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WHAT IS IT?

This is a replication of Per Bak's model of punctuated equilibria in evolution, as presented in "How Nature Works", and "Punctuated equilibrium and criticality in a simple model of evolution".

HOW IT WORKS

Species are arranged in a circle and assigned a single, random value between 0 and 1 to represent their fitness. Each time step, the species with the lowest fitness and it's two neighbors are selected for mutation, and they are each assigned a new random fitness.

HOW TO USE IT

Setup creates a ring of num-species species, and assigns them a random fitness value.

The plot "Fitness" plots a point for each species at their corresponding fitness.

"Species History" shows the mutation activity of the species selected by the species-plot slider.

"Population History" shows mutation activity across the whole population. Each point shows where a mutation occurs, allowing us to track the region of activity over time. The "Species History" could be found by examining points along a vertical line on this plot.

THINGS TO NOTICE

"Fitness" plot:
Over time, the mean fitness of the population increases. On this plot, we can see a block of points above some threshold, with only a handful of species below this (currently involved in mutations). This threshold can be shown analytically to asymptotically approach 0.667.

"Species History" plot:
For any chosen species, we can see a similar structure in their history; quiet periods of no activity puctuated by rapid bursts. Contrary to Darwin's belief that evolution would be a steady change, this is in agreement with data collected from fossils.

Additionally, the history neighboring species can be seen to have some similar features, gradually transforming into different shapes for more distant species.

"Population History"
After a short period where the population organizes itself above this critical fitness threshold, the population history takes on a fractal structure in space and time.

CREDITS AND REFERENCES

Phys. Rev. Lett. 71, 4083 (1993): Bak and Sneppen - "Punctuated equilibrium and criticality in a simple model of evolution"
Per Bak - "How Nature Works: The Science of Self-Organized Criticality"