i. In this assignment we created simulations of three different movement behaviors in order to find the best fit for the underlying process that produced the observed spatial (and temporal) patterns of two different species. By creating simulations that follow different sets of movement and using a pattern-oriented approach, we were able to determine which of the three movement theories (random, foraging, or flocking) most closely resembles the processes driving each species’ movement. The observed data regarding the two species’ movement consist of a snapshot of a spatial population distribution, and a graph showing average distance between nearest neighbors over time. By using these two patterns–one spatial and one temporal–we can narrow the possible patterns further than if relying on only a single pattern fit (Grimm et al 2005).
Species A exhibits a tightly clustered spatial distribution, and the distance between nearest neighbors displays a cyclical temporal pattern. Species B exhibits a looser clustered distribution, and a temporal pattern of gradually increasing, but tapering, distance between nearest neighbors.
ii. We created three different candidate simulations, each modeling a different movement pattern. The first simulated a random walk: the agents simply wandered across the landscape at random, without interacting with the landscape or each other. Since the edges of this model wrap, the agents could move freely in any direction, though their direction of movement could be constrained by the “Directed-Walk?” variable which limited agents to turns of less than or equal to 90 degrees. Both random walk models produced a spatial pattern (after a sufficient number of ticks) of randomly scattered agents, and a temporal pattern of gradually increasing, although tapering off, average distance to nearest neighbor (hereafter ADNN). (The Directed Walk model reached the upper bound of the ADNN more quickly.)
Random Walk Simulation: Spatial Distribution and ADNN over time.
The second model simulated a type of foraging behavior: each agent had an energy level depleted over time and replenished by moving over the green patches, with agents being moved to the nearest green patch when their energy reaches zero. Green patches are not altered by the agents; therefore the model contains agent-cell interaction but no agent-agent interaction (even indirectly). Nonetheless, this movement model produced a spatial pattern with distinct clusters (near the green patches), and the chart of the ADNN variable displayed a temporal pattern of periodically fluctuating values.
Foraging Simulation: Spatial Distribution and ADNN over time.
The third and final movement model that we built simulated flocking behavior: the agents attempted to match the speed and direction of nearby agents, leading to the gradual formation of groups of agents moving together. This model has agent-agent interaction, but the green patches do not play any role (i.e. no agent-cell interaction.) This movement model created a spatial pattern displaying a high degree of clustering; the temporal pattern in the value of ADNN showed (after an initial spike) a degree of short-term variation, with a long-term trend towards a smaller, more stable value.
Flocking Simulation: Spatial Distribution and ADNN over time.
iii. Each of the models generated a distinct combination of spatial and temporal patterns. Comparing the models’ patterns with the species’ patterns allows us to build hypotheses regarding the underlying mechanisms generating the observed patterns. Species A exhibits a clustered spatial distribution, with a ADNN increasing over time, though at a progressively slower rate. Both the Foraging and the Flocking model generated a clustered distribution, while the Random Walk did not. When comparing the temporal distribution, however, the Flocking model’s ADNN graph diverges sharply from the species A graph. Therefore, the Foraging model best describes both the spatial and temporal patterns of species A.
iv. Species B, in contrast, exhibits a spatial pattern of looser clusters and a temporal pattern of rapidly, then more gradually increasing ADNN. With the exhibited level of clustering, it is difficult to determine whether the distribution is truly an example of clustering or a clustered-seeming though still random distribution. Given the relatively tight clustering of the Flocking model, it does not describe species B’s pattern well. (Coupled with the temporal pattern, which diverges sharply from B’s, Flocking can be eliminated entirely.) The Foraging model appears to have the closest match to the somewhat clustered spatial distribution. However, once the temporal pattern is incorporated the Foraging model is no longer a strong candidate: the periodic fluctuations observed in the Foraging ADNN have no parallel in the species B graph. In contrast, the Random Walk ADNN graph shows the same trajectory of tapering increase as species B. Therefore, the Random Walk model best describes both the spatial and temporal patterns of species B.
v. A pattern-oriented modeling approach employs a succession of pattern-matching analyses to narrow a number of candidate models down to the model which best describes the unique set of patterns observed in the subject. By comparing not just the spatial or temporal patterns of the two species, but both, I was able to determine which of the three simulations best described the species’ movement patterns.
The models also suggest a further opportunity for data gathering: the Foraging model implies that resource distribution may have an impact on distribution. Further field work incorporating this insight will yield another pattern to be used in determining which models best describe the data, strengthening our understanding of the underlying processes at work.
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