7.8 Interpolation and Extrapolation from Samples
landscape level. Third, landscape configurations
change over time. Ecosystems that have restricted
extent today may become more extensive in the future. It is crucial to identify all segments of the
ranges of biotic and abiotic variability, whether
common or rare. Only then can all aspects of the
natural variability at landscape and regional levels
be considered for management and conservation
planning.
Gillison and Brewer (1985) argued that gradsect
design is more efficient than random and systematic
design in recovering rare elements of an ecological
pattern, because gradsects can recover significantly
more patterns at finer scales of distribution, increasing the likelihood of locating rarities. Two other reasons make SSRSs and MSSRSs more likely to locate rarities. First, because physical environments
are defined and mapped, less common environmental combinations are clearly identified and located (Austin and Heyligers, 1989, 1991; Bourgeron et aI., 1994a; Engelking et aI., 1994; Bunce et
aI., 1996a). Any biotic rarity associated with such
environments will be included in a survey. Second,
SSRSs and MSSRSs require intensive study of the
range of environmental variability in an area, and
this leads to a more thorough examination in the
field. Hence the probability of locating rare ecological elements is increased. Mills et al. (1996) detected 3 rare bat species out of a total of 13 species
recorded using MSSRS.
7.7 Sample Size and Configuration
Once sample sites have been selected, the size and
configuration of samples become critical components of standardized sampling methods (Legendre
and Legendre, 1998). Sampling at multiple scales
within a site allows quantification of the influence
of spatial scale on patterns such as local species diversity and provides better multiscaled analyses of
community composition and diversity (Whittaker,
1977; Fortin et aI., 1989; Podani et aI., 1993; Reed
et aI., 1993; Stohlgren et aI., 1995; Bellehumeur
and Legendre, 1998). A number of nested survey
designs have been used to measure spatially structured variation in a variety of organisms, including
tropical trees and mollusks (Bellehumeur and Legendre, 1998; Legendre and Legendre, 1998). Results indicate that it is useful to collect samples at
two or more different scales of observation, making possible the detection of nested structures
(Bellehumeur and Legendre, 1998; Legendre and
Legendre 1998). This approach can easily be integrated into SSRSs and MSSRSs. Finally, it would
101
be advantageous to use preliminary data to test the
impact of sample size and configuration on the results for a specific application. For example, Fortin
(1999) showed that quadrat shape and orientation
did not significantly affect the detection of boundaries in a forested landscape, although they might
have such an effect in other data sets.
Some multi scale sampling methods, such as the
20 by 50 m Whittaker plots widely used in vegetation studies (Stohlgren et aI., 1995), have flaws,
such as suboptimal plot shapes, nested plots with
different shapes at different sizes, and nonindependence of data where successively larger plots
are superimposed on smaller plots, that reduce their
effectiveness in detecting patterns (Stohlgren,
1994; Stohlgren et aI., 1995). Stohlgren et al.
(1995) introduced a modified-Whittaker vegetation
sampling method that avoids these problems and is
rapid and cost effective. The sampling method includes 1, 10, and 100-m 2 subplots within a 20 by
50 m (1000 m 2 ) plot, as in the Whittaker method,
but all plots have the same rectangular shape
and there is minimal plot overlap. The modifiedWhittaker plot design produced significantly higher
species diversity values than the Whittaker plot in
forest and prairie vegetation in Colorado and South
Dakota (Stohlgren et aI., 1995). The modifiedWhittaker method was also compared with several
rangeland sampling methods in shortgrass, mixed
grass, and tall grass prairie vegetation in the central
United States (Stohlgren et al., 1998). Parker transects, Daubenmire transects, and a large-quadrat
design proposed by the USDA Agricultural Research Service all significantly underestimated total
plant species richness and the number of native
species compared with the modified-Whittaker
method. In addition, the two transect methods missed
half the exotic species and captured only 36%
to 66% of the species detected by the modifiedWhittaker method. The modified-Whittaker method
was found to work equally well in sampling large or
small vegetation patches (Stohlgren et aI., 1997).
The size of the plots can be adjusted (e.g., from 20
by 50 m to 10 by 25 m) to accommodate sampling
in small patches (Stohlgren et aI., 1997).
7.8 Interpolation and Extrapolation
from Samples
Data collection efforts in most large areas are unlikely to be complete due to prohibitive costs.
Therefore, it is often necessary to use models to interpolate or extrapolate the survey results to areas
landscape level. Third, landscape configurations
change over time. Ecosystems that have restricted
extent today may become more extensive in the future. It is crucial to identify all segments of the
ranges of biotic and abiotic variability, whether
common or rare. Only then can all aspects of the
natural variability at landscape and regional levels
be considered for management and conservation
planning.
Gillison and Brewer (1985) argued that gradsect
design is more efficient than random and systematic
design in recovering rare elements of an ecological
pattern, because gradsects can recover significantly
more patterns at finer scales of distribution, increasing the likelihood of locating rarities. Two other reasons make SSRSs and MSSRSs more likely to locate rarities. First, because physical environments
are defined and mapped, less common environmental combinations are clearly identified and located (Austin and Heyligers, 1989, 1991; Bourgeron et aI., 1994a; Engelking et aI., 1994; Bunce et
aI., 1996a). Any biotic rarity associated with such
environments will be included in a survey. Second,
SSRSs and MSSRSs require intensive study of the
range of environmental variability in an area, and
this leads to a more thorough examination in the
field. Hence the probability of locating rare ecological elements is increased. Mills et al. (1996) detected 3 rare bat species out of a total of 13 species
recorded using MSSRS.
7.7 Sample Size and Configuration
Once sample sites have been selected, the size and
configuration of samples become critical components of standardized sampling methods (Legendre
and Legendre, 1998). Sampling at multiple scales
within a site allows quantification of the influence
of spatial scale on patterns such as local species diversity and provides better multiscaled analyses of
community composition and diversity (Whittaker,
1977; Fortin et aI., 1989; Podani et aI., 1993; Reed
et aI., 1993; Stohlgren et aI., 1995; Bellehumeur
and Legendre, 1998). A number of nested survey
designs have been used to measure spatially structured variation in a variety of organisms, including
tropical trees and mollusks (Bellehumeur and Legendre, 1998; Legendre and Legendre, 1998). Results indicate that it is useful to collect samples at
two or more different scales of observation, making possible the detection of nested structures
(Bellehumeur and Legendre, 1998; Legendre and
Legendre 1998). This approach can easily be integrated into SSRSs and MSSRSs. Finally, it would
101
be advantageous to use preliminary data to test the
impact of sample size and configuration on the results for a specific application. For example, Fortin
(1999) showed that quadrat shape and orientation
did not significantly affect the detection of boundaries in a forested landscape, although they might
have such an effect in other data sets.
Some multi scale sampling methods, such as the
20 by 50 m Whittaker plots widely used in vegetation studies (Stohlgren et aI., 1995), have flaws,
such as suboptimal plot shapes, nested plots with
different shapes at different sizes, and nonindependence of data where successively larger plots
are superimposed on smaller plots, that reduce their
effectiveness in detecting patterns (Stohlgren,
1994; Stohlgren et aI., 1995). Stohlgren et al.
(1995) introduced a modified-Whittaker vegetation
sampling method that avoids these problems and is
rapid and cost effective. The sampling method includes 1, 10, and 100-m 2 subplots within a 20 by
50 m (1000 m 2 ) plot, as in the Whittaker method,
but all plots have the same rectangular shape
and there is minimal plot overlap. The modifiedWhittaker plot design produced significantly higher
species diversity values than the Whittaker plot in
forest and prairie vegetation in Colorado and South
Dakota (Stohlgren et aI., 1995). The modifiedWhittaker method was also compared with several
rangeland sampling methods in shortgrass, mixed
grass, and tall grass prairie vegetation in the central
United States (Stohlgren et al., 1998). Parker transects, Daubenmire transects, and a large-quadrat
design proposed by the USDA Agricultural Research Service all significantly underestimated total
plant species richness and the number of native
species compared with the modified-Whittaker
method. In addition, the two transect methods missed
half the exotic species and captured only 36%
to 66% of the species detected by the modifiedWhittaker method. The modified-Whittaker method
was found to work equally well in sampling large or
small vegetation patches (Stohlgren et aI., 1997).
The size of the plots can be adjusted (e.g., from 20
by 50 m to 10 by 25 m) to accommodate sampling
in small patches (Stohlgren et aI., 1997).
7.8 Interpolation and Extrapolation
from Samples
Data collection efforts in most large areas are unlikely to be complete due to prohibitive costs.
Therefore, it is often necessary to use models to interpolate or extrapolate the survey results to areas