Lecture 1 - Introduction to Geometric Morphometrics
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Transcript of Lecture 1 - Introduction to Geometric Morphometrics
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Rychlik, L., G. Ramalhinho, and P. D. Polly. 2006. J. Zool. Syst. Evol. Res. 44: 339-351.
An introductionGeometric morphometrics
P. David PollyDepartment of Geology, Indiana(Biology and Anthropology)University, 1001 E. 10th Street, Bloomington, IN 47405, [email protected]://mypage.iu.edu/~pdpolly/
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Course websitehttp://www.indiana.edu/~g562/
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Spring 2014 Syllabus
Date Topic Assignments17#Jan#14 Introduction0to0Geometric0Morphometric0Methods0(GMM)
24#Jan#14 Applied:0Introduction0to0Mathematica Assignment01
31#Jan#14 Aopplied:0First0GMM0Analysis Assignment02
7#Feb#14 No0Meeting READING01
14#Feb#14 Applied:0Procrustes,0Principal0components0analysis0and0morphospaceAssignment03
21#Feb#14 Discussion:0Multivariate0tests0and02B#PLS0 READING02
28#Feb#14 Applied:0Multivariate0tests0for0GMM0(proposals0due) Assignment04
7#Mar#14 Discussion:0Randomization0and0Bootstrap READING03
14#Mar#14 Applied:0Bootstrapping0and0randomization0tests Assignment05
21#Mar#14 No0Meeting:00Spring0Break
28#Mar#14 Discussion:0Outlines0and0EDMA READING04
4#Apr#14 Applied:0Outline0analysis0and0EDMA Assignment06
11#Apr#14 Discussion:0Phylogenetic0trees0and0morphometrics READING05
18#Apr#14 Applied:0phylogenetic0trees0and0morphometrics Assignment07
25#Apr#14 Discussion:0evolutionary0and0growth0trajectories READING06
2#May#14 Applied:0Monte0Carlo0simulations Assignment07
5#May#14 Projects0Due:00Monday,0May05
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Computers and Mathematica®Laptops should be brought to class every week. The software we will use is compatible with both Mac and Microsoft operating systems.
General software: If possible, please install the following on your system: ImageJ (http://rsbweb.nih.gov/ij/ ), Adobe Creative Suite (especially Photoshop and Illustrator, http://iuware.iu.edu/ ), Microsoft Office or Mac iWork or OpenOffice (for spreadsheet programs, http://iuware.iu.edu/ ).
Mathematica®: Most of our work will be done in the Mathematica which is a mathematical and statistical application that does efficient computations, is flexible for customized analysis, has powerful graphics capabilities, and is easy to learn (compared to R, for example, which is an equivalent application). You can purchase a student license for Mathematica 8.04 at the IU Stat/Math Center at 410 Park Avenue for $30 (cash or check only). They will provide licence code and download link for installation.
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Participation 20% Assignments 20% Reading reports 10% Project proposal 10% (due 7 March) Project report 40% (due 5 May)
Grading
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
ProjectsThe focal assignment for the course is to carry out an original morphometric study that you will present as a written project paper. Ideally your project will be related to your broader research interests. During the first half of the course you will develop your study, with advice if you need/want it.
Project proposals are due mid semester. Proposals consist of a one to two page description of the aim and subject of your project, the source of your data, the question your study will try to answer, and the tools you’ll need to collect your data. Please feel free to consult me as you develop your proposal.
The final project report should be modelled on a scientific journal paper, with introduction to the problem, materials and methods, results, discussion, conclusion, references (cited properly in the journal format of your choice). Target length is 10-15 pages, including figures, tables, and references.
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Supplementary texts
Hammer, Ø. and D.A.T. Harper. 2006. Palaeontological Data Analysis. Blackwell Publishing, Oxford, United Kingdom.
Zelditch, M.L., D.L. Swiderski, H.D. Sheets, and W.L. Fink. 2004. Geometric Morphometrics for Biologists: a Primer. Elsevier Academic Press, San Diego, California.
MacLeod, N. 2012. Palaeo Math 101. A series of essays published in the Palaeontological Association Newsletter. http://www.palass.org/modules.php?name=palaeo_math
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
What are morphometrics?
Any quantitative measurement and analysis of morphological traits
Mandible Length (cm)
Man
dib
le H
eig
ht
(cm
)
Shrew
Marmot
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Geometric morphometricsthe quantitative representation and analysis of morphological shape using geometric coordinates instead of measurements
Component 1 Com
ponent 2
Shrew
Marmot
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
The Major Goal of Morphometrics:Measuring morphological similarity and difference
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Types of geometric representationOutlines (2D or 3D)Semilandmarks, sliding landmarks
3D surfaces
Landmarks (2D or 3D)
Polly, P. D. 2008. Adaptive Zones and the Pinniped Ankle: A 3D Quantitative Analysis of Carnivoran Tarsal Evolution. Pp. 165-194 in (E. Sargis and M. Dagosto, Eds.) Mammalian Evolutionary Morphology: A Tribute to Frederick S. Szalay.
Springer: Dordrecht, The Netherlands.
Polly, P. D. 2003. Paleophylogeography: the tempo of geographic differentiation in marmots
(Marmota). Journal of Mammalogy, 84: 369-384.
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Definitions
Landmark – any point described with cartesian coordinates (x, y, z) used to represent the shape of a structure.
Landmark (2) – any point that can be placed on a biologically or geometrically homologous point on the structure.
Semi-landmark – a point that is placed arbitrarily using an algorithm, often by defining endpoints at biologically homologous points and placing a specified number of semilandmarks between them.
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
0 10 0
10
5
5
X-axis
Y-ax
is
(2,5)
(4,8)
(5,2)
(6,8)
(6,2)
Landmarks
Landmarks are coordinate points used to represent a shape
They are quantified as Cartesian coordinates (x,y[,z])
At least 3 are required (two points make a line)
Example analyses: Relative Warps (PCA of landmarks), Euclidean Distance Matrix Analysis (EDMA) of distances between landmarks
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
0 10 0
10
5
5
X-axis
Y-ax
is
Outlines
Outlines are perimeters delimited by many points
They are quantified as Cartesian coordinates (x,y[,z]), often converted to angles
Many points are required to represent a shape
Example analyses: Semilandmarks, sliding semilandmarks, Eigenshape (PCA of outline), Fourier analysis
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Polly, P. D. 2008. Adaptive Zones and the Pinniped Ankle: A 3D Quantitative Analysis of Carnivoran Tarsal Evolution. Pp. 165-194 in (E. Sargis and M. Dagosto, Eds.) Mammalian Evolutionary Morphology: A Tribute to Frederick S. Szalay.
Springer: Dordrecht, The Netherlands.
Surfaces
Surfaces are the 3D surface of an object
They are quantified as Cartesian coordinates (x,y,z)
Many points are required to represent a shape
Example analysis: Eigensurface (PCA of surfaces), sliding semilandmarks
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Advantages to geometric representation
Results can be presented visually as a “shape” than tables of numbers
Data are easily collected from digital photographs
Size is mathematically removed from the analysis to focus on pure shape
X-axis
Y-ax
is
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Y-ax
is
X-axis
Y-ax
is
Vector Plot
Spline Plot
GMM results can be presented graphicallyTwo examples of graphically showing those differencesDifference in shape of mandibles
of shrew and marmot
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Marmot
Shrew
Traditional morphometrics mixes size and shapeThe size of the animal affects all measurements so that primary morphometric difference between two taxa is size rather than shape
Marmot
Shrew
0
5
10
15
20
25
Mill
imet
res
H L H L
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Marmot
Shrew
Geometric morphometrics removes size by rescalingShapes are enlarged or reduced to achieve a standard, equal size
Coordinates of rescaled landmarks show difference in relative position only
X-axis
Y-ax
is
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Disadvantages of geometric representationSize is completely absent from the analysis, and size may be biologically relevant
Only single rigid structures can be easily analyzed
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
-4.0 -2.0 0.0 2.0 4.0 Log body mass (kg)
Log
met
abol
ic ra
te (O
2 /hr
/g)
data from Eisenberg, 1981
Size is biologically importantand it may be of interest in a morphometric analysis
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Polly, P. D. 1998. Variability in mammalian dentitions: size-related bias in the coefficient of variation. Biological Journal of
the Linnean Society, 64: 83-99.
Size and shape may behave differentlySize or shape data may be appropriate for different analyses
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Only single rigid structures can represented with geometric morphometrics
Okay Not okay
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
A short history of geometric morphometrics....
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Albrecht Dürer (1471 -1528)
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
On Growth and Form, 1917
D’Arcy Thompson (1860-1948)
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Francis Galton (1822-1911)
1891: starts biometric laboratory at University College London
Biometric approach to genetics: regression & correlation
Composite portraiture: photographs of different subjects combined (through repeated limited exposure) to produce a single blended image
Anthropometry & differential psychology: quantitative analysis of fingerprints
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Modern Geometric Morphometric Methods (GMM)Development of landmark geometrics was driven by Fred Bookstein (long of University of Michigan, now Washington and Vienna)
Joined very productively by F. James Rohlf (Stony Brook)
Ian Dryden, Kanti Mardia, Les Marcus, and Dennis Slice have been important names in developing techniques and theory.
Bookstein was originally intent on creating a truly quantitative way of producing d’Arcy Thompson transformation grids.
Bookstein
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Steps in a geometric morphometric study
Study design
Data collection
Data standardization
Analysis
Results interpretation
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
How do you choose landmarks (or outlines, or surfaces)?1. The data must reflect a hypothesis
2. The data must represent the shape adequately
3. Landmarks must be present on all specimens
Measurement Error and Sample size
1. Measurement error (ME) always exists in any collection of data, but ME doesn’t matter if it is substantially less than the differences you want to measure.
2. Sample size required for a particular study depends on the within-group variation relative to differences between groups.
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
How many specimens do I need?
• Depends on the question being addressed
• Depends on the error in your data
• You need more specimens when the differences you want to measure are small compared to the variation within your group (natural or due to error)
• For sexual dimorphism in skulls of humans or other primates, 10 individuals of each sex might be enough
• For differences in genetic strains of mice where the mutation doesn’t obviously affect the skeleton, 50 individuals of each strain is more realistic
• For species that belong to different families or orders, 1 specimen per species is almost always sufficient
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
What morphometrics can’t answer for you..
• Morphometrics does not tell you what ‘large’ or ‘difference’ or ‘shape’ mean(These are definitions you must supply and your results depend upon them)
• Morphometrics does not tell you whether you unwittingly have two unrecognized groups in a single sample(Although comparison with known groups may help such an endeavour)
• How to identify cladistic characters(For the first two reasons combined)
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Examples of available software
Digitizing landmarks and outlines: tpsDIG, ImageJ
Superimposition: Morpheus (plus integrated in some below)
Outline analysis: Eigenshape, PAST
MANOVA: Statistica, PAST
Discriminant functions, CVA: Statistica, PAST
Principal components analysis of landmarks: tpsRELW, PST
Construction of trees: PHYLIP, PAUP, NTSYSpc, PAST
Simulations: Mathematica, R
Links and downloads at SUNY Stony Brook morphometrics site: http://life.bio.sunysb.edu/morph/
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Equipment: 2D outlines and coordinates
High-quality digital cameras
(resolution doesn’t matter as much as the possibility of lens distortion: test your camera first by photographing a piece of graph paper and looking for “fish eye” distortion)
Calipers or scale bar
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
Equipment: 3D outlines and coordinates
Reflex Microscope for collectingthree-dimensional landmarks, outlines and measurements (good for objects the size of a cat skull down to things about 2-5 mm long)
Microscribe robotic arm for collecting 3D landmarks and measurements (good for objects the size of a human skull down to a rat skull)
Department of Geological Sciences | Indiana University (c) 2012, P. David Polly
G562 Geometric Morphometrics
3D surfaces
Microscan Laser scanner for scanning surfaces (good for objects the size of a cat skull down to ones about 2-3 cm long)
NextEngine laser scanner (good for objects the size of a horse skull down to a single tarsal bone)