The concept of structural diversity
Jürgen Böhl and Adrian Lanz
Swiss Federal Institute for Forest, Snow and Landscape Research.
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Abstract
Silvicultural practices are developing towards sustainable management in many countries.
Environmental and other services provided by forest ecosystems have a significant
importance for society. As a result, the idea of a sustainable and multi-functional forestry has
almost replaced the understanding of forests as a source for timber. The Ministerial
Conference on the protection of forests in Europe (MCPFE) developed criterions for
sustainable forest management. Among these is the conservation of biological diversity in
forest ecosystems.
This paper defines structural diversity as the combination of tree species diversity and tree
heightclasses and introduces the reader to the concept of structural diversity as a possible
indicator for biodiversity of forest ecosystems.
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Introduction
Biodiversity is defined by the Rio declaration in 1992 as “the variability among living
organisms from all sources” and “the diversity within species, between species, and of
ecosystems”. This global definition makes monitoring biodiversity a challenge, since many
aspects of a given ecosystem have to be taken into account.
The term “diversity” is clearer defined. Kimminis (1987) gave a rather narrow definition that
diversity covers species richness and dominance in a system. Nagel (1976) described the
demands on a diversity measure by the example of species diversity.
1.
If a system contains only one species, the species diversity equals zero
2.
The maximum species diversity in a system occurs, if by given number of species n
all species are equally frequent
3.
Given two systems with equal distribution of species, species number n and species
number n-1, the species diversity of the system with species number n must be higher
4.
If there are multiple independent varying elements, the diversity of a pool of elements
must equal the sum of the diversities of the elements
In this paper, we define structural diversity as the combination of tree species and tree
heightclasses and we identify a diversity index that fulfils the demands described by Nagel
(1976) to measure structural diversity.
Structural diversity
The Shannon-Index (H’) determines diversity in a system using the number of appearing
types of a certain characteristic (for example tree species) and their frequency (Shannon,
1949). An increase of the number of types leads to a higher value of the index. The
maximum index value of H’ is reached, if the relative frequency pi is the same for all
appearing types. Pielou (1975) proved that the Shannon – Index fulfils the demands of a
diversity measure as stated by Nagel (1976).
n
H '( p1 , p2 ,..., pn ) = − ∑ pi ln( pi ) (1)
i =1
If we understand diversity in terms of structure, the structure of a given system is certainly
better described by more than one characteristic. This leads to the combined Shannon –
Index (H’1/2) for two appearing characteristics i and j in a system (for example tree species
and tree heightclasses).
n
n
H '1/ 2 = − ∑∑ pij ln( pij ) (2)
i =1 j =1
H’1/2 may be hard to interpret. A rise in index values can originate from only one of the
considered characteristics or from both. This leads to the Transinformation (T), which allows
an interpretation of H’1/2 (Nagel, 1976).
T = H '1 + H '2 − H '1 / 2 (3)
T is in the same unit as the index itself. To get a better measure for comparison reasons, T is
equalized by its maximum value. This leads to the Interconnection Coefficient (K).
K=
2T
H '1 + H '2
(4)
K is a number between 0 and 1. K = 1 means the characteristics are ideal coupled. If K = 0
there is no connection between the characteristics. With K*=-K+1, K* increases as the
structure of the system becomes more diverse.
Example
Figure 1 and Table 1 give an interpretation example of the introduced indices. If we only look
at the indices H’species and H’heightclass we are not able to find differences in the two forests A
and B. Intuitive speaking, forest B appears to be more divers than forest A. H’species/heightclass
gives a possibility to order the forests A and B in terms of structural diversity. If we interpret
H’species/heightclass together with K*, we can also see the reason for the higher value of the
diversity index H’species/heightclass. The conclusion of this example is that forest B is more diverse
than forest A, because the two elements height and species are not coupled.
In the example, the concept of quantifying structural diversity for comparing two different
forest stands has been illustrated. In analogy, it is also possible to analyze changes of
structural diversity by comparing the same stands at two different points in time.
A
B
Figure 1:
Interpretation of indices on two hypothetical forest stands. In both stands we
find only two species and only two heightclasses. The values of the indices are printed in
Table 1.
Since in forest A the tree height is coupled with species, T equals H’species/heightclass. For the
same reason K* equals zero. In forest B T is zero, since H’species/heightclass is the sum of H’species
and H’heightclass.
Table 1:
Values of the diversity indices for the two forest stands in Figure 1; Forest B is
more diverse than forest A, because the characteristics tree species and tree heightclasses
are not coupled.
H’species H’heightclass H’species/heightclass T
K*
A
0.69
0.69
0.69
0.69
0
B
0.69
0.69
1.38
0
1
Conclusions
The combined Shannon-Index (H’species/heightclass) is an abstract measure of diversity and lacks
of a direct ecological interpretation – as for example the number of species. However, the
abstract measure can be used to order different communities or the same community in
different points in time in terms of more or less diverse.
Next step: application and test with Swiss National Forest Inventory data.
Reference
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Neumann, M. and Starlinger, F. (2001) The significance of different indices for stand
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