The variable gr represents the maximum rate of growth of the tree.

Your model diagram should now look like this:

In this expression, the value 25 is the maximum size the tree will reach. It’s growth rate will fall from the maximum given by gr at the start of the simulation. This form of mathematical expression is a convenient way of achieving this desired behaviour of rapid initial growth reducing as the final maximum size is reached.

This submodel will represent a population of trees. However, rather than calling it “trees”, it is conventional to name the class of objects after one individual, so here we call it “tree”.

Your model diagram should now look like this:

Note that the submodel boundary now has an extra line on the top-and-left, and on the bottom-and-right. This is a visual signal that Simile now represents this as a “population submodel”.

Since we will now be simulating the growth of several trees, we are giving each one a different growth rate, randomly selected between 0.1 and 0.3. This could reflect, for example, differences in the soil conditions where each tree grows, or genetic differences between trees.

This is used to specify the initial number of trees (i.e the number at time zero). If we didn’t put this into our model, then our population would start off empty, i.e. with no trees.

We are stating that two new trees are created every year.

Your model diagram should now look like this:

This states that a tree will “die” (be eliminated from the model) when its size exceeds 17.

You should see multiple lines on the graph. Each line represents the growth of a single tree. Note that each line has a different slope, since each tree has a randomly different growth rate (as determined by the variable gr). Note also that each year two new trees are created, and that trees disappear when their size value exceeds 17.

Your model diagram should now look like this:

Notice how the influence arrow crosses the submodel boundary.

Be very careful to get the brackets right. The outer (round) brackets enclose the argument for the built-in function sum( ), which can find the total value of an array of a list. In this case, we want the sum( ) function to find the total value of a list of size values, one for each tree. It’s a “list” rather than an “array” of values, because the number of trees (and hence the number of values to be summed) is not fixed, but changes over time. Simile uses braces {....} to denote a list, and square brackets [....] to denote an array.

In additional to the plot for the growth of individual trees, you should see a graph with a single line for the total size of all the trees, rising smoothly up, then bouncing around an asymptotic value. Why does it show this behaviour? First, trees are growing and more are being added, with none dying. Later, the growth of existing trees and the addition of new (small) ones is balanced by the sporadic death of big trees. The top of the curve is not smooth because the time it takes for a tree to die depends on its growth rate, which is randomly determined.

We imagine a 1 hectare plot, with the trees on the left-hand side: i.e. their x-coordinate is between 0 and 50 m. The actual x-coordinate for each tree is randomly determined.

The trees can be anywhere between the front and the back of the 1 hectare plot. Hence, the y-coordinate for each tree is randomly determined between 0 and 100 m.

You should see a gridded area, with five lollipops on it, representing the five trees created at initialisation time.

Now, you can the trees growing, new trees being created, and trees dying off when they reach the threshold height. Note that we have not changed the mathematical nature of the model. All we have done is to change the way we visualise its behaviour — but this has a dramatic effect on our appreciation of what’s going on.