Assignment 3
Q1: Describe in 4-5 sentences the utility of using a pattern oriented modeling approach for understanding the observed patterns of both species.
In our scenario we have two observed spatial and temporal patterns that characterize the systems of interest, yet we don’t understand the processes that gave rise to these patterns.
The goal of pattern oriented modeling(POM) approach allows the researcher to contrast theories of agent level behaviors to compare how these well these behaviors reproduce the patterns observed in the real world and eliminate the theories that are found to be incompatible with the observed patterns (Grimm et al., 2005). The utility of the method is to produce models that are more structurally realistic; this realism extends the model’s credibility. Serendipitous secondary applications for the model may result from the increased realism such as revealing new understanding of an ancillary aspect of the system (Grimm et al., 2005).
Q2: For each movement model, describe how agent interactions lead to emergent patterns in both space and time.
Random Walk:
In this model the agent do not interact with each other; the turtle agents simply move about their environment as directed by their movement parameters defined in the by the command Directed Walk. In the “on” state, this command limits the directions of forward movement of the agents. At each time step agents choose a new travel direction randomly between 0 – 180 degrees from the previous heading. The result of this behavior is gauged by measuring the mean nearest neighbor distance for each of the turtle agents; here, in the “on” state the mean nearest neighbor distance increased as the simulation went on. The graph (Figure 1) shows this increase eventually slows and stabilizes into a consistent range after > 200 time steps. When “Directed Walk” is “off” the turtles movement is not constrained. At each time step the turtle changes its heading randomly in any direction. This movement behavior has a similar spatial and temporal patterns, with the exception that the mean nearest neighbor distance remains much lower throughout the simulation (Figure 2).
Video 1. Random Walk Model, Directed Walk: On
Video 2. Random Walk Model, Directed Walk: Off
Foraging:
The foraging model is a modified version of the Random Walk model: The movement patterns are identical in the both the Directed Walk “on” and “off” states. There are a few key differences between Random Walk and Foraging: Turtles have a limited amount of energy and must interact with one of the five patches randomly designated as “food” to regain energy to continue foraging, or face death after 200 steps without finding food (although in this simulation, upon death, turtles are immediately reborn from the food patches). When Directed Walk is “on” the behavior is much like that of Random Walk, although after 200 steps a significant portion of the turtles die. Once they have been reborn from the food patches they are able to remain in a steady population and soon establish a mean nearest neighbor distance that is steady for however long the model runs (Figure 3). With Directed Walk “off” the behavior follows a similar trend, however the nearest neighbor distance is noticeably reduced from the “on” state (Figure 4).
Video 3. Forage Model, Directed Walk: On
Video 4. Forage Model, Directed Walk: Off
Flocking:
This model uses a more complicated turtle movement protocol. Once turtle movement has been initiated the turtles have parameters that control their behavior and direct them to either move away from each other if they are too close ( < 1 patch apart), or if they are at a greater distance from one another, they attempt to align their heading to their nearest neighbor, and then maintain directional coherence with their nearest neighbors heading. Since all the turtles are attempting to align their direction of travel with that of their neighbors they are all able to eventually swarm together and maintain a very small nearest neighbor distance. Within a few hundred time steps all the turtles are organized into a pattern that they will maintain for as long as the simulation runs (Figure 5).
Video 5. Flocking Model, Directed Walk: On
Q3: Which movement model best describes the patterns observed for species A? Why?
The Flocking model best describes the pattern for species A. Like in the graph of species A, the graph of the flocking model shows that the turtles quickly organized into a pattern that has a low nearest neighbor distance that remained relatively constant with a narrow range of variation (again, see Figure 5). Additionally, the spatial patters of species A was highly clustered, this pattern is consistent with the behavior of the turtles in the flocking model (see Figure 6 for the patterns of species A and B).
Q4: Which movement model best describes the patterns observed for species B? Why?
The Random Walk model with the Directed Walk in the “on” state best describes the pattern for species A. The graph of species A shows as time increases the nearest neighbor distance increases to a high value until a point is reached when the agents are in a relatively dispersed spatial pattern and the graph flattens out. This is similar to what is seen in the Random Walk model with the Directed Walk in the “on”. The variation seen in the graph (Figure 1) is not present in the curve seen in species B, but a general pattern that matches can be seen. Its worth noting that the Random Walk with the Directed Walk in the “off” state, and the Foraging model in both Directed Walk states showed a similar pattern, but the Random Walk model with the Directed Walk in the “on” state was the strongest match for the patterns of species A.
Q5: How did a pattern oriented modeling approach allow you to determine the answers to (iii) and (iv)?
In the Pattern-Oriented Modeling approach, described by Grimm et al. (2005, p. 987), patterns are understood as the expression of the system indicating the processes that underpin the system and give the system its character. They say the information about the system is “coded” in these patterns. The codes to the behaviors of species A and B are visualized by the nearest neighbor distance graph and the map, of sorts, of the spatial arrangement of the agents. Similarly testing multiple hypotheses was important to determining the processes that best fit the models. This was especially evident in determining the process that created the pattern most similar to species B. There were three other patterns that, while they had a resemblance to the species B patterns, weren’t as strongly articulated as was the pattern seen for Random Walk model with the Directed Walk in the “on” state. If we had tested just one of the processes and the resulting graph was an approximate match, we may have concluded that that process was correct, but not as well understood as we had thought. Comparing multiple processes allowed for a wider range of outcomes, and in so doing, the strongest candidate emerged.
References:
Grimm, V. et al. (2005). Pattern-oriented modeling of agent-based complex systems: lessons from ecology. science, 310(5750), 987-991