# Detecting Associations between Archaeological Site Distributions and Landscape Features: A Monte Carlo Simulation Approach for the R Environment

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## Abstract

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^{2}test) or are difficult to apply correctly (regression analysis). Monte Carlo simulation, devised in the late 1940s by mathematical physicists, offers a way to approach this problem. In this paper, we apply a Monte Carlo approach to test for association between Lower and Middle Palaeolithic sites in Hampshire and Sussex, UK, and quarries recorded on historical maps. We code our approach in the popular ‘R’ software environment, describing our methods step-by-step and providing complete scripts so others can apply our method to their own cases. Association between sites and quarries is clearly shown. We suggest ways to develop the approach further, e.g., for detecting associations between sites or artefacts and remotely-sensed deposits or features, e.g., from aerial photographs or geophysical survey.

## 1. Introduction

^{2}test) do not seem suitable, as the expected frequency of samples in each class is a function of the proportional size of the class, rather than the proportion of landscape area occupied by the landscape features. A further problem, which frequently confounds analysis of archaeological site distribution data, is the low degree of accuracy and precision of the point data within a dataset. This is especially a problem with large, integrated databases, like those maintained under the Valetta Convention, for example, the UK’s county-level Historic Environment Records (HER). This is usually due to the low degree of precision of the original recorded coordinates (e.g., UK six-figure grid references), which are often derived from record cards or paper maps, or simply from the lack of precise knowledge about the location. While these problems are well known, satisfactory solutions remain elusive.

## 2. Research Background: Understanding Archaeological Site Distributions

#### 2.1. Overview

^{2}test, which are not really appropriate for spatial distributions, and more complicated approaches, like regression analysis, which require experience and care in application in order not to fall into one of a number of well-documented traps. Monte Carlo simulation, once difficult to do before the advent of powerful computers, is something of an intermediate approach, as it allows a test of association of one spatial data set against another in a way that is fast, intuitive and robust, and does not require immersion in statistical modelling. Monte Carlo approaches have been variously applied in archaeological contexts (see, e.g., [15,16]) but are not as widely used as they might be, probably because the procedure is not integrated as standard in GIS software, and a straightforward description of the process with worked examples has so far not been published. In this paper, we seek to address this gap by showing the utility of the approach by application to a simple research question—whether the spatial distribution of Lower and Middle Palaeolithic sites in Hampshire and Sussex can be shown to be associated with 19th and earlier 20th-century quarries recorded on historical topographic maps.

#### 2.2. Monte Carlo Simulation

## 3. Materials and Methods

#### 3.1. Study Area

#### 3.2. Study Aims

- The location of the Palaeolithic finds is, in many cases, uncertain.
- Many quarries are small—the fairly low precision of the recording of findspots means that finds might not coincide with the mapped location of the quarry from which they probably came.
- Not all quarrying activities are recorded on the maps.
- The fourth edition map was only partially available in digital form at the time the digitizing work was undertaken. Many tiles and areas of this map were missing from the dataset used, so later quarries are likely to have been omitted.
- Not all Palaeolithic sites are directly derived from quarries. Some have arrived in the hands of collectors as a result of natural processes, such as erosion.
- Quarries have been digitised without consideration for their depth or purpose, as determining this information would have been unreasonably time-consuming. Consequently, the dataset includes a number of quarries which do not impact any Pleistocene deposits (e.g., hilltop chalk quarries).

#### 3.3. Workflow

#### 3.3.1. Georeferencing and Digitising of Quarries

#### 3.3.2. Adding Buffers to Account for Uncertainty

#### 3.3.3. Random Sites Generation

#### 3.3.4. Overlay and Frequency Determination

#### 3.3.5. Script Programming

## 4. Results

## 5. Concluding Discussions

^{2}test, which are difficult to successfully apply in a spatial context, and more developed analyses involving various kinds of regression. For testing association between archaeological sites and multiple explanatory variables, regression approaches are likely to be superior to this simple Monte Carlo test. However, the need to obtain and process suitable data, and the absence of obviously applicable explanatory variables for archaeological periods where climate, vegetation and landforms are all unrecognisably different from today, means that the Monte Carlo simulation approach described here is useful in a very wide variety of analysis contexts. For example, one very simple application, analogous to the case presented here, might be to investigate the association between cropland and archaeological sites detected by aerial photography, e.g., in the UK (e.g., [33]). As hot, dry years are known to provide ideal conditions for detection of archaeological sites from cropmarks on arable land, a clear association between arable land and archaeological sites might be expected. On the other hand, this would be expected to show some variation, depending on the type of crop and the type of site. A very strong association between sites and arable land might indicate a significant under-representation of archaeological sites on different land cover types, e.g., pasture, allowing different kinds of aerial remote sensing techniques (e.g., LIDAR) to be targeted to these areas.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Technical Description of the MCSites Tool

#### Appendix A.1. Data Import and Analysis Preparation in R

#### Appendix A.2. Generation of Random Points Inside Study Area

#### Appendix A.3. Buffering Sites and Random Points to Account for Uncertainty

#### Appendix A.4. Overlay Features Layer with Sites and Random (Simulated) Sites

#### Appendix A.5. Run Monte Carlo Simulation

## Appendix B

## Appendix C

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**Figure 1.**(

**a**) Hampshire and Sussex in Southern England; (

**b**) the Sussex/Hampshire coastal corridor catchment area; (

**c**) Eastern Solent-focussed study area; (

**d**) Palaeolithic sites of the study area, showing modern-day elevation above sea level, mapped by frequency of lithics discovered at each site. Highest lithic yield sites are named, with lithic counts following in parentheses.

**Figure 2.**Observed sites, random sites and uncertainty buffers. Inner (100 m diameter) buffers were used in this analysis. The greater the uncertainty, the larger the buffer, and hence, the higher the probability of intersection between sites and quarries.

**Figure 3.**No. of recorded Palaeolithic sites (total n = 57) intersecting with quarries, versus number of random sites (total n = 57) intersecting with quarries, for 1000 Monte Carlo simulation runs (Run No. 1 in Table 1, below). Test No. 1001 is the 57 recorded Palaeolithic sites. Site/quarries intersection counts for Monte Carlo simulation shown in blue, recorded sites in red.

**Table 1.**Monte Carlo Simulation test results for 8 simulation passes of 1000 runs. Note how increasing the size of the uncertainty buffer increases the number of hits for both recorded sites and randomly simulated sites.

Run Number | Number of Simulations | Mean Frequency | Median | Mode | Min | Max | Recorded Sites | Uncertainty (m) |
---|---|---|---|---|---|---|---|---|

1 | 1000 | 2.323 | 2 | 2 | 0 | 8 | 19 | 100 |

2 | 1000 | 2.206 | 2 | 2 | 0 | 8 | 19 | 100 |

3 | 1000 | 2.233 | 2 | 2 | 0 | 8 | 19 | 100 |

4 | 1000 | 2.304 | 2 | 2 | 0 | 8 | 19 | 100 |

5 | 1000 | 2.243 | 2 | 1 | 0 | 8 | 19 | 100 |

6 | 1000 | 4.371 | 4 | 4 | 0 | 15 | 22 | 200 |

7 | 1000 | 4.27 | 4 | 4 | 0 | 12 | 22 | 200 |

8 | 1000 | 4.28 | 4 | 4 | 0 | 15 | 22 | 200 |

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**MDPI and ACS Style**

Hewitt, R.J.; Wenban-Smith, F.F.; Bates, M.R.
Detecting Associations between Archaeological Site Distributions and Landscape Features: A Monte Carlo Simulation Approach for the R Environment. *Geosciences* **2020**, *10*, 326.
https://doi.org/10.3390/geosciences10090326

**AMA Style**

Hewitt RJ, Wenban-Smith FF, Bates MR.
Detecting Associations between Archaeological Site Distributions and Landscape Features: A Monte Carlo Simulation Approach for the R Environment. *Geosciences*. 2020; 10(9):326.
https://doi.org/10.3390/geosciences10090326

**Chicago/Turabian Style**

Hewitt, Richard J., Francis F. Wenban-Smith, and Martin R. Bates.
2020. "Detecting Associations between Archaeological Site Distributions and Landscape Features: A Monte Carlo Simulation Approach for the R Environment" *Geosciences* 10, no. 9: 326.
https://doi.org/10.3390/geosciences10090326