## 2 Notes on the Theory, Method and Data
### A Simple Test Model: Strength of the Gravity Signal
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**No.**} & \multicolumn{1}{c}{**Site/Area \({}^{*}\)**} & \multicolumn{1}{c}{**Active \({}^{**}\) (BP)**} & \multicolumn{1}{c}{**Latitude \({}^{***}\) N**} & \multicolumn{1}{c}{**Longitude \({}^{**}\)**} & \multicolumn{1}{c}{**Height \({}^{*}\)**} & \multicolumn{1}{c}{**References**} \\ \hline
1 & El Adam Playa & 10,500–7300 \({}^{\text{a}}\) & \(22^{\circ}38^{\prime}32^{\circ}\) & \(30^{\prime}04^{\prime}46^{\prime\prime}\) & 175 & [29] \\ \hline
2 & Bargat El-Shab Playa &
\begin{tabular}{c} 10,500–7300 \({}^{\text{b}}\) \\ 7300–5500 \({}^{\text{c}}\) \\ \end{tabular} & \(22^{\circ}24^{\prime}14^{\prime\prime}\) & \(30^{\prime}37^{\prime}49^{\prime\prime}\) & 215 & [37; 38] \\ \hline
3 & Kiseiba (Pleistocene) \({}^{\text{c}}\) & 500,000–3000,000 \({}^{\text{a}}\) & \(22^{\circ}40^{\prime}40^{\prime\prime}\) & \(30^{\prime}59^{\prime}10^{\prime\prime}\) & 200 & [28] \\ \hline
4 & Kiseiba (Holocene) & 10,500–7300 \({}^{\text{a}}\) & \(22^{\circ}44^{\prime}49^{\prime\prime}\) & \(30^{\prime}2^{\prime}28^{\prime\prime}\) & \(<\)180 & [28; 29] \\ \hline
5 & El Baalad Playa & 10,500–7300 \({}^{\text{b}}\) & \(22^{\circ}44^{\prime}54^{\prime\prime}\) & \(30^{\prime}16^{\prime}20^{\prime\prime}\) & 175 & [29] \\ \hline
6 & El Gebal El Beid Playa & 10,500–7300 \({}^{\text{a}}\) & \(22^{\circ}51^{\prime}38^{\prime\prime}\) & \(30^{\prime}43^{\prime}25^{\prime\prime}\) & 160 & [27; 29] \\ \hline
7 & El Gebal El Feel Playa & 10,500–7300 \({}^{\text{a}}\) & \(22^{\circ}28^{\prime}35^{\prime\prime}\) & \(29^{\circ}55^{\prime}18^{\prime\prime}\) & 200 & [29] \\ \hline
8 & El Ghorab Playa &
\begin{tabular}{c} 10,500–7300 \({}^{\text{a}}\) \\ 7300–5500 \({}^{\text{a}}\) \\ \end{tabular} & \(22^{\circ}48^{\prime}38^{\prime\prime}\) & \(30^{\prime}13^{\prime}09^{\prime\prime}\) & 140 & [28; 29] \\ \hline
9 & El Kortein Playa & 10,500–7300 \({}^{\text{a}}\) & \(22^{\circ}41^{\prime}19^{\prime\prime}\) & \(30^{\prime}46^{\prime}15^{\prime\prime}\) & 175 & [27; 29] \\ \hline
10 & Gebel Nabta Playa &
\begin{tabular}{c} 10,500–7300 \({}^{\text{b}}\) \\ 7300–5500 \({}^{\text{c}}\) \\ \end{tabular} & \(22^{\circ}30^{\prime}49^{\prime\prime}\) & \(30^{\prime}39^{\prime}27^{\prime\prime}\) & 190 & [27; 29] \\ \hline
11 & Nabta Playa &
\begin{tabular}{c} 10,500–7300 \({}^{\text{f}}\) \\ 7300–5500 \({}^{\text{c}}\) \\ \end{tabular} & \(22^{\circ}31^{\prime}56^{\prime\prime}\) & \(30^{\prime}44^{\prime}58^{\prime\prime}\) & 175 & [27; 29] \\ \hline
12 & Ramlah Playa &
\begin{tabular}{c} 10,500–7300 \({}^{\text{f}}\) \\ 7300–5500 \({}^{\text{c}}\) \\ \end{tabular} & \(22^{\circ}41^{\prime}32^{\prime\prime}\) & \(30^{\prime}30^{\prime}04^{\prime\prime}\) & 140 & [39] \\ \hline \hline \end{tabular} \({}^{*}\)Usually, a playa (the flat-floored bottom of an undrained desert basin that becomes at times a shallow lake) with a cluster of archaeological localities along its edges or close to its center. \({}^{**}\) Two main periods of the Holocene occupation of the Eastern Sahara according to [24] (their figure 3b–d) and the previous study by [PERSON] et al. [4] with the earlier period overlapping with the Early (-500–7300 bp) and Middle (-7100–6600 bp) Nedilithic and the later with the Late (-6500–5800 bp) and Final (-5700–4500 bp) Nedilithic of the regional archaeological sequence [29]. \({}^{***}\) Geodetic coordinates from Google Earth in the international WGS 84, north latitude N, east longitude E, position of each playa preferred to that of the associated archaeological localities; presented up to arc-seconds, although this precision is not realistic. \({}^{*}\) rounded to 5 m, accounting for the real accuracy of the topographic models available (Section 2.4.2). _italics_ indicate heights estimated using Google Earth. asl (m) above (present) sea level in meters. \({}^{\text{c}}\) location on a small plateau ca. 20 m above surrounding terrain. \({}^{\text{a}}\) both earlier and later part of the Early Neolithic. \({}^{\text{b}}\) only later part of the Early Neolithic (the local climatic optimum). \({}^{\text{c}}\) both Late and Final Neolithic. \({}^{\text{d}}\) only Middle Neolithic. \({}^{\text{e}}\) only Late Neolithic. \({}^{\text{f}}\) both earlier and later part of the Early Neolithic and Middle Neolithic.  
\end{table}