## Simulation

• A method of practice, trial and error learning, and exploration.

Imagine learning to play the piano without ever touching a piano or practicing the hand movements required to play. What if you were expected to play a difficult concerto after extensive exposure (perhaps a semester) to only verbal and written descriptions of how other people play? Such a teaching style would make learning to play the piano very difficult because there would be no opportunity for practice, trial and error, or exploration. You would not have the opportunity for direct experience nor incremental improvement of your understanding. Unfortunately, this is exactly how science courses are taught to some degree. You are expected to learn and remember concepts with only limited opportunity for directly observing principles in action. In fairness, this is partly due to the difficulty of carrying out some of the experiments or observations that originally lead someone to discover and understand an important principle.

In the field of population genetics computer simulations can be used to effectively demonstrate many fundamental genetic processes. In fact, computer simulations are an important research tool in population genetics. Therefore, when you conduct simulations you are both learning by direct experience and learning using the same methods that are used by researchers. Simulations allow us to view how quantities like allele frequencies change over time, observe their dynamics, and determine whether a stable end point is reached: an equilibrium. With simulations we can view dynamics (change over time) and equilibria over very long periods of time and under a vast array of conditions in an effort to reach general conclusions. Without simulations, it would be impossible for us to directly observe allele frequencies over such long periods of time and in such diverse biological situations.

Simulations are an effective means to understand some of the fundamental predictions of population genetics. Mathematical expressions are frequently used to express dynamics and equilibria in population genetics, but the equations alone can be opaque at first. Simulations provide a means to explore the relationships among variables that are summarized in the compact language of mathematics. Many people feel that a set of mathematical equations is much more meaningful after having the chance to explore what they describe with some actual numerical values. Simulation provides the means to explore what equations predict and can make learning population genetics an easier, more rewarding experience.

Carrying out simulations has the potential to make the expectations of population genetics much more accessible and understandable. Conducting simulations is not much extra work, especially once you get into the practice of using the text and simulation software in concert. You can approach simulations as if they are games, where each one shows a visual scene that helps to solve a puzzle. In addition, simulations can help you develop a more intuitive understanding of population genetic predictions so you do not have to approach the expectations of population genetics as disembodied or unanimated "facts."

It is important to approach simulations in a systematic and organized fashion, not as just a collection of buttons to press and text entry boxes to be filled in on a whim. It is absolutely imperative that you understand the meaning behind each variable that you can control as well as the meaning of the results you obtain. To do so successfully you will need to be aware of both specific details and larger patterns, or both individual trees and the forest that they compose. For example, in a simulation that presents results as a graph, it is important that you understand the details of what variables are represented on each axis and the range of axis values. Sometimes these details are not always completely obvious in simulation software, requiring you to use both your intuition and knowledge of the population genetic processes being simulated.

Once you are comfortable with the details of a simulation, you will also want to keep track of the "big picture" patterns that emerge as you view simulation results. Seeing these patterns will often require that you examine the results over a range of conditions. Try approaching simulations as experiments by changing only one variable at a time until you understand its effects on the outcome. Changing several things all at once can lead to confusion and an inability to see cause-and-effect relationships, unless you have fully understood the effects of indi vidual variables. Finally, try writing down parameter values you have tried in a simulation and sketching or tabulating results on paper as you work with a simulation. Use all of your skills as a scientist and student when conducting simulations and they will become a powerful learning tool. Eventually, you may even use scripting and programming to carry out your own simulations specifically designed to explore your own genetic hypotheses.

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