An Animal Population Simulation & Mathematical Modeling Activity for Secondary Mathematics Majors

David Thompson (Bayard Middle School) & Diana Cheng (Towson University)

Our students

• Undergraduate students: pre-service middle & secondary mathematics & science teachers

• Graduate students: in-service middle & secondary mathematics teachers

Common Core State Standards for Mathematical Practice

• Modeling with Mathematics: how the biological phenomenon of population change can be modeled graphically – Experiment which mimics species’ changes in

population– Hypothesize & test ways to increase the population by

changing relevant parameters • Using appropriate tools strategically: Computer software

& spreadsheets, graphing calculators

Total # of Species & Threatened Species

Source: IUCN Red List

Quantities considered for classifications

% population reduction in 10 years Mature

population size

Reduction in geographic range

IUCN Red List Categories (2001)

Criteria for Threatened Levels(IUCN, 2001)

Tiger: Endangered since 1986

Bald Eagle—Removed from the Endangered Species List in 2007

A Hands-On Simulation Experiment

• Beads:– White beads: mature female

species.– Red beads: mature male

species.– Black beads: incapable of

reproducing (too old, or not mature enough)

• Collect data & analyze it: determine the curve of best fit using a graph and R2 values.

• Come up with a plan to try to get their species to make a full recovery.

http://tinyurl.com/p673fr7– Access spreadsheet– Access handouts

A Technology-Enhanced Experiment

Vortex 10 software– Developed by the IUCN

Conservation Breeding Specialist Group & the Chicago Zoological Society

– Provided at no cost– http://vortex10.org/

Vortex10.aspx

• Some parameters:– Initial population size– Carrying capacity– % of adult females /

males breeding– Mortality rates– # of offspring per female

Explorations on Vortex 10 software

• What combinations of parameters will allow you to simulate the following:– A stable population– An increasing population– A decreasing population

• Find the equations of best fit for each of these scenarios

• Where appropriate, identify the threatened level classification for your species

• What parameters (or combinations thereof) will increase/decrease the rate of a population’s change?

• What initial settings will allow for 2 of each species to replenish the earth? (“Noah’s Ark”)

Sample response to Noah’s Ark

• 10 iterations

• Initial Population Size: 2• Carrying Capacity: 1000• Reproduction Rate: 100% of

females breeding

Additional explorations

Research the population data of three types of species (stable, increasing, decreasing). – Graph the populations’ data.– Determine ways to predict the population size in 10

years. – What factors have been causing the populations’

changes?