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hypercycle

by Joerg Hoehne (Submitted: 09/15/2004)

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WHAT IS IT?

This model simulates a hypercycle described by Eigen and Schuster 1979. A hypercycle is a prebiotic model which shows how stable structures (e.g. life forms) can or will emerge because of cyclic support of self replicating molecules to other self replicating molecules. This model can simulate up to 10 different molecule types.
The original concept of a hypercycle was critized by John Maynard Smith because a parasite molecule will destroy a hypercycle. Hogeweg and Boerlijst showed 1990 by using a cellular automata a hypercycle will be stable despite by an 'infection' of a parasite because of the spatial structures a hypercycle will emerge.

Rules:
a) A cell (patch) filled with a molecule (state > 0) has in every cycle a certain chance to become empty (denoted by state 0). This probability is given by the global constant decay (slider).

b) Every empty cell (patch) can be filled by a molecule of the surrounding neighbours (north, west, south, east) or remains empty.

c) Every molecule has in a cycle of a run a certain chance to reproduce itself. This is defined by the constant s[i] where [i] denotes the i_th entry for the corresponding molecule i. The value for every s[i] is 1.

d) Due to the hypercycle a molecule gets some support to reproduce itself if its predecessor is in the neighbourhood. This support value is 100 which raises the probability a molecule will reproduce itself into an empty cell.

e) Using a parasite molecule will give more support of one state to the parasite state as any other state will receive.

HOW IT WORKS

This model uses no turtles. The patches are the cells of the cellular automata. The models runs through every patch for which the next state will be computed. After all some sort of diffusion to simulate the molecule drift is computed by exchanging the next states of neigbour patches. After all next states have been computed als patches set these as the current state.

The state 0 (displayed black) denotes an empty patch. The state 1 (red) will denote a parasite molecule if the parasite option is activated.

The parasite will be simulated by changing the support values. Usually the support for 5 states is:

1 supports 2.
2 supports 3.
3 supports 4.
4 supports 5.
5 supports 1.

Introducing a parasite will change these rules to
1 supports none.
2 supports 3.
3 supports 4.
4 supports 5.
5 supports 1 and 2.
The support of 5 for 1 is higher than the support of 5 for 2.

For the general idea how this model works please refer to
Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites.
Physica D, 48: 17-28.
You'll find a link to a pdf document containing this artice at the end of this page.

HOW TO USE IT

Use the control elements from top to down and left to right. But read the following information first!

Doing a run:
Press set-up. Press open-movie if you like to save a movie. Press go. Press go again. Press close-movie (if you have pressed open-movie before).

SLIDERS:

hc-states:
Number of hypercycle states which are used in the current settings. This slider is only effective pressing the setup button.

support-factor-parasite:
The support factor a parasite is given by the last state.

frame-skip:
To accelerate display frames can be skipped. n frames are skipped during display where n denotes the value of the slider. A value of 0 will skip no frame.

SWITCHES:

Parasites:
Only effective during pressing the setup button. If parasites are used in this model the state 1 will be the parasite state. The internal tables become different values according to run a parasite state in this model or not.

BUTTONS:

setup:
The setup button initialize the model. Some internal tables are computed according to the settings of some sliders and switches. The number of states, which can't be changed later on, in this model is set pressing the setup button; also the patches are randomly initialized with states.

open movie:
Rudimentary support for movies. Pressing this button a movie file will be created. You can only choose the path. Open a movie will only write the graphical output of the patches into the movie file.
IMPORTANT: Open a movie AFTER you have setup the simulation.

close movie:
Closes the movie and writes the movie with the name 'capture.mov' in the prior selected directory.

add parasites:
Adds the number of parasites defined by the choice add-parasites to the model. This button is only effective if the switch 'Parasites' has been turned on during pressing the setup button.
The patches are choosen randomly so there is no guarantee exactly 'add-parasites' number of patches will be 'converted' to a parasite.

one cycle:
Running this model exactly one cycle.

go-for:
Running this model exactly for the number of cycles given in the choice 'cycles'.

go:
Running this model forever until this button is pressed again.

THINGS TO NOTICE

Wait for the emerging spirals. This model may run very slowly but structures will emerge only with screen-sizes greater 50.

THINGS TO TRY

This section could give some ideas of things for the user to try to do (move sliders, switches, etc.) with the model.

EXTENDING THE MODEL

This section could give some ideas of things to add or change in the procedures tab to make the model more complicated, detailed, accurate, etc.

NETLOGO FEATURES

This section could point out any especially interesting or unusual features of NetLogo that the model makes use of, particularly in the Procedures tab. It might also point out places where workarounds were needed because of missing features.

RELATED MODELS

This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.

CREDITS AND REFERENCES

This model was developed by Joerg Hoehne in September 2004 in the intention to learn the concepts and programming features of NetLogo.

email: hoehne@thinktel.de
Any suggestions, questions, bug reports, corrections (especially typos, grammar, unknown words etc.) and feedback are welcomed.

References:
[Book, out of print] Gerhard, Martin ; Schuster, Heike: Das digitale Universum. Vieweg Verlag, 1995

[Book, out of print] Eigen, Manfred ; Schuster, Peter: The Hypercycle - A Principle of Natural Self-Organization. Springer, 1979

[link]: http://www-binf.bio.uu.nl/publications/1991.html
where you find the following interesting link to
http://www-binf.bio.uu.nl/pdf/Boerlijst.pd91-48.pdf
Spiral wave structure in pre-biotic evolution: Hypercycles stable against parasites.
Physica D, 48: 17-28.

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