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[screen shot]

If clicking does not initiate a download, try right clicking or control clicking and choosing "Save" or "Download".(The run link is disabled for this model because it was made in a version prior to NetLogo 6.0, which NetLogo Web requires.)


This model investigates the evolutionary success of mutant foragers that have a selective advantage/disadvantage compared to indigenous foragers.

Miniscule biases can translate to large evolutionary advantages in certain regions of parameter space.


Foragers travel around, consuming food (green patches). Food consumed is related to the energy accumulated by the parameter 'pJ-per-food'. If a forager accumulates energy Vrep, it splits into two identical foragers. If a forager falls to energy 0, it dies by starvation. Food units are replenished with probability 'algae-birth-rate' (expressed as a percentage) after every time step.

It can be shown that this ecosystem has a non-trivial equilibrium, where populations stabilise, and that this equilibrium is stable in all parameter space. After the populations of foragers and food stabilise, we introduce a mutant and allow the simulation to run until either the mutant successfully invades the indigenous population or goes extinct.


The Buttons:

Press the 'setup' button. A number of indigenous foragers appear, user-defined by the parameter 'initial-indigenous.' Indigenous foragers are blue in color.

Press the 'go' button. The indigenous foragers travel about the world, consuming food, accumulating energy, and reproducing or starving. The food unit population dips as the foragers become more populous. Eventually, both food unit and forager populations stabilise.

Press the 'introduce-mutant' button. A single mutant forager appears. Mutant foragers are red in color. The mutant has a selective advantage/disadvantage over indigenous foragers, as defined by the 'mutant-advantage' slider. The specific advantage/disadvantage that mutants hold over indigenous foragers is that mutants are able to obtain more/less energy per food unit consumed (pJ-per-food is slightly altered). If 'mutant-advantage' is 1, the mutants and indigenous are identical.

Allow the simulation to run until the entire forager population is composed of indigenous or mutant foragers.

Turn on the plot-populations? to help gauge when the food density has achieved equilibrium. After the mutant has been introduced, turn the switch off to speed up the simulation.

The make-movie button allows the user to 'film' a short segment of the program in action. This is useful if you want to include this animation in a powerpoint presentation.

The Parameters:

initial-indigenous = the starting number of foragers in the environment.

algae-birth-rate = the probability (percent chance) that an empty patch will have its food unit replenished on a time step.

mutant-advantage = the amount of energy obtained per food unit consumed with respect to the indigenous foragers. If mutant-advantage = 1, the mutants and indigenous are equivalent.

pJ-per-food = the energy obtained by indigenous foragers per food unit consumed.

pJ-per-time = the metabolic cost of foragers per time step.

Vrep = the amount of energy needed for a forager to reproduce by binary fission. Forager offspring begin their lives with energy Vrep / 2.

show-mutant-energy? = an option to watch all mutants' energy change as they forage.

show-indigenous-energy? = an option to watch all indigenous' energy change as they forage.

plot-populations? = an option to watch the populations of indigenous foragers, mutant foragers, and food units evolve in time. Use this option to determine when the ecosystem has achieved stable equilibrium.


Changing the amount of energy per prey consumed and/or the amount of energy spent per time step will change the equilibrium food unit and forager populations accordingly.

The overall forager population remains approximately constant due to the ecological constraint of limited food availability. This allows us to approximate the ecosystem as a Moran process.

If mutants are only very slightly advantaged over the indigenous, then absorption could take a very long time to occur, sometimes over 24 hours!

In certain regions of parameter space, tiny changes in parameter values lead to drastic changes in fixation probability. In other regions, however, fixation probability is not sensitive to changes in some parameters. For example, when pJ-per-food = 1, then mutant-advantage = 1.003 will almost certainly lead to fixation. When pJ-per-food = 5, then mutant-advantage = 1.003 only leads to fixation with probability 1/4. This discrepancy is not due to the total population size; on the contrary, the fixation probability for advantaged mutants is virtually independent of the population size. This discrepancy illustrates that the fixation of advantageous mutations is almost certain in more predictable environments.

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