Transcript Chapter 3

CHAPTER 3
Community Sampling and Measurements
Tables, Figures, and Equations
From: McCune, B. & J. B. Grace. 2002. Analysis of
Ecological Communities. MjM Software Design,
Gleneden Beach, Oregon http://www.pcord.com
Table 3.1. Cutoff points for cover classes. Question marks for cutoff points
represent classes that are not exactly defined as percentages. Instead, another
criterion is applied, such as number of individuals. Cutoffs in parentheses are
additional cutoffs points used by some authors.
Name
Cutoff points, %
Notes
References
Arcsine squareroot
0 1 5 25 50 75 95 99
Designed to approximate an
arcsine squareroot
transformation of percent
cover.
Muir & McCune (1987,
1988)
Braun-Blanquet
0 ? ? 5 25 50 75
Uses two categories of low
cover not exactly defined as
percents. Commonly used in
Europe.
Braun-Blanquet (1965),
Mueller-Dombois &
Ellenberg (1974)
Daubenmire
0 (1) 5 25 50 75 95
Widely used in western U.S. in
habitat-typing efforts by U.S.
Forest Service and many other
studies.
Daubenmire (1959)
Domin
0 ? 1 5 10 25 33 50 75
One category of low cover not
exactly defined as percent.
Krajina (1933); MuellerDombois & Ellenberg
(1974)
Hult-Sernander
(modified)
0 (.02 .05 .10 .19 .39 .78)
1.56 3.13 6.25 12.5 25 50
75 ...
Based on successive halving of
the quadrat.
Oksanen (1976)
Figure 3.1 Expected percent frequency of presence in sample
units (SU) as a function of density (individuals/SU).
Relative density of species j is the proportion of the p
species that belong to species j:
RD j =
Density j
p
 Density
j=1
j
These relative measures are commonly expressed as
percents, by multiplying the proportions by 100, for
example:
Relative density j % =
100  Density 
j
p
 Density
j=1
j
Importance values are averages of two or more of the
above parameters, each of which is expressed on a
relative basis. For example, a measure often used for
trees in eastern North American forests is:
IV% = (Relative frequency + relative dominance +
relative density) / 3
Table 3.2. Example of identical importance values
representing different community structures.
Species 1
Species 2
Relative Density
42
8
Relative Dominance
10
44
Sum
52
52
IV%
26
26
Box 3.1. Example of stand description, based on individual tree data from fixedarea plots. The variance-to-mean ratio, V/M, is a descriptor of aggregation, values
larger than one indicating aggregation and values smaller than one indicating a
more even distribution than random. The variance and mean refer to the number of
trees per plot. IV and other measures are defined in the text.
Raw data for three tree species in each of four 0.03 hectare plots. Each
number represents the diameter (cm) of an individual tree.
Species
Carya glabra
Plot 1
Plot 2
23
22
24
Cornus florida
Quercus alba
13
17
44
Plot 3
Plot 4
31
10
10
12
10
11
12
20
11
30
10
32
Box 3.1, cont.
Frequencies, counts, total basal areas, stand densities, and stand basal areas.
Species
Carya glabra
Cornus florida
Quercus alba
Totals
Freq.
No. BA (dm2)
Trees
3
3
4
4
6
8
20.0
5.6
38.8
10
18
64.4
Freq.%
75
75
100
Density
Trees/ha
BA
dm /ha
33.3
50.0
66.7
166.9
46.4
323.3
150.0
536.56
2
Box 3.1, cont.
Relative abundances, importance values, and variance statistics.
Relative Abundance
Species
Carya glabra
Cornus florida
Quercus alba
Frequency
30.0
30.0
40.0
Number of quadrats
Empty quadrats
Quadrat size
Area sampled
Average BA/tree
BA/hectare
Trees/hectare
Trees/quadrat
=
=
=
=
=
=
=
=
Density
22.2
33.3
44.4
Variance
Dominance
31.1
8.7
60.3
4
0
0.030 hectares
0.120 hectares
3.577 dm2
5.366 m2/hectare
150
4.5
IV(%)
27.8
24.0
48.2
no. trees
0.67
1.67
0.67
V/M
0.67
1.11
0.33
All species
1.00
0.22
Table 3.3. Average accuracy and bias of estimates of lichen species richness
and gradient scores in the southeastern United States. Results are given
separately for experts and trainees in the multiple-expert study. Extracted
from McCune et al. (1997). N = sample size.
% Deviation from expert
Activity
N
Species
richness
Score on
climatic
gradient
Score on
air quality
gradient
% of expert
Bias
Acc.
Bias
Acc.
Bias
Reference plots
16
61
-39
4.4
+2.4
11.1
-10.5
Multiple-expert study,
experts
3
95
-5
3.6
+3.6
4.7
-4.7
Multiple-expert study,
trainees
3
54
-46
8.0
+8.0
5.0
-5.0
Certifications
7
74
-26
2.7
+2.4
2.1
-2.1
Audits
3
50
-50
10.3
+3.7
6.0
+2.7
If Sobs is the observed number of species, xobs is the
observed value of variable x, and xtrue is the true value of
parameter x, then:
Species capture,% = 100 ( S obs / S true )
100 |xobs - xtrue|
Accuracy, % =
xtrue
100 ( xobs - xtrue )
Bias, % =
xtrue
Table 3.4. Raw data for two-dimensional example of accuracy and bias,
plotted in Figure 3.2.
Person
x
y
Person
x
y
1
3.0
5.2
4
0.9
-0.4
1
4.0
5.1
4
-0.6
1.1
1
4.0
2.6
4
-1.1
-2.0
2
0.9
-0.7
5
-2.7
-1.0
2
0.1
-2.9
5
-3.1
-1.2
2
0.4
-2.9
5
1.3
-1.9
3
0.0
0.0
6
3
0.6
0.3
4
3
-2.1
-1.6
1
1
1
2
Y
4
Figure 3.2. Two-dimensional example of
accuracy and bias. Each person (1, 2,.. ,5)
aims at the center (0,0), representing the
“true value.” Deviations are measured in
two dimensions, x and y.
0
3
4
2
3
5 5
3
-2
4
5
2 2
-4
-4
-2
0
2
X
4
6
Table 3.5. Inaccuracy and bias for two-dimensional
example (Fig. 3.2).
Inaccuracy
(Ave.
distance
Average bias
Person
to 0,0)
x
y
1
5.75
3.67
4.30
2
2.32
0.47
-2.17
3
1.10
-0.50
-0.43
6
1
1.51
-0.27
-0.43
5
2.84
-1.50
-1.37
4
1
2
4
Y
4
1
0
3
4
2
3
5 5
3
-2
4
5
2 2
-4
-4
-2
0
2
X
4
6
Table 3.6. Tradeoffs between few-and-large and many-andsmall sample units.
Few-and-large
Many-and-small
Bias against cryptic
species
Higher. There is a hazard that
some species, particularly
cryptic species, are inadvertently
missed by the eye.
Lower. Small sample units force
the eye to specific spots,
reducing inadvertent observer
selectivity in detection of
species.
Degree of visual
integration
High. The use of visual
integration over a large area is an
effective tool against the
normally high degree of
heterogeneity, even in
"homogeneous" stands.
Low. Minimal use is made of
integrative capability of eye,
forcing the use of very large
sample size to achieve
comparable level of
representation of the community.
Inclusion of rare to
uncommon species
High. Visual integration
described above results in
effective "capture" of rare
species in the data.
Low. Unless sample sizes are
very large, most rare to
uncommon species are missed.
Table 3.6. (cont.)
Accuracy of cover
data on common
species
Lower. Cover classes in large
sample units result in broadly
classed cover estimates with
lower accuracy and precision
than that compiled from many
small sample units.
Higher. More accurate and
precise cover estimates for
common species.
Bias of cover
estimates for rare
species
High (overestimated).
Low.
Sampling time
Varies by complexity and degree
of development of vegetation.
No consistent difference from
many-and-small.
Varies by complexity and degree
of development of vegetation.
No consistent difference from
few-and-large.
Analysis time
Faster. With a single large plot,
data entry at site level leads
directly to site-level analysis.
Slower. Point data or microplot
data require initial data reduction
(by hand, calculator, or
computer) to site-level
abundance estimates.
Table 3.6. (cont.)
Analysis options
Estimates of within-site variance Within-site variance estimates
are poor or impossible,
are possible as long as sample
restricting analyses to individual units are larger than points.
sites as sample units.
Recommendations
The extreme case (single large
plot) is most useful with
extensive (landscape level)
inventory methods. In many
cases it is better to compromise
with a larger number of mediumsized sample units.
The extreme case (point
sampling) is most useful when
rare to uncommon species are of
little concern and accurate
estimates are desired for
common species. In most cases
a compromise by using a smaller
number of larger sample units is
better.
The following formula rescales aspect to a scale of zero to
one, with zero being the coolest slope (northeast) and one
being the warmest slope (southwest).
1 - cos ( - 45)
Heat load index =
2
where  = aspect in degrees east of true north. A very
similar equation but ranging from zero to two, was
published by Beers et al. (1966).
The plane-corrected distance D' for a distance D on an
angle of S above the horizontal is:
D' = D/cos S.