number of individuals, basal area, etc. If number of individuals is used to calculate proportions, the maximum H' occurs when number of individuals is evenly distributed among height or DBH classes. When basal area is used to calculate proportions, the maximum H' occurs with an inverse J frequency distribution. Classification of tree size (height or DBH) into classes has been criticized because it is somewhat arbitrary and results in loss of information (Staudhammer and LeMay 2001).
Variance (S2), measuring tree size variation in a stand, can be calculated as
(2)
where xi is height or DBH for ith tree; is the mean of xi in the stand. The above equation can be further modified to account for differences in basal area between different tree sizes (see Staudhammer and LeMay 2001).
- Horizontal distribution patterns
a) Defining patterns
Random (Poisson) - location of any one tree does not influence the location of another individual
Clumped or aggregate or underdispersed - presence of an individual increases the chance of another nearby
Uniform or regular or hyperdispersed - presence of an individual decreases the probability of another individual of very nearby or far away
b) Quantifying horizontal structural patterns
Analysis of horizontal structure requires mapping of trees in a stand and assigning co-ordinates to each stem. The most commonly used statistical analysis is the Clarke-Evans aggregation index (Clark and Evans 1952). It relates the observed mean distance of all trees to the respective nearest neighbors, to the mean distance expected under a random (Poisson) spatial distribution. The expected distance (Dexp) to the nearest neighbor is related to the actual number of trees in the test area by:
(3)
with a standard error (Dse) calculated as
(4)
Observed mean distance (Dobs) from each individual to its nearest neighbor (di) is
(5)
Statisitcal test for significant deviation from a random pattern is
(6)
where n = the number of trees in the test area, A = the area of the test plot in square metres. If C< 1.96, trees are considered randomly spaced, C values below –1.96 indicate a clumped pattern, and C values about 1.96 a uniform pattern. Modification of the Clark and Evans' method to correct for irregularly shaped plot boundaries was discussed by Zenner (2000). Examples to calculate the Clark and Evans' index are provided in Appendix 1.
- Quantifying stand structure in three-dimensional space
A three-dimensional approach, called Structural Complexity Index (SCI), was proposed by Zenner (2000). Trees in a stand are represented as three-dimensional irregularly spaced points (x, y = horizontal coordinates, z = tree sizes such as heights or DBHs). Three horizontally adjacent points in this x, y, z space can be connected to form a triangular surface. When extended across a stand of trees, they form a network of non-overlapping triangles.
The SCI is defined as the sum of the surface areas of all triangles (ATi) divided by the horizontal ground area covered by all triangles (Ai) in a stand.
(7)
This method allows the comparison of stands based on the distribution of size differences of neighboring trees. The larger the SCI, and the more complex the structure. Theoretically, if there are three stands, one with a clumped horizontal structure, one random, and one uniform in which trees have exact the same heights in each respective stand, what would their SCI values be?
E. References
Clark, P.J., and F.C. Evans. 1952. Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35:445-453.
Shannon, C.E., and W. Weaver. 1949. The mathematical theory of communication. University of Illinois Press, Urbana, Illinois.
Staudhammer, C.L., and V.M. LeMay. 2001. Introduction and evaluation of possible indices of stand structural diversity. Canadian Journal of Forest Research 31:1105-1115.
Zenner, E.K. 2000.Do residual trees increase structural complexity in Pacific Northwest coniferous forests. Ecological Applications 10:800-810.
Appendix 1. Examples for calculating horizontal structure.
Tree No. / Observed distance to nearest neighbor (m)Stand 1 / Stand 2 / Stand 3
1 / 1.5 / 0.5 / 2.5
2 / 1.8 / 0.7 / 2.5
3 / 1.1 / 0.5 / 2.5
4 / 1.3 / 1.0 / 2.5
5 / 2.4 / 0.8 / 2.5
6 / 1.4 / 0.5 / 2.5
7 / 1.3 / 0.6 / 2.5
8 / 1.2 / 0.9 / 2.5
9 / 1.4 / 1.0 / 2.5
10 / 1.5 / 0.6 / 2.5
11 / 0.9 / 0.8 / 2.5
12 / 1.4 / 1.0 / 2.5
13 / 1.5 / 0.6 / 2.5
14 / 1.7 / 0.5 / 2.5
15 / 2.0 / 1.0 / 2.5
Dexp / 1.291 / 1.291 / 1.291
Dse / 0.176 / 0.176 / 0.176
Dobs / 1.493 / 0.733 / 2.500
C / 1.147 / -3.162 / 6.854
Classification / Random / Clumped / Uniform
Note: Plot area is 100 m2.
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