**UM's ITME**

Institute of Theoretical and Mathematical Ecology

Institute of Theoretical and Mathematical Ecology

core graduate course

(interdisciplinary among math, biology and marine science)

**Learn to frame biological problems mathematically**

The goal of this course is to train a generation of bio-mathematical bridge crossers who can frame biological issues in mathematical terms. We aim to train empiricists how to think mathematically about ecological issues and to train mathematicians how empiricists think about ecological/biological issues, while both learn the fundamentals of theoretical ecology and learn to work with each other. The only way to learn mathematical concepts is to work problems. Lab sessions on Fridays may be used to get focused on problems. You have to invest solo time throughout the semester in trying to solve problems. Homework and lab assignments related to the topics will be given from the text books and from supplementary materials.

3 credits, (Lecture/Computer Lab)

Two semester sequence.

Fall for single populations. Spring for species interactions and communities

Next time offered: Fall 2018-Spring 2019.

Sample syllabus Fall below

Two semester sequence.

Fall for single populations. Spring for species interactions and communities

Next time offered: Fall 2018-Spring 2019.

Sample syllabus Fall below

BIL630-F(7427),GH(7428) / MTH 786- F(7427),GH(7428)

SYLLABUS 1.0 Fall 2016

MW 1:25- 2:15 (Cox 217) & M 2:30-5:00 (Cox 108)

BLACKBOARD will be used to share materials and exchange communications

Main faculty:

Dr. Carol C. HORVITZ and Dr. Chris COSNER

carolhorvitz@miami.edu

gcc@math.miami.edu

Other faculty of the ITME:

Dr. Shigui Ruan, Dr. Stephen Cantrell,

Dr. Don De Angelis,

Dr. Don Olson, Dr. Jerry Ault,

Dr. David Van Dyken

Books

Case, T. J. 2000. An Illustrated Guide to Theoretical Ecology, Oxford University Press

Ellner, S.P. and J. Guckenheimer, 2006. Dynamic Models in Biology. Princeton University Press.

*Otto, S. P. and T. Day, 2007, A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, Princeton University Press

link to supplementary materials: http://www.zoology.ubc.ca/biomath/

*Kot, M. 2001. Elements of Mathematical Ecology. Cambridge University Press.

Renshaw. E. 1991. Modelling Biological Populations in Space and Time. Cambridge University Press.

Roughgarden, J. 1998. Primer of Ecological Theory. Prentice-Hall, Inc.

* main text books for the course. Others are supplementary and pdf’s or hard copy of excerpts will be supplied to you.

Topics (First semester of a two semester sequence)

I. Introductory Workshop (4 wks: Aug 22 -Sept 21 )

Holidays: Labor Day Sep 5

A. Background: mathematical concepts and usefulness for ecology

1. Introduction to modeling using a case history of HIV

..................... Otto and Day, Chapter 1

2. Constructing a model: basic elements

Formulate a biological question mathematically

Mathematical relationships : words, equations, graphs, codes, numerics

....................Otto and Day, Chapter 2

B. MATLAB

Command line, scripts, work space, basic functions, etc.

................. (Otto and Day, Chapter 4

for discussion of graphical/numerical approaches)

C. Calculus, powers and logarithms

D. Differential equations and derivatives as linear approximations

..................... Otto and Day, Primer 1

E. Probability density functions

...................... Otto and Day, Primer 3

II. Dynamics of unstructured single species models (5 wks: Sept 26 – Oct 27)

Holidays: Fall Recess Oct 20-21

A. Continuous time

Density independence - exponential

Density dependence - logistic, Allee harvest models

Equilibria and stability and bifurcation

...... Kot, Ch 1-2; Roughgarden, pdf, Otto and Day Ch. 5

B. Discrete Time

Density independence - geometric

Density dependence - logistic, Ricker, Beverton-Holt

Equilibria and stability and bifurcation

..... Kot, Ch 4; Roughgarden, pdf, Otto and Day Box 4.2, Ch. 5;

C. Detecting density dependence from data

.............. Roughgarden, pdf

D. Stochasticity: environmental and demographic stochasticity;

Birth-death process stochastic models.

................ Kot, Chapter 3

................Renshaw, pdf

III. Structured models for a single species (4 wks: Oct 31 – Nov 30)

Holidays: Thanksgiving Break Nov 21-25

A. Age-structured models

......Kot, Section E; Otto and Day, Chapter 10

B. Stage-structured models

...... Caswell, pdf; Crowder et al., pdf

C. Further topics

1. McKendrick-von Foerster p.d.e. models

............. Kot, Section E

2. Integral equations models

3. Other types of structure (metabolic, genetic)

IV. Final projects: preparation and presentation

(Dec 6 – Dec 14, includes reading day and final exams period).

Project presentation symposium on Final Exam Date: Wed Dec 14 2:00-4:30pm

Philosophy

The goal of this course is to train a generation of bio-mathematical bridge crossers who can frame biological issues in mathematical terms. We aim to train empiricists how to think mathematically about ecological issues and to train mathematicians how empiricists think about ecological/biological issues, while both learn the fundamentals of theoretical ecology and learn to work with each other. The only way to learn mathematical concepts is to work problems. Lab sessions on Fridays may be used to get focused on problems. You have to invest solo time throughout the semester in trying to solve problems. Homework and lab assignments related to the topics will be given from the text books and from supplementary materials.

We recommend that you take lots of notes on lectures, readings, class discussions, and computer labs. We encourage you to ask questions throughout the course and to discuss issues with one another and with us.

PIE (Periodic Iterated Exercises)

Every now and then (dates TBA) we will ask you to apply what you learned by doing some short written exercises at home on your own that will be handed in for us to review. These will be quiz-like, open-book, open-notes, but not team work. They will be your individual work. We will make recommendations for you to revise your answers and then we will collect the revised answers to review as well. You will have 1 week to complete each one and 1 week to complete your revision after receiving our comments.

Final Project

Everyone will participate in a team project at the end of the semester. The goal of the project is to give you the opportunity to apply what you have learned during the semester to a particular problem. Each team member is expected to contribute uniquely and to participate in both the research and the presentation of the results. The topic of the project and the team membership will be decided upon by the faculty, although everyone is encouraged to suggest topics. The faculty will assemble the teams to ensure as much as possible cross-disciplinary expertise.

Teams will have two weeks to work on the project. During this period, there will be some class periods devoted to working on the project, but it is expected that the team will get together outside of class time to work on and complete the project. The faculty will be available for consultation and encourage consultation early on in the process. The presentation will be made at a symposium during the final exam period, at which time a written report will also be handed in. The written report should include a brief description of the issue, and brief sections on background, methodology, statement of model in equation format, results, significance, as well as an appendix with computer code, if appropriate. The written report should be a digital file.

Grades

Grades will be based on the PIE's and the Final Projects.

Applied Math Seminar: Tuesday 12:30

Attendance at this seminar is required when the topic is mathematical biology.

(Come back for the second semester: Topics will include: species interactions, community structure, spatially structured models).

SYLLABUS 1.0 Fall 2016

MW 1:25- 2:15 (Cox 217) & M 2:30-5:00 (Cox 108)

BLACKBOARD will be used to share materials and exchange communications

Main faculty:

Dr. Carol C. HORVITZ and Dr. Chris COSNER

carolhorvitz@miami.edu

gcc@math.miami.edu

Other faculty of the ITME:

Dr. Shigui Ruan, Dr. Stephen Cantrell,

Dr. Don De Angelis,

Dr. Don Olson, Dr. Jerry Ault,

Dr. David Van Dyken

Books

Case, T. J. 2000. An Illustrated Guide to Theoretical Ecology, Oxford University Press

Ellner, S.P. and J. Guckenheimer, 2006. Dynamic Models in Biology. Princeton University Press.

*Otto, S. P. and T. Day, 2007, A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, Princeton University Press

link to supplementary materials: http://www.zoology.ubc.ca/biomath/

*Kot, M. 2001. Elements of Mathematical Ecology. Cambridge University Press.

Renshaw. E. 1991. Modelling Biological Populations in Space and Time. Cambridge University Press.

Roughgarden, J. 1998. Primer of Ecological Theory. Prentice-Hall, Inc.

* main text books for the course. Others are supplementary and pdf’s or hard copy of excerpts will be supplied to you.

Topics (First semester of a two semester sequence)

I. Introductory Workshop (4 wks: Aug 22 -Sept 21 )

Holidays: Labor Day Sep 5

A. Background: mathematical concepts and usefulness for ecology

1. Introduction to modeling using a case history of HIV

..................... Otto and Day, Chapter 1

2. Constructing a model: basic elements

Formulate a biological question mathematically

Mathematical relationships : words, equations, graphs, codes, numerics

....................Otto and Day, Chapter 2

B. MATLAB

Command line, scripts, work space, basic functions, etc.

................. (Otto and Day, Chapter 4

for discussion of graphical/numerical approaches)

C. Calculus, powers and logarithms

D. Differential equations and derivatives as linear approximations

..................... Otto and Day, Primer 1

E. Probability density functions

...................... Otto and Day, Primer 3

II. Dynamics of unstructured single species models (5 wks: Sept 26 – Oct 27)

Holidays: Fall Recess Oct 20-21

A. Continuous time

Density independence - exponential

Density dependence - logistic, Allee harvest models

Equilibria and stability and bifurcation

...... Kot, Ch 1-2; Roughgarden, pdf, Otto and Day Ch. 5

B. Discrete Time

Density independence - geometric

Density dependence - logistic, Ricker, Beverton-Holt

Equilibria and stability and bifurcation

..... Kot, Ch 4; Roughgarden, pdf, Otto and Day Box 4.2, Ch. 5;

C. Detecting density dependence from data

.............. Roughgarden, pdf

D. Stochasticity: environmental and demographic stochasticity;

Birth-death process stochastic models.

................ Kot, Chapter 3

................Renshaw, pdf

III. Structured models for a single species (4 wks: Oct 31 – Nov 30)

Holidays: Thanksgiving Break Nov 21-25

A. Age-structured models

......Kot, Section E; Otto and Day, Chapter 10

B. Stage-structured models

...... Caswell, pdf; Crowder et al., pdf

C. Further topics

1. McKendrick-von Foerster p.d.e. models

............. Kot, Section E

2. Integral equations models

3. Other types of structure (metabolic, genetic)

IV. Final projects: preparation and presentation

(Dec 6 – Dec 14, includes reading day and final exams period).

Project presentation symposium on Final Exam Date: Wed Dec 14 2:00-4:30pm

Philosophy

The goal of this course is to train a generation of bio-mathematical bridge crossers who can frame biological issues in mathematical terms. We aim to train empiricists how to think mathematically about ecological issues and to train mathematicians how empiricists think about ecological/biological issues, while both learn the fundamentals of theoretical ecology and learn to work with each other. The only way to learn mathematical concepts is to work problems. Lab sessions on Fridays may be used to get focused on problems. You have to invest solo time throughout the semester in trying to solve problems. Homework and lab assignments related to the topics will be given from the text books and from supplementary materials.

We recommend that you take lots of notes on lectures, readings, class discussions, and computer labs. We encourage you to ask questions throughout the course and to discuss issues with one another and with us.

PIE (Periodic Iterated Exercises)

Every now and then (dates TBA) we will ask you to apply what you learned by doing some short written exercises at home on your own that will be handed in for us to review. These will be quiz-like, open-book, open-notes, but not team work. They will be your individual work. We will make recommendations for you to revise your answers and then we will collect the revised answers to review as well. You will have 1 week to complete each one and 1 week to complete your revision after receiving our comments.

Final Project

Everyone will participate in a team project at the end of the semester. The goal of the project is to give you the opportunity to apply what you have learned during the semester to a particular problem. Each team member is expected to contribute uniquely and to participate in both the research and the presentation of the results. The topic of the project and the team membership will be decided upon by the faculty, although everyone is encouraged to suggest topics. The faculty will assemble the teams to ensure as much as possible cross-disciplinary expertise.

Teams will have two weeks to work on the project. During this period, there will be some class periods devoted to working on the project, but it is expected that the team will get together outside of class time to work on and complete the project. The faculty will be available for consultation and encourage consultation early on in the process. The presentation will be made at a symposium during the final exam period, at which time a written report will also be handed in. The written report should include a brief description of the issue, and brief sections on background, methodology, statement of model in equation format, results, significance, as well as an appendix with computer code, if appropriate. The written report should be a digital file.

Grades

Grades will be based on the PIE's and the Final Projects.

Applied Math Seminar: Tuesday 12:30

Attendance at this seminar is required when the topic is mathematical biology.

(Come back for the second semester: Topics will include: species interactions, community structure, spatially structured models).