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CHAPTER 5
Species on Environmental Gradients
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
Figure 5.1. Hypothetical species abundance in response to an environmental
gradient. Lettered curves represent different species. Figure adapted from
Whittaker (1954).
Figure 5.2. Hypothetical linear responses of species abundance to an environmental
gradient. Lettered lines represent different species.
Three major problems with community data
1. Species responses have the zero truncation
problem.
Figure 5.3. The zero truncation problem.
Three major problems with community data
1. Species responses have the zero truncation
problem.
2. Curves are “solid” due to the action of many other
factors.
Figure 5.4. A “solid” response curve. Points
represent a species abundances.
Three major problems with community data
1. Species responses have the zero truncation
problem.
2. Curves are “solid” due to the action of many other
factors.
3. Response surfaces can be complex: polymodal,
asymmetric, or discontinuous
1.2
Sp 1
Cover,
%
0.8
0.4
0.0
2.0
Figure 5.5. Scatterplot of
abundance, measured as cover, of
four species in relation to a
gradient. Each point is a plot.
Least-squares linear regression
lines and fitted envelope lines are
shown.
Sp 2
Cover,
%
1.0
0.0
2.0
Sp 3
Cover,
%
1.0
0.0
2.0
Sp 4
Cover,
%
1.0
0.0
Gradient
Number of plots
80
70
60
50
40
30
20
10
0
0
10
20 30 40 50
Basal area, dm2 /plot
60
Figure 5.6. Frequency distribution of abundance for a typical tree species in a forest in
southern Indiana. The abundance data are basal areas in about 90 plots. Note that most
plots do not contain the species, but a few plots have large amounts of the species.
Abundance
Abundance
Sp 2
Sp 1
3
2
1
0
2
1
0
4
4
3
3
Sp 2
Sp 2
3
10 20 30 40 50
Environmental Gradient
2
1
10
20 30 40 50 60
Environmental Gradient
70
2
1
0
0
0
2
Sp 1
4
0
2
Sp 3
4
4
4
Abundance
Abundance
Sp 2
Sp 3
0
0
Sp 2
Sp 1
3
2
1
0
Sp 2
Sp 3
3
2
1
0
0
10 20 30 40 50
Environmental Gradient
0
4
4
3
3
Sp 2
Sp 2
Figure 5.7. Bivariate species distributions
from species responses to environmental
gradients. Left column: two positively
associated species. Right column: two
negatively associated species. (A) 
Positively associated species following
Gaussian ideal curves. (B)  Negatively
associated species following Gaussian ideal
curves. (C)  Bivariate distribution of
species abundances corresponding to A. (D)
 Bivariate distribution of species abundances
corresponding to B. (E)  Positively
associated species with “solid” responses to
the environmental gradient. (F)  Negatively
associated species with “solid” responses to
the environmental gradient. (G)  Bivariate
distribution of species abundances
corresponding to E. (H)  Bivariate
distribution of species abundances
corresponding to F.
4
4
2
1
0
0
2
Sp 1
4
20 30 40 50 60
Environmental Gradient
2
1
0
10
0
2
Sp 3
4
70
Figure 5.8. The dust bunny distribution in
ecological community data, with three levels
of abstraction. Background: a dust bunny is
the accumulation of fluff, lint, and dirt
particles in the corner of a room. Middle:
sample units in a 3-D species space, the three
species forming a series of unimodal
distributions along a single environmental
gradient. Each axis represents abundance of
one of the three species; each ball represents a
sample unit. The vertical axis and the axis
coming forward represent the two species
peaking on the extremes of the gradient. The
species peaking in the middle of the gradient
is represented by the horizontal axis.
Foreground: The environmental gradient
forms a strongly nonlinear shape in species
space. The species represented by the vertical
axis dominates one end of the environmental
gradient, the species shown by the horizontal
axis dominates the middle, and the species
represented by the axis coming forward
dominates the other end of the environmental
gradient. Successful representation of the
environmental gradient requires a technique
that can recover the underlying 1-D gradient
from its contorted path through species space.
Figure 5.9. Comparison of the normal and
dust bunny distributions. Upper left.
the bivariate normal distribution forms an
elliptical cloud most dense near the center
and tapering toward the edges. The more
strongly correlated the variables, the more
elongate the cloud. Upper right. the
bivariate dust bunny distribution has most
points lying near one of the two axes. A
distribution like this results from two
overlapping “solid” Gaussian curves (Fig.
5.4). Lower left. the multivariate
normal distribution (in this case 3-D)
forms a hyperellipsoid most dense in the
center. Elongation of the cloud is
described by correlation between the
variables. Lower right. the multivariate
dust bunny has most points lying along the
inner corners of the space. Two positively
associated species would have many
points lying along the wall of the
hypercube defined by their two axes.
Normal
Dust bunny
2-D
Sp 2
Sp 1
Sp 1
3-D
Sp 3
Sp 2
Sp 1
Sp 3
Sp 1
6
Species 1
5
4
3
2
1
0
0
2
4
6
Species 2
Figure 5.10. Plotting abundance of one species against another reveals the
bivariate dust bunny distribution. Note the dense array of points near the origin
and along the two axes. This bivariate distribution is typical of community
data. Note the extreme departure from bivariate normality.
[0, 18, 2]
Sp B
0
Sp C
0
[0, 0, 0]
Sp A
Figure 5.11. Nature abhors a vacuum. A sample unit with all species removed is
usually soon colonized. The vector shows a trajectory through species space. The
sample unit moves away from the origin (an empty sample unit) as it is colonized. In
this case, species B and a bit of species C colonized the sample unit. As in this
example, successional trajectories tend to follow the corners of species space.
0.1
0.0
r -0.1
-0.2
-0.3
0
20
40
60
80
100 120
Number of added 0,0's
Figure 5.12. The consequence for the correlation coefficient of adding
(0,0) values between species.
Box 5.1. Basic properties of ecological community data.
1. Presence or abundance (cover, density, frequency,
biomass, etc.) is used as a measure of species performance in
a sample unit.
2. Key questions depend on how abundances of species
relate (a) to each other and (b) to environmental or habitat
characteristics.
3. Species performance over long environmental gradients
tends to be hump-shaped or more complex, sometimes with
more than one hump.
4. The zero-truncation problem limits species abundance as a
measure of favorability of a habitat. When a species is
absent we have no information on how unfavorable the
environment is for that species.
Basic properties, cont...
5. Species performance data along environmental
gradients form “solid” curves because species fail for
many reasons other than the measured environmental
factors.
6. Abundance data usually follow the “dust bunny”
distribution, whether univariate or multivariate; the data
rarely follow normal or lognormal distributions.
7. Relationships among species are typically nonlinear.
Table 5.1. Solutions to multivariate analytical challenges posed by the basic properties of ecological community data
(Box 5.1). The various classes of problems and their solutions are explained in the remainder of this book.
Class of problem
Example solution, appropriate for
community data
Solutions based on a linear model,
usually inappropriate for community
data
Measure distances in
multidimensional space
Sørensen distance (proportionate
city-block distance)
Euclidean distance or correlationbased distance
Test hypothesis of no multivariate
difference between two or more
groups (one-way classification)
MRPP or Mantel test, using
Sørensen distance
one-factor MANOVA
Single factor repeated measures,
randomized blocks, or paired sample
blocked MRPP
randomized complete block
MANOVA, repeated measures
MANOVA
Partition variation among levels in
nested sampling
nonparametric MANOVA
(=NPMANOVA)
univariate nested ANOVA
Two-factor or multi-factor design
with interactions
NPMANOVA
MANOVA
Evaluate species discrimination in
one-way classification
Indicator Species Analysis
Discriminant analysis
Extract synthetic gradient
(ordination)
Nonmetric multidimensional scaling
(NMS) using Sørensen (Bray-Curtis)
distance
Principal components analysis
(PCA)
Assign scores on environmental
gradients to new sample units, on
basis of species composition
NMS scores
linear equations from PCA