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## NetLogo User Community Models

## WHAT IS IT?

This is a model to study the effect of spatial pattern formation on dynamics of cyclic competition between species. Such "intransitive loops" are for instance observed in competitive dominance between coral species (see Johson & Seinen, 2002). The model is taken from Boerlijst & Hogeweg, 1995, who studied "hypercycles with negative interactions".

## HOW TO USE IT

The model can be started with "random start", which seeds the field with 90% coverage with equal numbers of each species. During each tick, all patches are updated. During an update empty patches can obtain an offspring from a randomly chosen neighbor patch, and occupied patches can die due to a dominant species in a neighbor patch.

## HOW IT WORKS

In the model a variable number of species can be simulated, who form one large cycle of competitive dominance, where species 1 > 2 > 3 > ... > n > 1. Every time step each patch chooses a random neighbor (out of the 8 direct neighbors). If the patch is empty it produces an offspring of the species in the neighbor patch. If the patch is full, it determines whether the neighbor contains the dominant species. If this is the case the patch becomes empty with high probability (50%). Note that there is also a 5% change of background mortality in the absence of dominance.

## THINGS TO NOTICE

Start with a system with 3 species. Notice that the cyclic dominance is reflected in a spatial pattern formation that quickly is established, and where each species sits directly behind the species that it dominates. Note that this description only applies to a system of 3 species. For other number of species other patterns emerge, which can be found via "things to try".

## THINGS TO TRY

Change the number of species and restart the field. First study the pattern with 2 species, and than try to understand what happens if the system consists of 4 species. If this is clear, you can go to a system of 5 species. Here, you have to carefully study the spatial succession of the species (i,.c. which species is locally overtaking the previous dominant species?). Can you understand this order of succession?

Now study what happens if you vary the relative dominance of species 1 over species 2. This can be done by adjusting the slider "comp-factor-species-1". First try this in a system with 3 species. What would you expect if species 1 becomes more aggressive towards species 2? Check your prediction (set comp-factor-species-1 to 1.5) and try to explain!

Check what happens to the dynamics of the system if the dominant species can directly overgrow the patch of the other species. This can be done by setting the switch "direct-overgrowth". How does this affect the 3 species system? How does this direct overgrow affect the dynamics for systems with other number of species?

Note that with the direct overgrowth the system resembles the spatial Hypercycle dynamics. I have also uploaded a Netlogo model for that system.

## REFERENCES

Boerlijst, M.C.; Hogeweg, P. , Attractors and Spatial Patterns in Hypercycles with Negative Interactions (1995) Journal of theoretical Biology, volume 176, pp. 199 - 210.
https://doi.org/10.1006/jtbi.1995.0191

Johnson, C.R., Seinen, I., 2002. Selection for restraint in competitive ability in
spatial competition systems. Proc. R. Soc. London B 269, 655–663.
https://doi.org/10.1098/rspb.2001.1948

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.