introduction to numerical methods in community ecology

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introduction to numerical methods in community
ecology

• 01.18.20

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data collection

• what do you want to know??
• determine sampling methods/procedures
• layout sites/plots
• record species presence
• record physical/environmental characteristics

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data collected now what?
Community data (vegetation, organisms, etc)
Environmental data (pH, slope, cover, etc)
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matrices and dimensionality
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what do you want to know???

• generically, relationships about how a change in
  vegetation/organism communities is associated
  with a change in an environmental
  variable/gradient

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what do you want to know???

• Goals of Community Analysis
• Summarize the information of complex datasets
  efficiently (i.e., pattern detection in the sense
  of Kenkel et al. 1989)
• Reveal trends and relationships (e.g.,
  distribution of species relative to environmental
  gradients)
• Generate hypotheses about causal relationships
  (why does species x occur where it does?)

notes from Wentworth BO565 (2005)
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ask the expert!!!
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community formats

• Cover
• Presence-absence
• Richness
• Relative abundance, density, frequency
• Biomass
• Density
• Frequency
• Composition
• Importance value
• Basal Area (veg only)

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variable formats

• Categorical
• Observations (i.e. soil type)
• Group definition (i.e. treatment/control)
• Ordinal
• Ranked loss of statistical power but avoids
  distributional assumptions
• Measured
• Discontinuous (i.e. cover classes)
• Continuous (i.e. cover)

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data transformations
ADJUSTS THE EFFECT OF RARE AND ABUNDANT
SPECIES TO REMOVE EFFECTS OF OUTLIERS

• Monotonic
• Log
• Square-root
• Power
• Relativization
• coefficient of variation
• maximum
• mean
• Rare species delete?
• Rule of thumb? lt5 of sample

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ecological distances

• Measure of dissimilarity of sites
• analogous to constructing the triangular mileage
  triangle (EXCEPT MULTIDIMENSIONAL!!)

(McCune and Grace 2002)
http//www.hm-usa.com/distance/usa.html
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distance measures

• Sorenson (Bray-Curtis, Czekanowski)
• Jaccard
• Euclidean
• Chi-Square
• Correlation distance
• Relative Sorenson, Euclidean

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Euclidean (Pythagorean) distance

• may not be best for ecological datasets why??

Figure (McCune and Grace 2002)
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Sorenson (Bray-Curtis)

• shared abundance/total abundance
• probably most popular distance measure

Figure (McCune and Grace 2002)
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Sorensen Index (qualitative)

• Consider two plots, A and B
• A B
• species 1 Cs 2w/(ab)
• species 2 4/(43)
• species 3 0.57
• species 4 Ds 1-Cs
• species 5 0.43
• w species in common 2
• a species in A 4
• b species in B 3

Example from Wentworth Lecture Notes 2005
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A Distance Matrix

• Our complex community data may now be summarized
  in a distance matrix
• A B C D
• A .00 .43 1.0 .15
• B .00 .57 .28
• C .00 .85
• D .00

Example from Wentworth Lecture Notes 2005
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Ecological distances so what?

• Defining groups (today) classification
• Stepwise/not stepwise
• Hierarchical or non-hierarchical
• Agglomerative or divisive
• Polythetic or monothetic
• Identifying patterns (thursday) ordination
• direct
• indirect

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defining groups - numerical classification

• Stepwise
• or
• non-stepwise

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defining groups - numerical classification

• Or
• non-hierarchical no subgroups (reduction of
  within group variance)

• Hierarchical - has subgroups (dendrogram)

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defining groups - numerical classification

• Agglomerative assembles from bottom up
• or
• Divisive divided from top down

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defining groups - numerical classification

• Polythetic - (use all variables in data set)
• or
• monothetic (use presence/absence of key species)

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classification - cluster analysis
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classification - cluster analysis

• start with the distance matrix
• find two least dissimilar units (shortest
  mileage)
• link the two units into a single unit
• recompute distance matrix
• return to step (2)
• stop when all plots belong to single group

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group linkage
rules for defining how across-plot distances are
measured

• Nearest neighbor
• Farthest neighbor
• Median
• Group average
• Centroid
• Wards (minimum variance)
• Flexible beta
• McQuittys method

List from (McCune and Grace 2002)
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comparing groups attribute by groups

• comparison of traditional averages of community
  attributes

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comparing groups MRPP

• MRPP Multi-response Permutation Procedures
• Nonparametric based on ranks advantage because
  no distributional assumptions
• Ho no difference between two (or more) groups,
  example treatment (fertilized) vs. control
  (unfertilized)
• Provides a measure of effect size, and a
  p-value

(McCune and Grace 2002)
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comparing groups indicator species analysis

• detects the ability for individual species to
  indicate environmental conditions
• based on species abundance and frequency of
  occurrence in a group
• Spartina alterniflora ? salinty
• Damselflies ? fine root hairs

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comparing groups discriminant analysis

• attempts to identify which environmental
  variables are reliable predictors of group
  membership
• high salinity? Spartina alternaflora
• fine root hairs ? damselflies

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comparing groups discriminant analysis

• limited applicability due to
• Parametric assumes
• Homogenous within-group variances
• Multivariate normality (within groups)
• Linearity (among all variables)
• Requires pre-defined groups (training set)
  prior probabilities