This page explores the utility of pattern-oriented modeling in the context of another NetLogo model.

Part 1: Describe (in 4-5 sentences) the utility of using a pattern-oriented modeling approach for understanding the observed patterns of both species.

Grimm et. al describe pattern-oriented modeling as means to make bottom-up modeling more ‘rigorous and comprehensive’ by including in a model the necessary agents and mechanisms that allow a certain pattern to emerge. Simply put, this means that instead of trying to replicate the decision-making processes of agents and then observing the pattern that emerges when these agents interact, we work backwards. Instead, we find a pattern we would like to replicate and program our agents and environment to make the desired pattern emerge.

By striving to replicate a pattern, we are able to insightfully include in our model relevant parameters, agent attributes, and mechanisms that will allow us to decode the internal architecture of a system.

In the context of our two species, we may compare species’ movement patterns with a model that represents these patterns. When comparing the observed pattern with the simplified, modeled one, we begin to learn something about agent interaction and system structure by the ways we chose to build our model.

Part 2: For each movement model, describe how agent interactions lead to emergent patterns in both space and time.

1. Random Walk

In the ‘random walk’ model, agents move about the space freely, disregarding both food sources (green patches) and other agents. Despite this, a spatial pattern eventually emerges; as time goes on, agents move further away from the origin (the center of the environment, where they began), and gain distance from one another.

This pattern is more obvious when our ‘directed-walk’ dial is on. In this case agents move away from the origin quickly, and disperse into a random spatial pattern within seconds.

We see that in the latter model, it takes much less time for the agents to disperse. This variability in time may be reduced to a matter of geometry and probability. Essentially, these agents advance forward .25 patches, and pick a random direction to turn within 90 degrees to their left or right, when the ‘directed-walk’ switch is on. If this range of angle-movement were to be larger, (e.g. when we switch off the ‘directed walk’ dial) we can the dispersal of agents to happen slower, as the turtles now have the opportunity to turn a larger distance in a shorter amount of time, and to backtrack.

In either case, both the temporal and spatial patterns are dominated by stochastic movement, and therefore can be categorized as a random pattern.

2. Foraging

The pattern that emerges in in the foraging model is largely dictated by the location of green patches and the chosen movement of the turtles (whether or not an agent’s walk is directed). This movement pattern can be characterized as a ‘clustered’ pattern, and can be seen in the video below.

Without the directed-walk constraint, the turtles move slowly away from the center, and remain close to one another for a longer period of time. When the turtles run out of ‘energy,’ instead of dying, they are transported to the nearest green patch (or food source). Because turtles tend to run out of energy around the same time, they edge closer towards the green patches seasonally. However, the temporal pattern becomes more cyclical over time, as agents encounter food sources at different times.

We also notice that when the directed-walk switch is on, agents disperse much quicker and populate more food sources faster than if their trajectories were entirely random. Compare the video below with the previous video to see the disparity.

3. Flocking

The pattern that emerges out of the flocking model is dictated by agent interaction entirely, and is much more involved and complex than the previous two movement patterns.

When flocking, each agent recognizes it’s nearest neighbor (another agent within a 3-unit radius ) and either aligns with and follows this neighbor if it more than one unit away. If its nearest neighbor is within one unit of the particular agent, the agent changes its trajectory, heading away from that neighbor and potentially leaving the flock.

This movement pattern obviously results in a clustered spatial pattern. These clusters grow in population size over time, but disperse periodically when enough agents are too close to their neighbors. Temporally, this pattern appears and dissipates in a cyclical fashion, as we cannot tell exactly when a flock may disperse.

Part 3: Which movement model best describes the patterns observed for species A? Why?

To determine the movement pattern of species A, we are given both the spatial and temporal patterns of the species’s movement. We can see from the graphs that the species has a clustered spatial distribution. This automatically rules out our ‘random-walk’ movement-pattern, as utter randomness does not (always) result in clustering.

Next, we look at the plot of nearest-neighbor-distance vs. time. Generally, if agents are dispersed throughout the environment evenly, our nearest-neighbor distance would be a large value. If this number is low, all (or most) agents will be close to others, forming clusters. Given this information, we can imagine that this species is dispersing and clustering seasonally, or over a repeated period of time.

Our flocking model best displays the oscillation of distance in this species’ movement pattern. As described in the 3rd section of Part 2, flocking model results in periodic clustering and dispersal of agents throughout time.

Below is a video of both the flocking model and plot that allows us to draw a comparison between the spatial and temporal patterns between our model, and the movement pattern of species A.

 
Part 4: Which movement model best describes the patterns observed for species B? Why?

Our ‘random-walk’ movement model represents the movement pattern of species B. Since agents move independently of other agents and food sources, their spatial and temporal pattern is dictated entirely by probability. We can see in the graph above that the average distance between neighbors increases constantly, but the rate at which it increases is actually lessening as time goes on. The decrease in rate is due to the bounds of our environment–that we are dealing with limited space. If the environment was infinitely large, we could see agents traveling further and further away from each other indefinitely. However, in our model agents can only get so far away from one another, and this distance is the threshold that both our agents and species B encounter.

Part 5: How did a pattern-oriented modeling approach allow you to determine the answers to parts 3 and 4?

By approaching this problem through a pattern-oriented perspective we provided ourselves with a useful set of tools for ‘decoding’ the internal organization and mechanism of these species’ movement patterns.

Specifically, we are given two patterns described by the plots and graphs shown above (in parts 3 and 4 respectively), and are given a model of real-world phenomena that may replicate the movement-pattern of a species.

We take notes of the key distinguishing features of these patterns, such as the continuously broadening oscillation of the ‘average nearest neighbor distance’ in species A, or the logarithmic pattern of distance seen in the species B, and look for these patterns in our own model. If we find a match, we are able to make assumptions about agent behaviors and interactions and how they influences their movement pattern.