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Model : SpatialOrg
Simile version : 3.1+
Date added : 20040105
Keywords :
Spatial organization ;
Spatial modelling ;
Multiinstance submodel ;
Multiagent systems ;
The model SpatOrg implements ideas about the information theoretic measure developed to quantify spatial organization (Krivov et al., 2003). The model illustrates the spatial organization by an example of flocking. To begin with, consider the correlations between the spatial events S^{k}_{i,t,x,y}(a) (where k corresponds to any of the spatial events: 'arrival at', 'stay put', 'departure from' and 'absence at' the site (x, y associated with the agent a of species i, in a two dimensional space, at time t) and the coupling of the set of all spatial events pertaining to the agents of species C_{i} that happened at site (x, y) at time t. The index of spatial organization is calculated as follows:
The value SC_{i(t, x, y)}represents the correlation between the arrival, staying put, departure and absence at a site(x, y) of the agents of species C_{i} at time t. The intuitive interpretation of AMI (average mutual information) suggests that, if these events are correlated, then the behavior of species C_{i} is organized, and the value of SC_{i(t, x, y)} will be high.
The model SpatialOrg is the first of a series of models to be developed as a demonstration of the quantifying measures. The main challenge of this model is to calculate the probabilities. The probabilities are estimated as the ratio of the number of times the event occurs to the total number of time intervals. The calculation of probabilities (submodel:patch (grid_cell)) included following steps:
The SpatOrg model space is a collection of cells arranged in a regular twodimensional lattice of size 10x10=100 cells. The spatial index is calculated for every cell based on the correlations of spatial events performed by the individuals/agents. The number of individuals/agents is equal to 20. However, the model could be modified for a varying population as well.
Simulistics is indebted to Anju Dahiya (adahiya@uvm.edu) for permission to include this model in the catalogue. Please contact Anju Dahiya for more information about the model.
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SpatOrg.sml 
A separate list of the model equations is available.
The figure 1. shows spatial importance index of a species for 10,000 time steps at a regular interval of 100 time steps. The model run without the flock submodel and on removing the related links to the individualofspecies submodel brings down the spatial index significantly. Different hypothetical cases of ecological systems are considered to illustrate the spatial importance index. The results are in preparation for a publication.
Figure 1. Spatial importance index at 10000 time steps
Figure 2. Screenshot of animation window showing agents after few runs.
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