introducing mathematical modeling in an undergraduate ecology laboratory mathematical biology...

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

/1

1

B

CCr

dt

dC

CK

BBr

dt

dB

C

BBirds

Cats

Trying an Example

/1

1

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

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