Community Analysis of Duke Forest Vegetation using PCOrd
Annemarie Nagle
Biology 112
12/5/05
Introduction
Computer modeling and statistical analysis have become extremely valuable tools in the
modern field of ecology. Whereas ecologists have traditionally characterized forest communities
using environmental gradients that dictate species distribution, and have been forced to examine
community structure strictly through the lens of obvious causal relationships between these two
factors, the advent of statistical analysis software allows more sophisticated and objective
comparison of complex data. In these situations where causal relationships between
environmental or other factors and species presence and abundance are unknown or assumed to
be unknown, analysis programs like S-PLUS and PCord allow ecologists to analyze relationships
within their data and allow them to create an accurate picture of complex variable interactions
that would be nearly impossible without these tools.
In this analysis, PCord was used to examine the community structure of a large section of
Duke Forest, in Durham and Orange Counties, North Carolina. Tree species presence and
abundance data was collected for 106 plots in the Duke Forest, and corresponding environmental
data was measured in each plot as well. Preliminary analysis consisted of obtaining the optimal
number of axes through which to examine the data, and looking at possible correlations between
species distribution and environmental variables. Next, a grouping system was created, which
placed the plots into various categories based on their relationships to one another. Finally,
indicator species analysis was used to characterize these groups and obtain an idea of their
structure.
Methods
Stem counts of woody species in Duke Forest plots were used to obtain frequency data
for 56 tree species, while environmental sampling methods measured pH, calcium, magnesium,
potassium, aluminum, manganese, phosphate, and organic matter content, sand, silt, clay, aspect,
slope, distance from water and water content, solar radiation, and elevation.
Using PCord, a step-down ordination was carried out to determine the minimal number of
axes that would accurately represent trends in the data in an interpretable number of dimensions.
Sorenson (Bray-Curtis) analysis was used. Results of this test ordination were examined to
ensure minimal stress values and low instability. The optimal number of axes (3) was selected
and used to create a focal run for the data. See Table 1 for ordination settings.
Setting
NMS Step-down Run
Distance measure
Sorensen (Bray-Curtis)
Number of axes
6
Number of runs real data
20
Stability Criterion
0.0005
Max # iterations
400
Iterations to evaluate stability
20
Initial step length
0.20
Table 1. NMS settings for step-down and focal ordinations.
NMS Focal Run
Sorensen (Bray-Curtis)
3
20
0.0005
400
20
0.20
The data obtained from the NMS focal run was used for preliminary comparison of
assigned axes and environmental and species variables. Biplots and r values for individual
species correlations with the assigned axes were accessed under the Graph Ordination menu of
PCord.
Next, cluster analysis was performed to show relationships among plots and attempt to
define a number of community types based on species composition represented in the data.
Settings for the cluster analysis are shown below in Table 2. Cluster analysis output was
examined to ensure minimal values of percent chaining in the data.
Setting
Distance measure
Linkage method
Add group membership variable
Beta
Group membership level
Write all higher level groupings
Table 2. PCord cluster analysis settings.
Cluster Analysis
Sorensen (Bray-Curtis)
Flexible beta
Yes
-0.25
6
Yes
In order to determine which level of grouping was the most biologically significant and
useful, a Monte Carlo Test was performed at 1000 runs for each possible level of grouping (3-6
groups). P-values from the Monte Carlo Test were then examined to determine which number of
groups was best. A maximum number of significant (p ≤ 0.050) p-values and a minimal average
of p-values was used as indicator of the best number of groupings.
Indicator species analysis was performed on the species abundance data using the number
of groups shown to be optimal in the Monte Carlo Test by examining abundance, frequency,
indicator, and p-values of species within the group.
Results
Three axes were selected for the focal ordination via the step-down run. Stress values at
three axes were slightly less than optimal at 15.95997 (values less than or equal to ten are
preferred). Instability values were very good, however, at 0.00046. Despite sub-optimal stress
values, the slope of the scree plot shown in Figure 1 provides a clear picture as to why three
dimensions were selected. The minimum number of dimensions corresponding to minimal
increase in stress value is desired, and as one can see with fewer than three dimensions levels of
stress being to increase rapidly.
Step-Down NMS Scree Plot
40
Real Data
Stress
30
20
10
0
1
3
5
Dimensions
Figure 1. NMS scree plot showing optimal 3 dimensions for focal run.
Examination of cluster analysis results indicated that the analysis was a good
representation of groupings in the data, and provided valuable information regarding
relationships in groups. Percent chaining was low, at only 1.66%.
Number of Groups
Average p-value
Number Significant p-values
3
0.158786
22
4
0.152929
11
5
0.169357
21
6
0.129429
28
Table 3. Summary of p-values from Monte Carlo Test to determine the appropriate number of
groups for use in indicator species analysis. The lowest average p-value and highest number of
significant p-values was seen in six groups, so this grouping was selected.
Summary: 6 Group Analysis
Distance (Objective Function)
1.6E-02
5.1E+00
100
75
1E+01
1.5E+01
2E+01
25
0
Information Remaining (%)
00001
PSP37
00018
00021
00574
00004
00008
00014
00002
00005
00007
00509
00520
00016
00024
00023
00033
00010
00031
00020
00042
00019
00069
00517
PSP36
00555
00581
00598
00589
00571
00579
00009
00012
00011
00015
00017
00022
00067
00618
00513
00514
00620
00537
00619
00501
00504
00524
00502
PSP88
PSP86
00508
PSP87
00617
PSP35
PSP34
00081
00606
00590
00510
00596
00512
00511
00607
00621
00608
00609
00003
00612
00616
00611
00614
00615
00622
00624
00575
00593
00582
00013
00029
PSP44
PSP61
00503
00507
00025
00026
00583
00584
00585
00032
00505
00506
00625
PSP10
00027
00587
00518
00588
00602
00515
PSP43
00028
00516
00030
00610
00613
00623
50
Group6
1 3 12 36 37 87
Figure 2. Cluster dendrogram color-coded to show groupings of sample plots into six categories.
TreeLong_NMS
Group6
1
3
12
36
37
87
LIST
Axis 3
CACR
QUPR
QUAL
Axis 2
Figure 3. PCord biplot of axes 2 and 3 showing plots colorcoded by group membership and
corresponding species.
TreeLong_NMS
Group6
1
3
12
36
37
87
LIST
Axis 3
CACR
LITU
FAGR
JUVI
QUST
QUAL
Axis 1
Figure 4. PCord biplot of axes 1 and 3 showing plots colorcoded by group membership and
corresponding species.
TreeLong_NMS
Group6
1
3
12
36
37
87
JUVI
QUST
Axis 2
LITU
FAGR
QUPR
Axis 1
Figure 5. PCord biplot of axes 1 and 2 showing plots colorcoded by group membership and
corresponding species.
TreeLong_NMS
group6
1
3
12
36
37
87
Axis 3
Mg-A
Ca-A
pH
Elev
Dist-H2O
Axis 2
Figure 6. PCord biplot of axes 2 and 3 showing plots colorcoded by group membership and
corresponding environmental variables.
TreeLong_NMS
Axis 3
group6
1
3
12
36
37
87
Mg-A
Ca-A
Dist-H2O
Axis 1
Figure 7. PCord biplot of axes 1 and 3 showing plots colorcoded by group membership and
corresponding environmental variables.
TreeLong_NMS
group6
1
3
12
36
37
87
Axis 2
pH
Axis 1
Figure 8. PCord biplot of axes 1 and 2 showing plots colorcoded by group membership and
corresponding environmental variables.
Species
Abbreviation
QUPR
PITA
FRAX
Species Name
Quercus prinus
Pinus taeda
Fraxinus sp.
Abundance
Frequency
0
84
1
0
100
100
Indicator
Value
98.6
83.6
73.6
p-value
0.001
0.001
0.001
Max
Group
36
87
37
FAGR
PIVI
ULAL
JUVI
ILDE
LIST
QUST
CECA
LITU
ULRU
CACR
OSVI
QUAL
MORU
CAOV
PIEC
QURU
QUCO
OXAR
QUVE
QUMI
COFL
CAGL
CATO
ACRU
PRSE
QUPH
CAOL
NYSY
ACNE
QUSH
PLOC
PRAM
CRMA
CACO
CEOC
DIVI
ILOP
CAPA
ACSA
BENI
ULAM
QUMA
QUFA
JUNI
MATR
CACA
SAAL
Fagus grandifolia
Pinus virginiana
Ulmus alata
Juniperus virginiana
Ilex decidua
Ligustrum sinense
Quercus stellata
Cercis canadensis
Liriodendron tulipifera
Ulmus rubra
Carpinus carolina
Ostrya virginiana
Quercus alba
Morus rubra
Carya ovata
Pinus echinata
Quercus rubra
Quercus coccinea
Oxydendrum arboreum
Quercus velutina
Quercus michauxii
Cornus florida
Carya glabra
Carya tomentosa
Acer rubrum
Prusus serotina
Quercus phellos
Carya ovalis
Nyssa sylvatica
Acer negundo
Quercus shumardii
Platanus occidentalis
Prunus americana
Crataegus marshallii
Carya cordiformis
Celtis occidentalis
Diospyrus virginianus
Ilex opaca
Carya pallida
Acer saccharum
Betula nigra
Ulmus americana
Quercus marilandica
Quercus falcata pagodaefolia
Juglans nigra
Magnolia tripetala
Carya carolinaeseptenrionalis
Sassafras albidum
0
69
7
63
0
3
59
0
0
0
0
0
1
0
0
39
0
0
0
0
0
0
0
1
4
12
6
0
0
0
0
0
0
0
0
0
19
0
0
0
0
0
19
3
0
0
0
0
100
67
100
0
100
100
0
0
0
0
0
67
0
100
100
0
0
0
33
0
67
67
100
100
33
100
0
67
0
0
0
0
0
0
0
100
0
0
0
0
0
67
33
0
0
0
73.1
69.2
66.4
63
61.8
59.7
59.1
58.9
58.3
48.7
48.6
45.2
44.4
42.9
39.4
38.8
37.7
37.4
37.2
35.5
35.3
34.5
34.4
34
33.3
32.8
29
28
27.7
27.3
27.3
26.1
25
23.2
21.8
21.6
18.8
18.4
18.1
15.2
14.8
14.5
13.7
13.2
12.6
10.3
9.1
0.001
0.003
0.004
0.001
0.002
0.001
0.001
0.007
0.001
0.011
0.016
0.013
0.001
0.031
0.056
0.029
0.051
0.027
0.03
0.029
0.008
0.033
0.065
0.096
0.059
0.209
0.029
0.15
0.236
0.028
0.038
0.047
0.054
0.042
0.052
0.123
0.291
0.2
0.058
0.35
0.145
0.24
0.281
0.443
0.259
0.159
0.22
12
87
3
37
3
3
87
37
12
3
3
37
1
37
87
87
37
36
36
1
3
1
37
87
1
37
87
37
36
3
3
3
37
3
3
37
87
12
36
12
3
3
87
1
3
12
3
0
0
9.1
0.729
1
QUNI
CRUN
AMAR
ILAM
CRAT
Quercus nigra
Crataegus uniflora
Amelanchier arboreum
Ilex ambigua
Crataegus sp.
0
0
0
0
0
0
0
0
0
0
8.4
7.7
7.5
6.3
5.9
0.272
0.315
0.578
0.585
0.536
Table 4. Summary statistics of Monte Carlo Test and indicator species analysis for six groups
sorted by IV.
Discussion
Cluster analysis allowed the beginnings of characterization of possible tree communities
in the Duke forest. By examining a series of biplots of species and environmental variables
overlaid on plot arrays color-coded to reflect group membership, possible defining environments
and compositions were identified for the groups. We were also able to better assess outliers or
misleading trends in the data.
Groups were not constructed by taking into account environmental variable relationships
between the plots, but were solely based upon species composition and distribution. However, it
is widely recognized that environmental variables often influence individual species
distributions, so it is valuable to compare group relationships with these variables. The groups
labeled 37(blue) and 36(pink) seemed to lie along a pH gradient, with 37 on the positive end and
36 on the negative. Group 12(light blue) may have a weaker positive correlation with pH.
Group 1(red) is one of the largest groups, and seems to be correlated with Dist-H20 and Mg-A,
as it seems Group 3(green) is as well. Group 1 has a positive correlation with Dist-H20 and a
negative correlation with Mg-A, while group 3 has the opposite. Groups 36 and 37 are also
located in the region of group 1, and appear to have similar but less strong correlations with the
two variables. Aluminum also seems to occur most frequently in group 1.
Acer rubrum was highly correlated with Axis 2. When viewed with its groupings,
however, Acer rubrum seems to occur in many of the groups (most abundantly in 12 and 36),
and so possibly may be viewed as abundant everywhere and less weight given to its correlation
with the axis. Carpinus carolina occurs most abundantly in groups 12 and 3, so may be
characterized by higher pH and longer distance from water and higher values of Mg-A. Fraxinus
sp. is found almost exclusively in group 37, which may be present where pH values are higher.
Ligrustrum sinense is found in groups 3 and 12. Liriodendron tulipifera, although not
corresponding strongly to any axis seems to fall primarily in group 12. A number of oak species,
Quercus alba, Quercus velutina, and Quercus stellata seem to occur at the highest frequency in
group 1. Quercus prinus is located almost exclusively in group 36. Ulmus alata appears to be
nearly exclusively in group 3. Group 87 (yellow) was difficult to assign qualities due to lack of
trends in environmental or species content, and due to it being the smallest group in the analysis.
Visual examination of the data discussed above provided insight as to what may drive
community structure and what characterizes the six types of communities defined by the
analysis. However, the statistics provided by the Monte Carlo and Indicator Species analyses are
able to give us a more objective picture of species composition in the created groupings. Pvalues are powerful indicators of the likelihood that a pattern observed has occurred by chance.
Low p-values (here, for p ≤ 0.050) tell us that our results are significant and have real meaning.
3
36
1
3
37
Abundance (fidelity) and frequency (constancy) can be combined to give indicator values, which
discuss the degree to which a particular species is diagnostic for the grouping that it is placed in.
Abundance is the percentage of the total occurrence of a species that is found within the group of
interest. Frequency refers to the percentage of the plots within the group of interest that contain
a species. A perfect indicator species for a group would only be present in the group of interest
(100% of its abundance) and would be present in every plot contained within the group
(frequency would also be 100%). Our analyses returned no perfect indicator species. The
species with the maximum IV reported (98.6), Quercus prinus, did not occur in any of the plots
and so can be omitted. However, Pinus taeda, with an IV of 83.6, seems to be a nearly perfect
indicator for the group 87. Pinus virginiana is also a good indicator (IV= 69.2) species of group
87. The existence of two strong indicators from the Pinus genera may indicate that this group
represents communities characterized by dominance of pines. For group 37, Juniperus
virginiana is the best indicator (IV= 63). These were the closest indicators to “perfect” reported
by the data.
Indicator species for the other groups were farther from “perfect”. The best indicator
reported for Group 3 was Ulmus alata (IV=66.4). The highest IV in Group 1 was only 44.4,
which belonged to Quercus alba. There did not seem to be any meaningful indicator species for
the other two groups, 36 and 12.
From this data, it appears that Pinus taeda and Pinus virginiana may be used with
relative confidence as indicator species for the community type contained in grouping 87.
Juniperus virginiana could also be a valuable indicator. It is possible that this number of
groupings was still too small to explain the patterns seen on the landscape of Duke Forest, or that
the communities may be too similar or the scale of sampling too small to separate the data into
distinct groups with unique indicator species. Groups that do not appear to have any correlation
to any measured environmental variables may be characterized by variables that were not tested.
Further analysis is needed to determine the characteristics of the individual groups and possible
biotic or abiotic explanatory factors contributing to observed species distributions.