TENTATIVE COURSE OUTLINE
1. Definitions and assumptions
2. Describing forms: boundaries and landmarks
Mathematical models of boundaries
Conics , polynomials , and circular functions
Radial functions, tangent angles, and medial axes
Fourier and elliptical-Fourier functions
Modeling sets of forms: landmark configurations
Characters and homology
Landmarks and other points
Conventional character sets
Mapping functions
From distances to landmarks
Triangulations, trusses, and Euclidean distance matrices
Choleski factorization and multidimensional scaling
Procrustes superimposition
Shape spaces
Descriptions in three dimensions
Proportions and ratios : resisting the temptation
Fractals and L- systems : self-similar forms
Technology of measurement
3. Allometry and scaling
Size
Shape
Size-and-shape, and shape-minus-size
4. Very quick, bare-bones overview of:
Inferential hypothesis testing and statistical assumptions
Randomization tests
Optimization
5. Covariance patterns
Covariation and correlation
Predictive and major -axis regression
Principal component analysis
Multivariate allometry
Morphological spaces and predicted forms
6. Factor models and size/shape decomposition
Path analysis
Factor analysis
Shear and Burnaby size-adjustment procedures
Discriminant and canonical-variate analysis
Size-invariant (“size-free”) discriminant analysis
Canonical correlation analysis
Partial least -squares regression
Eigenshape analysis
7. Geometric transformations
Vector methods
Elastic deformation and affine transformations
Shape coordinates
Thin-plate splines
Decompositions of deformations: warps
8. Ontogenetic trajectories
Organisms as four-dimensional (space/time) objects
Allometry: form- change as a function of size
Growth: form- change as a function of time
Heterochrony and morphological spaces
9. Morphometric data and phylogenetic inference
Estimating phylogenetic trees
Parsimony, consistency, and morphometric data
Punctualism vs. random walk
Discrete methods: coding morphometric data
Continuous methods: parsimony and maximum- likelihood
Character evolution
Mapping continuous characters onto trees
Mapping trees onto morphological spaces
Heterochrony revisited
Evolutionary rates
Rates of what?
Punctualism vs. gradualism: ends of a continuum
10. Other related issues that we probably won’t get to but should
Quantitative genetics and Mendelian quantitative trait loci (QTLs)
Pattern formation and morphogenesis
Bilateral asymmetry
Reaction-diffusion (Turing) models of pigmentation patterns
Kinematic and fluid-dynamic growth models
Biomechanical models
CALENDAR
| M |
Aug 27 |
First class |
| M |
Sep 3 |
Labor day, no class |
| M |
Sep 28 |
Exam 1 |
| F |
Oct 12 |
Fall break, no class |
| M |
Oct 29 |
Exam 2 |
| M |
Nov 19 |
Library assignment due |
| F |
Nov 23 |
Thanksgiving break, no class |
| M |
Dec 3 |
Last class |
| T |
Dec 11, 5:30pm |
Final Exam |
| Th |
Dec 13 |
Final written paper due (5 p.m.) |
LIBRARY ASSIGNMENT
Locate and read 10 journal articles involving morphometric applications and
found in the
literature pertaining to your personal interests or organisms. From these,
choose the one “best”
paper based on the following criteria: (1) that it involve a biological problem
of interest to you;
and (2) that it apply a morphometric methodology to solve the problem .
Write a short (2–5 page) critique of the paper. Briefly state its objectives and
indicate why
you found the problem to be an interesting one. Decide whether the quantitative
morphological
approach taken by the author(s) is appropriate to the solution of the problem ,
and whether the
author’s conclusions are warranted. Describe any limitations or unwarranted
assumptions.
Append a copy of the paper (or of relevant portions, if it’s lengthy) to your
report.
Provide an annotated bibliography (including complete citations and short
abstracts) of the
other nine papers examined but not selected.
You are encouraged to submit your paper, and the journal paper on which it is
based,
electronically rather than as hardcopy.
FINAL PROJECT
The final project will consist of a morphometric analysis of a data set and will
result in a
written report. The nature of the question, source of the data, and kinds of
analysis employed are
all quite flexible. The question will probably concern some aspect of
morphological variability
or discrimination, and the data set may be your own or one obtained from the
literature. The only
requirements are that it be adequate and sufficiently large to test the
hypothesis in question.
The primary requirement of the project is that the data and analysis must
address one or
more specific morphological hypotheses or questions, which are to be
studied using an
appropriate quantitative method of analysis . Analytic procedures can be either
exploratory
(exploring the structure of the data) or confirmatory (formally testing a
hypothesis). The
primary goal is logical clarity , not number crunching. The data may
derive from your own
research, past or present, but if so you must carry out an analysis different
from any that you’ve
done in the past. The idea is to do and learn something new, not rehash
something old.
The report need not be lengthy but should be written in standard scientific
format (i.e., with
abstract, introduction, methods, results, and discussion). It should include a
short, general
description of the problem, a paragraph or two in length, with enough
background information
to allow me to understand what question you're asking, why you’re asking it, and
why you find it
interesting; justification of methods of analysis, including any data
transformations (if used); a
list of the assumptions underlying the study, both biological and
statistical, and an assessment of
the importance of each assumption in strengthening or weakening the final
conclusions; a
description of the analytic procedures (methods); tabular and graphic
summaries of results; and
conclusions, including a discussion of how the assumptions affect your
confidence in the results.
You are encouraged to submit your paper electronically rather than as hardcopy.
