Genetic drift simulation

Consider how the model is working

As you are working through the models, start thinking about how our modelling decisions are representing the process of a population passing on its genes from parents to offspring over time. Some of the choices we are making are not terribly faithful representations of how a real biological population would work. Ask yourself questions such as:

Is population size really going to stay exactly the same in a real population over 500 generations? If not, why are we keeping it constant in our models?
What kind of organism might the simulation best represent? Broadcast spawners are aquatic animals that release sperm and eggs into the water, where fertilization occurs - is this the kind of organism we are simulating?
Is the way we are selecting males and females to breed realistic? Are every male and female in a population equally likely to mate with one another?
Do most species breed and then die, with no overlap in generations? So all offspring produced usually survive to adulthood?
There is no natural selection in these models, only drift. How might the results be different for genes that are subject to natural selection?

But, simulation models have some distinct advantages that justify their use.

Simulation models allow us to run experiments that aren't possible in real populations. We may be able to do field work that tests whether gene frequencies are varying over time in a population with random mating, but a single population will only have a single pattern of change over time. Our ability to run multiple identical runs to see what happens in general is tremendously beneficial. Additionally, many processes we want to study take a very long time to complete, and we can't study them in real time - a species that takes a year to mature and reproduce can't be followed over 500 generations by any one researcher (and no studies that I'm aware of have been continued for 500 years).
Simulation models allow us to isolate variables. Being able to isolate variables by holding everything else constant is a very important principle of experimental design, and we have an unrivaled ability to isolate variables in a simulation model. For example, we're holding population size constant, knowing that in real populations it will usually vary from generation to generation. Although a constant population size may not be very realistic, if we were not able to hold population size constant we wouldn't be able to tell how much of the variation in allele frequency was due to random mating and how much was due to fluctuation in population size over time.
We can explore the consequences of the things that we know. We know that when there is random mating we expect drift, but how does an increase in population size affect the rate of loss of alleles to drift? What happens if instead of a closed population (with no immigration or emigration) there is immigration into the population?

As long as the way the model works is not so completely unrelated to how biological systems work to the point that we will be misled by using them it can be very useful to use models to help us understand real populations.

You can address questions like this in the Discussion of your papers when you're talking about potential problems with the model, or limitations on what we can learn from it.

First variation: Double the population size

Genetic drift is a random sampling process, and random sampling tends to have the largest effects at small sample sizes. We might expect that if we have more individuals in the population it will take longer for an allele to go to fixation on average, and we'll have more runs that don't go to fixation at all. We'll test this by doubling the population size from 100 to 200.

Save your drift_sim_n100_time_to_fixation spreadsheet as a new file, called "drift_sim_n200". MAKE SURE YOU SAVE AS A MACRO ENABLED WORKSHEET, OR YOUR MACROS WILL BE LOST. We will now modify the simulation by increasing the population size to 100 males and 100 females each.

Start with the Simulation sheet.

1.Copy and paste the male and female parent generation alleles below the current set of 50. This will double the size of the population, but the frequencies of all the genotypes will be the same as before.

2. Extend the ID numbers to 100.

3. Increase the number of Breeder male and females to 100 each. In addition to increasing the rows to 100, make sure you update the randbetween() function to select from all 100 of the males and females.

Also, check that the lookups used to select the breeder alleles are pointing to the full set of 100 males and females.

4. Increase the number of Offspring males to 100 (the increase in female offspring will be done by the program).

Statistics sheet

Check all the formulas. If they point to a cell range in Simulation, adjust them to the new ranges (they should go to 104 instead of 54, and are based on 200 individuals with 400 alleles, instead of 100 individuals with 200 alleles). The change will affect the allele frequencies, and heterozygosity calculations, but not allelic diversity (which is based just on the frequencies in the Statistics sheet).

Results sheet

There are no formulas to update, only results recorded by the program. Nothing to change here.

Original sheet

Copy the new Parent Population with 100 males and 100 females to the Original sheet before you run the simulation so that the initial population is set up correctly.

Macro

Open the macro and check each cell reference to either the Simulation or Original sheets to make sure they're updated to reflect this larger population size. None of the cell ranges will change in Statistics or Results, so you don't need to change those.

Debug

Put a break at the first line of code after the Loop line that closes the Do While loop. Step through the Do While loop a couple of generations to make sure everything is working (position your screen so you can see that the full 100 males and 100 females are being copied, and that all 100 individuals in the Original sheet are being used to reset to initial conditions between runs), then run until the program hits your break point and step through the last couple of steps to make sure the For...Next "j" loop commands still work too. Do this at least twice through the For...Next loop.

Run the program, and interpret the results

It should be ready to go, so run it. When it's done you should see that the average amount of time to fixation is longer, and more runs will not have gone to fixation than before.

This model will run a little slower - since there are more rows in the sheet all the recalculations will take a little longer, and fewer runs will go to fixation, so most will run the full 500 generations. As long as your status bar counter is increasing don't interrupt the program.

You will again only have a full set of allele frequencies for the final run, so graph them as an example of the pattern of change in allele frequencies that occurs when there are 200 individuals in the population. Use the time to fixation and alleles fixed from the full set of 100 runs to address how population size affects the rate of loss of genetic diversity that happens due to genetic drift (get the same statistics as you did for the n100 time to fixation model).

Second variation: immigration

When an individual moves to a new population, it brings its genes along with it. Immigrants can thus restore lost alleles, and may be able to prevent alleles from being lost in the first place by increasing the frequencies of rare alleles.

Immigration has a smaller effect on big populations than on a small population, because a single pair of alleles is a smaller contribution to a big gene pool than a small one. Big populations also lose alleles to genetic drift more slowly than small populations do (as you should have seen with your n200 model, above). These two factors offset one another perfectly in theory, such that a single immigrant per generation is expected to prevent loss of alleles to drift regardless of the size of the population. This next version of the model will explore whether 1 immigrant per generation is enough to avoid loss of alleles in our simulated population.

1. For this modification, start with your drift_sim_n100_time_to_fixation file. Save it as "drift_sim_n100_immigration" (macro enabled - don't forget!). Make sure you start with the n100 simulation, not the n200 simulation you just completed, we just want to add immigration without increasing the population size.

2. In sheet "Simulation", we need to change the last row of male Breeders to simulate a migrant entering the pool of breeders. We will assume that the migrant comes from a large, outbred, genetically diverse population that has an equal frequency of all five of the alleles originally present in our population - in other words, the population the immigrant comes from looks just like the initial population we are simulating, but is large enough that there is no change in allele frequencies over time.

We can simulate a single immigrant entering the population each generation by generating the alleles for the final male Breeder like so (enter this formula in cells J54 and K54):

=choose(randbetween(1,5), "A", "B", "C", "D", "E")

The randbetween() function will generate a random integer number between 1 and 5, and then the choose() function will use the randomly selected number to choose from the set of five alleles. Each allele has an equal chance of being selected, so the immigrant is coming from a population with allele frequencies that are all equal at 0.2 and don't change over time.

Write the label "immigrant" to cell I54 to label this male.

The rest of the simulation should be the same - this male will produce offspring like all the rest. Bear in mind that although we are simulating one immigrant into the population, the way we simulate breeding by copying the male offspring and paste-specialing their values to create female offspring causes this immigrant male breeder to always have exactly two offspring each generation. Other parents can either have none (if their numbers aren't selected) or multiple (if their numbers are selected several times). We could instead have added the immigrant male to the parent population and then selected him at random like the rest, but the "one immigrant per generation" rule of thumb expects that the immigrant will successfully breed - if an immigrant enters the population and doesn't breed they have no effect on the gene pool, and it will generally take more than one immigrant to avoid loss of diversity to drift if some of them don't breed. You can mention this in your writeup.

3. Run the program. Since there is no change to the macro you know that it works, and you can simply run the program at this point, no need to debug.

4. Summarize the results, as you did for the other simulations. However, the pattern of change in heterozygosity and allelic diversity are quite different, so produce a graph for these as well as the allele frequencies for the final run. Use the time to fixation and allele fixed results for the full 100 sets of runs to address how immigration typically affects loss of genetic diversity due to drift.

Assignment

And with that, you're done with the simulations for the genetic drift project. Now you can write up a report of your results according to the instructions posted on Canvas, and will turn in all four of your simulations (n100, n100_time_to_fixation, n200, and n100_immigration) along with a Word file with your written report.

Genetic drift simulation - steps 3 and 4