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## WHAT IS IT?

This is a simple model of how mutation rates and population sizes affect the rate of evoution.

Every time step (tick) is a generation, where each organism reproduces asexually, and its offspring inherit its fertility. 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 the 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 -0.1 and 0.1 (with uniform distribution), and adds that to the parent's fertility rate. In this way, the offspring's fertility maybe slightly higher or slightly lower than its 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 LOG-MUTATION0-RATE slider sets the probability that an organism's fertility rate changes at reproduction. This is log base 10, so -1 = 0.1 and -2 = 0.01, and so on.

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

The POPULATION plot displays the number of organisms currently in the population.

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

The RUN-EXPERIMENT button lets you experiment with many trials at the same settings. This button outputs the number of ticks it takes for the average fertilty of the population to rise above 4. At that point, the world is cleared and another run begins with the same settings. This way you can see the variance of the number of generations until the population evolves that high level of fertility.

## THINGS TO DO

Set the starting log mutation rate to -2 (i.e., set the mutation rate to 0.01) and the carrying capacity to 200. Run an experiment and for at least 3 runs, record the number of generations it takes for the average fertility in the population to exceed 4.

Now increase the log mutation rate to -1 and rerun the experiment. Does the population evolve faster or slower? Why?

Now set the carrying capacity to 1000 and rerun the experiment. Does the larger population evolve faster or slower? Why?

## EXTENDING THE MODEL

If you want to download the model and change the code, try changing the range by which the fertility changes. Or change the degree of mutation from a uniform distribution to a Normal distribution.

## 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.

## COPYRIGHT AND LICENSE

Copyright 1997 Uri Wilensky.


This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001.

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