Building your own model is a requisite component to this investigation. It is during the model building, testing, and corrective phase of construction that the reflective and analytical skills of model building are learned:)

Remember the end of the quarter is next Friday:

This is the last day to turn in late work for 50% credit.

Students can do up to 2 current event synopses: 10 pts. each

This is the last day to turn in late work for 50% credit.

Students can do up to 2 current event synopses: 10 pts. each

**How can mathematical models be used to investigate the relationship between allele frequencies in populations of organisms and evolutionary change?**

“Mathematics is biology’s next microscope, only better …” (Cohen 2004)

It is not hard to understand the value of microscope technology to biology and how this technology opened up entire new worlds of biological understanding. However, for some, it is not as easy to see the value of mathematics to the study of biology. Like the microscope, math and computers provide tools to explore the complexity of biology and biological systems, offering deeper insights to and understanding of what makes living systems work. Even the incredible complexity of evolution in populations is illuminated by relatively simple mathematical equations, several of which are based on the Hardy-Weinberg (H-W) equilibrium. Students (and their teachers) have traditionally found the topic of population genetics in an introductory biology class to be challenging, due in part to the fact that for the last couple of generations biology has been thought of as the science with only a minimal mathematics foundation — particularly in comparison to chemistry or physics. Modern biology, however, is vastly different.

In the first part of this investigation, the students will build a spreadsheet that models how a hypothetical gene pool changes from one generation to the next. This model will allow for the exploration of parameters that affect allele frequencies, such as selection, mutation, and migration.

Quantitatively describe the biological system.

On pages 30-38 read and follow the guidelines for building your mathematical model. Think about the spreadsheet functions you are incorporating and how they help you model this particular system.

On a separate sheet of cellulose; answer the bulleted elements for this activity

Testing your mathematical model- pg 37: follow the guidelines for your model- in this case by adding several generations. Answer the following questions for this section:What factors can cause allele frequencies to change in a population? (Hint: There are many.) How could you model these factors using your spreadsheet?

The second part of the investigation you are asked to generate your own questions regarding the evolution of allele frequencies in a population. Then you will explore (heading down the rabbit hole:) possible answers to those questions by applying more sophisticated computer models.

In this second part, you can use your newly built model or use more sophisticated models available on the Internet to answer your own questions; see the suggested online options that follow. In this option, while you are not building the model, you are applying your knowledge of models to explore questions about population genetics.

AlleleA1: Jon Herron from the University of Washington has created a simulation called AlleleA1 along with documentation. It is available for free at

http://faculty.washington.edu/herronjc/SoftwareFolder/AlleleA1.html

Deme 1.0 and 2.0: Another Excel model with more sophistication than the model you built in class, Deme 1.0 and 2.0 with documentation are available at http://bioquest.org/esteem/esteem_details.php?product_id=193,

where you need to establish an account (free) before you can download it. It works in Excel just as the spreadsheet model you created earlier.

■■Designing and Conducting Your Investigation

By this point you’ve been able to use your model to explore how random chance affects the inheritance patterns of alleles in large and small populations. Perhaps you’ve also been able to find some interesting patterns in how alleles behave across generations. At the end of the last section you were asked what factors can cause allele frequencies to change in a population and how you would model them. Choose one of your answers, and try it out using your spreadsheet. This may involve adding multiple columns or rows along with a few extra operations. Keep the life cycle of your hypothetical population in mind as you develop additional strategies. With your new spreadsheet model, generate your own questions regarding the evolution of allele frequencies in a population. From these questions (noted in your lab notebook), you need to develop hypotheses that you can test — those that allow you to easily manipulate the parameters of population size, number of generations, selection (fitness), mutation, migration, and genetic drift. Collect sufficient data by running your model repeatedly.