By: Ruud Sperna Weiland, Mark Voschezang, Wouter Meering. Freek van den Honert, Thomas Start
The Bak-Sneppen model is based on co-evolution. It consists of network of species. Every species has a fitness value and at each iteration the species with the lowest fitness is selected to go extinct. Its direct neighbours (connected nodes in the network) will go extinct as well. The extinct species are replaced by new species that have new (random) fitness values.
Wiki: Bak-Sneppen
We have extended the model to allow for spatial interactions. This is achieved by creating a spatial lattice that contains a distinct Bak-Sneppen model on each lattice point. During each extinction update in the local Bak-Sneppen models a Bernoulli trial (coin toss) is held to determine whether the new species is completely new (i.e. mutation), or originates from a neighbouring lattice point (i.e. migration). Thus, species can move over the lattice.
Several parameters are introduced to control this behaviour:
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P: float in [0,1]The probability of mutation. The probability of migration is thus (1-P). Lower values allow species to spread out more. -
fitness-migration correlation: float in [0,1]This controls the speed at which the relative (local) fitness of species can change during migration. -
migration prioriy: least fit | random | fittest
This video shows the effect of this parameter on the spreading of species over the lattice.
The jupyter notebook Experiments.ipynb contains a number of experiments and can be viewed online. First install dependencies.
pip3 install -r requirements.txt
Then start the jupyter server.
jupyter notebook
The major classes are Lattice and BS which represent the lattice and Bak-Sneppen models, respectively. They are located in the directory src.
The directory results contains some images and videos, which are displayed below.
This model exhibit patterns similar to the species-area curve, with comparable power law slopes as observed in nature.
The effect of the parameters fitness-migration correlation and migration priority on the power law slope of the species-area curve.
The model features both local and global avalanches.
These can grow system wide (i.e. O(1) perturbations can have O(N) effects)
The parameter migration priority has a strong effect on convergence after initialization and on the critical (i.e. average) fitness.
