Zed Langston
April 21, 2015
Assignment 3: Pattern-Oriented Modeling with Agents

Description:

This is a Pattern-Oriented Model (POM) to determine what processes cause the observed spatial and temporal pattern of two different species.  The three processes (movement theories) that could be responsible for the observed patterns are flocking, foraging or random walking movement.  The model was built in NetLogo and will be used to look at the processes that closely replicate the observed patterns.  The agents move around the landscape to find available resources losing energy as they move.  In the foraging model, the initial agent variables start with 200 energy and will get an additional 200 energy after finding food resources (from five randomly placed patches).  If any turtle loses all energy (energy = 0) before finding a food resource, the model is built so that agent will move directly to a food source.  In the random walk model, agents move around either taking random left/right turns at 90 degrees (directed-walk) or in a random right direction between 0 – 359 degrees.  In the flocking model, agents move towards the closest other agents but are required to maintain a minimum distance or change directions.  At setup for any of the mobility models, 20 agents are placed at the extent origin and the agents move outwards to resource patches following the rules of one of the movement models.  There is a built-in model parameter that affects agent movement in the random walk or foraging models that can be switched to directed movement (random left or right turn at 90 degrees) or switched off for random movement (random right movement between 0 – 359 degrees).  The stochastic asynchronous updates should not affect the overall emergence over many runs.  It should be noted with the foraging model using directed movement the mean Nearest Neighbor Distance (NND) appears to be more than the random movement NND.

Questions:

1) The utility of using a POM for understanding the observed patterns is that all three theories can be tested and contrasted within the same explicit model to find the theory of best fit.  Using a POM based on agents allows the observer to look at the overall patterns resulting from interactions of the autonomous agents to give an idea of the underlying organization to understand which theory best applies to each of the species.  The model structure gives the ability to emulate the interactions of the observed agent behavior patterns of the species over space and time (emergent patterns) to deal with some of the uncertainty inherent in all models.  The emergent patterns indicate the processes that cause the emergent patterns (agent influence and self-organization based on local rules and individual decisions).  Furthermore,  the strength of using a POM is that the observed patterns could help to calibrate the model so that we can replicate the phenomenon of movement and bracket the outcomes.

2)  In the flocking model, agent interactions lead to emergent patterns that are clustered in space over time by following three rules coherence (attraction), separation (repulsion) and alignment (imitation) based on the mutual influence among the agent and the nearest agent (neighbor) using the NND as a type of feedback.  In this model, agents adjust their behavior and self-organize by aligning and/or cohering or separating using their state and that of the next closest neighbor (agent) to match the speed and direction to that of the nearest neighbor movement (influence).  These agent interactions result in similar cohesive and aligned (directional) movements over space and time because of path dependence and influence.

 

In the foraging model, the agent interactions lead to emergent patterns in space and time because of the interactions while looking for some resource in their environment to get energy.  The agents move at random 90 degree left or right turns or using directed random right turn movement (directionally 0 – 359 degrees) to find the food resources (patches) over the landscape.  Each agent tries to get to the food resource, if no food resource is available, the agents continue to move.  If the agent energy reaches null, than the agent moves directly to the closest available resource.  This mobility theory simulates resource competition among agents with the exception that in this model, no agent dies and the five resource areas are always available.  The agent interactions lead to emergent patterns over space and time because of the agents path memory and the recognition of a food resource that leads to the mutual influence between agents when trying to find resources in the environment.  The emergent pattern tends to be clustered because agents find efficient paths or change paths indicating to other agents that resources are somewhere else or conversely that a resource has been found (feedbacks).

 

In the random movement model, the agent interactions lead to emergent patterns that are dispersed in arrangement in space over time by moving around the landscape in either a random (movie and top image set) or directed way (bottom image set).  In the directed random right movement process, turtles make left or right 90 degree turns moving .25 patches.  In the random movement process, turtles move in a direction between 0 – 359 degrees .25 patches.  Movement is based on random individual decisions, on where to move, based on the agents current state, the neighbors state and the state of the local environment.  This model leads to a somewhat dispersed spatial pattern with some minor clusters with fluctuating but increasing NND over time.

3)  The model (theory) that best describes the observed patterns for species A is the flocking model because the NND fluctuates but remains low (matching the temporal pattern) while maintaining clustered groupings (the spatial pattern).  This model seems to fit the observed spatial and temporal phenomena better than the other theories.  The NND is low when an agent tries to mimic the next closest agent but fluctuates to a higher peak as groupings get farther away from each based on the local rules and influence of the nearest neighbor and autonomous agent path dependence.  The random walk model does appear to match the temporal pattern but does not match the spatial pattern well while the foraging model does not appear to match the temporal pattern but fits the spatial pattern.  Therefore, both the random walk and foraging models were excluded as a possible process explanation for the observed phenomenon.

 

4)  The model (theory) that best describes the observed patterns for species B is the random walk movement model because there is a more dispersed spatial pattern and a higher NND.  Initially, there is a rapid increase in NND as the agents move outwards from the origin increasing the NND distance.  As the agents move farther away from the starting point and each other, the NND becomes more stabilized because the agents have reached the largest average separation distance based on the closest neighbor and specified environmental extent.  With many model runs, the plotted simulations will approximate the curve.  The movie and image set below show a directed random walk model.  The foraging model did not fit the temporal or spatial pattern well for most runs while the flocking model exhibits a temporal minimum and maximum fluctuation distance between peak and valley.  Therefore, these two later models were excluded as a possible process explanation for species B.

 

5)  A POM approach allowed for a spatial simulation of multiple theories (pattern processes) to be tested, compared and contrasted by emulating the observed patterns of the two species.  The model uncertainty is addressed by looking at the difference of high and low emergent patterns (using the plot) using the parameter setting for two of the contrasting theories (attempting to visually bracket the results using the upper and lower limits from many model runs).  Using these methods, the model is more realistic reducing uncertainty associated with an observed real-world phenomena.  POM allowed for examining and contrasting the three competing mobility process theories to find (infer and reproduce) the closest similar spatial and temporal patterns to those of the observed phenomena.