# Integrating Point Process Models, Evolutionary Ecology and Traditional Knowledge Improves Landscape Archaeology—A Case from Southwest Madagascar

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Point Process Modeling for First-Order Properties

_{i}), the better the model. Stepwise selection determines the best fitting model by evaluating how each covariate affects the fit of the overall model and dropping covariates if they result in a higher AIC or BIC score [82].

#### 2.2. GIS Analysis

#### 2.3. Point Process Modeling for Second-Order Properties

## 3. Results

#### 3.1. Point Process Modeling of First-Order Properties

_{i}= 0.256 and ΔBIC = 0 and W

_{i}= 0.848. Table 3 shows the covariate estimates for PPM3.

#### 3.2. GIS Analysis

_{arch}= the archaeological probability value, Dpth

_{BR}= depth to bedrock, D

_{RO}= distance to rock outcrops, D

_{i}= distance to offshore islands, D

_{w}= distance to water/ocean, D

_{c}= distance to coral.

#### 3.3. Point Process Modeling of Second-Order Properties

_{i}of 1. The unweighted model with area interaction (PPM7) is worse at predicting archaeological patterns than PPM8, with ΔAIC and ΔBIC of >500 and W

_{i}of 0. Weighted Model 3 without area interaction (PPM5) performs substantially worse than PPM8, with ΔAIC and ΔBIC of >2300 and W

_{i}of 0. The residual K-function indicates that the best fitting model (PPM8) still underestimates second-order clustering at distances ≥ 1500 m (Figure 9).

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map of study region in southwest Madagascar. The region contains the Velondriake Marine Protected Area and has been increasingly documented by archaeologists over the past several years.

**Figure 2.**Illustration of iterative modeling process. This method permits for simultaneous and constant re-evaluation of the current predictive model and interpretation of the archaeological record.

**Figure 3.**

**Left**: shows the unweighted predictive raster without resampling depth to bedrock data from 150 m to 10 m.

**Right**: shows the results of the unweighted predictive raster after resampling depth to bedrock data from 150 m to 10 m. Resampling makes the results more easily interpretable and by extension, usable for archaeological survey.

**Figure 4.**First order intensity of archaeological deposits (per m

^{2}) as a function of different environmental variables using nonparametric smoothing (rho-hat test). Euclidian distance measurements were used for distance (m) calculations.

**Figure 5.**First order intensity of archaeological deposits (per m

^{2}) weighted by artifact counts as a function of different environmental variables using nonparametric smoothing (rho-hat test). Likewise to the unweighted rho-hat tests, bedrock, islands and rock outcrops have the highest absolute intensity values, while dunes and vegetation have the lowest.

**Figure 6.**Results of testing for second-order interaction using K-, G- and PC-functions compared to 39 simulated realizations of complete spatial randomness (CSR). Black line is the empirical function for archaeological deposits, the red-dashed lines is the theoretical expectation under the null model of CSR, the grey shaded region is the simulation envelope (equivalent to p = 0.05).

**Figure 7.**Map of raw and kernel-smoothed Pearson residual values of PPM3, PPM4 and PPM1. Note that the smoothed Pearson residuals for PPM3 and PPM4 contain more values of 0 (indicating a better fit), while PPM1 has more values greater than and less than 0, indicating more over- and under-fitting. Archaeological points are overlaid on top of the raw residual maps (black dots).

**Figure 8.**Results of the residual K- and G-function tests on PPM1 (the Davis et al. [49] model) and best fitted models PPM3 and PPM4. Both PPM3 and PPM4 perform better than the Davis et al. algorithm but still overestimate clustering between points at some distances.

**Figure 9.**Residual K-function test of the best-fitting unweighted PPM with an area interaction parameter and the best-fitting weighted PPM with an area interaction parameter. Both models performed better with area interaction than without and the weighted model yields the best results.

**Table 1.**List of different variables incorporated in Davis et al. [49] and the models developed in this paper.

Variable | Davis et al. [49] | This Study |
---|---|---|

Vegetative Productivity | Yes | Yes |

Coral Reefs | Yes | Yes |

Offshore Islands | Yes | Yes |

Distance to the Ocean | Yes | Yes |

Paleodunes | Yes | Yes |

Rocky outcrops | No | Yes |

Depth to bedrock | No | Yes |

**Table 2.**Results of comparing the different inhomogeneous Poisson point process models using ΔAIC, ΔBIC and their associated weights. PPM3 and PPM4 were the best fitting models according to stepwise model selection using Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC), respectively. We chose PPM3 (bold text) because it is the simpler of the two models PPM1 (italicized) represents the Davis et al. ([49]) model. Df = degrees of freedom; W

_{i}= information criterion weight value.

Model | Variables | Df | ΔAIC | W_{i} | ΔBIC | W_{i} |
---|---|---|---|---|---|---|

PPM3 | coral, water, islands, rocky shoreline, depth to bedrock | 6 | 1.13 | 0.256 | 0 | 0.848 |

PPM4 | vegetation, coral, water, islands, rocky shoreline, depth to bedrock | 7 | 0 | 0.452 | 3.55 | 0.143 |

PPM2 | vegetation, dunes, coral, water, islands, rocky shoreline, depth to bedrock | 8 | 0.88 | 0.292 | 9.12 | 0.009 |

PPM1 | vegetation, dunes, coral, water, islands | 6 | 3486.97 | 0 | 3485.84 | 0 |

PPM0 | Complete spatial randomness (Poisson Process) | 1 | 6074.78 | 0 | 6050.20 | 0 |

**Table 3.**Results of the chosen best fitting model (PPM3), including the parameter estimates and standard errors with a 95% confidence interval for each covariate. S.E. = standard error. CI95 = 95% confidence interval.

Estimate | S.E. | CI95 Low | CI95 Hi | Ztest | Zval | |
---|---|---|---|---|---|---|

Intercept | −10.3513 | 0.24798 | −10.8373 | −9.865255 | <0.0001 | −41.7427 |

Coral | −0.0118 | 0.00133 | −0.014358 | −0.0092 | <0.0001 | −8.8633 |

Water/Ocean | 0.0112 | 0.001354 | 0.008508 | 0.0138 | <0.0001 | 8.2433 |

Offshore Islands | 0.0043 | 0.000952 | 0.002429 | 0.0062 | <0.0001 | 4.5132 |

Rocky outcrops | −0.0004 | 0.000061 | −0.000504 | −0.0003 | <0.0001 | −6.3179 |

Depth to Bedrock | −0.0205 | 0.001075 | −0.022596 | −0.0184 | <0.0001 | −19.0557 |

**Table 4.**The formulas and respective covariate weights for each predictive model and the results of ground truthed results from the Davis et al. [49] study in relation to each modified algorithm. The best performing model (bolded) produces the most true positives and highest overall values in areas with confirmed archaeological deposits (Table 5). D

_{v}= distance to vegetation (measured by SAVI) and D

_{d}= distance to paleodunes.

Algorithm | Formula | True Positive (#) ^{1} | False Positive (#) ^{1} | # Artifacts (High Prob.) | #Artifacts (Medium Prob.) | # Artifacts (Low Prob.) |
---|---|---|---|---|---|---|

Davis et al. [49] | $\frac{1}{{\mathrm{D}}_{\mathrm{V}}+{\mathrm{D}}_{\mathrm{i}}+{\mathrm{D}}_{\mathrm{c}}+{\mathrm{D}}_{\mathrm{w}}+{\mathrm{D}}_{\mathrm{d}}}$ | 29 | 7 | 654 | 332 | 141 |

Unweighted Model | $\frac{1}{{\mathrm{Dpth}}_{\mathrm{BR}}+{\mathrm{D}}_{\mathrm{RO}}+{\mathrm{D}}_{\mathrm{i}}+{\mathrm{D}}_{\mathrm{c}}+{\mathrm{D}}_{\mathrm{W}}}$ | 28 | 3 | 886 | 102 | 160 |

Weighted Model 1 | $2.5\left(\frac{1}{{\mathrm{Dpth}}_{\mathrm{BR}}}\right)+2\left(\frac{1}{{\mathrm{D}}_{\mathrm{RO}}}\right)+2\left(\frac{1}{{\mathrm{D}}_{\mathrm{v}}}\right)+1.75\left(\frac{1}{{\mathrm{D}}_{\mathrm{i}}}\right)+1.75\left(\frac{1}{{\mathrm{D}}_{\mathrm{c}}}\right)+1\left(\frac{1}{{\mathrm{D}}_{\mathrm{w}}}\right)+1(\frac{1}{+{\mathrm{D}}_{\mathrm{d}}})$ | 31 | 7 | 955 | 144 | 49 |

Weighted Model 2 | $3\left(\frac{1}{{\mathrm{Dpth}}_{\mathrm{BR}}}\right)+2.5\left(\frac{1}{{\mathrm{D}}_{\mathrm{RO}}}\right)+2\left(\frac{1}{{\mathrm{D}}_{\mathrm{v}}}\right)+2\left(\frac{1}{{\mathrm{D}}_{\mathrm{c}}}\right)+1.75\left(\frac{1}{{\mathrm{D}}_{\mathrm{i}}}\right)+1\left(\frac{1}{{\mathrm{D}}_{\mathrm{w}}}\right)+1(\frac{1}{+{\mathrm{D}}_{\mathrm{d}}})$ | 23 | 2 | 813 | 136 | 199 |

Weighted Model 3 | $\mathbf{2.5}\left(\frac{\mathbf{1}}{{\mathrm{Dpth}}_{\mathrm{BR}}}\right)+\mathbf{2}\left(\frac{\mathbf{1}}{{D}_{\mathrm{RO}}}\right)+\mathbf{1.75}\left(\frac{\mathbf{1}}{{D}_{v}}\right)+\mathbf{1.5}\left(\frac{\mathbf{1}}{{D}_{i}}\right)+\mathbf{1.5}\left(\frac{\mathbf{1}}{{D}_{c}}\right)+\mathbf{1}\left(\frac{\mathbf{1}}{{D}_{w}}\right)+\mathbf{1}\left(\frac{\mathbf{1}}{+{\mathbf{D}}_{\mathbf{d}}}\right)$ | 32 | 7 | 957 | 138 | 53 |

Weighted Model 4 | $2.5\left(\frac{1}{{\mathrm{Dpth}}_{\mathrm{BR}}}\right)+2\left(\frac{1}{{\mathrm{D}}_{\mathrm{RO}}}\right)+1.75\left(\frac{1}{{\mathrm{D}}_{\mathrm{v}}}\right)+1.75\left(\frac{1}{+{\mathrm{D}}_{\mathrm{d}}}\right)+1.5\left(\frac{1}{{\mathrm{D}}_{\mathrm{i}}}\right)+1.5\left(\frac{1}{{\mathrm{D}}_{\mathrm{c}}}\right)+1\left(\frac{1}{{\mathrm{D}}_{\mathrm{w}}}\right)$ | 32 | 7 | 957 | 138 | 53 |

^{1}True and false positives are based on “high” probability values (i.e., where the algorithm expects the most material to be found). Medium and low probability values are not considered in these calculations (i.e., the algorithm expects that you might find material but you might not, thus it cannot be counted as a “true” positive or negative). Qualitative probability scores were derived from a natural breaks method [87] on the generated quantitative values.

**Table 5.**Descriptive statistical values for raster probability values at known archaeological deposit locations (n = 1030) for each created predictive model.

Model | Total Average | Median | Mode | Standard Error |
---|---|---|---|---|

Unweighted | 0.00924 | 0.00243 | 0.00038 | 0.00024 |

Weighted 1 | 0.04769 | 0.03150 | 0.01762 | 0.001486 |

Weighted 2 | 0.03182 | 0.01487 | 0.00106 | 0.000992 |

Weighted 3 | 0.04769 | 0.03150 | 0.01762 | 0.001486 |

Weighted 4 | 0.04467 | 0.03148 | 0.01762 | 0.001392 |

Weighted 5 | 0.02545 | 0.01189 | 0.00085 | 0.000793 |

**Table 6.**Results of comparing 6 PPMs using ΔAIC, ΔBIC and their associated weights. Four PPMs (5, 6, 7 and 8) are comprised of predictive rasters created in ArcGIS. The other 2 (PPM0 and PPM9) represent CSR and area interaction processes without environmental covariates. The weighted model with area interaction (a second-order property) performs better than all other models. Df = degrees of freedom; W

_{i}= information criterion weight value.

Model | Variables | Df | ΔAIC | W_{i} | ΔBIC | W_{i} |
---|---|---|---|---|---|---|

PPM8 | Area interaction, Weighted Model 3 * | 3 | 0 | 1 | 0 | 1 |

PPM7 | Area interaction, Unweighted Model ** | 3 | 507.96 | 0 | 508.12 | 0 |

PPM5 | Weighted Model 3 * | 2 | 2376.92 | 0 | 2371.23 | 0 |

PPM6 | Unweighted Model Raster ** | 2 | 3230.97 | 0 | 3225.28 | 0 |

PPM9 | Area interaction, CSR | 2 | 7632.29 | 0 | 7627.76 | 0 |

PPM0 | Complete Spatial Randomness (CSR) | 1 | 13,174.52 | 0 | 13,164.14 | 0 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Davis, D.S.; DiNapoli, R.J.; Douglass, K.
Integrating Point Process Models, Evolutionary Ecology and Traditional Knowledge Improves Landscape Archaeology—A Case from Southwest Madagascar. *Geosciences* **2020**, *10*, 287.
https://doi.org/10.3390/geosciences10080287

**AMA Style**

Davis DS, DiNapoli RJ, Douglass K.
Integrating Point Process Models, Evolutionary Ecology and Traditional Knowledge Improves Landscape Archaeology—A Case from Southwest Madagascar. *Geosciences*. 2020; 10(8):287.
https://doi.org/10.3390/geosciences10080287

**Chicago/Turabian Style**

Davis, Dylan S., Robert J. DiNapoli, and Kristina Douglass.
2020. "Integrating Point Process Models, Evolutionary Ecology and Traditional Knowledge Improves Landscape Archaeology—A Case from Southwest Madagascar" *Geosciences* 10, no. 8: 287.
https://doi.org/10.3390/geosciences10080287