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Course Objectives:
- Ecological theory provides a rigorous conceptual framework for understanding the complexity
observed across both natural and managed 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.
This course offers motivated students an appreciation of Theoretical Biology. Furthermore, the
curriculum prepares any interested students for graduate study of Ecology.
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Students should acquire familiarity with basic ecological concepts, by
learning to formulate and explain introductory mathematical models of Ecology.
Students should gain an understanding of the mathematical analysis of
[1] single-population growth in constant and fluctuating environments, [2] interspecific competition,
[3] predator-prey interaction, and [4] advance of infectious disease.
Students should understand how predictions deduced from theory
guide empirical work in "hypothetico-deductive" science.
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..
... despite the field's reputation as a soft science, nearly all of biology
is now ripe for quantitative analysis ...
Phillips, R., Quake, S., Physics Today, May 2006.
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Students should realize that this course addresses quantitative,
organizing concepts fundamental to population biology. Hence the course does not
include focused study of envirommental problems or conservation technologies.
For an intelligent discussion of of contemporary environmental challenges, see
Vermont Law School's Environmental Watch List.
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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:
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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. A fraction of each student's final grade is earned through
following course procedures; points are lost by failing to complete assignments on time
and by disruptive behavior in class (talking, sleeping, ...).
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Texts:
- 1. Gotelli, N.J. 2008. A Primer of Ecology, 4th Edition.
Dr. Gotelli's book provides a clear, 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. An alternative, with which this class has
far less experience, is a
commercial web site.
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 material in Dr. Alstad's book. Remember that books can be
purchased (new or used) and that a limited number of copies may be avialble for semester-long rental.
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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 address the associated
text material.
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
Whoever despises the high wisdom of mathematics nourishes himself on delusion.
da Vinci, 1489.
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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
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 equates with 25% of the course grade (hence, 50% in total).
In-class quizzes, each graded pass/fail, collectively equate to 15% of the
course grade.
The project report contributes the 30% of the course
grade. Following course procedures (see above) earns the final 5% of the
course grade.
Students accumulating 90 or more of the 100 available "points" will earn a final grade of A;
most students find this goal challenging.
Each test will be administered approximately seven (7) days after competion of the lectures
presenting topics covered by the test.
Test 1 will be presented on Monday, 17 October 2011.
Test 2 will be presented on Friday, 18 November 2011.
The course does not include a final exam.
Test 1: percentile scores.
Test 1 + Test 2: percentile scores;
letter grades only approximate.
- Syllabus
