Eigensurface Analysis a new way to analyze

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Eigensurface Analysisa new way to analyze
model morphological data
Norman MacLeod Department of Palaeontology, The
Natural History Museum
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Morphometric Analysis
Example Dataset Neogene Bivalves
Astarte mutabilis
Astarte obliquata
Astarte omalii
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Morphometric Analysis
Landmarks
Outlines
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Morphometric Ordination
2D Landmarks
2D Outlines
M 4
M 4
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Morphometric Ordination
2D Landmarks
2D Outlines
Sample Mean
Sample Mean
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Morphometric Ordination
2D Landmarks
2D Outlines
A. mutabilis Mean
A. mutabilis Mean
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Morphometric Ordination
2D Landmarks
2D Outlines
A. obliquata Mean
A. obliquata Mean
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Morphometric Ordination
2D Landmarks
2D Outlines
A. omalii Mean
A. omalii Mean
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Morphometric Analysis
Example Dataset Neogene Bivalves
Astarte mutabilis
Astarte obliquata
Astarte omalii
Do these look like species that intergrade
morphologically?
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Morphometric Analysis
Astarte mutabilis
Astarte obliquata
Astarte omalii
Do these look like species that intergrade
morphologically?
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Problems with Landmarks Outlines

• Landmarks should be used to examine the location
  of structures in 2D or 3D.
• Outlines should be used to examine the shapes of
  objects or character peripheries in 2D or 3D.
• But many specimens, organs, structures, and/or
  characters are of interest to systematists
  because of their surface geometries.

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Problems with Landmarks Outlines
Astarte mutabilis
Astarte obliquata
Astarte omalii
Landmarks and outlines fail to capture important
distinctions between these species because these
sampling protocols dont assess differences in 3D
surface geometry.
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Challenges for Surface-based Morphometrics

• Need to locate xyz points on surfaces of
  specimens.
• Need to arrange the points That represent
  surfaces in a way that ensures inter-specimen
  topological correspondence.
• Need to analyze these data in a way that
  supports ordination and modeling.

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3D Data Collection
Konica-Minolta VIVID 910
Alicona Infinite-Focus Microscope (IFM)
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Morphometric Analysis
Landmarks
Outlines
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3D Surface Data Collection
Astarte mutabilis
Astarte obliquata
Astarte omalii
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Eigensurface Analysis

• Specification of an adaptive surface-sampling
  grid composed of topologic-ally corresponding,
  3D, semi-landmark points.
• Generalized least-squares (GLS) superposition of
  semi-landmark point grid.
• Shape variation summarized as Procrustes
  shape-covariance matrix.
• Singular value decomposition (SVD) of
  shape-covariance matrix.

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Sampling Net Assembly
Astarte mutabilis
Astarte obliquata
Astarte omalii
m86
m86
m86
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GLS Superposition
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Singular Value Decomposition

• Singular values - Analogous to eigenvalues,
  quantify lengths of singular vectors
• Eigensurfaces ( singular vectors) - analogous
  to eigenvectors, quantify relation of major
  direction of shape variance to original variables
• Eigensurface scores - covariance between each
  measured shape and the set of eigensurfaces

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Astarte 3D Dataset
Astarte mutabilis
Astarte obliquata
Astarte omalii
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3D Relative Warps Ordination
A. mutabilis
A. obliquata
A. omalii
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3D Eigenshape Superposition
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3D Eigenshape Ordination
A. mutabilis
A. obliquata
A. omalii
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Eigensurface Superposition
Ten-point Grid
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Eigensurface Ordination
Ten-point Grid
A. mutabilis
A. obliquata
A. omalii
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Alternative Ordinations
3D Landmarks
3D Outlines
3D Surfaces (10 pt. grid)
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Astarte 3D Dataset
Astarte mutabilis
Astarte obliquata
Astarte omalii
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Eigensurface Ordination
Thirty-Point Grid
Ten-Point Grid Size
A. mutabilis
A. obliquata
A. omalii
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Eigensurface Modeling
ESurf-1
ESurf-2
ESurf-3
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Eigensurface Variables ...

• ... can be created from any set of 3D coordinate
  data (e.g., laser scans, optical scans, optical
  stereo scans, CT scans)
• ... can be subjected to statistical hypothesis
  tests
• ... can be represented as images and used as
  input to automated class recognition
  routines/computer vision systems (e.g., neural
  nets)
• ... can be combined with external data to
  quantify morphological correlations with
  function, ecology, behavior, etc.
• ... can be assessed and/or corrected for
  phylogenetic autocorrelation

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Range of Applications

• Estimation of 3D mean shapes
• Analysis of surface shape variance
• Functional morphology, ecomorphology, behavioral
  morphology, morphological biogeography,
  developmental morphology
• Biostratigraphy
• Tempo and mode of morphological change
• Allometry, allomery
• Character analysis, reconstruction of ancestral
  morphology, comparative analysis
• Morphological integration, disparity analysis

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Shape Transformation Grids
Thompsonian Transformation Grid
Thin-Plate Spline
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Eigensurface Modeling
ESurf-1
ESurf-2
ESurf-3
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Eigensurface Analysisa new way to analyze
model morphological data
Norman MacLeod Department of Palaeontology, The
Natural History Museum