AMATH 536  |  Schedule  |  Instructor  |  Flyer  |  Handout  |  Content  |  Outline  |  Textbooks  |  References  |  Prerequisites  |  Grading  |  Homework  |  Calendar  |  Notes  
  
     

AMATH 536



Spatial Models in Ecology and Epidemiology



Spring 2014






Schedule








SLN:

10232




Days:

M, W, F




Time:

10:30-11:20 am




Room:

DEN 206









Instructor








Name:

Mark Kot




Office:

230B Lewis Hall




Phone:

(206) 543-0908




Fax:

(206) 685-1440




Email:

mark_kot@comcast.net











Office Hours:

M, W, F, 11:45-12:45 pm












Flyer



Here is a



course flyer



to help you remember this course.




Handout

Handout




Content



This course will cover models for the growth and dispersal of biological populations.


Topics will include population persistence, climate-induced range shifts, rates of spread of invading


organisms, and pattern formation.  We will consider random walks, reaction-diffusion equations,


and integrodifference equations.  If time permits, we will also look at branching random walks,


coupled map lattices, and cellular automata.  


Please see the class
outline
for further details regarding class content.










Course Catalog




Outline






Formulating spatial models:




  • 
Random walks

    


  • 
Reaction-diffusion equations

    


  • 
Integrodifference equations

    



Core problems:




  • 
Population persistence.

    

What is the critical patch size for an endangered population?

    


  • 
Range shifts.

    

Can populations keep pace with climate-induced range shifts?

    


  • 
Spread rates

    

How quickly do invading populations spread?

    


  • 
Pattern formation.

    

Can spatial patterns in density arise from trophic interactions
and dispersal in homogeneous environments?

    


  • 
Age and stage structure.

    

How do age and stage structure, in growth and dispersal, affect the answers to the above questions?

    




Textbooks



There is no required textbook.



I will instead provide detailed, typeset lecture notes.




References






Helpful Reference Books:




  • 
Banks, R. B.  (1994)

    
Growth and Diffusion Phenomena: Mathematical Frameworks and Applications. 

    
Springer-Verlag, Berlin, Germany.

    

UW Library Catalog

    


  • 
Barber, M. N. and Ninham, B. W.  1970.

    
Random and Restricted Walks: Theory and Applications.    

    
Gordon and Breach, New York, New York, USA.

    

UW Library Catalog

    


  • 
Berg, H. C.  (1993)

    
Random Walks in Biology. 

    
Princeton University Press, Princeton, New Jersey, USA.

    

UW Library Catalog

    


  • 
Britton, N. F.  (1986)

    
Reaction-Diffusion Equations and Their Applications to Biology. 

    
Academic Press, London, UK.

    

UW Library Catalog

    


  • 
Cantrell, R. S. and Cosner, C.  (2003)

    
Spatial Ecology via Reaction-Diffusion Equations 

    
John Wiley & Sons, Chichester, UK.

    

UW Library Catalog

    


  • 
Dieckmann, U., Law, R., Metz, J. A. J.  (2000)

    
The Geometry of Ecological Interactions: Simplifying Spatial Complexity. 

    
Cambridge University Press, Cambridge, UK

    

UW Library Catalog

    


  • 
Edelstein-Keshet, L.  (1988)

    
Mathematical Models in Biology 

    
Random House, New York, NY.

    

UW Library Catalog

    

Edelstein-Keshet, L.  (2005)

    
Mathematical Models in Biology 

    
SIAM, Philadelphia, PA.

    

UW Library Catalog

    


  • 
Hughes, B. D.  (1995)

    
Random Walks and Random Environments.  Volume 1: Random Walks. 

    
Oxford University Press, Oxford, UK.

    

UW Library Catalog

    


  • 
Ibe, O. C.  (2013)

    
Elements of Random Walk and Diffusion Processes. 

    
John Wiley & Sons, Hoboken, NJ

    

UW Library Catalog

    


  • 
Klafter, J. and Sokolov, I. M.  (2011)

    
First Steps in Random Walks: From Tools to Applications. 

    
Oxford University Press, Oxford, UK.

    

UW Library Catalog

    


  • 
Kot, M.  (2001)

    
Elements of Mathematical Ecology. 

    
Cambridge University Press, Cambridge, UK.

    

UW Library Catalog


    


  • 
Logan, J. D.  (2001)

    
Transport Modeling in Hydrogeochemical Systems. 

    
Springer-Verlag, New York, New York, USA.

    

UW Library Catalog

    


  • 
Logan, J. D.  (2008)

    
An Introduction to Nonlinear Partial Differential Equations. 

    
John Wiley & Sons, Hoboken, New Jersey, USA.

    

UW Library Catalog

    


  • 
McGlade, J.  (1999)

    
Advanced Ecological Theory: Principles and Applications. 

    
Blackwell Science, Oxford, UK.

    

UW Library Catalog

    


  • 
Mendez, V., Campos, D., and Martumeus, F.  (2014)

    
Stochastic Foundations in Movement Ecology: Anomalous Diffusion, Front Propagation and Random Searches. 

    
Springer, Berlin, Germany.

    

UW Library Catalog

    


  • 
Murray, J. D.  (2002)

    
Mathematical Biology I:  An Introduction. 

    
Springer, Berlin, Germany

    

UW Library Catalog

    


  • 
Murray, J. D.  (2003)

    
Mathematical Biology. II: Spatial Models and Biomedical Applications. 

    
Springer-Verlag, New York, New York, USA.

    

UW Library Catalog

    


  • 
Okubo, A. and Levin, S. A.  (2001)

    
Diffusion and Ecological Problems:  Modern Perspectives. 

    
Springer-Verlag, New York, New York, USA.

    

UW Library Catalog

    


  • 
Rudnick, R. and Gaspari, G.  (2004)

    
Elements of the Random Walk:  An Introduction for Advanced Students and Researchers. 

    
Cambridge University Press, Cambridge, UK.

    

UW Library Catalog

    


  • 
Sattenspiel. L.  (2009)

    
The Geographic Spread of Infectious Diseases: Models and Applications. 

    
Princeton University Press, Princeton, New Jersey, USA.

    

UW Library Catalog

    


  • 
Smoller, J.  (1994)

    
Shock Waves and Reaction-Diffusion Equations. 

    
Springer-Verlag, New York, New York, USA.

    

UW Library Catalog

    


  • 
Tilman. D. and Kareiva, P.  (1997)

    
Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. 

    
Princeton University Press, Princeton, New Jersey, USA.

    

UW Library Catalog

    


  • 
Shigesada, N. and Kawasaki, K.  (1997)

    
Biological Invasions: Theory and Practice. 

    
Oxford University Press, Oxford, UK.

    

UW Library Catalog

    


  • 
Turchin. P.  (1998)

    
Quantitative Analysis of Movement: Measuring and Modelling Population Redistribution in Animals and Plants 

    
Sinauer Associates, Inc., Sunderland, Massachusetts, USA.

    

UW Library Catalog

    


  • 
Weiss, G. H. (1994)

    
Aspects and Applications of the Random Walk 

    
North-Holland, Amsterdam, Netherlands

    

UW Library Catalog

    




Prerequisites



There are no formal prerequisites, but this is a graduate course.



You will see large doses of probability theory and partial differential equations.



It will help if you have had some exposure to these topics.




Grading



Homeworks account for 70% of the final grade.



You have the option of writing a term paper or of taking a take-home final exam.



Your term paper or take-home final accounts for 30% of the final grade.




Homework



Homework are due one week from the date of assignment.



Homeworks constitute 70% of the final grade.



Write up your homework alone, not as a group!







Calendar



Important Dates








Monday
March 31
First Day of Classes




Monday
May 26
Memorial Day (No Class)




Friday
May 30
Take-Home Final Available




Friday
June 6
Last Day of Lectures




Monday
June 9
Take-Home Final or Term Paper Due (11:30 am)









Notes