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## WHAT IS IT?

This model show the Equilibrium Theory of Island Biogeography (ETIB) in practice.
By either creating a random assortment of islands or using a preset layout designed to demonstrate the extremes of the model, the model tracks over time the species richness of islands as different species migrate from the mainland. The model aims to demonstrate that island size and distance from the mainland are both key componements in an islands eventual equilibrium of species richness, using preset models and a very fast iteration speed to quickly demonstrate these equilibriums and thier variability.

## HOW IT WORKS

The model assumes that the west border of the world space is 'mainland' and generates a new species (represented by a butterfly) to attempt to outmigrate from a random point on the mainland every iteration. It is assumed that another migration of an identical species to an island would be negligable in effecting species survival rates, and so when tracking species richness and the inhabitants of an island, if an identcal species reaches the island, it is ignored. The number of different species in the model can be adjusted with a slider before and while running the model. If one of the butterflies reaches an island it is assumed that that species will alyaws migrate to the island (except in cases where the species is already there as discussed). There is also variability in the flight path of the butterflies meaning further out islands may sometimes be out of reach. This variability can also be adjusted via the use of a slider. If a butterfly makes it to the east border of the world without finding an island, it is assumed the species starved before finding any land to migrate to, and the next iteration begins without any new migration occuring. Similarly, every butterfly is assigned a food number that allows them to travel the corresponding distance before starving and dieing. This figure can also be tweaked using a slider. Species that have migrated to islands will also begin to die out randomly as the model runs. This is determined by the size of the island as well as the number of other species currently on the island, and the extremety of both these factors in effecting extinction rates can be amplified or reduced by adjusting the species-docilness and species-space-requirements sliders.

## HOW TO USE IT

When setting up the model you can either select one of the Example Island Setups to see the theory clearly demonstrated or you can select the Random Setup button to create a completely random set of islands to test the theory on.

If you are using an example setup the number of island and max island size will be decided for you, but if you want to completely customise your random island setup the number-of-islands and max-island-size sliders allow you to alter how many islands you will generate, and the maximum size they can randomly be assigned.

species-space-requirements and species-docileness are both used to raise or lower the extinction rates on islands. Raising species-space-requirements will mean more clashes occur over territory and extinction rates will become more common, particularly on smaller islands. raising species-docileness will mean species are less aggressive towards other species and will reduce extinciton rates universally accross all islands. The default values given for these sliders are designed to best display the theory in action but they cam be tweaked if the user desires to see more extreme or subtle effects.

The number-of-species slider will change how many possible species can migrate to the islands while the model runs. A larger number of species will better demonstrate the different levels of equilibria for each island.

max-bird-flight-distance determines how far the butterflies can travel before starving and dying. If you wish to amplify or reduce the effect that distance from mainland has on island migration rates this is a good slider to tweak.

bird-flight-variability can also be used to alter how extremely the distance from mainland of an island effects migration rates. A large flight variability makes butterflies a lot less likely to make it very far from the mainland whereas a very low variability ensure the butterflies will travel in a much straighter path, meaning they reach the distant islands with ease.

The Show-Island-Names? and Show-Inhabitants? switches can be turned on or off depending on whether you want to see the names of islands and thier current number of species or not. Leaving them on allows you to easily keep track of migration and extinction as it happens, as well as easily compare the islands in the model to thier lines on the graph.

Once you have the model setup as you'd like, simpy click Go and the model will begin to iterate very quickly through the migration extinciton cycle. If you wish to see individual mogrations occuring or the graphs plotting real time changes then turn down the speed slider into the slower option.

## THINGS TO NOTICE

As the model runs you will hopefully see that islands further from the mainland will experience less migration, and smaller islands will have a much higher extinction rate than larger islands.

## THINGS TO TRY

Once you have a feel for how different islands species richness will change over time try turning off labels on the model and running a random island setup. Then try identifying what island is which by looking at the species richness of each island over time on the graph before turning the labels back on.

Try playing with all the sliders to see how it effects the model, when is the ETIB clearly demonstrated the most? When is it not apparent at all? Can you break the model by changing a certain combination of sliders?

## EXTENDING THE MODEL

To truly test every custom island layout that interests the user, more island setup customization would be fantastic to extend the model, potentially allowing the user to click to place any islands they want.

Adding a bar graph that tracks the species richness of each island as the model runs would also be a welcome addition, as it can be rather difficult to interpret the line graph as the model iterates so quickly and the colours clash.

## NETLOGO FEATURES

The model uses the in-radius command to see if butterflies are touching any part of an island when checking for migration. In the pure form of the model island size isnt a relevant detail for migration, only extinction rates, so reverting the model back to only counting the center of an island as a hit could be an interesting experiment.

## RELATED MODELS

## CREDITS AND REFERENCES

http://ccl.northwestern.edu/netlogo/docs/index2.html

http://www-personal.umich.edu/~dallan/nre220/outline15.htm

https://en.wikipedia.org/wiki/The_Theory_of_Island_Biogeography

http://users.clas.ufl.edu/mbinford/geoxxxx_biogeography/literatureforlinks/simberloff_1974_etib_annurev.es.05.110174.pdf

https://www.fs.fed.us/rm/pubs/rmrs_p021/rmrs_p021_163_171.pdf

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