Immigration

The Immigration symbol is used to specify the creation of new instances of a population submodel during the course of a simulation. In contrast to the Reproduction symbol, which specifies this in per instance terms (i.e. the creation of new instances per existing member of the population), the Immigration symbol determines the total number of new instances that are created. Note that the process adding new individuals need not be an actual immigration from another place -- it could be anything that causes new members of a population, unrelated to existing individuals, to appear throughout a run.

Immigration belongs to the group of symbols known as channels. The symbol's icon represents a bird on the wing.

How to add an Immigration symbol

The immigration symbol only has meaning in the context of a population submodel. Therefore, it makes sense to construct a population submodel first, then add the immigration symbol to it. This is not strictly necessary: you can add the immigration symbol first, then construct a submodel around it, then make the submodel into a population submodel, but it is better practice to construct the population submodel first.

See Adding node-type elements.

Rules

• The immigration symbol can receive influence arrows from anywhere in the model, including from within the same submodel. This information is then be used to calculate the current value for the rate of creation of new instances of the population. If the influence arrow comes from within the same population, then this input will be presented (in the Equation dialogue window) as a list, not as a scalar. See below for the reasons for this, and what you should do about it.

• You can include as many immigration symbols as you like. In real-world terms, each one corresponds to a separate process leading to the new instances being created: for example, some new trees can appear in a forest from seeds blowing in from outside the forest, while others can appear from a forester planting seedlings.

• It is possible to draw an influence arrow from the immigration symbol to another element. The usual use of this is with the channel_is( ) function. The value of the immigration symbol is the value of its equation.

Interpretation

The immigration symbol it is used to determine the creation of new instances of a population submodel. This must be in terms of whole numbers: you cannot have a part of a new individual. And yet, the value for the immigration term can be a floating-point number, e.g. 1.3. So how does Simile use this value to calculate the creation of new instances?

The value of the immigration symbol's equation is the number of new instances created over the course of one time unit. Typically the time step is not the same as a time unit, so each time step the value of an internal variable is incremented by the immigration symbol's value divided by the number of time steps in a time unit. If this value is one or greater, the integer part of the number is subtracted from it and that number of new individuals are added to the population. The fraction part remains to be incremented on the next time step.

In order that a model with many immigration processes behaves realistically rather than adding all new individuals synchronously, the internal variable for each one is initialized to a random fraction between 0 and 1. Thus there is a possibility that a new individual will arrive through immigration in any time step, even if the value of the channel is small.

Immigration events

An immigration symbol can be either continuous or discrete event valued. If any influences from events or squirts terminate on the immigration symbol, it is discrete event valued. In this case it will be evaluated in the same way as an event or squirt. When the event occurs, the value will be added to the latency (fraction remaining after previous additions) and new individuals added to the popualtion immediately if the result is 1 or greater.

Avoiding random behaviour

You might well feel uncomfortable with the non-deterministic nature of the process. To avoid any random variation between runs, you can make sure that the value of the equation for immigration divided by the number of time steps in a time unit is always a whole number, which will result in exactly that number of individuals being added each time step. The length of the time step is selected when running the model, and can be found with the dt() function.

If using discrete event valued immigration channels, all you need to do is make sure the event magnitude is integer valued, as the time step size does not affect the result of an addition event.

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