# Systems of Interaction between the First Sedentary Villages in the Near East Exposed Using Agent-Based Modelling of Obsidian Exchange

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{n}(called the neighbor distance) from each other, are assumed to be permanently linked (Figure 2). This would draw a regular network of exchange, where any node is exclusively connected with its neighbors. However, in order to test the viability of more complex exchange networks, some nodes were also allowed to connect to more distant partners in our trials. In this case, for each time step, each node is given (with probability ${p}_{t}$) the possibility to create or renew one of the $n$ distant links it has with any of the villages which are further away than ${d}_{n}$ from it but within a distance ${d}_{t}$ (which represents a maximum travel distance). This introduces a dynamic generation of long-distance links that are not fixed in time but evolve dynamically during the simulation.

## 3. Sensitivity Analysis of the Model

- Number of villages (N).
- The distance defining neighborhood (${d}_{n}$).
- The limit for distance of exchange/production link (${d}_{t}$).
- The number of distant links per village (n).
- The function of decrement in obsidian acquisition ($r$) related to distance.
- The rate of obsidian exchange/consumption in each village ($c$).

## 4. Modelling Results

- The distance of exchange link: Ethnographic examples reveal long trade expeditions to reach contact partners located at distances between four and 10 days walking [29,30,31]. For example, direct access to sources for acquiring salt or stone blades in ethnographic contexts of primitive trade among archaic farming communities in NG implies expeditions of four to seven days walking [31,32]. Considering a medium distance of 20 km walking per day, we estimate 180 km as a reasonable maximum distance of a production/exchange trip (${d}_{t})$ in our model.
- The rate of obsidian exchange/consumption in each village ($c$): The study of archaeological remains has demonstrated beyond a doubt that obsidian was both consumed and exchanged, and therefore had a use and an exchange value. As ethnographic examples show, the proportion of one value with respect to the other was most likely contextual. For example, among the Anga of NG, the price of a commodity (which is directly related to the exchange value) depends on its rarity, on the political relationships between groups (the price is higher for enemies) and, in the case of utilitarian commodities (which obsidian was in the context we are researching), on the degree of necessity for its use. Another important element which influences the exchange value of a commodity is the likelihood of providing other commodities in exchange. Among the Kapau and Langimar groups from NG, Baruya salt is consumed but not exchanged because these groups own the production monopoly on stone axes and adzes, which are other commodities that can be used for exchange [30]. Most obsidian remains are recovered from archaeological sites in the form of used and discarded tools, while very few obsidian caches that could represent material ready for exchange have been found. This seems to indicate, generally speaking, that the exchange value was not higher than the use value. As both values were important, we have chosen a rate of 50% for each site in our standard model.
- The distance defining neighborhood (${d}_{n}$): Ethnographic examples show [32] that most transactions take place between villages which are located at a distance of one or two days walking. Thus we have chosen 50 km as the limit of a “neighborhood” (${d}_{n})$.

## 5. Comparing Model Results and the Archaeological Data

## 6. Archaeological Implications

## 7. Conclusions

## Supplementary Files

Supplementary File 1## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Maps with the quantity of obsidian present in the Pre-Pottery Neolithic A (

**left**) and Pre-Pottery Neolithic B (

**right**) sites.

**Figure 2.**Attachment dynamics with interaction distances ${d}_{n}$ (neighbor distance) and ${d}_{t}$(maximum travel distance).

**Figure 3.**Multi-parameter representation of the simulation results for the ODLb (Optimized Distant Link) model. The quantity of obsidian reaching different distances (see legends) from the production region is plotted as a function of four different parameters. Each single point in the plots corresponds to one single choice in the parameter space computed according to the Latin Hypercube Sampling (LHS). The dependence on $c$ is shown in the horizontal axis. The dependence on $n$ is shown by changing the shape of the points (squares for $n=1$ , circles for $n=2$ and triangles for $n=3$). The dependence on $N$ correspond to the size of the points (with smaller points corresponding to $N=150$ and larger ones to $N=350$). The dependence on ${d}_{t}$ is represented by changing the gray color in a linear scale where ${d}_{t}=0$ corresponds to “white” and the maximum value ${d}_{t}=220$ km corresponds to “black”.

**Figure 4.**ODLa (

**left**) and ODLb (

**right**) model results as a function of the total number of villages $N$, compared with Pre-Pottery Neolithic A (PPNA) and Pre-Pottery Neolithic B (PPNB) obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Figure 5.**ODLa (

**left**) and ODLb (

**right**) model results as a function of decrement in obsidian acquisition ($r$) related to distance, compared with PPNA and PPNB obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Figure 6.**ODLa (

**left**) and ODLb (

**right**) model results as a function of the number of distant links per node $\mathrm{n}$, compared with PPNA and PPNB obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Figure 7.**ODLa (

**left**) and ODLb (

**right**) model results as a function of the neighbor distance ${d}_{n}$, compared with PPNA and PPNB obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Figure 8.**ODLa (

**left**) and ODLb (

**right**) model results as a function of the maximum travel distance ${\mathrm{d}}_{\mathrm{t}}$, compared with PPNA and PPNB obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Figure 9.**ODLa (

**left**) and ODLb (

**right**) model results as a function of the exchange/consumption rate in each village (c), compared with PPNA and PPNB obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Figure 10.**Modelling of networks resulting from the regular network (down-the-line) exchange model, the Optimized Distant Link model with preferential attachment based on the quantity of distant links (ODLa) and the Optimized Distant Link model with preferential attachment based on the quantity of obsidian (ODLb) compared with PPNA and PPNB obsidian archaeological data. The Y axis is represented in a logarithmic scale.

**Table 1.**Clustering coefficient and path length in the three explored models of obsidian exchange compared to an equivalent random network.

Path Length (Number of Nodes) | Local Average Clustering Coefficient | |
---|---|---|

Regular network (Down-the-line) | 15.8 ± 12.6 | 0.61 ± 0.21 |

Optimized Distant Link (ODLa) | 9.51 ± 8.74 | 0.49 ± 0.18 |

Optimized Distant Link (ODLb) | 5.10 ± 2.84 | 0.45 ± 0.16 |

Random network | 2.91 ± 1.79 | 0.035 ± 0.021 |

**Table 2.**Degree of correspondence (average individual deviation with respect to data regression) between the three models explored and the PPNA and PPNB archaeological datasets (We have fit the PPNA and PPNB data to an exponential regression curve. Regression was calculated from 23 archaeological sites for the PPNA and 42 for the PPNB (see supplementary materials Table S1). For the PPNA: function 100 * exp(−9,9E−3x), with a standard error of 1.12; and for the PPNB: function 100 * exp(−7,7E−3x), with a standard error of 0.73. We calculated the distance (measured in terms of standard deviation) between the regression curve and the archaeological data, and between the regression curve and the results of our models).

Average Individual Deviation with Respect to PPNA Data Regression | Average Individual Deviation with Respect to PPNB Data Regression | Average Individual Deviation with Respect to Model Prediction | |
---|---|---|---|

PPNA data | 1.12 | - | - |

PPNB data | - | 0.73 | - |

Regular network | 2.75 | 3.49 | 2.88 |

Optimized Distant Link (ODLa) | 1.90 | 2.12 | 0.28 |

Optimized Distant Link (ODLb) | 1.38 | 1.00 | 0.22 |

**Table 3.**Ratio of obsidian to flint in relation to site size (small: <1.2 ha; medium: 1.2–5.3 ha; big: >5.3 ha) at PPNB sites that are more than 500 km from obsidian sources.

Small | Medium | Big | All Sites | |
---|---|---|---|---|

PPNA | 0.009 | 1.465 | (no data) | 0.233 |

PPNB | 0.073 | 0.398 | 2.410 | 0.703 |

All periods | 0.023 | 0.703 | 2.410 | 0.437 |

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**MDPI and ACS Style**

Ortega, D.; Ibáñez, J.J.; Campos, D.; Khalidi, L.; Méndez, V.; Teira, L.
Systems of Interaction between the First Sedentary Villages in the Near East Exposed Using Agent-Based Modelling of Obsidian Exchange. *Systems* **2016**, *4*, 18.
https://doi.org/10.3390/systems4020018

**AMA Style**

Ortega D, Ibáñez JJ, Campos D, Khalidi L, Méndez V, Teira L.
Systems of Interaction between the First Sedentary Villages in the Near East Exposed Using Agent-Based Modelling of Obsidian Exchange. *Systems*. 2016; 4(2):18.
https://doi.org/10.3390/systems4020018

**Chicago/Turabian Style**

Ortega, David, Juan José Ibáñez, Daniel Campos, Lamya Khalidi, Vicenç Méndez, and Luís Teira.
2016. "Systems of Interaction between the First Sedentary Villages in the Near East Exposed Using Agent-Based Modelling of Obsidian Exchange" *Systems* 4, no. 2: 18.
https://doi.org/10.3390/systems4020018