A2

In this exercise, I will explore the effect of preference level on a Segregation model in NetLogo. One of the most interesting and valuable aspects of the segregation model developed by Shelling is its sensitivity to thresholds of individual preference. For the purpose of this set of models, I’ve held the population at 2000 for most of the examples, for reasons explained near the end of this exercise.

Agents in this model chose movements based on a preference for proximity to other agents of like kind. This means that at every time step, the entire population is asked whether its neighborhood is suited to its individual preferences. As soon as there are not any agents who are dissatisfied with their surroundings, the model ends.

When the preference level is low there is relatively little activity, and around 26% desired similarity there is a transition from very little reorganization to more substantial reorganization and an emergent pattern.

However, at this lower bound of the preference spectrum, there is not a clear threshold. Starting at around 10% preference, model runs do result in a more segregated landscape. At low preference (below 30% or so) incremental changes do occur, but they are subtle. Perhaps the best way to measure the development of the model as the preference is raised is the average number of time steps that pass before the model comes to an end. By this metric, around 16% preference the model changes from a predominantly 2-5 time step pattern to a 4-9 time step pattern.

Again at 26%, the model changes from a pattern than rarely progresses beyond 9 steps, to one that is almost always over 10 steps. This pattern continues and around 51% preference we can start to see buffer regions start to appear between the differently colored agent groups where the members of both groups are moving closer to their own, implying movement away from the other.

There is however an abrupt change at an upper limit of preference. Above 75% the model will only occasionally resolve to a stable state and instead agents move around the landscape, perpetually dissatisfied with their neighbors. In this model run, preference is set to 75% and it takes several seconds (at normal speed) for the model to complete. Notice the emergent pattern appears relatively quick and then there are many time steps spent finding the final positions.

Moving the preference level up a single percentage point to 76% has a rather dramatic effect. This is a classic example of nonlinearity and the dynamic of threshold effects. Instead of finding a stable pattern, there is a constant reshuffling of agents across the landscape.

From the above discussion, it seems likely that adjusting the level of preference that each turtle has to have in order for the model to stop is the most important control that we have over the final state of the model. The reality is that this is partly controlled by the number of of turtles. I chose not to explore that relationship fully, but decreasing the number of agents per unit area appears to push the thresholds in preference to higher values. For instance, moving the number of turtles to 1200 (as opposed to 2000) increases the sudden upper threshold to 81%.

In addition there are measurements which allow us to evaluate the magnitude and nature of the effect of preference. The “unhappy ratio” is one interesting metric of the model progression. This particular ratio is quite sensitive changes in the spatial arrangement, because the numerator decreases and denominator increases simultaneously. At the low levels of preference, the relationship between % unhappy and % similar is strongly nonlinear in time, but is mostly logarithmic or exponential. Basically, under about 70% preference, each early time step results in a vastly decreased value of the ratio indicating that the % unhappy decreases very quickly as time proceeds and % similar increases very quickly. Each step changes by a less and the % unhappy and % similar approach 0 and 100% respectively. The result is that even small fluctuations in the two measurements are accentuated in the ratio.

 

 

 

Above, the most profound changes in the ratio occur within the first few time steps and subsequent changes take longer. This is consistent through the middle range of preference, but just before the 76% threshold, the pattern begins to disintegrate.

In general this exercise demonstrates an important aspect of threshold behavior in complex systems. This is a emergent pattern as well, in which only the simple rules governing agents’ self-interest needed to produce the complex behavior. In this complex system abrupt changes in behavior can result from small corresponding changes in the input parameters. These abrupt changes in behavior are not evenly distributed or arbitrary, but reflect mathematical relationships of the probabilistic nature of agent-based rules.