Complexity Explorables | Repliselmut

 

Source: Complexity Explorables | Repliselmut

 

“Repliselmut”

Yet another Complexity Explorable on evolution

An organic simulation of the replicator-mutator equation

EXPLORABLES

by Dirk Brockmann , Santa Fe Institute*

This explorable illustrates how variation and selection in a population of replicating organisms naturally leads to a gradual increase in the population’s overall fitness. The explorable simulates a system that is captured (to some extent) by the Replicator-Mutator Equation which is both, a generalization of the famous Replicator Equation and the Quasispecies Equation.

This explorable is similar to the Explorables “Maggots in the Wiggle Room” and “A Patchwork Darwinge”that illustrate key features of evolution. In those two explorables individuals of different species interact directly in a competitive way. Here however, individuals do not interact directly. They merely reproduce at different rates proportional to their fitness and die at equal rates. So competition is only indirect.

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This is how it works

Initially the system has a population of 100 individuals all of the same kind (same color and fitness). When the system runs each individual in the population replicates at a rate proportional to its fitness. Each individual can also die at a constant rate so eventually replication and death balance when the population is around 400.

While this is happening, mutations can occur. At a rate you can set with the mutation rate slider an individual can have a baby with a different fitness indicated by a different color. A new species is born. The new species can have a lower or a higher fitness with symmetric probability. How much the variation of fitness can be for a newborn species can be controlled with the variation magnitude slider. The third slider Selection Strength controls how sensitive the difference in reproduction rate between species depends on their fitness difference.

Fitness dynamics

As the system unfolds you will see that every now and then new species emerge with a fitness higher than all the other species and oftens they “take over” the entire population until yet another new strain emerges that repeats the process.

In the plot below the controls every species in the system is represented by a dot in the same color on the fitness axis. The larger, more transparent circle represents the fraction of that species in the entire population. When species go extinct a little white dot below the axis is drawn, so one can see the series of extinction events.

The large red dot is the average fitness of the population. As time passes, the average fitness of the population increases steadily, despite the fact that mutations do not favor higher fitness.

* Acknowledgements

This explorable was coded in part in the atrium of the Santa Fe Institute when I was a guest there in July 2019. I want to thank Jenna Marshall for hosting me and the Santa Fe Institute as a whole for providing such a great and inspiring environment.

Source: Complexity Explorables | Repliselmut