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Ecology and EvolutionTutorials
September 2005– August 2006
Workshops Page
Tutorial 1: September
7-9 and September 12-13
Tree Reconstruction and Coalescence Theory (including computer
lab)
Organizers: Dennis Pearl
and Paul Fuerst
Presentation materials (Dennis Pearl):
PDF1, PDF2,
PDF3, PDF4,
PDF5
Tentative Schedule
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Wednesday September 7th
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| 9:00 - 10:00 a.m. |
Introduction, models,
alignments, diagnostics |
Paul Fuerst |
| 10:30 - 11:30 a.m. |
| 2:00 - 3:00 p.m. |
Computer lab: CLUSTAL &
ModelTest |
Paul Fuerst |
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Thursday September 8th
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| 9:00 - 10:00 a.m. |
Parsimony |
Paul Fuerst &
Dennis Pearl |
| 10:30 - 11:30 a.m. |
Maximum Likelihood |
| 2:00 - 3:00 p.m. |
Computer Lab: PHYLIP &
PAUP* |
Paul Fuerst & Dennis Pearl |
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Friday September 9th
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| 9:00 - 10:00 a.m. |
Comparing methods,
Resampling, diagnostics |
Paul Fuerst &
Dennis Pearl |
| 10:30 - 11:30 a.m. |
| 2:00 - 3:00 p.m. |
Computer Lab: PAUP* |
Paul Fuerst & Dennis Pearl |
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Monday September 12th
|
| 9:00 - 10:00 a.m. |
Bayesian Methods |
Dennis Pearl |
| 10:30 - 11:30 a.m. |
| 2:00 - 3:00 p.m. |
Computer Lab: MrBayes |
Dennis Pearl |
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Tuesday September 13th
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| 9:00 - 10:00 a.m. |
Coalescence Theory |
Dennis Pearl |
| 10:30 - 11:30 a.m. |
Computer Lab: Coalescence |
Paul Fuerst |
Abstract:
Phylogenetic trees are commonly used to describe
the evolutionary history of a group of species, and may also be
used to study rapidly evolving individual organisms such as certain
viruses, bacteria or parasites. These trees are high-dimensional,
non-real-valued data objects, with a specific pattern of built-in
dependencies that violate the assumptions of many traditional
methodologies and thus provide a rich source of statistical and
mathematical challenges. This tutorial will provide an introduction
to the area illustrated with some interesting and important biological
problems that can be addressed using phylogenetic techniques.
Reference:
Felsenstein, J (2003) Inferring Phylogenies. Sinauer
Associates
Tutorial for Workshop 4:
March 9-10, 2006
Reaction - Diffusion Models
Organizer: Chris Cosner
Reaction-Diffusion equations have been used extensively
in mathematical ecology as models for the dynamics and interactions
of spatially distributed populations. They provide a way of translating
assumptions about local rates of movement, reproduction, and mortality
into global conclusions about the persistence of populations and
the structure of communities. They can be derived as continuum
limits of spatially discrete stochastic processes. They can incorporate
boundary conditions that describe edge-mediated effects. There
are three major types of phenomena that can arise in reaction-diffusion
models: traveling wavefronts, the formation of patterns in homogeneous
space, and the presence of lower bounds on the sizes of domains
that will support nonzero solutions or solutions with spatial
patterns. Thus, they can be used to address issues related to
biological invasions, spatial patterning, and critical patch size.
The analysis of reaction-diffusion equations involves a mixture
of ideas from dynamical systems and the theory of partial differential
equations. Many reaction-diffusion equations have monotonicity
properties arising from the maximum principle which allow comparisons
between solutions. The stability of their equilibria is typically
determined by the signs of principal eigenvalues of related elliptic
partial differential operators. Information about the stability
of equilibria often can be used to analyze the overall structure
of the set of equilibria or the asymptotic behavior of solutions
by means of bifurcation theory and persistence theory. The derivation,
interpretation, and analysis of reaction-diffusion models will
be discussed, along with the essential background ideas from
partial differential equations and dynamical systems. Applications
to biological invasions, spatial patterning, and spatial effects
influencing the persistence or coexistence of populations will
be described. The material will be drawn from various sources,
a few of which are listed below.
1. R.S. Cantrell and C. Cosner (2003), Spatial
Ecology via Reaction-Diffusion Equations. Wiley.
2. J. D. Murray (2004), Mathematical Biology I
and II. Springer.
3. A. Okubo and S. Levin (2001), Diffusion and
Ecological Problems: Modern Perspectives. Springer.
Presentation Materials: PDF1, PDF2, PDF3, PDF4, PDF5, PDF6, PDF7, PDF8, PDF9, PDF10, PDF11, PDF12
Schedule
Thursday, March 9 |
| 9:00am-12:00pm |
Chris Cosner presentations (with short breaks) |
| 12:00pm-1:30pm |
Lunch Break |
| 1:30pm-5:00pm |
Chris Cosner presentations (with short breaks) |
Friday, March 10 |
| 9:00am-12:00pm |
Chris Cosner presentations (with short breaks) |
| 12:00pm-1:30pm |
Lunch Break |
| 1:30pm-5:00pm |
Chris Cosner presentations (with short breaks) |
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