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## NetLogo User Community Models

## WHAT IS IT?

This is a simple model of the evolution of mutation rate and population size.

Every time step (tick) is a generation, where each organism reproduces asexually, and its offspring inherit its fertility and its mutation rate. If the population rises above the terrain's carrying capacity, organisms randomly die (starve) until the population is reduced below the terrain's carrying capacity.

Each time an organism is born, there is a probability, set the by its mutation rate, that the offspring's fertility will differ from the parent's. If the fertility of the offspring does mutate, the model chooses a random number between 0 and 0.2 (with uniform distribution), and subtracts that from the parent's fertility rate. So all mutations are deleterious. In addition, a random number is chosen between 0.5 and 1.5 (with uniform probability) and that number is multiplied against the parent's mutation rate to determine the offspring's mutation rate. So the offspring's mutation rate may be up to 50% lower or 50% higher than the parent's.

## HOW TO USE IT

Always use the SETUP button at the start of these models to initialize the population of organisms.

The CARRYING-CAPACITY slider sets the carrying capacity of the terrain. The model is initialized to have a total population of CARRYING-CAPACITY.

The GO button runs the model. Clicking it again stops the model.

The FERTILITY plot shows a histogram of the fertilities in the population.

The MUTATION RATE plot shows the average mutation rate in the population over time.

The RUN-EXPERIMENT button lets you experiment with many trials at the same settings, stopping at 5,000 ticks and reporting the average mutation rate.

## THINGS TO DO

Set the starting carrying capacity to 100. Run the model for a while to see what happens to the average mutation rate in the population. Does it increase or decrease? Why?

Run an experiment and for at least 5 runs with a carrying capacity of 100, record the exponent on the average mutation rate and the aveage fertility to 4 decimal places.

Now increase the carrying capacity to 1,000 and run another experiment for at least 5 runs. Calculate the average order of magnitude (exponent) of the mutation rates. Does the larger population evolve a lower or higher mutation rate? Why?

Calculate the average fertility across your runs. Does the larger population evolve a lower or higher fertility? Why?

## EXTENDING THE MODEL

If you want to download the model and change the code, try changing the range by which the fertility changes and the mutation rate change.

What happens if 1% of the mutations are beneficial, increasing the mutation rate? What happens if half of them are?

## HOW TO CITE

This model is based on Wilensky's Simple Birth Rates modelm, and was extended by Carlo C. Maley in 2018.

To cite the original model itself:

* Wilensky, U. (1997). NetLogo Simple Birth Rates model. http://ccl.northwestern.edu/netlogo/models/SimpleBirthRates. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)