Properties of Community Data in Ecology

1
Properties of Community Datain Ecology
Adapted from Ecological Statistical Workshop,
FLC, Daniel Laughlin
2
Community Data Summary

• Community data matrices
• Species on gradients
• Problems with community data
• Normality assumptions

Key questions to keep in the back of your
mind 1. How do species abundances relate to each
other? 2. How do species relate to environmental
gradients?
3
Community data matrices
or Molecular marker
Independent sample units
SPARSE
(abundance or presence/absence used as a measure
of species performance)
Traits
4
Full Community Dataset
n of sample units (plots) p of
species t of traits e of
environmental variables or factors d of
dimensions
n x p
n x e
n x t
n x d
plots in species space
plots in envir space
plots in trait space
traits in species space
plots in reduced species space
t x p
t x e
used for species in environmental space (AE)
traits in envir space
e x p
species in reduced plot space
d x p
Ordination can address more questions than how
plots differ in composition
5
Species on environmental gradients
Gaussian ideal - peak abundances, nonlinear -
this is challenging to analyze
Linear responses to gradients - okay for short
gradients
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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 curves can be complex
4. High beta diversity
5. Nonnormal species distributions

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Major Problems with Community Data
1. Zero truncation
2. Solid curves

• species responses truncated at zero
• only zeros are possible beyond limits
• no info on how unfavorable the environment is
  for a species

• curves are typically solid envelopes rather
  than curves
• species is usually less abundant than its
  potential (even zeros are possible)

8
Major Problems with Community Data
3. Complex curves -polymodal, asymmetric,
discontinuous
Average lichen cover on twigs in shore pine bogs
in SE Alaska.
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High beta diversity

• Beta diversity the difference in community
  composition between communities along an
  environmental gradient or among communities
  within a landscape

10
Whittakers (1972) Beta Diversity
? number of species in composite sample (total
number of species) ? average species richness
in the sample units No formal units, but can be
thought of as number of distinct communities
The one is subtracted to make zero beta diversity
correspond to zero variation in species
turnover. Rule of thumb ßw lt 1 are low, ßw gt 5
are high
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Are species distributions normal?

• Univariate normality (its what were used to)
• Bivariate normality (its easy to visualize)
• Idealized community data
• Real community data
• Multivariate normality (straightforward extension
  of bivariate normality to multiple dimensions)

12
Univariate normality
Skew 0 Kurtosis 0
Normality can be assessed by skewness
(asymmetry), and kurtosis (peakiness)
13
Skewness

• Community data will nearly always be positively
  skewed due to lots of zeroes
• Linear models require skew lt 1
• Assess skewness of data in PCORD (Row and Column
  Summary)

14
Positively skewed distribution typical of
community data
HYVI
PLHE
HYIN
15
Bivariate Normality
Views from above
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Bivariate Species Distributions
positive association
negative association
bivariate distribution is non-linear
dust bunny distribution-plotting one species
against another (lots of points near orgin and
along axes)
Idealized Gaussian species response curves
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Bivariate Species Distributions
positive association
negative association
dust bunny distribution
dust bunny distribution
Realistic data with solid response curves
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Bi- and Tri-variate Distributions
Bivariate normal distribution forms elliptical
cloud
Bivariate distribution with most points lying
near one or two axes
Multivariate normal distribution (hyperellipsoid)
Multivariate dust bunny distribution
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Dust bunny in 3-D species space
Environmental gradients form strong non-linear
shape in species space
20
A cluster within the cloud of points (stands)
occupying vegetation space. B 3 dimensional
abstract vegetation space each dimension
represents an element (e.g. proportion of a
certain species) in the analysis (X Y Z
axes). A, the results of a classification
approach (here attempted after ordination) in
which similar individuals are grouped and
considered as a single cell or unit. B, the
results of an ordination approach in which
similar stands nevertheless retain their unique
properties and thus no information is lost (X1 Y1
Z1 axes). Key Point Abstract space has no
connection with real space from which the records
were initially collected.
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Multivariate Normality

• Linear algebra easily extends these concepts into
  multiple dimensions
• Most multivariate methods assume multivariate
  normality (linear ordination methods)
• Ecological data are seriously abnormal
• Thus, we will often require different methods