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IMA Workshop

From Individual to Aggregation: Modeling Animal Grouping

From Individual to Aggregation: Modeling Animal Grouping

June
7-11, 1999

Mathematics Department

University of British Columbia

http://www.math.ubc.ca/people/faculty/keshet/keshet.html

keshet@math.ubc.ca

**
Simon A. Levin**

Department of Ecology and Evolution Biology

Princeton University

simon@eno.princeton.edu

http://www.eeb.princeton.edu/~simon/

and

**
Mark Lewis**

Department of Mathematics

University of Utah

mlewis@math.utah.edu

http://www.math.utah.edu/~mlewis/

Patterns of aggregation, including schools of fish, flocks of birds, and herds of ungulates, are among the most striking patterns in biology. How do such patterns arise from decisions taken at the level of individuals? A promising approach begins from Lagrangian (e.g. Newtonian) descriptions of individual responses to the environment and to each other, derives macroscopic descriptions, and proceeds to Eulerian descriptions. The mathematical issues will involve Lagrangian/Eulerian connections, moment closure and other methods for proceeding from small to large scales.

**All
talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.**

Monday | Tuesday | Wednesday | Thursday | Friday |

MONDAY, JUNE 7 | ||
---|---|---|

8:30 am | Registration and Coffee | Reception Room EE/CS 3-176 |

9:10 am | Fadil
Santosa, Fred Dulles, and Simon A. Levin |
Introduction |

9:30 am | Mark
Lewis University of Utah |
Workshop Overview |

10:00 am |
Hidekatsu Yamazaki Tokyo University of Fisheries |
Lagrangian Simulation of Planktonic Swimming Behaviours |

11:00 am | Coffee Break | Reception Room EE/CS 3-176 |

11:30 - 12:30 pm | Daniel
Grunbaum University of Washington |
Population-level Advection-Diffusion Equations for Biased Random Walks by Individuals and Groups |

Short Talks | ||

2:00 pm |
Christopher Cosner University of Miami |
The Effects of Spatial Grouping on the Functional Response of Predators |

2:15 pm |
Frithjof Lutscher Universitaet Tubingen |
A Simple Model for Schooling Fish and its Effect on Predation |

2:30 pm |
James Watmough University of Victoria |
Can PDE Models Describe Migratory Locust Swarms? |

2:45 pm | Coffee Break | Reception Room EE/CS 3-176 |

3:00 pm |
Odo Diekmann Utrecht University |
Reflections on Epidemic Models |

3:30 - 4:00 pm |
Steven Ellner North Carolina State University |
Spatial Dynamics and Persistence in a Model Tri-trophic System |Talk |

4:15 pm | IMA Tea |
IMA East, 400 Lind Hall A variety of appetizers and beverages will be served. |

TUESDAY, JUNE 8 | ||

9:15 am | Coffee | Reception Room EE/CS 3-176 |

9:30 am | Will
Wilson Duke University |
Consuming, Grouping, and Coexisting |

10:30 am | Coffee Break | Reception Room EE/CS 3-176 |

11:00 - 12:00 pm | Mercedes
Pascual University of Maryland |
Determinism and Spatial Scale: Aggregating Individuals into Densities in Oscillatory Systems |

Short Talks | ||

2:00 pm | Donald
B. Olson University of Miami |
Aggregation and Aggretion |

2:30 pm | Victor
Padron Universidad de Los Andes |
Effect of Aggregation on Population Recovery Modeled by a Diffusion-Advection Equation |

2:45 pm | Emily
Silverman University of Washington |
Mixed-Species Aggregations of Waterfowl |

3:00 pm | Carl
Simon University of Michigan |
Favored Places in the Selfish Herd |

3:15-3:30 pm | Sharon
R. Lubkin North Carolina State University |
Chemotactic Bacterial Pattern Formation |

3:45 pm | Informal Video Session | IMA East Seminar room, Lind Hall 409 |

WEDNESDAY, JUNE 9 | ||

8:45 am | Coffee | Reception Room EE/CS 3-176 |

9:00 am | Karl-Peter
Hadeler University of Tübingen |
Reaction Transport Equations as Models for Spread and Reactions |

10:00 am | Angela
Stevens Max-Planck-Institute for Mathematics in the Sciences |
Hyperbolic v Parabolic Models for Chemotaxis (Individual and Population Density Based Models) |Talk |

11:00 am | Coffee Break | Reception Room EE/CS 3-176 |

11:30 - 12:30 pm | Hans
G. Othmer University of Utah |
Continuum Taxis Equations Based on Individual Behavior |

1:30 - 6:30 pm | David
Tilman University of Minnesota |
Field Trip to the Cedar Creek Natural History Area
This will be a trip led by Professor Tilman to see a research facility he directs located north of the Twin Cities. See http://www.lter.umn.edu/ for more details about this site. Driving time will be about 50 minutes each way and the group will leave at 1:30 pm from the lobby of the Radisson Metrodome. |

THURSDAY, JUNE 10 | ||

9:15 am | Coffee | Reception Room EE/CS 3-176 |

9:30 am | Paulien
Hogeweg University of Utrecht |
From Individual Decisions to Aggregates and from Aggregates to Indivudual Dicisions |

10:30 am | Coffee Break | Reception Room EE/CS 3-176 |

11:00 am - 12:00 pm | Shay
Gueron Technion - Israel Institute of Technology |
Birth and Death Processes and Mass Action Laws in Biology and Chemistry: AN Interacting Particle Systems Approach |

2:00 pm | Vincenzo
Capasso University of Milan |
From the Individual Behaviour Subject to Stochastic Fluctuations to the PIDE Describing The Global Behaviour Of an Aggregating Population |

3:00 pm | Coffee Break | Reception Room EE/CS 3-176 |

Short Talks | ||

3:30 pm | Sandy
Anderson University of Dundee |
From Populations to Indviduals: Applications of Continuum and Discrete Models in Cancer Growth |

3:45 pm | Ricardo
Diaz University of Northern Colorado |
Flocking Kinematics and Nonlinear Fluid Flow Equations: Some Exact Analytic Solutions |

4:00 pm | Ulrike
Schuldenzucker University of Bonn |
From a Skein of Individuals to Partial Integro-Differential Equations |

4:15 - 4:30 pm | Thomas
Hillen University of Utah |
Moment Closure of Reaction Transport Equations |

6:00 pm | Workshop
Dinner |
Dinner will be catered by Cossetta's, a local Italian Restaurant. It will be held outside on the east side of Lind Hall and will feature a variety of Italian entrees and salad. |

FRIDAY, JUNE 11 | ||

9:15 am | Coffee | Reception Room EE/CS 3-176 |

9:30 am | Alexander
Mogilner University of California-Davis |
Quantitative Modeling of Bacterial Aggregation Based on `Energy Taxis' |Talk |

10:30 am | Coffee Break | Reception Room EE/CS 3-176 |

10:45 - 11:45 am | Paul
Moorcroft Princeton University |
Mechanistic Models for Animal Home Ranges |

11:45 am - 12:15 pm | Leah
Edelstein-Keshet University of British Columbia |
Workshop Summary |Summary |

Monday | Tuesday | Wednesday | Thursday | Friday |

Name | Department | Affiliation |
---|---|---|

Kevin Anderson | IMA | University of Minnesota |

Sandy Anderson | Mathematics | University of Dundee |

Don Aronson | Mathematics | University of Minnesota |

Bruce Ayati | IMA | University of Minnesota |

Steve Cantrell | Mathematics and Comp. Science | University of Miami |

Vincenzo Capasso | Mathematics | University of Milan |

Chris Cosner | Mathematics & Computer Sciences | University of Miami-College of Arts & Sciences |

Kim Cuddington | Zoology | University of Guelph |

Gregory J. Davis | Natural and Applied Sciences-Mathematics | University of Wisconsin - Green Bay |

Ricardo Diaz | Mathematical Sciences | University of Northern Colorado |

Odo Diekmann | Utrecht University | |

Kevin Drury | Biological Sciences | University of Notre Dame |

Fred Dulles | Institute for Mathematics and its Applications | |

Leah Edelstein-Keshet | Mathematics | University of British Columbia |

Stephen Ellner | Statistics | North Carolina State University |

Daniel Grunbaum | Zoology | University of Washington |

Shay Gueron | Mathematics | Technion-I.I.T. |

Karl Hadeler | Lehrstuhl fur Biomathematik | Universitat Tubingen |

Thomas Hillen | Mathematics | University of Utah |

Paulien Hogeweg | Theoretical Biology/Bioinformatics | University of Utrecht |

Eli Holmes | Zoology Department | University of Washington |

Henri Laurie | Applied Maths | University of Cape Town |

Simon A. Levin | Ecology and Evol. Biology | Princeton University |

Mark Lewis | Mathematics | University of Utah |

Sharon Lubkin | Biomathematics Program | North Carolina State University |

Frithjof Lutscher | Lehrstuhl fur Biomathematik | Universitat Tubingen |

Urmila Malvadkar | Applied and Computational Math | Princeton University |

Douglas Meade | Mathematics | University of South Carolina |

Willard Miller | Institute for Mathematics and its Applications | |

Alexander Mogilner | Mathematics | University of California-Davis |

Denis Mollison | Act. Maths & Statistics | Heriot-Watt University |

Paul Moorcroft | Princeton University | |

Mike Neubert | Biology Department | Woods Hole Oceanographic Institute |

Claudia Neuhauser | School of Mathematics | University of Minnesota |

Donald B. Olson | Rosenstiel School of Marine & Atmos. Science | University of Miami |

Hans G. Othmer | Mathematics | University of Utah |

Victor Padron | Departamento de Matematicas | Universidad de Los Andes |

Keiko Parker | US West | |

Mercedes Pascual | Center of Marine Biotechnolgy | University of Maryland |

Virginia Pasour | Biomathematics | North Carolina State University |

Kathleen Rogers | IMA | University of Minnesota |

Ulrike Schuldenzucker | University of Bonn | |

Emily Silverman | University of Washington | |

Carl Simon | Mathematics Department | University of Michigan |

Angela Stevens | Max-Planck-Institute for Mathematics in the Sciences | |

Steven Viscido | Biological Sciences | University of South Carolina |

James Watmough | Mathematics and Statistics | University of Victoria |

Warren Weckesser | IMA | University of Minnesota |

Hans Weinberger | Mathematics | University of Minnesota |

Will Wilson | Zoology | Duke University |

Ralf Wittenberg | IMA | University of Minnesota |

Hidekatsu Yamazaki | Ocean Sciences | Tokyo University of Fisheries |