Introducing Mathematical Modeling in an Undergraduate Ecology Laboratory
Mathematical Biology Modeling Group
School of Mathematical Sciences &
School of Biological Sciences
J. Fielder
The Ecology Class
• 4 credits; 3 hours/week lecture, 1 three-hour lab/week
• Juniors and Seniors• 25-30 students• Mostly biology
majors• Our modeling lab
supplemented the population dynamics unit
Why Math Modeling in Ecology?
• Historically important role of math in ecology
• Our group focuses on math applications in ecology
• Models of invasive species
en.wikipedia.org http://www.chthonic.f9.co.uk/b3ta/underage.jpg
The Problem of Feral Cats: Kerguelen Islands (Chapuis 1995)
en.wikipedia.org/wiki/Port-aux-Français
• 60 winter inhabitants• up to 120 summer
inhabitants
• 5 founder cats?...• 25 years later…30,000 cats
Birds killed per year?
> 3 million per year!
glennmci.brinkster.net
Control of Feral Cats• Culling & trapping are expensive• Time-consuming• Labor intensive• Controversial
• Disease– Feline Immunodeficiency Virus (FIV)– Feline Leukemia Virus (FeLV)
• Retrovirus found worldwide • Spread by coming in contact with saliva, urine,
feces, and nasal secretions (American Association of Feline Practitioners and Cornell Feline Health Center, 2006)
www.wildliferesearchmanagement.com.au
Introducing Predator-Prey Models: Logistic Growth
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1
B
CCr
dt
dC
CK
BBr
dt
dB
C
BBirds
Cats
Trying an Example
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B
CCr
dt
dC
CK
BBr
dt
dB
C
B
Starting Values
Graph of (Cat, Bird) Trajectory
Cats
Birds
What happens if a cat disease is introduced to the
system?
??/
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1
B
CCr
dt
dC
CK
BBr
dt
dB
C
BBirds
Cats
Differential equations for FeLV
Mathematica Simulator
• Can run from any computer (with Mathematica Player download)
• 12 parameters (run by sliders)• Initial populations controlled by
pointer. http://www.unco.edu/NHS/mathsci/facstaff/Champion/Math/AlienCats/
Benefits of the Collaboration
• Mathematicians learned about applications of mathematics in Ecology
• Learned that technology made the mathematics more accessible
• Extended depth of mathematics that the Biologists could be involved with
• More efficient, saved time• Feedback from the students was
positive