For example, dominance of a stand by many small-diameter trees would suggest that the stand has only recently been established, perhaps following some form of disturbance event. Alternatively, presence of some very large diameter trees with representation of trees in smaller diameter classes might be interpreted as mature or ‘old-growth’ forest, within which continuous recruitment is taking place (Spies 1997, Spies and Turner 1999). However, it should be noted that the size and age of trees are not necessarily closely related. Trees growing on adverse sites or subjected to a high intensity of browsing can grow very slowly, leading to much greater variation in age than in size. Stands that appear to be even-aged on the basis of their diameter distributions may in fact have been recruited over a prolonged period.
For this reason, caution should always be exercised when interpreting diameter measurements in terms of ages; ideally both age and size should be measured.
Uneven-aged stands are typically characterized by the presence of a large num- ber of trees in smaller-diameter size classes with decreasing frequency as the size class increased. This form of size–frequency relationship is often referred to as an
‘inverse-J’ shape (Figure 3.12) and is often an objective of approaches to sustain- able forest management. If a particular tree species displays such a size distribution, then continuous recruitment can generally be inferred, suggesting that the popu- lation is viable as sufficient regeneration it taking place for the population to be maintained. Techniques for studying forest dynamics and the population viability of tree species are described in detail in Chapters 4 and 5.
Stand diameter distributions can be represented mathematically by probability density functions. A number of different functions have been used, including normal, exponential, binomial, Poisson, Pearl, Reed, Schiffel, and Fourier series (Husch et al. 2003). Details of the use of these functions are provided by Johnson
100 80 60 40 20
0 1 2 3 4 5 6 7 8 9 10 11 12 Size class
No. individuals
Fig. 3.12 Inverse-J structure of a forest stand, illustrated by plotting the number of individuals in each size class. The inverse-J structure is characterized by larger numbers of smaller individuals than of larger individuals. (After Peters 1994, http://www.panda.org.)
(2001) and Schreuder et al. (1993). The most widely used function in relation to analysis of forest stand data is the Weibull function (see, for example, Soehartono and Newton 2001), which can be expressed as follows (Husch et al. 2003):
where f(D)is the probability density, ais a location parameter (theoretical mini- mum population value), bis a scale parameter, cis a shape parameter, and Dis the diameter.
The Weibull function can exhibit a variety of different shapes depending on the value of c(Husch et al. 2003):
● c1, inverse J-shape
● c1, exponential decreasing
● 1c3.6, positive asymmetry
● c3.6, symmetric
● c3.6, negative asymmetry.
The parameters of the Weibull distribution can be derived directly from diam- eter measurements. Parameter ais usually set to the smallest value of diameter observed. An algorithm for recovering the other two parameters of the function is provided by Burk and Newberry (1984).
3.7.2 Height and vertical structure
The vertical structure of a forest stand refers to its structural complexity, which is influenced by the presence of different plant life forms (such as vines and epi- phytes), the arrangement of leaves on branches, and the amount and distribution of leaves, branches, and twigs, at different heights (Brokaw and Lent 1999).
Vertical structure has a major influence on the provision of habitat for wildlife.
Quantitative methods for assessing vertical structure in this context are described in Section 7.3.
Foresters traditionally classify the crown position of trees according to the fol- lowing simple scheme (Oliver and Larson 1996):
● dominant, where tree crowns extend above the general canopy level and are not physically restricted from above
● co-dominant, where crowns form the general level of a forest canopy and are somewhat crowded by other adjacent trees
● intermediate, where trees are shorter, but their crowns extend into the general canopy that is primarily composed of the crowns of dominant and co-dominant trees
● suppressed(overtopped), where crowns lie entirely below the general level of the canopy and are physically restricted from above.
This classification is subjective, and can be difficult to apply in practice, but is widely used.
f (D)c
b
冢
Dab冣
1/ce[(Da)/b]cCharacterizing stand structure | 115
Ecologists have traditionally described the vertical structure of forest stands through profile diagrams. Some excellent examples are provided in Richards’ classic work on tropical rain forests (Richards 1996). The method involves marking out a rectangular strip of forest, typically at least 60 m long with a width of 10 or 20 m.
The positions of all trees above 5 m height are then mapped and their diameters recorded. Height and crown width are then recorded by using the methods described above. These measurements are used to produce a diagram of a vertical section through the forest. Richards (1996), who was one of the people responsible for developing the method, was well aware of its limitations: it is difficult to select a site that is truly representative of a particular forest, and it is of limited value as a source of quantitative information. However, profile diagrams do capture something of the vertical structure of forest stands, and are an effective way of illustrating its complexity.
Average canopy height can be obtained by calculating a mean value of all trees, or a sample of trees in the stand. Mean values can be weighted according to the position of trees in the canopy, for example whether they are classified as dominant or co-dominant, or according to their basal area (Husch et al. 2003).
3.7.3 Leaf area
Measurements of leaf area may be expressed as a quantity (m2), or more typically, asleaf area index(LAI), which is the leaf area per unit ground area, usually defined in units of m2m–2. LAI is an important structural attribute of forest ecosystems because of its role in influencing exchanges of energy, gas, and water and physio- logical processes such as photosynthesis, transpiration, and evapotranspiration. It is therefore very widely used in ecophysiological investigations. As noted in Chapter 2, LAI can be estimated from remote sensing data, and is also an import- ant component of many process-based models of forest dynamics (Chapter 4) (Running et al. 1989, Chen and Cihlar 1995).
In the field, LAI can be estimated by using a wide variety of different instru- ments and techniques. These have been reviewed by a number of authors (Chason et al. 1991, Larsen and Kershaw 1990), and most recently by Bréda (2003), who noted that LAI is difficult to quantify because of large spatial and temporal vari- ability. Methods developed for estimating LAI may be grouped into direct and indirect methods.
Direct or semi-direct methods described by Bréda (2003) include:
● Direct measurement of leaf area, using either a commercially available leaf area meter or a defined relation between leaf area and some other measured variable. In the latter approach, leaf area is typically measured on a subsample of leaves and related to dry mass—viaspecific leaf area(SLA, cm2g–1), for example—then the total dry mass of leaves collected within a known ground- surface area is converted into LAI by multiplying it by the SLA.
● Relation between foliage area and sapwood area. This is based on the hypothe- sis that leaf area is in balance with the amount of conducting tissues, and
therefore allometric relations can be developed. Because of the difficulties of measuring conducting area, sapwood area is often replaced by more readily measured variables, such as dbh. Estimating allometric relations through destructive sampling is generally a reliable method of deriving LAI for a given experimental site, but different relations may need to be established for different years. Examples of this approach are provided by Medhurst and Beadle (2002) and Pereira et al. (1997).
● Collection of leaf litter. In deciduous stands, leaves can be collected in traps of known collecting area distributed below the canopy during leaf fall. Litter should be removed from the traps at least every second week to avoid losses and decomposition. Collected litter is dried (at 60–80 C for 48 h) and weighed, and the dry mass of litter calculated as g m–2. Leaf dry mass at each collection date is converted into leaf area by multiplying the collected biomass by the SLA. LAI is the leaf area accumulated over the period of leaf fall. As leaves can be sorted, litter collection enables the contribution of each species to total leaf area index to be assessed. The depth of fresh leaf litter can also be assessed by using a point quadrat method, by inserting a needle into the litter layer and counting the number of leaves that it touches.
Indirect methods infer LAI from measurements of the transmission of irradiance through the forest canopy, and are based on statistical descriptions of the arrange- ment of leaves. Two main approaches may be differentiated: radiation measure- ment methods, which assume that leaves are randomly distributed within the canopy, and ‘gap fraction’-basedmethods that are dependent on estimating leaf angle distributions (Bréda 2003). Radiation measurement methods require meas- urement of irradiance both incident on the canopy and below the canopy; LAI is calculated from an extinction coefficient which is influenced by the total leaf area present within the canopy, as well as by canopy architecture and stand structure.
Further details of these methods, including the analytical equations used in LAI estimation, are presented by Bréda (2003). A number of commercial sensors are available that use gap fraction-based methods of estimating LAI (Table 3.1).
Although it should be noted that these sensors were primarily developed for use with crop plants, they may also be adapted for use with forest canopies.
A further indirect method involves the use of hemispherical photographs, with supporting digital analysis. The use of hemispherical photographs to characterize forest light environments is considered further in section 4.5.2.
Comparisons between direct and indirect methods indicate a significant under- estimation of LAI by the latter techniques in forest stands, mainly because of clumping of leaves and the contribution of stem and branches. Reports indicate that the degree of underestimation varies from 25% to 50% depending on the characteristics of the stands. The sampling strategy adopted also has a major influ- ence on the accuracy of the results, as the spatial heterogeneity of forest canopies is often very large (Bréda 2003). However, direct methods are all very labour-inten- sive (Fassnacht et al. 1997) and require many replicates to produce a precise result;
they are therefore costly in terms of time and money.
Characterizing stand structure | 117
3.7.4 Stand volume
Measurement of the volume of wood produced by a forest stand is of fundamental importance to forestry, and consequently foresters have developed a variety of methods for estimating it. Particular efforts have been directed towards developing functions for stem volume and taper that allow estimates to be made from rela- tively simple measurements. Details of these functions are provided by Avery and Burkhart (2003), Husch et al. (2003), and West (2004). Stem volume is less important to forest ecologists, but as it is used for estimation of stem biomass and carbon content, a brief overview of the principal methods used in volume estima- tion is presented here (see also section 7.2).
The main method used to measure tree stem volume is the sectional method, which involves measuring the stem in relatively short sections, determining the volume, and each then summing these values to produce an estimate of total volume (West 2004). The volume of a stem section is determined by measuring its length, and the stem diameter at the lower end of the section (‘large end diameter’), the upper end (‘small end diameter’) and/or at the midpoint of the section. These measurements are used to estimated volume by using one of three formulae (West 2004):
● Smalian’s formula:
VSl
(
dL 2dU2
)
/8Table 3.1 Characteristics of four commercially available sensors that can be used for indirect estimation of LAI (adapted from Bréda 2003).
Principle Sensor Company URL
AccuPAR Gap fraction 80 PAR sensors Decagon www.decagon.com or sunflecks distributed Devices,
along a Pullman, USA 0.90 m rod
DEMON Gap fraction Detector CSIRO, www.cbr.clw.csiro.au/
zenith angles sighted at Canberra, pyelab/tour/demon.htm from the sun the sun Australia
at different angles to the vertical
LAI-2000 Gap fraction Fish-eye Li-Cor, www.licor.com for each sensors with Lincoln,
zenith angle five concentric Nebraska, acquired rings of sensors USA simultaneously
SunScan Gap fraction 64 PAR sensors Delta-T www.delta-t.co.uk or sunflecks distributed Devices Ltd.,
along a 1 m rod Cambridge, UK
● Huber’s formula:
● Newton’s formula:
where VSis the volume of a section of a stem, lis the length of the section, dLis the stem diameter at the lower end of the section, dUis the diameter at the upper end of the section, and dMis the diameter midway along the section.
These formulae provide accurate estimates of stem volume so long as the stem is circular in section or the stem is shaped in the form of a quadratic paraboloid.
A variety of stem taper functions have been developed to accurately describe stem shape, but for most tree species the quadratic paraboloid is a reasonable approxi- mation to the actual shape of tree stems, and for this reason these three functions are still in widespread use (West 2004). Of the three, Newton’s is generally the most accurate because it uses the most information in the calculation.
Most measurements of tree stem volume use section lengths of 0.5–1 m for large trees; shorter lengths are used for smaller trees. Stem diameters can be measured by the methods described in section 3.6.2.
‘Importance sampling’ or ‘centroid sampling’ methods offer an alternative to the sectional method. These methods require the stem dbh to be measured (D0) together with total height (H). A further measurement of stem diameter is required high on the stem (D1). The location of this measurement point can be selected by either importance sampling or centroid sampling approaches. These involve application of the following formulae.
First, the value Kis determined as:
where HLis the lower height and HUis the upper height of the stem section for which the volume estimate is required. The height at which the required upper stem diameter is to be measured (HS) is then determined as:
If importance sampling is used, then Nis a randomly selected value in the range 0–1. If the centroid method is used, then N0.5 (the centroid being the position along the stem section above which half of the section volume lies) (West 2004).
Once HShas been determined, the diameter at that height must be measured (DS), by using one of the methods in section 3.6.2 (such as an optical dendrome- ter). The stem volume (VLU) between HLandHUcan then be determined as:
This method is relatively simple, as it requires few diameter measurements to be made. The entire stem can be treated as a single section, or it can be divided into a
VLUK
(
DSDI/DO)
2/[
8(
HHS)]
HSH兹
(
HHL)
2NK K2H(
HUHL)
HL2HU
2
VS/
(
dL24dM
2dU
2
)
/24VSl dM 2/4
Characterizing stand structure | 119
series of sections and estimates obtained for each. Care should be taken to measure upper diameters accurately, and measurements should be made above any but- tresses or stem swelling present near the base of the tree.
3.7.5 Stand density
Stand density refers to the number of trees within a given area. This can be most simply obtained by counting the number of trees present within a stand and measuring its area, then dividing the former by the latter. However, basal area and the extent of crown cover can also be used as measures of stand density. Stand density is of great importance to forest management, primarily because of its importance in determining the volume of timber likely to be obtained from a particular stand. Consequently foresters have developed a range of metrics for describing it, including various measures of relative spacing, stand density indices, crown competition factors, and stocking diagrams. Details are provided by forest mensuration textbooks such as Avery and Burkhart (2003) and Husch et al.
(2003).
As noted earlier (section 3.5), distance measures are often used to estimate stand density. For example, Patil et al. (1979) proposed a plant density estimator based on point-to-plant distances that produces consistent results. Barabesi and Fattorini (1995) showed for various spatial plant patterns that an improvement over simple random sampling can be achieved by estimating plant density by a ranked set sampling of point-to-plant distances.
Two main issues should be borne in mind when measuring plant density (Bullock 1996). First, it may be difficult to differentiate individuals of clonal plants; in such cases, the number of ramets (i.e. shoots or stems) tends to be counted, rather than the number of genets (i.e. distinct genotypes, which usually can only be differentiated if information from molecular markers is available; see section 6.5.1). Second, measures of density that fail to take into account differ- ences in the size of individual plants may give ecologically misleading results. For example, if a herbaceous species were to be compared with a tree species, it might demonstrate a much higher density in terms of number of individuals, but be much less important in terms of its contribution to the structure of the forest stand. For this reason, combined measures of density and plant size are often pre- ferred. The commonest of these is cover, which is a measure of the above-ground parts of the plant (such as the tree canopy) when seen from above (for methods of estimating canopy cover, see section 3.6.4; methods for assessing the cover of understorey vegetation are described in section 7.7).
The 3/2 law of self-thinning has attracted a great deal of interest from both foresters and ecologists, because it is one of those rare things in ecology—a straight line. Usually, the logarithm of mean tree volume or mass is plotted against the logarithm of the number of trees per unit area. For stands undergoing density- dependent mortality (‘self-thinning’), the slope of the line is approximately 3/2 (Kershaw and Looney 1985).