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Supplementary Methods The following Zenodo repository contains all the necessary material to reproduce the results reported in the text: https://zenodo.org/doi/10.5281/zenodo.10061466. At a high level, the file resistance-resilience.RProj can be opened within RStudio to access and run the entire workflow. 1. Contents The Supplementary Information is organised into six main folders: data - radiocarbon date tables for 16 regions. scripts - R scripts for running Bayesian MCMC models, statistical modelling of results, and producing outputs. fits & output - the results of running the above scripts. figures & supplement – figures and tables produced for the main text and for the Extended Data. 2. Data Raw data for the MCMC analysis can be found in the data folder, comprising 18 tables (.csv format) of archaeological radiocarbon dates with accompanying metadata. 3. Analysis Bayesian MCMC Code for performing Bayesian Markov Chain Monte Carlo analysis on aggregated radiocarbon data (mcmc.R). Please note that, given the long processing time and memory requirements for each MCMC fit, the script contains code to reproduce a single example: Southeastern Norway. This is one of the smaller datasets (617 dates), and takes approximately ~6 hours to complete on an Intel(R) Core(TM) i5-9600 CPU @ 3.10GHz with 16 GB of DDR3 RAM. However, any of the 18 radiocarbon datasets can be substituted in this script and the parameters altered per Table S1 to obtain posteriors for any case study. The output folder contains the full results of the Bayesian MCMC analysis: MCMC diagnostics, parameters, posterior checks, and resistance-resilience metrics collected on each fit, including traceplots, Rhat, and ESS checks. Resistance-resilience metrics Code for the resmet() function is also contained in the mcmc.R file. resmet() is an adaptation of Edinborough et al.'s post-hoc statistical test for demographic events in written and oral history (https://doi.org/10.1073/pnas.1713012114). The inspiration for this function - p2pTest() in rcarbon - is for use with objects of class ‘SpdModelTest’. This function extends the principle to ‘spdppc’ objects. Following Riris and De Souza (ref. 12), Nimmo et al. (ref. 52), Cantarello et al. (ref. 53), and Van Meerbeek et al. (ref. 11), this will perform post-hoc tests for resistance and resilience on marks of an ‘spdppc’ object over all periods where SPDs are below growth model expectations ('downturns'). These two metrics are defined as the ability to absorb disturbances and "bounce back" following disturbances, respectively. They are normalised relative to the value of the SPD at the start of the interval of interest and fully described in the Methods section of the main text. The function outputs a data frame containing the value of both metrics, as well as the duration, end- and start-times of downturns, and the time to SPD minimum, all in calendar years Before Present. Parameter 'LD' (short for lag/duration) is the Time to SPD minimum normalised by the downturn duration - which we term 'Pace' in the main text. Raw results on individual posterior predictive checks can be found in the mcmc_metrics subfolder. resistance-resilience_metrics.csv contains the compiled, cleaned, and annotated dataset used in statistical modelling. Statistical Modelling Code for performing linear mixed-effect modelling on resistance-resilience metrics is contained in the statisticalmodelling.R file. It generates fitted models and diagnostics from the file resistance-resilience_metrics.csv. 4. Display items Figures and tables for the main paper text and the Materials & Methods can be found in the relevant sub-folders. The plotting.R script produces Figures 2-3 and Figures S1-7. Supplementary references 53. Nimmo, D.G., R. MacNally, S.C. Cunningham, A. Haslem, A.F. Bennett. Vive la résistance: reviving resistance for 21st century conservation. TREE 30, 516-23 (2015). https://doi.org/10.1016/j.tree.2015.07.008 54. Cantarello, E., A.C. Newton, P.A. Martin, P.M. Evans, A. Gosal, M.S. Lucash. Quantifying resilience of multiple ecosystem services and biodiversity in a temperate forest landscape. Ecol. Evol. 7, 9661-75. https://doi.org/10.1002/ece3.3491

The interest in testing different survey methods within the framework of the IPAAST project was motivated by three objectives: identifying evidence of rural life in the hinterland of the Roman colony of Augusta Emerita, with special attention to forms of resilience and diversification of agrarian activities beyond the areas of highest productivity of the alluvial plain of the Guadiana River. assessing the composition and depth of soils in the area in order to evaluate the representativeness of surface finds and perform a regression analysis to assess the potential distribution of arable lands in the area from Roman times to the present. combining geophysical methods commonly used in precision agriculture and archaeology in order to evaluate their interoperability and the complementary information they can provide. Attention was focused on a sector of the estate where two elements were coincident 1) preliminary evidence suggested the estate’s highest concentration of archaeological finds. 2) land plots within the estate used for grazing where LIFE Adapt experiments were undertaken. This area encompassed approximately. 6.5 ha. 2 geophysical methods for the exploration were used: Magnetic survey: a 2 sensors gradiometer system was used (Grad602 Bartington). Data sets: RC_MAG 01 Vector limits of survey area. 02 Vector point file of vertices of survey area. 03 Grid composite. 04 Raster interpolation of magnetic data. Electromagnetic induction with a EM38Mk2 by Geonics. Data sets: RC_EMI01. 01 Vector limits of survey area 02 Vector file of point data (raw data) 03 Raster interpolation of quad-phase (conductivity) 0,5m 04 Raster interpolation of quad-phase (conductivity) 1m 05 Raster interpolation of in-phase (magnetic susceptibility) 0,5m 06 Raster interpolation of in-phase (magnetic susceptibility) 1m RC_EMI02. 01 Vector limits of survey area 02 Vector file of point data 03 Raster interpolation of quad-phase (conductivity) 0,5m 04 Raster interpolation of quad-phase (conductivity) 1m 05 Raster interpolation of in-phase (magnetic susceptibility) 0,5m 06 Raster interpolation of in-phase (magnetic susceptibility) 1m

Abstract of presentation given at the CAA2023 conference, Amsterdam, 3-6 April 2023.

Supplementary information

Data and code version submitted to the journal. The dataset included here provides a collection of archaeological sites from three areas in modern Iraq (Haditha dam, Mosul dam, Hamrin dam). In addition, this repository provides reproducible analyses in the form R scripts, JavaScript code for Google Earth Engine and QGIS models.

These data were collected by Soyl Ltd as part of a commercial agricultural soil survey. They were reprocessed by the University of Ghent ipaast team.

JavaScript code used in the geospatial analysis searching for Paititi. The code, coupled with the provided data, allows studying the distribution of morphometric characteristics of terrain for specified point samples by making a chart and exporting the derived terrain products as GeoTiffs. In theory, it can bring insights on where to look for ancient settlements of Inca and other Andean cultures. You must run the code inside the Google Earth Engine, a free-to-use cloud computing platform for processing satellite imagery and other Earth observation data. It requires you to have a Google account and a related Earth Engine account. To successfully apply this code, you also need to have basic experience with coding and GIS. Please, read the README.md file for more details. Links Paititi Research Google Earth Engine GitHub Repository

This data provides the basis for the report titled "Ready for integrated sustainable agricultural land management? Are practitioners in archaeology and agriculture informed, willing, enabled, and motivated to change how they work with remote and near-surface sensing data to collaboratively address contemporary challenges in sustainable agricultural land management? " Data were collected in compliance with the University of Glasgow's Research Ethics Policy (Application #100200154). As stated in the Methods section of this report: "The participatory survey was conducted between May 2021 and October 2022. Location: The preponderance of stakeholders engaged with are professional practitioners or researchers based in the UK, Belgium, Italy, Cyprus, Spain and France. Sessions occurred remotely (online/phone), as well as on site, during workshops at the University of Glasgow, the Dalswinton Estate, Dumfries, and Manor Farm, Yedingham. Participants Selection: A sub-group of 51 high-level participants were selected from a greater network of 86 stakeholders who were engaged with during the ipaast project. Sector: Farmers, researchers, heritage managers, geophysicists, remote sensing specialists, statisticians, soil scientists, service providers, sensor developers, and data archivists, who all deal directly, or indirectly with datasets relating to the measurement of soil and/or plant properties (physical, chemical, microbial) were represented (Table 1) Expertise: Engagement with mid- to late- career specialists was prioritised, with many participants having over 20 years of experience and most having over 10 years of experience (including time during the PhD). Interview method Engagement with stakeholders was primarily through one-to-one interviews and structured workshop discussions, conducted either in person, or remotely over video conference or phone. In some instances, participants provided written input (see Table 2 summary). Follow-up interviews or written exchanges were used to clarify or continue discussions when required. A semi-structured approach to interviews and discussions was preferred, with a mix of general questions (see sample questions), as well as questions specifically tailored to the participants specialist background and experience. Sample Questions: What types of sensing data do you use/collect? Where/how do you access/collect these data? What are your main aims/applications in using or collecting these data? How often do you access/collect, or anticipate accessing/collecting, these data to be useful to you? What spatial resolution is necessary for these data to be useful to you? What, if anything, would encourage/discourage you from sharing your data? What kinds of additional data types or additional information (metadata) might help you to better understand and use data which you have previously collected or received? What do you see as the main impacts, if any, of ecosystem service frameworks and/or recent changes to rural/environmental regulations on your work? What attitudes to sensing data do you see from other stakeholders in rural affairs? Documentation: Where viable, interviews and workshop discussions were recorded and transcribed; alternatively, notes were made during engagement by either the interviewer and/or dedicated participant observers (e.g. at workshops). Where notes were used, specific quotes and summary reports were checked with the participants for accuracy. " Please see the linked report for details on the analysis and key findings.

Figure 3 The proposed workflow technology stack for the SDR.