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Predator-mediated coexistence

by Felix Baerlocher (Submitted: 11/4/2003)

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PREDATOR-MEDIATED COEXISTENCE (Felix Baerlocher, fbaerlocher@mta.ca)

WHAT IS IT?

This model is based on Caswell (1978). It examines the effect of a predator on the coexistence of two competitors. The graphics window contains a variable number of brown resource patches and blue non-resource patches. Brown patches allow survival and reproduction of the two competitors, called "winner" and "loser", respectively. A third agent, "predator" preys on both winners and losers present on a brown patch. Blue patches do not contain any food, they may represent barriers between food patches. When a winner and a loser land on the same brown patch, the loser gets killed. Once a winner is established on a brown patch, it cannot be displaced, except by a predator. When a predator arrives on a brown patch, it will kill both winners and losers, and, in the process, gain energy.
Newly hatched offspring wander randomly until they find a brown patch. If the patch is empty, it can be colonized by either winner and loser; if it already contains a winner, losers cannot colonize it. Predators can colonize (and will empty) any patch with losers, winners, or both.
When the model is run with only winners and losers, winners almost always win, except when there are very few brown patches and the migration parameters are set very low.
When a predator is added, the length of time that winner and loser can coexist, increases. By emptying patches occupied by the superior competitor, the predator creates new opportunities for the inferior competitor.
Important concepts that can be illustrated are the difference between open and closed systems, equilibrium vs. nonequilibrium systems, trade-offs between rapid reproduction and wide dispersal vs. superior competitiveness, etc.
An advantage of this model over Caswell's original model is that spatial arrangement of resource patches is explicit. Their numbers and arrangements,combined with mobility of the agents, can greatly influence the final outcome. In the current setup, they are distributed randomly; this could easily be modified by producing clumps of patches, separated by variable distances.
The predator can be generalized to a disturbance (which would no longer allow its extinction). The model could then provide a simple illustration of the intermediate disturbance hypothesis (Connell 1978)

Caswell, H. (1978) Predator-mediated coexistence: a nonequilibrium model. American Naturalist 112, 127-154.
Connell, J.H.(1978) Diversity in tropical rainforests and coral reefs. Science 199, 1302-1310.

HOW TO USE IT?

Click the SETUP button to set up the the two competitors (winner, loser), the predator (predator) and the resources patches.
Click the GO button to start the simulation.
There are 11 sliders. nwinner, nloser and npredator control the initial numbers of the three species, npatches controls the initial number of brown resource patches.
nrepro, wrepro, and prepro control the number of offspring released during hatching.
wjmp, ljmp, pjmp controls the maximum number of fd steps that might be taken during random movement.
pmax controls the upper limit where reproduction by the predator is no longer possible.
(Note: Changes in the DENSITY slider do not take effect until the next SETUP.)

THINGS TO NOTICE

Begin with the following settings: nwinner = nwloser = 400. npredator = 0;wrepro = 5, lrepro = 5, prepro = 1, npatch = 500. pmax = 250. wjmp = 1, pjmp = 20, ljmp = 20. pmax = 250. The loser generally goes extinct within 20 - 50 turns.
Now add 250 predators. Winner usually goes extinct after a few 100 turns.
Now begin with 500 patches. Coexistence of all 3 species is extended.

EXTENDING THE MODEL

Try arranging brown patches in a certain order (e.g., a large contiguous block in the center, with a few smaller blocks distributed randomly. Replace predator by an physical/chemical disturbance (no need to reproduce).

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