This model is a predator prey model with sharks and minnows, which illustrates the principle of evolution. The minnows are programmed with certain behaviors, such as movement, feeding, reproduction, evading sharks and more complex behaviors that can lead to schooling under certain conditions. Sharks hunt minnows and feed on them. The parameters that determine the minnow behaviors evolve as minnows die and are born.
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This model is a predator prey model with sharks and minnows, which illustrates the principle of evolution. The minnows are programmed with certain behaviors, such as movement, feeding, reproduction, evading sharks and more complex behaviors that can lead to schooling under certain conditions. Sharks hunt minnows and feed on them. The parameters that determine the minnow behaviors evolve as minnows die and are born.
The model Sharks_and_Minnows has more details about the shark and minnow population dynamics, including the parameters that determine how sharks and minnows reproduce, feed, and move, and how minnows evade sharks and school. In this model the parameters that govern these behaviors are specified as a “genome” for each minnow, rather than being specified by sliders on the interface. The genome is specified as a list of parameter values. Initially each minnow has a randomly assigned genome and consequently the minnows do not exhibit particularly effective shark evading or schooling behavior. However, sharks hunt and eat minnows and the survivors reproduce. In addition, some minnows reproduce more rapidly, depending on how much energy they consume and food they eat. New minnows inherit the genome of their parent, but with some small mutation, determined by a particular mutation rate for each gene. As time passes the behavior of the minnows evolves to one that increases the chances of survival. The exact behavior that evolves can be different in different simulations.
Choose initial minnows and shark populations. Then choose the global parameters such as food-energy, plankton-growth-rate, birth-energy, drag-coefficient and metabolism and run the simulation. For some combinations the minnows will die out. Adjust them so that the population does not die out. Once you have relatively stable dynamics allow the simulation to run long enough for the evolutionary trend to become obvious. This may take some time. Eventually one color will come to dominate – this is survival of the fittest. After a bit longer the behavior of this “species” will also evolve.
Try varying the number of sharks that you add. The behavior that evolves will be quite different with one than it will be with many. You can remove sharks by clicking the button. You can add sharks by clicking on the world-view.
Occasionally the minnows will adopted schooling behavior and move as a group to avoid sharks. On other occasions they will evolve to swim faster than the sharks, but will not exhibit a tendency to school. Sometimes minnows do not evolve to be particularly effective at avoiding sharks, but instead evolve behaviors that help them reproduce rapidly. The behaviors that evolve depend on some global parameters, such as metabolism, food-energy, and the drag coefficient. For example, with the drag coefficient low, the minnows end up moving rapidly (since the energy cost of movement is not high). One thing to notices is that even when the global parameters are fixed, the minnows do not always evolve in the same direction.
If you run the simulation for a long time, the death rate will decrease, and the population of minnows will stabilize.
In this model, minnows often eventually evolve to evade sharks almost entirely. In nature the predators often evolve along with the prey. Sharks have parameters or genes that govern minnow hunting behaviors, such as burst speed and sight range, but these genes don't evolve in this simulation. For sharks to evolve there needs to be some mechanism for them to die if they are unsuccessful at catching minnows. It should be relatively simple to give sharks a genome similar to that of the minnows, and have new sharks hatch with slightly mutated genes. Having sharks evolve could setup the possibility for an "arms race" behavior where minnows and sharks become faster and faster, or minnows might simply learn to school more closely, or learn to turn more quickly.
This model is the second of two models on shark minnow population dynamics. The first one does not include evolution, but instead allows the user to choose the parameters and behaviors of the sharks and minnows.
Copyright 2006 David McAvity
This model was created at the Evergreen State College, in Olympia Washington
as part of a series of applets to illustrate principles in physics and biology.
Funding was provided by the Plato Royalty Grant.
The model may be freely used, modified and redistributed provided this copyright is included and it not used for profit.
Contact David McAvity at mcavityd@evergreen.edu if you have questions about its use.