Abstract
Ecological models are useful in modeling organizations and their competition over resources. However, the traditional approaches, particularly Blau space models, are restrictive in their dependence on a continuous space. In addition, these models are susceptible to indicating competition in sparsely populated areas of an ecology. To deal with these problems we propose a reconceptualization of Blau space that utilizes a cellular structure to model a wider number of variable types, and simple probabilistic urn models to evaluate competition between organizations. We briefly review the basic concepts of Blau Space, demonstrate the issues with traditional Blau space modeling, and present a new model referred to as the Hybrid model.
This work is supported by the Office of Naval Research Multidisplinary University Research Initiative (MURI) under grant number N00014-17-1-2675.
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Notes
- 1.
Traditionally, Blau space has been used to study “voluntary associations”, such as athletic clubs, social clubs, and religious organizations. However, the theory itself is applicable to all social organizations [3].
- 2.
- 3.
Produced using Blaunet Version 2.0.8.
- 4.
The underlying mathematical framework for Blau space is a modification of the Lotka-Voltera Ecological Competition model [2], which assumes of populations with a continuous and somewhat normal distribution of resources that they are consuming.
- 5.
This scaling might rely on MDS techniques or a Goodman RC-II model but is beyond the focus of this paper.
- 6.
The method proposed uses change in membership between two organizations as a proxy for competitive pressure, with the expectation that more organizations present in the neighborhood of a focal cell will result in more pressure for individuals to change their membership. See Fig. 2 for an example.
- 7.
We use the sampling with replacement implementation because the recruitment of one individual into an organization does not instantaneously make recruitment of another into the same organization less likely.
- 8.
The fraction of the focal cell that is updated in a given iteration is a tunable parameter.
- 9.
This process is similar to a cellular automata, where rule sets for updating a cell as “alive” or “dead” are based on the surrounding cells. In normal cellular automata models, it is the cell itself that is being updated, while in our model, it is entities within the cell that are being updated.
- 10.
All results reported herein use 10,000 iterations (i.e., 10,000 focal cell updates). This value is arbitrary as convergence criteria have not been defined, and thus analysts should engage in some degree of sensitivity analysis.
- 11.
Niche Volume is the total volume of Blau space taken by the niche or an organization. It is calculated by taking take volume of an organization’s niche divided by the total volume of the k-dimensional space. All metrics are calculated using post-simulation results.
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Harder, N.L., Brashears, M.E. (2019). A Hybrid Cellular Model for Predicting Organizational Recruitment in a k-Dimensional Space. In: Thomson, R., Bisgin, H., Dancy, C., Hyder, A. (eds) Social, Cultural, and Behavioral Modeling. SBP-BRiMS 2019. Lecture Notes in Computer Science(), vol 11549. Springer, Cham. https://doi.org/10.1007/978-3-030-21741-9_17
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