In this assignment, I analyze the effects of certain parameters on the emergent patterns in a very simple model.

The following model was created in NetLogo’s modeling platform, and simulates a very simple ‘ecosystem’ in which agents (or turtles) explore an environment populated with grassy (green) patches, and bare (black) patches.

In this model, turtles act on only a few primitive instructions, that is to move around the environment randomly, eat grassy patches when they are encountered, to reproduce when they have obtained a sufficient energy level and to die if they are depleted of energy.

This video shows the model playing through with ‘standard’ parameters. These are defined as follows: initial-turtles = 50, energy-from-grass = 10, birth-energy = 50.

From here on out, we will experiment with some parameter changes, and analyze the results of their effects on the emergent patterns as they occur.

Part 1: How does the variable ‘energy-from-grass’ affect the emergent patterns observed in this system? 

Simply put, the energy-from-grass parameter defines how many grass-patches a turtle will need to eat before it is able to reproduce. When a turtle ‘eats’ a patch of grass, its energy level is increased by an amount specified by the energy-from-grass variable. In tandem with the ‘birth-energy’ value, this parameter is one factor that defines how quickly the turtle population increases.

This video shows how a low ‘energy-from-grass’ value effects the model (5):

This video show the effects of a high ‘energy-from-grass’ value (50):

To better visualize this change, these graphs represent the population increase and grass-patch decrease over the course of 300 ticks:

energy-from-grass = 5                                     energy-from-grass = 50

Above are two graphs which represent the population increase and grassy-patch decrease over a 300-tick period. Each graph represents a different scenario where there the parameter in question has either a smaller or larger value than our standard model.

In both scenarios, we see a liner progression in turtle population emerge out of the initial population. This means that the rate remains static, while the population itself increases. However, it is apparent that the scenario where the energy-from-grass value has been increased, the population has rapidly expanded as well. Additionally in both instances, the overall amount of grass patches decreases, but never quite reaches 0.

In conclusion, we see that over the 300 ticks the higher the energy-from-grass value is, the more quickly turtles reproduce. This is because energy is less difficult to obtain, and gives the turtles more opportunities to reproduce.

Part 2: How does the variable “birth-energy” affect this pattern?

The birth-energy parameter defines the limit a turtle’s energy-level must reach before it is able to reproduce. For example, if the birth-energy value is 50, a turtle will need to eat enough grass until it has an energy-level of 50 before it reproduces. It thus acts as a limit to how often a turtle may reproduce. The higher the limit, the more difficult it is to reproduce.

Below are two more videos and two more graphs which illustrate the variation in behavior when this parameter is tampered with:

The model with a low ‘birth-energy’ value (5):

The model with a high ‘birth-energy’ value (50):

birth-energy = 50                                            birth-energy = 5

Again, we can see the rate remains largely static once the turtle population exceeds the number of grass-patches. However, we see a dramatic increase in population when the birth-energy value is lowered. And a similar population when the birth-energy increases. In both cases, the energy-from-grass rate has been restored to its original value of 10, but now the turtles require either more or less energy to reproduce. From these observations we may conclude that the birth-energy variable has a profound effect on the turtle population. A low birth-energy value causes the population to increase rapidly, while a higher birth-energy value restricts reproduction, and leads to a smaller turtle population at any given time.

Part 3: How does the initial turtle population affect the emergent pattern?

The initial turtle population has remarkably little effect on the long-term population size. Though the population (in any case) increases continuously, it will increase no faster with a larger initial population than with a small one.  

This video shows the population increase with a small initial population (5):

This video shows the population increase with a large initial population (100):

initial-turtles = 5                                                 initial-turtles = 100

In both cases, the emergent patterns presented in the standard model still exist–in 300 ticks, we see a linear progression in population once the turtle population exceeds the number of grass patches. But as mentioned earlier, the aggregate population at the end of the ticks is relatively the same (give or take a few turtles).