Biology 120:creating a modeling lab

Nathaniel Meyer, Louis Weiss, Lauren Shuler

Background

• Target Audience– Genetics, Evolution, & Ecology Students and teachers (Biology 120)

• Teaching Objectives– Provide an introduction to modeling and the systems perspective– Reinforce Understanding of population dynamics & the

Lotka-Volterra predator-prey model

• r- & k-selected species– Build the associated model and draw conclusions based on

findings

• Lotka-Volterra (predator-prey) oscillations– Given a model and an interface, allow the students to explore

system dynamics by systematically changing coefficients

Pedagogy

• Thought process– How can we best create a lab exercise that provides

enough information to give students a basis for exploring the concepts on their own?

– Is building or exploring more effective at first?– How do we avoid a recipe book lab?– What questions do we ask to stimulate the students?– Which concepts in the Biology 120 curriculum would

be most appropriate for a modeling lesson? • Which can be most effectively taught using modeling?• Which is the best vehicle to teach modeling?

Structure

• Presented background on modeling including STELLA software

• Introduced the systems perspective i.e. stocks, flows, and feedback

• Guiding steps through the exponential (r-selected species) model

• Expand the exponential model to include a carrying capacity (k-selected)

• Provide an interface for the Lotka-Volterra model

r-selected Species• Purpose of this model

– Introduce the students to the STELLA software and modeling– Create a simple model of exponential growth without a limiting resource

– Help them understand what ‘r’ means in “r-selected”• Formulation: Exponential Growth

– dN/dt = R*N– N=P*e^rt

Population

Net Growth

Growth Rate

Adding k (carrying capacity) to the model

• Purpose of this model– Expand the student’s knowledge of STELLA by creating a more complicated model– Help students understand what ‘k’ means in “k-selected”– Allow them to play with coefficients to see what factors most heavily affect the

system• Formulation: Logistic Growth

– dN/dt = r*N*(K-N) = r*N*K – C*N^2 (second order loss, first order growth)

Population Stock

Growth Inflow

K:Carrying Capacity

R:Birth Rate

Difference Coefficient

r- & k-selected species Interface

Exploring Lotka-Volterra• Purpose of this model

– Allow the students to explore predator-prey population dynamics using a previously created model

• Systematically change coefficients to examine the effect of each on system dynamics

– Address feedback loops and explore their implications in this model

PreyPredator (-)

Feedback Loop

Calibration• We roughly calibrated

the model to Hudson Bay pelt data to find the correct coefficient values.

• We then reset the values and challenged the students to calibrate the model as well.

Lotka-Volterra Predator-Prey Oscillations

0

100

200

300

400

500

600

700

800

900

0 5 10 15 20 25

time (years)

Har

es(x

1000

); L

ynx(

x100

0)

Hares (x10)

Lynx (x10)

Year Hares (x10) Lynx (x10)

0 300 40

2.7 470.2 60.1

5.4 700.2 90.8

8.1 770.4 350.2

10.8 360.3 590.4

13.5 200.6 410.7

16.2 180.1 190

18.9 210.4 130

21.6 220 80.3

24.3 250.4 90.1

27 270.1 70.4

29.7 400.3 80

32.4 570 120.3

35.1 760.6 190.5

37.8 520.3 450.7

40.5 190.5 510.1

43.2 110.2 290.7

45.9 70.6 150.8

48.6 140.6 90.7

51.3 160.2 100.1

54 240.7 80.6

Current Bio120 Student Reactions

• Fit the lab to the current Bio 120 lab structure (break down into separate parts)

• More explicit directions• Cover more of the material discussed in lecture• It would have been nice to see a simple

ecological model prior to constructing their own (phytoplankton + nutrients)

• Allow for more hypothetical thinking: maybe tell us to conceptualize a food web model

• We thought we could apply what we learned more extensively (i.e. analogies)

Conclusions

• We need to spend more time working directly with students who are unfamiliar with systems modeling.

• The balance between too much and too little information is difficult to achieve.

• This project and its integration into the biology program is entirely feasible.

In the Future

• Meet with the three BIO 120 lab instructors and John (during commencement, John?) to review our exercise and discuss improvements.

• Explore other possible biology topics to be used in this exercise.

• Give the lab to more biology students (without modeling background).