Download Ordination Analysis of Duke Forest Vegetation

Ordination Analysis of Duke Forest Vegetation
Duke Forest
North Carolina
Charles Schutte
December 5, 2005
Biology 112 Lab
Introduction:
The purpose of this analysis was to determine what species and
environmental variables define different communities in the Duke Forest. This
was done by performing an ordination on 106 sample plots containing 56 tree
species found within the study area. Ordination is a technique that allows
complicated relationships between many objects to be expressed more simply in
terms of several axes. These axes are created by placing the most similar
objects of the analysis near each other in the n-dimensional ordination space.
This analysis was carried out in four main steps. In the first step, rare
species were removed and an outlier analysis was performed to clean the raw
data. In the second step, a focal ordination was run. Groups were then identified
within the data. Finally, an indicator species analysis was performed to identify
the indicator species within each group.
Methods
The program PC-ORD was used in every step of this analysis. Before the
actual ordination was carried out, some effort was made to clean the raw data.
Species composition is used to define the communities we are trying to analyze.
A few dominant species tend to define this composition, which makes rare
species relatively unimportant to this analysis. As such, those species found in
fewer than five of the sample plots (which is approximately 5% of the 106 sample
plots, as recommended by McCune and Grace (2002)) were removed from the
analysis. The species removed were Acer negundo, Carya carolinae-septent.,
Carya pallida, Crataegus uniflora, Magnolia tripetala, Platanus occidentalis, and
Prunus americana.
Outlier analyses were performed on both the tree species data and the
environmental data. No sample plots were removed based on theses analyses
because there was insufficient data to justify their removal. No individual plot
was listed as an outlier with regards to both environmental and species
composition data.
With the new, cleaned data set, ordinations were performed. Ordination
orders all of the data points along one or multiple axes according to their relative
differences from one another. Non metric multidimensional scaling (NMS)
ordination, which was the type of ordination performed in this analyses, is a type
of ordination that makes no assumptions about the statistical distributions of
species within the samples.
Before the focal ordination was carried out, a step-down ordination was
performed with six axes to determine what number of axes to use in the focal
ordination. This carried out a number of iterations (maximum 400) of ordinations
with each number of axes and computed the average stress and instability for
each. Stress measures the divergence between the actual data and the
locations of the data in ordination space. Instability is the amount that stress
changes with each additional iteration. The scree plot in Figure 1 below shows
how stress changes as the number of axes used increases. The curve begins to
level out at three axes. Also, it can be seen in Table 1 that the stress values
were the most consistent for three axes. For these reasons, three axes were
used for the focal ordination.
Stress
Axes
Minimum
Average
Maximum
1
40.629
48.84
57.142
2
23.352
24.854
27.294
3
15.815
15.844
15.909
4
12.733
16.48
26.596
5
10.575
13.3
23.045
6
9.116
13.216
20.62
Table 1: Stress data used to create the scree plot in Figure 1.
TreeLong_NMSstep_CR
Real Data
40
s
s
e
r
t
S
20
0
1
3
5
Dimensions
Figure 1: Scree plot of the NMS step down ordination performed.
After the focal ordination was performed, a cluster analysis was performed
to divide all of the sample plots into up to twelve different clusters using PCORD’s cluster analysis tool. This tool grouped the data based on species
composition. The results for each possible clustering using from three clusters to
twelve clusters were evaluated using PC-ORD’s indicator species analysis tool.
This tool measures the abundance (or fidelity) and the frequency (or constancy)
of each species with respect to each cluster. Abundance is the percentage of the
abundance of a given species that occurs within a given group. Frequency is the
percentage of sample plots within a given group that contain individuals of a
given species. These two values are then multiplied to attain indicator values
ranging from zero to one hundred. A species with an indicator value of 100 is
considered to be a perfect indicator.
The p-values from the indicator species analysis, which are a measure of
the significance of the analysis, were compared for each clustering level from
three groups to twelve groups. The average p-values were compared along with
the number of significant indicator species. A species was defined as a
significant indicator if it had a p-value less than 0.5. A graphical representation of
this comparison is displayed in Figure 2 below. From this figure, it can be seen
that the clustering level with six groups achieves the lowest average p-value, and
the greatest number of significant indicator species. For this reason, this is the
grouping level that is used in the rest of this analysis.
Analysis of Groupings
0.35
0.3
0.25
0.2
Average p Value
# of Significant Indicators (/100)
0.15
0.1
0.05
0
0
2
4
6
8
10
12
14
# of Groups
Figure 2: Analysis of different grouping levels based on the average p-value and
the number of significant indicator species using data derived from PC-ORD’s
indicator species analysis.
The arrangement of the sample plots into six groups can be seen in the
cluster dendrogram in Figure 3 below. This grouping exhibits 1.45% chaining.
Chaining occurs when an individual data point is arbitrarily added to an existing
group, providing no meaningful information. Furthermore, no group required
more than 75% of the available data for its creation. This is further indication the
arranging the Duke Forest sample plots into six groups is a reasonable
manipulation of the data.
TreeLong_CR_6Groups
Distance (Objec tive Func tion)
1.6E-02
5.1E+00
100
75
1E+01
1.5E+01
2E+01
25
0
Information Remaining (%)
00001
P SP 37
00018
00021
00574
00004
00008
00014
00009
00012
00011
00015
00017
00002
00005
00007
00509
00520
00016
00024
00023
00033
00010
00031
00020
00042
00019
00069
00517
P SP 36
00555
00581
00598
00589
00571
00579
00003
00616
00022
00067
00618
00513
00514
00620
00537
00619
00612
00617
P SP 35
P SP 34
00501
00504
00524
00502
P SP 88
P SP 86
00508
P SP 87
00081
00606
00590
00510
00596
00512
00511
00607
00621
00608
00609
00013
00029
P SP 44
P SP 61
00503
00507
00025
00026
00583
00584
00585
00032
00505
00506
00625
P SP 10
00027
00587
00518
00588
00602
00515
P SP 43
00028
00516
00030
00610
00613
00623
00575
00593
00582
00611
00614
00615
00622
00624
50
Group6
1 3 12 36 37 61
Figure 3: Dendrogram of the six-group clustering used in this data analysis.
Results
Group
Species
IV
Oxydendrum arboreum
43
1
Quercus alba
42
Cornus florida
33
Quercus velutina
31
Quercus stellata
58
Juniperus virginiana
45
2
Quercus falcata
35
Pinus taeda
29
Pinus virginiana
26
3
Fagus grandifolia
71
Liriodendron tulipifera
55
4
Quercus prinus
96
Quercus coccinea
35
Fraxinus sp.
69
5
Cercis canadensis
54
Ostrya virginiana
44
Quercus rubra
36
Carpinus carolina
72
Ulmus alata
65
Liquidambar styriciflua
61
Ilex decidua
58
Ulmus rubra
56
6
Morus rubra
47
Carya cordiformis
32
Quercus michauxii
32
Celtis occidentalis
31
Crataegus marshallii
29
Quercus phellos
23
Betula nigra
21
Table 2: A list of all of the significant indicator species (having p less than 0.5) for
each group and their indicator values.
The importance values in Table 2 above are simply measures of how
good an indicator a particular species is for a particular group. Figures 4 and 5
below show a graphical representation of what these values mean. Quercus
prinus has a very high indicator value of 96 for Group 4. In Figure 5, it can be
seen from the size of the triangles representing the sample plots in Group 4
relative to the size of those representing the other groups that this species
appears to define Group 4. In contrast, Oxydendrum arboreum has an
importance value of 43 for Group 1. It is possible to see why this value is
relatively small from its representation in Figure 4. A smaller number of O.
arboreum individuals also appear in sample plots from Group 4, as well as
several plots from Group 3. However, it can also be seen that more individuals
exist in the Group 1 plots, and more plots from this group contain this species
than from any other group. This data shows that even the smaller importance
values listed in Table 2 above indicate an important relationship between an
individual species and its group.
TreeLong_NMSfoc_CR
TreeLong_NMSfoc_CR
Group6
1
3
12
36
37
61
2
2
s
i
x
A
0
10
20
Group6
1
3
12
36
37
61
s
i
x
A
30
0
20
40
60
80
Axis 1
OXAR
Axi s 1
r = -.159 tau = - .189
Axi s 2
r = .478 tau = .407
Axis 1
30
QUPR
20
Axi s 1
r = .014 tau = - .012
Axi s 2
r = .118 tau = .079
80
60
40
10
20
0
0
Figure 4: Overlay plot showing the
relative importance of Oxydendrum
arboreum to each sample plot
(IV = 43).
Figure 5: Overlay plot showing the
relative importance of Quercus pinus
to each sample plot (IV = 96).
TreeLong_NMSfoc_CR
Group6
1
3
12
36
37
61
QUAL
OXAR
2
s
i
x
A
QUST
JU VI
FAGR
LITU
Figure 6: Ordination graph
of the sample plots divided
into six groups and arranged
along Axes 1 and 2, with
vectors showing the stronger
relationships between certain
species and axes.
U LAL
C AC R
LIST
Axis 1
The ordination graph in Figure 6 above shows where each sample plot is
located in ordination space. It also contains information about where in the
ordination space each group exists, and how each species is related to the three
ordination axes. Keeping in mind which species are indicators for which group
(Table 2), it is also possible to attain a clearer idea of how each group is related
to each axis. Group 1 is correlated positively with Axis 2, while Group 6 exhibits
a negative correlation with this axis. Group 2 has a positive correlation, and
Group 3 a negative correlation, with Axis 1. Similarly, Group 4 can be positively
correlated, and Group 5 can be negatively correlated, with Axis 3, though a
graphical representation is not given here in the interest of space.
TreeLong_NMSfoc_CR
Group6
1
3
12
36
37
61
3
s
i
x
A
Figure 7: Ordination graph of
the sample plots divided into
six groups and arranged along
Axes 2 and 3, with vectors
showing the stronger
relationships between certain
environmental variables and
the axes.
Al
Elev
D ist-H2O
Mg -A
C a-A
Mn
pH
Axis 2
In the same way, inferences can be made about which environmental
variables are important to which axes by observing the vectors in the ordination
graph in Figure 7 above. Axis 1 is not included in this analysis because it did not
help to interpret the environmental data in any meaningful way. It appears that
Axis 2 is strongly influenced by the availability of water, and, to a lesser degree,
by elevation. Axis 3 is correlated with pH and the presence of certain minerals,
as well as elevation, and probably has something to do with soil chemistry.
By combining this information, it can be inferred, for example, that Group
1, being positively correlated with Axis 2, can tolerate being at a greater distance
from water than Group 6, which is negatively correlated with the same axis.
Similarly, Group 4 appears to be able to tolerate acidic soil, while Group 3 prefers
soils with higher pH. This data shows how environmental factors drive species
composition and the arrangement of forest communities across the Duke Forest.
Discussion
Group 1 has the characteristics of a Mixed Oak / Heath Forest. It occurs
on dry slopes and is composed of Quercus velutina (among other oak species)
Oxydendrum arboreum, and Cornus florida.
Group 2 is a Coastal Plain Dry-Mesic Southern Red Oak Slope Forest.
This forest community type is characterized by such species as Quercus stellata,
Quercus falcata, and Pinus taeda.
Fagus grandifolia and Liriodendron tulipifera individuals dominate group 3
sample plots. They can also be associated with higher soil fertility. This group
represents the Southern Mesic Beech – Tuliptree community type.
Group 4 is dominated by Quercus prinus, and is also represented by
Quercus coccinea. It can tolerate acidic, infertile soils. This is consistent with a
Northern Piedmont Low-Elevation Chestnut Oak Forest community type
(NatureServe Explorer, 2005).
Group 5 appears to have all of the characteristics of a Northern Hardpan
Basic Oak - Hickory Forest community, with the obvious exception that hickory
does not play an important role in its species composition. This community is
known to occur on weathered soils in the Piedmont, which can be found in the
Duke Forest (NatureServe Explorer, 2005). It is possible that a disturbance
specific to hickory trees, such as a disease or parasite that affects only hickory
trees, has removed the hickory trees from the sample plots in this group in the
Duke Forest.
Group 6 shares many of the same species with several forest community
types found across the country. All of these community types are wet,
bottomland forests, but none of them match geographically with the Duke Forest.
Group 6 was strongly associated with high water availability in the Duke Forest
samples. There are many more species serving as indicators for this group than
for any other. It is possible that most of these species rarely occur in the Duke
Forest. Group 6 probably represents all of the sample plots found near streams
or in low lying areas that flood periodically that are much wetter on average than
the rest of the Duke Forest. This allows many species to persist in these
relatively small and scattered areas that would not be able to otherwise.
References
McCune and Grace. 2002. Analysis of Ecological Communities. MjM Software.
Chapter 25.
NatureServe Explorer. http://www.natureserve.org/explorer/. December 5, 2005.