Simulistics

The same population is now represented by four compartments, one for each of four age classes. The first one represents the first year group, the second represents the number of animals aged 1-5 inclusive, the next animals aged 6-15 inclusive, and the fourth for all remaining animals. As before, the mortality rate per animal is independent of population size, but now depends on its age (there is a different m value for each age class). The reproductive rate per individual is still influenced by total population size, as well as now being different for each age class.

In this model, the population is represented by a single compartment, representing the total number of animals in the population or the population density (number per unit area). Reproduction is assumed to be density dependent (the reproductive rate per individual, r, declines as population size increases), whereas mortality is not (the mortality rate per individual, m, is independent of population size).

The following sequence of five models illustrates two things. First, it shows that one problem — that of modelling changing population size — can be approached in a variety of ways, based on quite different methods for representing the population. Second, it introduces you to a range of constructs that Simile provides for modelling, including the “population submodel”, array variables, and the “association submodel”.

For a more in depth look at some models have a look at the worked examples and a wide range of models with varying quality of documentation can be found in the model catalogue.

Multi-layer soil water model

This example shows the use of a fixed-membership multiple-instance submodel for modelling the movement of water through soil layers. Each instance represents one layer, and has a single compartment, for the amount of water in that layer. The array variable outside the submodel is used to transfer the water flowing out of one layer into the one below it.

Animal movement model

We represent a number of animals using a fixed-membership multiple-instance submodel (it is easy to make it into a population submodel, if you wanted a dynamically-varying population). Each animal has got three state variables, representing its current x,y coordinates and the direction it’s going. Its direction changes slightly from one time step to the next, and this, along with its speed is used to update its position. Each animal is constrained to stay within the area.

Fractal model of tree branching

Fractal branching models - frequently called Lindemeyer or L-system models - work by repeated application of the same branching rules. The Simile implementation uses a population submodel for the branch segments (intenodes), starting off with a single member (the base segment). An association submodel is used to define the relationship between one segment and its two daughters.

The behaviour of the model is visualised using a specially-developed display tool, showing the 3D structure of the simulated tree from the side and from the top.

Individual-based tree model

This model uses a population submodel to represent the trees in a forest stand. A simple, single-compartment model is used to simulate the growth of each tree, and this is summed outside the submodel to give the total volume of the stand of trees. The model also sets the initial number of trees in the population, the rate at which new trees are created, and the rule for killing off trees when they reach a certain size.

Individual-based model of population dynamics

This shows how amazingly simple it is to make an individual-based model of population dynamics in Simile. We simply create a population submodel, add in symbols for the initial number, birth and death. In this model, the probabilities of reproduction and death are age-dependent, and reproduction also depends on the total population size, which is simply obtained by summing the number of individuals.