Scheduling

In IBMs, individuals do certain things, and the sequence in which they do these things can be decisive for the resulting dynamics. An IBM's schedule describes the actions of the IBM and how they are executed. An action is a list of model entities, the processes performed by these entities, and the order in which the entities are processed. For example, the action feeding may be defined as the list of all individuals which feed, one after the other in a fixed order, in their habitat cell. Or, feeding might be an action where all individuals first move to the neighbor habitat which has most food and then feed and where the individuals are processed in a random order.

Fixed schedules, which are used in most IBMs, define a single order in which events always occur, that is, a cycle which is repeated at every time step. Dynamic schedules allow the order to be changed while the model executes. For example, an individual that has just had an interaction with a predator and survived may put itself on a higher rank in the model's schedule, which would mimic its fleeing behavior. Flow charts, which are often used to illustrate how a model works, usually refer to model processes itself, for example, dispersal, but not necessarily to the model's schedule and actions. Table 1 shows a typical schedule of an IBM. Most descriptions of schedules in the IBM literature are incomplete, which makes it impossible to reimplement and test the IBM independently.

Table 1 Scheduling of the coyote model of Pitt and co-workers as an example of how the schedule of IBMs is organized into actions and IF-THEN rules

Pack actions (executed by all packs)

• Check whether both an alpha male and an alpha female are present

• If both alphas exist, and it is April, produce offspring: create pups, the number of which is stochastic but also depends on pack size, and add them to the pack

• Check whether either alpha is replaced:

- If it is December, and there is a contender (another adult of the same sex in the pack), both the male and female alpha coyotes are at risk of being replaced

- Replacement is a stochastic function with the probability of being replaced increasing with the alpha's age

- If replacement occurs, the alpha becomes a transient and the contender becomes the new alpha

• Update the dispersal probability of each member according to its age and pack size

• Force death of pups less then 2 months old if the pack has no adults

Pack member actions (executed by all individual coyotes that belong to a pack)

• If the age of 2 months is attained, leave the den

• If the age of 6 months is attained, change from pup to beta adult

• Update the age-dependent mortality probability and determine whether death occurs

• If individual is a beta less than 2 years old, determine whether it leaves the pack, according to its dispersal probability

Transient coyote actions (executed by all individuals not belonging to packs)

• Update individual's mortality probability, depending on the total number of transients

• Determine whether death occurs

Pack alpha replacement actions (executed by packs that lack an alpha individual)

• If there are beta individuals of the appropriate sex in the pack, promote the oldest beta to alpha.

• Otherwise, select a transient of the appropriate sex and promote it to alpha.

• If there are no available transients, select a beta from another pack.

Modified from Pitt WC, Box PW, and Knowlton FF (2003) An individual-based model of canid populations: Modelling territoriality and social structure. Ecological Modelling 166: 109-121.

Reproduced from Grimm V and Railsback SF (2005) Individual-Based Modeling and Ecology. Princeton, NJ: Princeton University Press, with permission from Princeton University.

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