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

BCCr

dtdC

CKBBr

dtdB

C

BBirds

Cats

Trying an Example

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1

BCCr

dtdC

CKBBr

dtdB

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

BCCr

dtdC

CKBBr

dtdB

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