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Course Objectives:
- Ecological theory provides a rigorous conceptual framework for understanding the complexity
observed aross natural landscapes, and for constructing scientific analyses of applied problems.
The course therefore focuses on the core of this framework, a series of well-defined mathematical models
for the dynamics of single populations, and for the growth of ecologically interacting species.
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Students should acquire familiarity with basic ecological concepts, by
learning to recognize, formulate and interpret basic mathematical models of Ecology.
Students should gain an understanding of basic mathematical analysis of
[1] single-population growth, [2] interspecific competition, [3] predator-prey interaction, and
[4] advance of infectious disease. Students should understand how predictions deduced from theory
guide empirical work. Finally, students should appreciate how evolution
can shape ecological processes.
Students will demonstrate
achievement of these objectives by answering in-class quizzes, by
writing two in-class examinations, and by completing a
project analyzing one or more questions about population dynamics. Satisfactory
completion of the course should prepare a student for graduate study of the
subject.
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Course Prerequisites:
- BIO 212Y, Genetics.
MAT 106, Calculus (or higher) OR PHY 140, Mechanics (or higher).
BIO 212Y introduces students to the language of population genetics, evolution
and adaptation - necessary to advance in evolutionary ecology. A calculus course,
or physics with calculus, is just as essential for ecology. Students should have some
familiarity with derivatives, difference equations, and differential equations.
Testing will emphasize quantitative problems.
Students may find several of the links listed on
The Calculus Page useful.
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Advice/Classroom Procedures:
- Note that class meetings scheduled on either MONDAY or WEDNESDAY
convene in HU 137. However, class meetings scheduled on FRIDAY
convene in Biology 248A. Plan accordingly.
Class attendance is not mandatory. However, in-class quizzes need not be
announced prior to the date administered. Read and follow any University at Albany
guidelines for missing class when you feel ill.
If attending class, please arrive on time for lecture, and be quiet when lecture begins.
The course objectives are acquired more easily if reading assignments (see below)
are completed prior to lecture.
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Texts:
- 1. Gotelli, N.J. 2008. A Primer of Ecology, 4th Edition.
Dr. Gotelli's book provides a concise introduction to population dynamics and
related ecological models.
- 2. Alstad, D. 2001. Basic Populus Models of Ecology.
Dr. Alstad's book discusses population dynamics, examines a series of
epidemic models, and guides the student's numerical
investigation of ecological models. The book serves as a "laboratory manual" for
Populus, a useful, free software tool.
When downloading Populus you first may need to download and install a virtual running
environment; the website offers adequate guidance.
The two books overlap strongly in topics addressed, since both cover central issues of Ecology.
But the books differ in important ways. For example, Dr. Gotelli's book includes discussion of
field studies bearing on ecological theory; Dr. Alstad's book devotes a chapter to epidemics, a major
focus of population dynamics. Students might find Dr. Gotelli's book sufficient, since Populus
includes "help files," summarizing points from Dr. Alstad's book.
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Problem Sets:
- Both texts listed above present problems for solution.
To help students meet course objectives, links to a series of problem sets
are provided below. Most of the problems require analytical or
numerical solution. Solving
problems proves the best preparation for quizzes and tests. Think about and solve
the problems associated with particular topics as we study those topics.
Problem Set 1: Population estimation, Exponential growth
Problem Set 2: Geometric-mean growth, Logistic growth
Answer Sheet: Problem Set 2
Problem Set 3: Discrete-time logistic growth, Life tables
Answer Sheet: Problem Set 3
Problem Set 4: Population projection, Reproductive value
Problem Set 5: Metapopulation dynamics, Interspecific competition
Answer Sheet: Problem Set 5
Problem Set 6: Predator-prey dynamics, SIR epidemic
Answer Sheet: Problem Set 6
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Project:
- Each student will complete a project summarizing their analysis of an ecological model.
The project may involve (i) development of a new model, (ii) numerical investigation of the dynamics
of an existing model (Populus would prove useful here), or a similar exercise. For most students,
numerical verification of an ecological model's properties will meet the minimal requirement. The project
must be summarized in a ten-page document. The project report is due
Monday, 7 December 2009, the last class meeting.
View a one-page discussion of
project details.
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Grade Determination:
- Two (2) tests will be administered.
Each test contributes 30%
of the course grade. The project report contributes the 30% of the course
grade. In-class quizzes, each graded pass/fail, contribute the final 10%.
Students accumulating 90 or more of the 100 available "points" will earn a final grade of A;
most students find this goal challenging.
Test dates are 14 October 09 (Wednesday), and 23 November 09 (Monday).
The final classroom meeting(s) will be spent analyzing models selected for student projects.
The course does not include a final exam.
- Syllabus