ECOSSE

Background

Ecosse is a program that attempts to construct and model ecosystems that are made up of a collection of interacting species.

In this model, it is assumed that the only way two species may interact is through predation. Thus an ecosystem made up of a certain number of species can be modeled by looking at which species prey on which others. This can be visualized as a food web where all the species in an ecosystem are displayed along with links between those species that interact through predation.

These links can only point in one direction (i.e. two species cannot prey on each other) and they have an interaction strength associated with them. The greater this strength being, the more the two species are affected by each other.

For a given interaction, the predator's population has a negative effect on the prey's population and the prey's population has a positive effect on the predator's population. However the positive effect is, in general, not as large as the negative effect as a predator cannot convert the prey it eats into offspring with perfect efficiency.

As well as effects from interactions, species also have a natural death rate. Thus a species that is not preying on anything will eventually die out.

In addition to the normal species, there is a special species to signify the environment. This species' population is held fixed and it cannot be a predator. Anything that preys on this species can be seen as living off non-living resources present in the environment (e.g. Plants photosynthesizing sunlight). All the species that prey on the environment are assumed to be living off the same resource. This resource does not run out but there is a limited amount of it at any one time (i.e. There is a constant flow of resources into the ecosystem) and so the species that live off it are in competition with each other and themselves.

Ecosse attempts to construct stable food webs by first constructing large, random webs. These are invariably unstable, leading to a large number of species dying out (Species are removed from the web when their populations go below a certain number). However eventually, a collection of species will remain that form a stable food web and survive indefinitely. It is interesting to note that these surviving food webs share a lot of properties in common with food webs in real ecosystems.

The Applet

When using the applet, "Reset" generates an initial, random web of a size given by the "No. of Species" box. This can be generated using a random seed by selecting "Random", or you can select your own seed by selecting "Specify Seed" and typing it into the "Seed" box. The "Start" button starts the simulation and the "Stop" button pauses it.

A major feature of the random webs is their connectance. This is a number between 0.0 and 1.0 which specifies the probability that two species are connected and can be set using the "Connectance" box. For a web of a given size, there tends to be a certain connectance that, on average, produces the largest surviving webs. This ideal connectance gets smaller as the size of the initial web increases. The graph on the right gives an idea of what to expect for webs of initial sizes 10, 20 and 100 species (These figures were obtained with "Scale" set to 0.003).

In addition to the connectance, the efficiency with which predators convert prey to offspring can be d changed using the "Efficiency" box (A value of 1.0 would correspond to 100% efficiency).

The flow of resources from the environment can be changed using the "Environment" box and the initial population size for each species can be changed using the "Starting Population" box (This specifies the initial population for species feeding on the environment, all other species have population = efficiency*starting population). The "Scale" box gives the size of each time step in the simulation (The smaller the scale is, the closer iterating the equations approximates integration).

The applet displays the web and updates this display as the simulation runs. Each circle is a different species with the size of the circle corresponding to the logarithm of the population size at that moment. Green circles represent the environment which has a fixed population (Even though there are more than one green circle, they all represent the same species. This is to help spread the display out and make it less messy). Otherwise, species are blue if they are increasing in size and red if they are decreasing.

Interactions are displayed as arrows going from the prey to the predator with the size of the arrow corresponding to the strength of the interaction.

The display can be arranged by choosing "Arrange" and clicking on the "Start" button. This attempts to arrange the web in as clear a way as possible. It is recommended that you wait until a lot of species have died out before trying this as it is quite slow for large webs. Clicking on the display gives the web a small kick. This is useful if the web gets tangled when arranging. The positioning of the species in the display are for aesthetic purposes only and have no effect on the actual simulation.

Interaction Strength

In this program, the interactions between species are allowed to change in strength. This models the coevolution of the species in the web where it is assumed that all the species are constantly evolving to be better at catching their prey or avoiding their predators.

If all the species were evolving at the same rate then there would be no net change in the interactions between the species. This is known as the Red Queen Principle [named as such because of the observation to Alice by the Red Queen in "Through the Looking Glass" that, "in this place it takes all the running you can do, just to keep in the same place."]. However, the rate of evolution for the species will generally be different as smaller populations are under more pressure to evolve and so evolve faster. Also, a species evolving an advantage over a few species will tend to do better than a species trying to evolve an advantage over many.

The difference in evolution rates between two interacting species is translated into a change in the interaction strength to the advantage of the species with the higher evolution rate. However, the interaction between two species is not allowed to grow arbitraily large as, at some point, there will be barriers that a species cannot easily evolve past no matter how much pressure there is to do so [this is described as the Generalised Peter Principle in Principia Cybernetica Web].

In addition to evolving interactions, there are a few minor changes too. It is now possible to specify the number of species that feed on the environment (autotrophs). This makes it possible to look at webs with a high connectance but only a few autotrophs. Also, the environment is no longer displayed but instead, species that feed on the environment are coloured light/dark green for rising/falling population instead of blue/red. Finally, a prameter has been added called Link Cut Off. Any links with a strength below this value will be ignored when calculating the links per species [Links/S-1] and displaying the web.

The parameter Evolve Rate specifies how quickly the interactions evolve. To run the program without evolving interactions, set this parameter and the Link Cut Off parameter to 0.

References

"Evolution of stabilising weak links in food webs") by Graeme Ackland and Ian Gallagher is available (pdf).


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