Assignment 2

The Segregation model looks at the patterns of clustering that develop when an agent’s preference to be close to similar agents increases. The Segregation model environment is composed of agents known as turtles that occupy a 33×33 cell grid of black cells, called patches. Turtles are divided into two classes, seen here as yellow and blue arrows. At each time step, the turtles assess the percentage of similar colored turtles in their neighborhoods, defined as a 3×3 cell “Moore” neighborhood, and make a decision to either stay put or to move in hopes of discovering a more preferable neighborhood. Two adjustable parameters are responsible for the development of emergent patterns of segregation in the model.

Adjustable Parameters:

Population Number (PN): Total amount of turtles in the environment (range: n = 500 – 2,500).

Percent Similar Wanted (%SW): Percent of like turtles in neighborhood needed for turtle to be satisfied with its neighborhood (range = 0% – 100%).

Q1: What minimum level of self preference leads to emergent patterns of segregation?

Population Number (PN) is an important parameter in moderating the Percent Similar Wanted (%SW) value necessary to trigger the development of emergent patterns of segregation in this system. When the PN is low, satisfying the %SW condition and achieving a steady state is possible throughout the range of %SW values ( 0% – 100%). However, reaching a steady state does not mean that a clear visual pattern of segregation will emerge (see figure 1).

Increasing the the number of turtles in the system makes the emergent patterns easier to see, but perhaps more importantly, the increased population results in a clear threshold value of %SW needed to trigger emergent patterns. For the simulation runs that serve as the basis for my analysis here forward, the PN was held constant at n = 2500.

Segregation begins to appear when the value for Percent Similar Wanted (%SW) reaches 26%; at this level the segregation patterns become defined. Within ~25 time steps the patters of clustering of similar values appear where they had not been with the %SW only 1% lower. Additionally, when the threshold is reached the monitor for Percent Similar (number of similar turtles in neighborhood / total turtles in neighborhood) indicates that a a significant change in the pattern of turtles in the environment has taken place. Pre-threshold values of %SW (0% – 25%) result in Percent Similar values of ≤ 55 %, but once the %SW threshold has been reached Percent Similar values immediately increase to ~ 71% (see figures 2 & 3).

 

 

 

 

Q2: Does a specific threshold level exist that tips the system into an unstable state?

Here again, PN plays an important role in moderating the effect of the %SW parameter, when the PN increases and the unoccupied space decreases, a threshold value for %SW emerges that destabilizes the system. In an unstable system condition, turtles cannot find a place in their environment that satisfies the precondition of %SW. When the system is unstable no pattern of segregation emerges and the turtles constantly move randomly about their environment in a futile attempt to find a preferable neighborhood.
I have identified five system stability states that can take shape depending on the values of PN and %SW.

Low PN, High %SW: System stability with no emergent pattern
When the PN is at the minimum values (n = 500) the system will find stability, although it may take > 3000 time steps to do so. Yet, no emergent pattern of note is visible. There are too few individuals in the system for high-level system behavior to emerge.

High PN, Low %SW: System stability with no emergent pattern
In the Low %SW condition the turtles easily find a preferable neighborhood, but no segregation appears.

High PN, Emergent Range %SW: System stability with emergent pattern
Once the threshold for segregation is crossed the system finds a stable pattern of segregation, all the turtles find a place to stop in a neighborhood where 100% of the turtles are happy (see figure 4, and video).

High PN, Upper Margin of Emergent Range %SW: System semi-stable with emergent pattern
Near the upper threshold of the Emergent Range, the system takes on a semi-stable state. An emergent pattern of segregation is well developed, but a percentage of the turtles struggle to find a preferable neighborhood. This state could be called stable if one were to qualify state stability allowing for a certain number of unsettled turtles to exist in constant flux (see figure 5 and video).

High PN, Above Emergent Range %SW: System instability with no emergent pattern
Above the emergent threshold the system the emergent pattern breaks down and the pattern seen becomes totally random, and the percent of happy turtles becomes ~50%.
With the PN = 2500, the threshold %SW for the system becoming unstable is 76%. From 25% to 75% the system is stable, or semi-stable, but above 75% the turtles are unable to for a segregated pattern (see figure 6 and video).

Q3. How does increasing levels of self preference change the nature of segregation patterns that emerge?

Increasing the levels of %SW causes the emergent patterns of segregation to form larger and larger grouping clusters until the population is separated into two groups. In the low range of %SW many small groups of turtles are present and the clusters themselves are very irregular. When the range of %SW reaches the upper limit of stability the groupings have smoother edges and become completely segregated into two distinct groups. In the semi-stable range the turtles are never able to find a completely stable state and although the groups are highly differentiated the margins of the groups are in constant flux.

Q4: What does the change in the unhappy ratio at each time step tell you about the relationship between self preference and the number of similar neighbors in one’s neighborhood?

The relationship between self preference and the number of similar neighbors follows an inverse power curve. The initial phase of system self-organization takes place quickly as the neighborhoods become more homogenous, but the final stages of the development of the pattern take more time.

Q5: What general conclusions can be drawn from your answers to questions (i) to (iii)?

After examining the Segregation model and interpreting the results to determine what conclusions can be made specifically about this model, and complex systems more generally, a few themes became evident: (a) the role of population in facilitating emergence; (b) the role of model architecture in the observed results, (c) and more philosophically how do top-down influences affect complex systems behaviors –especially if one attempts to make inferences to the real world, and what does this tell us about the limitations of this model.

1. Numbers matter; varying the number of individuals in the environment, and in turn the related amount of surplus space in the environment led to very different system wide behaviors to take place. With population numbers set low, the primary parameter of interest, Percent Similar Wanted (%SW), was easy to satisfy. As the population increased towards the maximum, two threshold values of %SW emerged; the first resulting in the emergence of segregation and the second resulting in system-wide instability when %SW condition was impossible to satisfy. In a social science context, one may be interested in understanding how personal preference to be near like individuals affects the distribution of the socio-economic groups in society, a model such as this may help to explain the relationship of population density on the patterns of self-organized segregation that are observable in a urban area.

2. Continuing on the theme of the importance of numbers, the results I observed made me wonder if the intrinsic properties of the model’s representation of space can be see in the results. Specifically: Is there a relationship between the symmetrical shape of the Moore neighborhood used by turtles to evaluate their personal satisfaction and the threshold values of %SW? When the number of like neighbors needed to satisfy the %SW condition was equal to the number of cells on 1 side of the square shaped Moore neighborhood (3) emergent segregation followed, and when number of like neighbors needed to satisfy the %SW condition was equal to the number of cells on 3 sides of the square (7) instability resulted. Although I may simply be framing a coincidence as causal mechanism, if this relationship is present it would shed light on an important facet of this model (and of all types of GIS data representations) to be aware of when drawing conclusions: The mechanics of spatial representation can be the source of artifacts that can affect the set of results derived from your model, and if one is not careful, this too can infiltrate your conclusions.

3. Returning to the social science context, Segregation assumes that all agents have equal access to space in the environment and equal ability to move to accommodate their self-interest. This idealization ignores potent top down control mechanisms that constrain individual agents operating in societal and environmental systems. Therefore, inferences from this model about the role of the personal preference of local actors in observed patterns of segregation in of human systems should be made very cautiously, if at all. While this may seem like an obvious point, understanding the limitations of any method of inquiry is crucial for evaluating the utility of the information created as a source of new knowledge.