There are two main types of sampling unit that might be selected. The common- est approach is to use a fixed areamethod, which involves establishment of a field plot that may be square, rectangular, or circular in shape. Alternatively, a distance- basedsampling approach might be adopted, where the area sampled varies but the number of individuals sampled is fixed. These two approaches are considered in the following sections, followed by an evaluation of their relative merits. In add- ition, line transects are briefly considered. Examples of the application of different Sampling approaches | 93
Fig. 3.3 A differential GPS system. The antenna and GPS receiver are illustrated here. A reference station is also required (not illustrated), which consists of an additional GPS receiver and antenna. Such systems can provide location data with an accuracy of a few centimetres. However, accurate measurements may be difficult to obtain under a forest canopy. This instrument is manufactured by Leica Geosystems AG of Switzerland. (Photo by Harry Manley.)
sampling units to the assessment of tropical forest are provided by Dallmeier and Comiskey (1998a,b).
3.5.1 Fixed-area methods
● Circular plotsare widely used because a single dimension (the radius) can be used to define the perimeter (Husch et al. 2003). They can be established relatively easily, and are readily marked through use of a single post, stake, or other form of marker (although they may be more difficult to relocate in future, for the same reason). Plots may range from 10 to 10 000 m2in area. In general, smaller circular plots are more efficient than larger ones (Husch et al.
2003). The main problem with this shape of plot is the accurate determin- ation of the plot boundary. The best approach is to extend a tape measure from the centre of the circle, or use an electronic measuring device. Beers (1969) describes a method for establishing circular plots on a slope (which are elliptical in horizontal projection).
● Square plots offer an advantage over circular plots as the boundaries are straight lines, making it easier to determine whether or not an individual tree falls within the plot. To ensure that the corners of the plots are right angles, a compass or right-angle prism should be used. Plot limits can be established by measuring diagonals from the centre of the plot. As with circular plots, areas may vary from 10 to 10 000 m2; for ecological surveys, plots of 1 ha in area or less are typically used.
● Rectangular plotsare usually established by measuring distances from the cen- tral axis. Rectangular plots may be preferable in forests with difficult topog- raphy and large altitudinal variation (Husch et al. 2003). The word stripis sometimes used to refer to long rectangular plots. Although a strip may be divided into smaller subplots, the entire strip is equivalent to a single sampling unit, and for this reason separate smaller plots are generally preferred to strips as they provide greater statistical power for the same amount of effort.
Within fixed-area plots, different size classes of trees are sampled in proportion to their frequency. In natural forests, the number of smaller trees is often much larger than the number of large ones, and can take a great deal of time to measure.
Generally some form of subplot is used to sample the smaller trees, which is typ- ically nested within the larger plot. In circular plots, subplots can be established as concentric circles. For example, a plot design with concentric circles of 16, 64, 255, and 1018 m2can be used to measure seedlings, shrubs, small trees, and large trees, respectively (Husch et al. 2003). Similarly, in square plots, nested square sub- plots tend to be used. For example, within a 1 ha plot (100100 m) all large trees might be measured, whereas young trees could be surveyed in a subplot 2020 m, and seedlings within a subplot of 1010 m or 55 m, typically located in the corner of the main plot. Subplots do not necessarily have to be the same shape as the larger plot, and can be arranged according to a variety of fixed designs (Husch et al. 2003).
Krebs (1999) points out that the ratio of the length of edge of a plot to the area enclosed inside it varies with shape, as follows:
circle square rectangle
The edge effect is important because it can lead to counting errors, which can arise because it is sometimes difficult to determine whether an individual tree is inside a plot or not. Such errors are fewer in circular plots. However, in some studies longer, thinner (rectangular) plots may be preferred because they include greater habitat heterogeneity.
3.5.2 Line intercept method
This method has been widely used by ecologists for measuring the cover of plants along line transects (Krebs 1999). A line transectcan be established by pegging a measuring tape or cord across the area of interest. Estimates of cover are simply calculated as the fraction of the line length that is covered by the canopy of a par- ticular species. Density or abundance estimates are obtained by measuring the longest perpendicular width wfor each plant or sample unit intercepted. This width determines the probability that any individual plant will be bisected by the sampling line (Krebs 1999). Following Eberhardt (1978), population size can be estimated as:
where Nis an estimate of population size, Wis the width of the baseline from which transects begin, nis the number of transects sampled, wis the perpendicu- lar width of plants intersected, and kis the total number of plants intercepted on all lines (i1, 2, 3, . . ., k). To estimate the density of organisms for any shape of area, simply divide this estimate of numbers by the area studied (Krebs 1999). If a series of line intercepts are measured, each can be used to generate an estimate of population size, enabling confidence limits to be calculated, providing an estimate of variability.
3.5.3 Distance-based sampling
Distance sampling methods are used primarily for estimation of population dens- ities and abundances (i.e. the number of individuals of a particular species occur- ring in an area), although these methods can also be used for estimating other variables such as tree heights, basal area, and canopy cover. The methods focus on sampling a certain number of individuals, rather than a fixed area or plot. A com- prehensive description of different distance sampling methods is provided by Buckland et al. (2001) and Krebs (1999), although it should be noted that many of the methods described are more widely used for investigations of animal populations than for plants. A comparative analysis of the performance of various distance-based sampling approaches is provided by Engeman et al. (1994). Use of
N
冤
Wn冥 兺i1k 冢
w1冣
Sampling approaches | 95
these methods in forestry is described by Payandeh and Ek (1986). In each of these methods, the sampling locations should be selected by using a random or stratified random design, although Hall (1991) used a systematic design, with sample points arranged on a grid.
Distance methods most commonly used by forest ecologists include:
● Thepoint-centred quarter method, in which a sample is taken of four trees at each sample point by selecting the nearest tree within each of four 90 quad- rants around the sample point (usually defined using compass bearings) (Morisita 1954). An example is provided by Haridasan and de Araújo (1988).
Data for each sample point are pooled before analysis, by calculating the mean of the four distances from each sample point.
● Thenearest individual method, where the nearest tree to the sample point is located and the distance between it and the sample point is measured. Density of trees can be calculated according to the equation
density1/(2D2)2
where D2is the mean of the distances over all of the samples (Bullock 1996).
● Themultiple-nearest-tree technique, which is characterized by sampling multi- ple nearest neighbours to each sample point, rather than just one or four (Williams et al. 1969). Application of this method is described by Hall (1991) in montane forest in Tanzania. In this case, a sample was taken of the nearest 20 trees20 cm dbh occurring around each sample point, although results indicated that a sample of 15 trees would have provided sufficient precision.
Sample points were located 200 m apart to avoid any chance of overlap between the samples. Distances from the sample points to the trees were esti- mated by extending 50 m measuring tapes from each point.
● TheT-square sampling method, in which the distance is measured from the sample point to the nearest tree. A line is then drawn at right angles to the line from the sample point to the tree, and the nearest tree to the sample point positioned on the other side of this line is then measured (Figure 3.3) (Greenwood 1996).
● Thevariable-area transect approachinvolves extending a single rectangular plot until it includes the specified number of stems (Parker 1979). This method is considered by Engeman et al. (1994) to be the simplest and most practicable of the distance methods that they considered. Further refinements to the method are presented by Engeman and Sugihara (1998). Sheil et al. (2003) highlight some of the problems with this approach, such as the fact that transects may extend over large areas, complicating the analysis of relations between density measurements and site characteristics such as soil and topography. Sheil et al.
(2003) present a refinement of the variable-area transect method developed for rapid assessment of diversity in tropical forests, in which the sample unit is a cluster of cells, each of which is a modified variable-area transect; a set of deci- sions is used to define the sampling effort on the transects.
The following formula is used to estimate population density from data collected by the point-quarter method (Krebs 1999):
where Nis the estimate of population density, nis the number of sample points from which observations are made,and rijis the distance from random point ito the nearest organism in quadrant j(j1, 2, 3, 4; i1, . . ., n).
In methods where distances are measured between an organism and a fixed point, the following formula can be used to estimate density (Krebs 1999):
where Nis the estimate of population density, nis sample size, and xiis the distance from a random point ito the nearest organism.
For methods that calculate distances between the organism and nearest neighbours, the following formula can be used to measure density (Morisita 1957, Krebs 1999):
where riis the distance from an organism to its nearest neighbour.
For T-square sampling, the following formula can be used (Krebs 1999):
where ziis the T-square distance associated with a random point i.
Other equations for estimating densities for use with distance measures and corresponding estimates of variation are presented by Buckland et al. (2001), Husch et al. (2003) and Krebs (1999).
The use of distance (or plotless) methods to assess tree density is described by Bullock (1996), who recommends a minimum of at least 50 sample points for each estimate. He also points out one of the problems with distance measures: the sam- ple may be biased, because more isolated trees are more likely to be sampled. The T-square method can overcome this problem, and may therefore be preferred (Greenwood 1996) (Figure 3.4). Bullock (1996) also notes that it takes longer to obtain samples by using the point-centred quarter method than for the nearest- individual method, but the latter gives a more variable estimate and therefore the sample size needs to be higher for the same degree of accuracy. The techniques also work less well when rare species, which occur at very low densities, are being sur- veyed. In such cases, it can take an enormous amount of effort to locate individuals and measure distances from sample points.
N 2n
兺
(zi2)N n
兺
(ri2)N n
兺
(xi2)N4(4n1)
兺 (
rij2)
Sampling approaches | 97
3.5.4 Selecting an appropriate sampling unit
Many factors influence the choice of sampling unit, including cost-effectiveness, required accuracy and precision, resource availability, and ease of data analysis and presentation (Sheil et al. 2003). Kenkel et al. (1989) provide an overview of such factors. Most importantly, the choice of sampling unit varies with the objectives of the investigation and the characteristics of the forest being surveyed.
Establishment of field plots in forests that are dense, inaccessible, or located on steep topography can be physically very challenging; in such situations, either a small plot size or a distance-based method may often be preferred. Overall, distance-based methods tend to be faster and more efficient than establishment of fixed-area plots, but despite these advantages, the use of fixed-area plots is far commoner in forest ecology research.
Phillips et al. (2003) describe two standard plot-based methods that are widely used in tropical forest ecology, particularly for assessment of floristic diversity:
● The 1 ha method. This involves a one-time census of all stems10 cm in diameter in a 1 ha plot, which is usually square in shape.
● The 0.1 ha method.This involves sampling all stems2.5 cm diameter in 10 0.01 ha transects each of 250 m (as developed by Gentry 1982, 1988).
This method has been applied mostly, but not exclusively, in the neotropics.
Phillips notes that more than 650 0.1 ha inventories have been established in tropical forests to date, which compares with more than 700 1 ha plots surveyed throughout the tropics.
Another standard plot design particularly used for assessing plant diversity and cover is the modified-Whittaker plot (MWP). This approach employs subplots
N z
x O
P
Fig. 3.4 The T-square method. The black circles represent individuals of the study species. Ois the nearest individual to a random point P; Nis O’s nearest neighbour on the opposite side of the dashed line (which is perpendicular to the line OP). (From Greenwood 1996.)
with a variety of different uses nested within each other, and can provide accurate estimation of mean species cover and analysis of plant diversity patterns at multiple spatial scales (Stohlgren et al. 1995). Examples of this approach being used in forests are provided by Campbell et al. (2002) and Keeley and Fotheringham (2005). In the former study, which was done in lowland tropical forest, 0.1 ha MWPs were found to record species composition and abundance similar to that of 1 ha plots, and were equally effective at detecting rare species. In addition, MWPs were more effective at detecting changes in the mean number of species of trees10 cm dbh and of herbaceous plants.
A key aspect that should be considered is the relative efficiency of different methods—in other words, the amount of information gained per unit effort expended. This issue has received surprisingly little attention from ecological researchers, although foresters have long been aware of its importance (Avery and Burkhart 2002). Phillips et al. (2003) repeatedly sampled forests in two regions of Amazonia by 1 ha and 0.1 ha plot-based methods, and compared their perform- ance against the amount of effort required. Results indicated that the 0.1 ha method is more efficient for floristic assessment, but the authors also note that 1 ha plots still may be preferred in some situations, such as for ground-truthing remotely sensed measurements; they are also widely used in studies of forest dynamics (Condit 1998, Dallmeier and Comiskey 1998a, b). A key advantage of both of these methods is that their widespread use enables comparisons to be made with a range of other studies. On the other hand, the fact that they have been widely used by other ecologists does not in itself provide a strong justifica- tion for their use in a particular study. It may be that for the characteristics of a particular forest, or a specific set of objectives, some other approach might be more efficient.
This point is further illustrated by the work of Gordon (2005), who compared fixed area, distance-based, and ad hocmethods for the rapid inventory of tropical forest tree and shrub diversity in eight seasonally dry tropical forests sites in south- ern Mexico, with the aim of identifying priority sites for conservation. Results indicated that the 250 m protocol with 10 repetitions popularized by Gentry (1982) was relatively inefficient and lacking in statistical power. A 650 m protocol and fixed-count circular plots (equivalent to the variable area transect approach) were found to be more efficient, in terms of results obtained per unit effort. Preliminary surveys testing different methods are therefore to be recommended before committing substantial time and resources to a particular approach.
Hall et al. (1998) provide a detailed consideration of different sampling approaches for tropical forests. For determining stand density, many small plots are more efficient in terms of time required to establish and enumerate, and can provide similar precision to larger plots. There is a trade-off between total area to be surveyed and number and size of plots, which depends on the extent of variation between plots in comparison to the variation between sites that are to be compared. This trade-off point can best be estimated by doing a preliminary survey with different Sampling approaches | 99
plot sizes (Hall et al. 1998). In Amazonian Peru, Stern (1998) compared fixed-area plots following the strip transect design of Gentry (1982) with variable-area tran- sects; she used a total sample size of 50 stems for each of three size categories. Her conclusions were that the fixed-count plots were more flexible, particularly when different vegetation structures were encountered, but that strip transects had the advantage of being comparable to assessments from many other sites worldwide.
Kintet al. (2004) also found that equal or higher sample sizes are needed for plot sampling than for distance sampling to obtain the same degree of accuracy, and that distance methods were generally more efficient. However, plot-based sampling was more efficient for estimating stand structure at low to medium accuracy. Kint et al.
(2004) also demonstrated that, at least in the low-diversity forests in which they worked, minimum sample size is negatively correlated with tree density and is gen- erally lower in large stands than in small ones.
Choice of plot size and shape can have a major influence on the results obtained from the survey (Laurance et al. 1998a). For example, Condit et al. (1996) found that in tropical forests 5–27% more species were found in rectangular plots than in square plots of the same area, with longer and narrower plots increasingly diverse.
This result reflects the aggregated distributions of individual species, and indicates the importance of sampling the same number of stems if the objective is to make comparisons of diversity. In Mediterranean vegetation, however, Keeley and Fotheringham (2005) found no such difference between square versus rectangular plots. The size of the trees being measured can also have implications for plot design. For example, Gray (2003) found that in mature Douglas-fir forests, sam- ples of at least 40% of a stand (4 subplots of radius 18 m) were required to reduce errors for estimated density of large trees (122 cm dbh) below 25% of true density at least 66% of the time. However, for trees75 cm dbh, the standard inventory sample of 0.07 ha with 4 subplots of radius 7.3 m met this degree of accuracy for estimates of density and mortality.
It is also worth noting that there is an alternative to the use of either fixed-area or distance methods: a systematic or ad hocsearch of habitat. Searches are typically done by the surveyor walking around a site, looking for the target species or record- ing all of the species encountered. Usually, the search is timed so that the informa- tion gained can be corrected for the amount of survey effort expended. Timed searches can be further standardized by restricting the search to a specific area; an area might be subdivided into units and a sample of these selected randomly for surveying. This method is generally used to determine whether a particular species is present in a specific area (the absence of the species from the area, however, can be difficult to demonstrate conclusively) or to produce a checklist of the species present in an area. The approach is widely used in support of conservation plan- ning, particularly where information is needed on the distribution of rare or threatened species, or where a rapid assessment of floristic composition is required (see, for example, Schulenberg et al. 1999).
Searches suffer from the problems of bias (Nelson et al. 1990) because survey effort will not be equally distributed over the forest area, regardless of how carefully