From: McCune, B.

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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
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Figure 5.1. Hypothetical species abundance in
response to an environmental gradient. Lettered
curves represent different species. Figure
adapted from Whittaker (1954).
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Figure 5.2. Hypothetical linear responses of
species abundance to an environmental gradient.
Lettered lines represent different species.
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Three major problems with community data
1. Species responses have the zero truncation
problem.
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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.

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Figure 5.4. A solid response curve. Points
represent a species abundances.
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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

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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Figure 5.12. The consequence for the correlation
coefficient of adding (0,0) values between
species.
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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.
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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.
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