Cluster Analysis of Abiotic Environmental Characteristics

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Cluster Analysis of Abiotic Environmental
Characteristics

• Sandy Gillespie
• Holly Bernardo
• Nicole Soper Gorden

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The Data - Background
Open Area
Understory
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The Data - Background

• 32 plots (16 understory, 16 open area)
• Set of abiotic characteristics
• Percent canopy cover
• Soil moisture
• Soil pH
• Photosynthetically active radiation (ppf)

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The Data - Background

• Wanted to test how well the designations open
  area and understory represent true abiotic
  characteristics of the area
• In other words, do the abiotic characteristics
  cluster plots into those two groups?

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The Data - Screening

• Normality
• Canopy and ppf non-normal in univariate space
• But were working in multivariate space

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The Data - Screening

• Standardization
• Columns in different units!
• Column standardization
• Z-scores scale them all the same
• Outliers
• No univariate outliers
• No multivariate outliers (Bray-Curtis)

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The Data - Screening

• Correlations
• Spearman correlation coefficients
• Canopy and ppf
• Soil moisture and pH

Significant, with Plt0.0001
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The Data Distance Metric

• Chose Euclidean distance
• Continuous data
• No uninhabitable space
• No need to be proportional
• Correlations suggest Mahalanobis distance
• BUT only useful after clusters formed
• Balanced correlations (2 and 2)

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Hierarchal or Non-hierarchal?

• Sample size suggests HC
• 32 plots (small)
• Goals suggest NHC
• Looking for environmental clusters, not ranked
• We did both (exploratory)

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Non-Hierarchal Clustering

• Makes sense even with small of variables
• K-Means Expected of groups
• 1) specify seeds
• 2) all samples are assigned to nearest seed
• 3) compute centroids and variances
• 4) move samples to closest centroid
• 5) new centroids and variances
• Until the variance in each group no longer gets
  any smaller
• i.e. maximized the within group homogeneity

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Evaluating our choice of 2 clusters
Or maybe 3?
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3 clusters
So we ran the analysis both ways
2 clusters
Jaccard bootstrap mean 1 0.9716024 2
0.9242937 3 0.9385516
Jaccard bootstrap mean 1 0.9413424 2
0.9224089
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Box plots of the 2 cluster solution
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Box plots of the 3 cluster solution Despite our
original prediction of 2 groups, going to go with
3
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Polytheic Heirarchical Clustering
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Introduction

• While the purpose of this study was better suited
  to Non-Heirarchical clustering, the low number of
  entities means that HC might give interesting
  insight into relationships between 3 groups
  described by NHC

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Clustering strategy

• Goal Maintain original data structure
• Used Average Linkage
• Compared with Wards
• Also tried Diana Divisive clustering
• Reminder Still using Euclidian distance, for
  reasons mentioned above

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Results
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Evaluating the Cluster solution

• Average Linkage
• Agglomerative Coefficient 0.8026942
• Cophenetic Correlation 0.8381367
• Wards
• Agglomerative Coefficient 0.9732249
• Cophenetic Correlation 0.779189
• Wards has denser clusters - not surprising
• Average linkage has higher Cophenetic correlation
  - better representation of original data

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We decided to use the 3 cluster solution
3 Cluster solution is at obvious elbow
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Cluster Stability for 3 cluster solution
Evaluated using bootstrap
Clusterwise Jaccard bootstrap mean 1 1.0000
0.9975 0.9975 dissolved 1 0 0 0 recovered 1
100 99 99 Clusterwise Jaccard subsetting
mean 1 0.9923687 0.9574524 0.9801667 dissolved
1 0 3 1 recovered 1 99 90 97
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Describing the clusters
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This solution looks great, so wed expect the
same results with Divisive Heirarchical
Clustering, right?
Close, but not quite Divisive Coefficient
0.87 Coph. Corr 0.8138967 - Comparable to our
findings with Average Linkage
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26 looks like a moderate outlier in its canopy
cover, which may explain strange grouping in
Divisive method
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Hierarchal or Non-hierarchal?

• Consistent clustering with both
• HC more common for small sample size
• But small sample size can be used in either
• NHC makes the most sense ecologically
• Data is not hierarchal in nature

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Ecological Importance
Open Area
Understory

• 1 2 3 4 5
  6 7 8 9 10
  11 12 13 14 15
  16

17 18 19 20 21 22
23 24 25 26 27
28 29 30 31 32
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Ecological Importance

• Understory/open area cluster by light
• Understory is broken apart by soil moisture and
  pH
• Wet acidic
• Dry basic

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Ecological Importance

• 2 initial designations not full picture!
• Microhabitats in understory
• Important to measure several abiotic
  characteristics