An Exercise in Leaf Growth Modeling for Introductory Students
adapted from “Modeling Plant Growth” by Yaffa Grossman
Objectives:
- Describe how plants grow
- Explain how carbon is partitioned between vegetative organs during plant growth
- Describe the use of models in biological research
- Evaluate a model designed to predict the growth of leaves under different conditions
- Describe the advantages and disadvantages of using models in science
- Evaluate a model for leaf growth and propose alterations of the model to better reflect data
- Design an experiment to empirically test the plant growth model
- Describe an application of a plant growth model
Introduction:
Mathematical models are important tools to help biologists better understand how biological systems function. The purpose of this exercise is to examine the utility of a simple model designed by Yaffa Grossman (Beloit College) for predicting plant growth. This model is an Excel spreadsheet that, based on several assumptions, allows the user to calculate predicted leaf area, plant mass, or carbohydrate production over time.
The beauty of a model is that it enables a scientist to investigate and predict how a particular variable will impact a biological event. For example, we might want to know how global climate change might affect the growth a plant. If we have created a model for leaf growth that includes a factor for temperature, then by using our model we could predict how plants in the future may respond.
There is no guarantee that our model is valid. Thus, it is usually necessary to test the model to see if it conforms to reality. To do so, scientists will collect data to determine if the empirical results match the predictions of the model. If so, then we would know that model is valid and has great predictive value. However, if our empirical results don’t match, then we need to either determine if we made an experimental mistake or we need to revise our model to better fit the data.
An Exercise in Leaf Growth Modeling for Introductory Students
adapted from “Modeling Plant Growth” by Yaffa Grossman
Student Work Sheet
Part 1 Background: Observing Plant Growth
Describe what has changed physically between the seed and the mature plant stage.
Explain what the main/critical biological process(es) that contribute to these changes.
How do the physical changes relate to this biological process?
Draw a simple diagram of this relationship.
Part 2 Simple Model
You will design a model that will show you how plant leaf area changes over time
Setting up a Spreadsheet Model for plant growth
Defining your columns and rows
From the literature scientists have determined that this plant life span is approximately 3 weeks and have estimated the following values.
Constants
0.0013= g CHO/cm2 leaf area/day
235= cm2 new leaf area/g CHO/day
From your model produce a graph showing change in leaf area over time.
Compare the relationship seen on the graph with your answers in Part 1.
What additional variables could we include in our model to make it more realistic?
Part 3 Improving Initial Model
Compare the spreadsheet of the new model with the spreadsheet of the initial model.
Describe what has been added and explain why the additions are important considerations for plant growth.
Produce baseline graph from model. Graph leaf area against time. Keep a copy of this graph.
Choose one of the following variables and predict how it might affect plant growth.
Initial leaf area
Mass specific leaf area
% plant mass as leaf
Light
Temperature
CO2
Change the variable in the model and graph the results.
What is the impact of the change on leaf area?
Was your prediction supported? Explain why or why not.
Design an experiment to empirically test the plant growth model.
Part 4 Application of Model (PEACH)
Propose an application of this plant growth model.