Lab Overview - Brief description

Descriptions of the Quantitative Biology Labs

Project Goals

A set of quantitative biology laboratory exercises are being developed in an interdisciplinary effort between the Department of Biology and the Department of Mathematics and Statistics at Utah State University. Our goal is to create a series of quantitative biology labs applicable to students from high school biology up through advanced (senior) undergraduate courses. This page gives a brief description of the labs and associated tools we have prepared.

Each title in blue text links to a page which is either the actual lab material or is a more thorough description of some part of the project.

Note: This and the associated pages are, like the project itself, continually evolving. Not all of the planned labs have been implemented.

Directory of Quantitative Labs

The following directory of lab exercises are descriptions of the lab exercises. The description title links to the actual webpages that are used by the students in the laboratories while they are doing experiments and solving quantitative problems. We employ different pedagogical techniques in different courses. In the introductory classes we use a combination of small-group problem solving and enquiry-based instruction. During the lab, the instructors periodically convenes the class and discusses the status of the problem solution and re-focuses the small groups of students working on the problem. The pages present a series of steps to the students that must be completed before proceeding

to subsequent steps. Since some of the later steps provide answers to questions asked in prior steps, these latter pages have boxes to be completed by the students. This strategy forces students to think about the problem and also provides a record of the solution.

Some of the pages may be password protected, as a means of withholding information that students are asked to discover for themselves. We have found this to be less successful and are phasing out this method. If you wish to view a page which is password protected, send email to Jim Haefner.

BioMath Minor Quantative Labs

The Departments of Biology and Mathematics and Statistics have established a BioMath minor for students in both Departments. The minor requires completion of a team-taught course that integrates wet-lab experiments with mathematical modeling and computational analyses. These exercises have not yet been produced as webpages, but a brief description follows.

Epidemiology Game
Leaky Bucket
Fermentation
Predator-Prey Dynamics

Introductory Quantitative Labs with Links

Cell Osmosis

Osmosis (the diffusion of water across biological membranes) is taught in almost all introductory biology laboratories. It is a ubiquitous phenomenon of cells that can be demonstrated with relatively simple and inexpensive experiments. A typical laboratory experiment simply demonstrates the occurrence of the phenomenon. We extend this classic exercise in hypothesis testing by adding a predictive mathematical model.
Osmosis is usually treated early in the first term of an introductory biology course along with diffusion and plasmolysis. In our labs, the experiment uses a bag made from dialysis tubing partially filled with water and known, but variable, concentrations of sucrose. The bag is immersed in water, removed for weighing, and re-immersed in water until the next weighing. This is repeated for 5--6 weighing bouts over a period of about 40 minutes.
The interesting phenomena which the students eventually see are:
(1) water moves into the bag,
(2) the rate of water movement decreases with time as the internal sucrose concentration approaches that of the outside, and
(3) this rate depends on initial sucrose concentration.

The quantitative problem for the students to solve is to mathematically describe these observations. To solve this problem, they must create a mathematical model.

Without this quantitative component, an osmosis lab normally requires 1 lab period, but must be expanded to 2 lab periods to include the new material. In first lab period, we lead the students to create a mathematical model of a more familiar phenomenon: cooling of a body that is initially warmer than ambient temperature. This has two advantages; first, the students have an intuitive grasp of the process. Second, we motivate the cooling problem with a real-world scenario: how to tell if a cougar was shot legally (see the webpage for more details). With the aid of the lab instructors, the students are led through the experiments and data analysis to formulate Newton's Cooling Law for the rate of change of temperature of a beaker of water.
In the second lab period, students are presented with the osmosis phenomenon. They perform the weight gain experiment and are asked to create a model that describes its change. After the cooling example, they can see the similarities of the two processes and transfer skills they learned studying cooling to osmosis.
The webpages, with instructor guidance, lead students through a series of steps designed to help them solve the problems. The primary quantitative math skills that students learn are: graphing data and drawing "best fit" lines, finding slopes from data plots, transforming data to create linear relations, and iterating finite difference equations. The math and inference skills are re-inforced with homework problems.

Cell Osmosis
Osmosis (the diffusion of water across biological membranes) is taught in almost all introductory biology laboratories. It is a ubiquitous phenomenon of cells that can be demonstrated with relatively simple and inexpensive experiments. A typical laboratory experiment simply demonstrates the occurrence of the phenomenon. We extend this classic exercise in hypothesis testing by adding a predictive mathematical model. Osmosis is usually treated early in the first term of an introductory biology course along with diffusion and plasmolysis. In our labs, the experiment uses a bag made from dialysis tubing partially filled with water and known, but variable, concentrations of sucrose. The bag is immersed in water, removed for weighing, and re-immersed in water until the next weighing. This is repeated for 5--6 weighing bouts over a period of about 40 minutes. The interesting phenomena which the students eventually see are: (1) water moves into the bag, (2) the rate of water movement decreases with time as the internal sucrose concentration approaches that of the outside, and (3) this rate depends on initial sucrose concentration. The quantitative problem for the students to solve is to mathematically describe these observations. To solve this problem, they must create a mathematical model.	Without this quantitative component, an osmosis lab normally requires 1 lab period, but must be expanded to 2 lab periods to include the new material. In first lab period, we lead the students to create a mathematical model of a more familiar phenomenon: cooling of a body that is initially warmer than ambient temperature. This has two advantages; first, the students have an intuitive grasp of the process. Second, we motivate the cooling problem with a real-world scenario: how to tell if a cougar was shot legally (see the webpage for more details). With the aid of the lab instructors, the students are led through the experiments and data analysis to formulate Newton's Cooling Law for the rate of change of temperature of a beaker of water. In the second lab period, students are presented with the osmosis phenomenon. They perform the weight gain experiment and are asked to create a model that describes its change. After the cooling example, they can see the similarities of the two processes and transfer skills they learned studying cooling to osmosis. The webpages, with instructor guidance, lead students through a series of steps designed to help them solve the problems. The primary quantitative math skills that students learn are: graphing data and drawing "best fit" lines, finding slopes from data plots, transforming data to create linear relations, and iterating finite difference equations. The math and inference skills are re-inforced with homework problems.

Back to Directory; Lab Home; BioMath Home

Light Extinction in a Lake

This is the first of a two-part lab exercise. Providing a strong motivation for a quantitative problem is essential to hold student interest. The motivating question that this series of lab exercises answers is: How much photosynthesis occurs in a Bear Lake Utah in one day? This lake is a local, clear lake with which students are familiar and we further motivate the problem by comparing it to a local, shallow, and very turbid reservoir impacted by high nutrient runoff from local dairy operations. We begin by asking students to think conceptually about the causal factors that limit photosynthesis in natural environments like lakes. They do this by creating a concept map (see the webpages) of photosynthesis in a small group activity. The instructor then leads a class discussion to simplify the (usually) complex diagrams.
Light is certainly one of the important variables that determine lake photosynthesis, and the first step in answering the lake question is to aswer the question: How does light change with depth in a lake? This lab exercise leads students to consider two quantitative models of extinction (linear and exponential

decrease with depth). The students must use elementary reasoning and visualization of functions to eliminate one of the equations.
The remaining equation, the Beer-Lambert Law, is examined quantitatively using aquaria, dye, and quantum light meters. Light is shone horizontally through a series of 3 aquaria filled with water, and light intensity is measured at the light source and at end of each aquaria. The students are asked to determine the quantitative differences between water columns with and without dye. This leads them to the problem of estimating the light extinction coefficient in the Beer-Lambert equation. They calibrate this equation using logarithm transformations and fitting their data to a straight line.
The math skills they use are: graphing data and drawing "best fit" lines, finding slopes from data plots, transforming data using logarithms to create linear relations, and iterating finite difference equations. Homework problems re-inforce these skills.

Light Extinction in a Lake
This is the first of a two-part lab exercise. Providing a strong motivation for a quantitative problem is essential to hold student interest. The motivating question that this series of lab exercises answers is: How much photosynthesis occurs in a Bear Lake Utah in one day? This lake is a local, clear lake with which students are familiar and we further motivate the problem by comparing it to a local, shallow, and very turbid reservoir impacted by high nutrient runoff from local dairy operations. We begin by asking students to think conceptually about the causal factors that limit photosynthesis in natural environments like lakes. They do this by creating a concept map (see the webpages) of photosynthesis in a small group activity. The instructor then leads a class discussion to simplify the (usually) complex diagrams. Light is certainly one of the important variables that determine lake photosynthesis, and the first step in answering the lake question is to aswer the question: How does light change with depth in a lake? This lab exercise leads students to consider two quantitative models of extinction (linear and exponential	decrease with depth). The students must use elementary reasoning and visualization of functions to eliminate one of the equations. The remaining equation, the Beer-Lambert Law, is examined quantitatively using aquaria, dye, and quantum light meters. Light is shone horizontally through a series of 3 aquaria filled with water, and light intensity is measured at the light source and at end of each aquaria. The students are asked to determine the quantitative differences between water columns with and without dye. This leads them to the problem of estimating the light extinction coefficient in the Beer-Lambert equation. They calibrate this equation using logarithm transformations and fitting their data to a straight line. The math skills they use are: graphing data and drawing "best fit" lines, finding slopes from data plots, transforming data using logarithms to create linear relations, and iterating finite difference equations. Homework problems re-inforce these skills.

Back to Directory; Lab Home; BioMath Home

Photosynthesis and Light

The second lab period answers the question with which the students were originally presented. Once the behavior of light in the water column is understood, the students are asked to determine the effect of different light levels on the rate of photosynthesis. To answer this, they use Elodea in an inexpensive manometer exposed to different levels of light. The response variable is volume of oxygen produced in a finite time interval. Measurements of oxygen production are performed at fixed distances from a light source.
In this preparation, the data typically show an asymptotic relation with increasing light levels (i.e., manometers near the light source). The students are asked to create an equation that matches this relationship. Again, the students must estimate the coefficients of the equation from their data. This requires that they again use a logarithm transformation to create a straight line relationship.

At the end of the two lab periods, the students know how light changes with depth and how photosynthesis changes with light.
The last step is a group problem-solving exercise done out of class to solve the problem of the lake. The students must synthesize their knowledge of the effect of dept on light and the effect of light on photosynthesis to determine the amount of photosynthesis at several discrete water depths. By adding the photosynthesis at each depth, they calculate total photosynthesis. As homework exercises, they are given actual light extinction data from Bear Lake Utah with depth and area data to calculate a final answer to the question.
The math skills they learn from this last step are: unit conversions, summation (integration), synthesizing two different equations and experimental results, organizing and performing moderately complex calculations.

Photosynthesis and Light
The second lab period answers the question with which the students were originally presented. Once the behavior of light in the water column is understood, the students are asked to determine the effect of different light levels on the rate of photosynthesis. To answer this, they use Elodea in an inexpensive manometer exposed to different levels of light. The response variable is volume of oxygen produced in a finite time interval. Measurements of oxygen production are performed at fixed distances from a light source. In this preparation, the data typically show an asymptotic relation with increasing light levels (i.e., manometers near the light source). The students are asked to create an equation that matches this relationship. Again, the students must estimate the coefficients of the equation from their data. This requires that they again use a logarithm transformation to create a straight line relationship.	At the end of the two lab periods, the students know how light changes with depth and how photosynthesis changes with light. The last step is a group problem-solving exercise done out of class to solve the problem of the lake. The students must synthesize their knowledge of the effect of dept on light and the effect of light on photosynthesis to determine the amount of photosynthesis at several discrete water depths. By adding the photosynthesis at each depth, they calculate total photosynthesis. As homework exercises, they are given actual light extinction data from Bear Lake Utah with depth and area data to calculate a final answer to the question. The math skills they learn from this last step are: unit conversions, summation (integration), synthesizing two different equations and experimental results, organizing and performing moderately complex calculations.

Back to Directory; Lab Home; BioMath Home

Optimal Foraging

This is a three lab exercise that integrates predator functional responses and optimal foraging. The motivating question and principle is: "Do fish forage optimally?"
In the first lab period, the general problem is introduced with a discussion of the evolution of animal foraging behavior. This is followed by a discussion of food item choice when a predator is faced with two items having respectively high energy content plus long handling times (juicy hamburgers) versus low energy content plus short handling times (bags of peanuts). The discussion addresses the situations when the density of each is very low and very high.
Once the students' intuition is clear, they perform a series of experiments that replicate and extend C.S. Holling's original disc equation experiments using sandpaper discs thumbtacked to white foam poster board. See the lab webpage for details. The data from these experiments are used to estimate handling times and attack rates. The experiments are performed so as to produce Type I, II, and III functional responses. Homework exercises are assigned. Finally, the experiments are repeated using discs with two energy and handling time levels at different densities. The results illustrate that more energy is

gained by consuming the disc type that has the highest profitability (energy content divided by handling time), even if it has less absolute energy content.
In the second lab period, the equations for optimal foraging are developed. These equations describe the energy gained by three foraging strategies as density of prey changes. At low density, the strategy to consume all prey encountered returns the greatest energy rate. At high density, the strategy to consume only the most profitable prey returns the greatest energy rate. The prey density at which the lines cross is the density where the predator should change its foraging behavior, if it is an optimal forager.
This is a lot of algebra for the students, so at the end of the second lab and in preparation and practice for the third lab period, students measure the handling times of guppies foraging on Daphnia or brine shrimp (depending on prey local availability).
In the third week, the theory is tested with experiments in which guppies are presented with two size classes of prey at 3 densities. After the experiments, the instructor engages the students in a discussion of the original question. The students complete a short lab report.

Optimal Foraging
This is a three lab exercise that integrates predator functional responses and optimal foraging. The motivating question and principle is: "Do fish forage optimally?" In the first lab period, the general problem is introduced with a discussion of the evolution of animal foraging behavior. This is followed by a discussion of food item choice when a predator is faced with two items having respectively high energy content plus long handling times (juicy hamburgers) versus low energy content plus short handling times (bags of peanuts). The discussion addresses the situations when the density of each is very low and very high. Once the students' intuition is clear, they perform a series of experiments that replicate and extend C.S. Holling's original disc equation experiments using sandpaper discs thumbtacked to white foam poster board. See the lab webpage for details. The data from these experiments are used to estimate handling times and attack rates. The experiments are performed so as to produce Type I, II, and III functional responses. Homework exercises are assigned. Finally, the experiments are repeated using discs with two energy and handling time levels at different densities. The results illustrate that more energy is	gained by consuming the disc type that has the highest profitability (energy content divided by handling time), even if it has less absolute energy content. In the second lab period, the equations for optimal foraging are developed. These equations describe the energy gained by three foraging strategies as density of prey changes. At low density, the strategy to consume all prey encountered returns the greatest energy rate. At high density, the strategy to consume only the most profitable prey returns the greatest energy rate. The prey density at which the lines cross is the density where the predator should change its foraging behavior, if it is an optimal forager. This is a lot of algebra for the students, so at the end of the second lab and in preparation and practice for the third lab period, students measure the handling times of guppies foraging on Daphnia or brine shrimp (depending on prey local availability). In the third week, the theory is tested with experiments in which guppies are presented with two size classes of prey at 3 densities. After the experiments, the instructor engages the students in a discussion of the original question. The students complete a short lab report.

Back to Directory; Lab Home; BioMath Home

Intermediate Quantitative Labs

DNA Fingerprinting and Guilt

This is a two lab period exercise using computer simulation and lectures. The primary learning goal is to have students learn and apply basic hypothesis testing skills. The motivating question is: "Did O. J. Simpson commit murder?"
The discussion begins with applications of a series of computer simulations written in Java and delivered over the internet. These programs simulate sampling from normal distributions with different means, variances, and sample sizes. The purpose is to illustrate the resultant cumulative distributions that emerge for the

difference between two samples. These distributions are used to compute the probability that the null hypothesis is false. Students are assigned homework based on the computer programs.
In the second lab period, a lecture describes likelihood functions and develops the fundamental equation for the likelihood that the DNA left at the crime was observed given the suspect left the DNA. This begins with a discussion of conditional probabilities in the context of forensic evidence and the nature of legal guilt.

DNA Fingerprinting and Guilt
This is a two lab period exercise using computer simulation and lectures. The primary learning goal is to have students learn and apply basic hypothesis testing skills. The motivating question is: "Did O. J. Simpson commit murder?" The discussion begins with applications of a series of computer simulations written in Java and delivered over the internet. These programs simulate sampling from normal distributions with different means, variances, and sample sizes. The purpose is to illustrate the resultant cumulative distributions that emerge for the	difference between two samples. These distributions are used to compute the probability that the null hypothesis is false. Students are assigned homework based on the computer programs. In the second lab period, a lecture describes likelihood functions and develops the fundamental equation for the likelihood that the DNA left at the crime was observed given the suspect left the DNA. This begins with a discussion of conditional probabilities in the context of forensic evidence and the nature of legal guilt.

Back to Directory; Lab Home; BioMath Home

Plant and Leaf Growth
The plastochron and leaf plastochron indices are methods to measure the age of whole plants and individual leaves based on their morphology rather than chronological age. They have been particularly useful for detailed studies of whole shoot and leaf development. Since the indices are based on measurements of exponential plant growth, they provide an opportunity to demonstrate the value of applying mathematics to a biological problem. In this exercise, students are presented the theoretical basis of the indices followed by practice in	calucating the indices for Xanthium strumarium (cocklebur) plants of various ages. The exercise demonstrates the potential variability in plant growth and the restuls of an exponential growth rate. The quantitative skills emphasized include: graphing and "best fit" estimates of slopes, logarithm transformations of data, and drawing scientific conclusions from quantitative data.

Back to Directory; Lab Home; BioMath Home

Bird Flight
This exercise is distributed over several weeks in an ornithology class. The exercise is assigned to small groups within the class. The motivating question is: "How can small birds migrate long distances without eating?" For example, more than 50 species of small songbirds and even the 3 g. Ruby-throated Hummingbird fly 1000km (600m) across the Gulf of Mexico. There are no stopping points along the way to rest or refuel. This feat is so amazing that for a long time scientists believed that hummingbirds flew around the gulf and many birdwatchers believed that they rode on the backs of larger birds. The mathematics is presented in a lecture format and results in basic parabolic relationship between energy consumption and flight speed. Then, given the amount of energy	available at the beginning of the trans-oceanic migration, the distance that can be traveled is computed. To provide an empirical component, each group is given the thawed carcass of a small bird that migrates across the Gulf of Mexico. Each group's problem is to determine for this bird during a spring crossing of the Gulf 1. what is the best choice for V (velocity of flight), 2. what is this bird's range at the best speed, 3. what is this bird's range when flying against a 25 mph headwind and 4. under what conditions (its own physiological state and meteorological conditions) should this bird initiate migration?

Back to Directory; Lab Home; BioMath Home

Advanced Quantitative Labs

Microbial Catabolite Repression

Most bacteria are capable of controlling the action of genes that code for the production of enzymes that catabolize (breakdown) growth compounds (e.g., glucose). In particular, the lac operon in E. coli is repressed in the presence of glucose to prevent the production of enzymes needed to catabolize other, less energetically rich, compounds. When glucose is exhausted, the genes coding for enzymes of the secondary substrate are transcribed. The experimental test for this phenomenon involves growing bacteria in a combination of substrates (e.g., glucose and lactose) and periodically measuring beta-galactosidase activity.
An analysis problem arises because both activity level per

cell and total bacterial population size increases during the experiment. As a result, the experiment is analyzed using the slopes of regressing enzyme activity against bacteria counts. The slopes are the primary data of interest.
The quantitative component of the lab exercise involves the statistical analysis of slopes. We present the statistical theory and spreadsheet manipulations needed to test the statistical differences among the slopes of different experiments.
The math skills reinforced are: statistical tests, cumulative probability distributions, logarithm transformations, spreadsheet manipulations.

Microbial Catabolite Repression
Most bacteria are capable of controlling the action of genes that code for the production of enzymes that catabolize (breakdown) growth compounds (e.g., glucose). In particular, the lac operon in E. coli is repressed in the presence of glucose to prevent the production of enzymes needed to catabolize other, less energetically rich, compounds. When glucose is exhausted, the genes coding for enzymes of the secondary substrate are transcribed. The experimental test for this phenomenon involves growing bacteria in a combination of substrates (e.g., glucose and lactose) and periodically measuring beta-galactosidase activity. An analysis problem arises because both activity level per	cell and total bacterial population size increases during the experiment. As a result, the experiment is analyzed using the slopes of regressing enzyme activity against bacteria counts. The slopes are the primary data of interest. The quantitative component of the lab exercise involves the statistical analysis of slopes. We present the statistical theory and spreadsheet manipulations needed to test the statistical differences among the slopes of different experiments. The math skills reinforced are: statistical tests, cumulative probability distributions, logarithm transformations, spreadsheet manipulations.

Back to Directory; Lab Home; BioMath Home

Leaf Heat Budgets

Photosynthesis, like most biological processes, is dependent on temperature. The question addressed in this lab exercise is: "What are processes by which a leaf gains and loses heat?" The two variables examined empirically are leaf size and stomatal conductance.
This is a two lab period exercise. In the first lab period the basic equations of heat balance in a leaf are presented. The physical processes considered are black body radiation, absorbance, evaporative cooling, convection, and conductance. Some of these terms have positive or negative contributions and their sum must equal zero.
After the theory is presented, the following variables

are measured in the lab: leaf temperature, vapor pressure, wind speed, leaf size, stomatal conductance, and absorbed radiation. Other parameters are known physical constants or are given to the students.
The students perform an experiment that varies leaf size and stomatal conductance to determine the temperature of the leaf. In addition, they use a simulation program that allows them to vary key variables to observe their effects on leaf temperature.
The primary math skills obtained are: graphing, managing complex computations, parameter sensitivity analysis, and drawing conclusions from quantitative predictions.

Leaf Heat Budgets
Photosynthesis, like most biological processes, is dependent on temperature. The question addressed in this lab exercise is: "What are processes by which a leaf gains and loses heat?" The two variables examined empirically are leaf size and stomatal conductance. This is a two lab period exercise. In the first lab period the basic equations of heat balance in a leaf are presented. The physical processes considered are black body radiation, absorbance, evaporative cooling, convection, and conductance. Some of these terms have positive or negative contributions and their sum must equal zero. After the theory is presented, the following variables	are measured in the lab: leaf temperature, vapor pressure, wind speed, leaf size, stomatal conductance, and absorbed radiation. Other parameters are known physical constants or are given to the students. The students perform an experiment that varies leaf size and stomatal conductance to determine the temperature of the leaf. In addition, they use a simulation program that allows them to vary key variables to observe their effects on leaf temperature. The primary math skills obtained are: graphing, managing complex computations, parameter sensitivity analysis, and drawing conclusions from quantitative predictions.

Back to Directory; Lab Home; BioMath Home

Michaelis-Menten Coefficients

This is a three part lab exercise with outside computer work. In the first part, the Michaelis-Menten equations are derived from the basic chemical rate equations. In the second week, statistical methods for estimating the two parameters are presented. This involves a discussion of linear regression. The main point of the exercise is to compare parameter estimates for different methods of transforming the Michaelis-Menten equation to a

linear form. In outside class homework, these linear regression estimates of the parameters are compared to estimates from nonlinear regression using the SAS statistical package. The third component is an experiment in which students measure enzyme activity and use the different methods to estimate the parameters.

Michaelis-Menten Coefficients
This is a three part lab exercise with outside computer work. In the first part, the Michaelis-Menten equations are derived from the basic chemical rate equations. In the second week, statistical methods for estimating the two parameters are presented. This involves a discussion of linear regression. The main point of the exercise is to compare parameter estimates for different methods of transforming the Michaelis-Menten equation to a	linear form. In outside class homework, these linear regression estimates of the parameters are compared to estimates from nonlinear regression using the SAS statistical package. The third component is an experiment in which students measure enzyme activity and use the different methods to estimate the parameters.

Back to Directory; Lab Home; BioMath Home

Island Biogeography

This is a 2 lab period exercise in which students physically simulate organisms colonizing islands of different sizes and distances from a mainland. Student data are then used to test the island biogeography theory of MacArthur and Wilson. In the first lab period, the basic theory is presented to show that immigration rate decreases and emigration rate increases as

the number of species on the island increases. Students solve for the equilibrium species number. They fit their data to these lines based on a simulation of island colonization. The data are obtained by throwing labeled plastic disks (petri dish halves) at squares delineated by string on a lawn. Overlapping dishes represent extinctions; disc labels define species.

Island Biogeography
This is a 2 lab period exercise in which students physically simulate organisms colonizing islands of different sizes and distances from a mainland. Student data are then used to test the island biogeography theory of MacArthur and Wilson. In the first lab period, the basic theory is presented to show that immigration rate decreases and emigration rate increases as	the number of species on the island increases. Students solve for the equilibrium species number. They fit their data to these lines based on a simulation of island colonization. The data are obtained by throwing labeled plastic disks (petri dish halves) at squares delineated by string on a lawn. Overlapping dishes represent extinctions; disc labels define species.

Back to Directory; Lab Home; BioMath Home

BioMath Minor Quantitative Labs

Epidemiology Game

Students creat rules for the spread of a disease in terms of frequency and spatial extent of infection. Using a plastic template with hexagons, randomized infected and non-infected individuals are represented by marks on the template. The infection rules

determine the numbers of infected individuals in the next iteration. Mathematical models of the dynamics of infected indivdiuals are created, calibrated, and tested with additional games.

Epidemiology Game
Students creat rules for the spread of a disease in terms of frequency and spatial extent of infection. Using a plastic template with hexagons, randomized infected and non-infected individuals are represented by marks on the template. The infection rules	determine the numbers of infected individuals in the next iteration. Mathematical models of the dynamics of infected indivdiuals are created, calibrated, and tested with additional games.

Back to Directory; Lab Home; BioMath Home

Leaky Bucket

"How long will a leaky bucket leak before the leaky bucket leaks no longer?" Students are given plastic containers (milk jugs) in whose side a small hole near the bottom has been filled. They measure the rate of flow over time and fit these

data to a series of models one of which is based on Torricelli's Law. They are then presented with a new bucket with a different type of orifice (e.g., rectangular) and asked to predict the emptying time.

Leaky Bucket
"How long will a leaky bucket leak before the leaky bucket leaks no longer?" Students are given plastic containers (milk jugs) in whose side a small hole near the bottom has been filled. They measure the rate of flow over time and fit these	data to a series of models one of which is based on Torricelli's Law. They are then presented with a new bucket with a different type of orifice (e.g., rectangular) and asked to predict the emptying time.

Back to Directory; Lab Home; BioMath Home

Fermentation

Students design and execute experiments in which yeast are grown in different initial concentrations of glucose. They measure

yeast and glucose over time, and use these data to calibrate models of the system.

Fermentation
Students design and execute experiments in which yeast are grown in different initial concentrations of glucose. They measure	yeast and glucose over time, and use these data to calibrate models of the system.

Back to Directory; Lab Home; BioMath Home

Predator-Prey Dynamics

Paramecium aurelia and Didinium spp are grown together in small containers and their numbers counted daily.

Data from these experiments and others form the basis of testing a family of simple predator-prey models.

Predator-Prey Dynamics
Paramecium aurelia and Didinium spp are grown together in small containers and their numbers counted daily.	Data from these experiments and others form the basis of testing a family of simple predator-prey models.

Back to Directory; Lab Home; BioMath Home