# The impact of climate change on the agriculture and the economy of Southern Gaul: New perspectives of agent-based modelling

Nicolas Bernigaud, Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi, Laurent Bouby, Philippe Leveau, Loup Bernard, Delphine Isoardi

<figure><img src="image_1.png" /></figure>

## To cite this version:

Nicolas Bernigaud, Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi, et al.. The impact of climate change on the agriculture and the economy of Southern Gaul: New perspectives of agent-based modelling. PLoS ONE, 2024, 19 (3), pp.1-24. 10.1371/journal.pone.0298895. halshs-04530599

HAL Id: halshs-04530599

https://shs.hal.science/halshs-04530599

Submitted on 3 Apr 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
RESEARCH ARTICLE

# The impact of climate change on the agriculture and the economy of Southern Gaul: New perspectives of agent-based modelling

Nicolas Bernigaud<sup>1*</sup>, Alberte Bondeau<sup>2</sup>, Joël Guiot<sup>1</sup>, Frédérique Bertoncello<sup>3</sup>, Marie-Jeanne Ouriachi<sup>3</sup>, Laurent Bouby<sup>4</sup>, Philippe Leveau<sup>5</sup>, Loup Bernard<sup>6</sup>, Delphine Isoardi<sup>5</sup>

1. CNRS, IRD, INRA, Coll France, CEREGE, Aix-Marseille Université, Aix-en-Provence, France,
2. Institut Méditerranéen de Biodiversité et d'Écologie Marine et Continentale (IMBE), Aix-Marseille Université, CNRS, IRD, Avignon Université, Aix-en-Provence, France,
3. CNRS, CEPAM, Côte-d'Azur Université, Nice, France,
4. CNRS, Institut des Sciences de l'Evolution-Montpellier (ISEM), Montpellier Université, Montpellier, France,
5. CNRS, Centre Camille Julian (CCJ), Aix-Marseille Université, Aix-en-Provence, France,
6. CNRS, Archimède UMR, Strasbourg Université, Haute-Alsace Université, Strasbourg, France

* bernigaud.nico@orange.fr

<figure><img src="image_1.png" /></figure>

<figure><img src="image_2.png" /></figure>

OPEN ACCESS

**Citation:** Bernigaud N, Bondeau A, Guiot J, Bertoncello F, Ouriachi M-Jeanne, Bouby L, et al. (2024) The impact of climate change on the agriculture and the economy of Southern Gaul: New perspectives of agent-based modelling. PLoS ONE 19(3): e0298895. https://doi.org/10.1371/journal.pone.0298895

**Editor:** John P. Hart, New York State Museum, UNITED STATES

**Received:** March 6, 2023

**Accepted:** January 31, 2024

**Published:** March 27, 2024

**Peer Review History:** PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0298895

**Copyright:** © 2024 Bernigaud et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Data Availability Statement:** The Netlogo model ROMCLIM with the other files are available in

## Abstract

What impact did the Roman Climate Optimum (RCO) and the Late Antique Little Ice Age (LALIA) have on the rise and fall of the Roman Empire? Our article presents an agent-based modelling (ABM) approach developed to evaluate the impact of climate change on the profitability of vineyards, olive groves, and grain farms in Southern Gaul, which were the main source of wealth in the roman period. This ABM simulates an agroecosystem model which processes potential agricultural yield values from paleoclimatic data. The model calculates the revenues made by agricultural exploitations from the sale of crops whose annual volumes vary according to climate and market prices. The potential profits made by the different agricultural exploitations are calculated by deducting from the income the operating and transportation costs. We conclude that the warm and wet climate of the Roman period may have had an extremely beneficial effect on the profitability of wine and olive farms between the 2nd century BCE and the 3rd century CE, but a more modest effect on grain production. Subsequently, there is a significant decrease in the potential profitability of farms during the Late Antique Little Ice Age (4th-7th century CE). Comparing the results of our model with archaeological data enables us to discuss the impact of these climatic fluctuations on the agricultural and economic growth, and then their subsequent recession in Southern Gaul from the beginning to the end of antiquity.

## Introduction

The evidence of a warming climate between the 3rd century BCE and the 2nd century CE based on various continental and oceanic paleoclimate proxies [1–3] has led to questions about its
RESEARCH ARTICLE

# The impact of climate change on the agriculture and the economy of Southern Gaul: New perspectives of agent-based modelling

Nicolas Bernigaud<sup>1*</sup>, Alberte Bondeau<sup>2</sup>, Joël Guiot<sup>1</sup>, Frédérique Bertoncello<sup>3</sup>, Marie-Jeanne Ouriachi<sup>3</sup>, Laurent Bouby<sup>4</sup>, Philippe Leveau<sup>5</sup>, Loup Bernard<sup>6</sup>, Delphine Isoardi<sup>5</sup>

1. CNRS, IRD, INRA, Coll France, CEREGE, Aix-Marseille Université, Aix-en-Provence, France,
2. Institut Méditerranéen de Biodiversité et d'Écologie Marine et Continentale (IMBE), Aix-Marseille Université, CNRS, IRD, Avignon Université, Aix-en-Provence, France,
3. CNRS, CEPAM, Côte-d'Azur Université, Nice, France,
4. CNRS, Institut des Sciences de l'Evolution-Montpellier (ISEM), Montpellier Université, Montpellier, France,
5. CNRS, Centre Camille Julian (CCJ), Aix-Marseille Université, Aix-en-Provence, France,
6. CNRS, Archimède UMR, Strasbourg Université, Haute-Alsace Université, Strasbourg, France

* bernigaud.nico@orange.fr

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

OPEN ACCESS

**Citation:** Bernigaud N, Bondeau A, Guiot J, Bertoncello F, Ouriachi M-Jeanne, Bouby L, et al. (2024) The impact of climate change on the agriculture and the economy of Southern Gaul: New perspectives of agent-based modelling. PLoS ONE 19(3): e0298895. https://doi.org/10.1371/journal.pone.0298895

**Editor:** John P. Hart, New York State Museum, UNITED STATES

**Received:** March 6, 2023

**Accepted:** January 31, 2024

**Published:** March 27, 2024

**Peer Review History:** PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0298895

**Copyright:** © 2024 Bernigaud et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

**Data Availability Statement:** The Netlogo model ROMCLIM with the other files are available in

## Abstract

What impact did the Roman Climate Optimum (RCO) and the Late Antique Little Ice Age (LALIA) have on the rise and fall of the Roman Empire? Our article presents an agent-based modelling (ABM) approach developed to evaluate the impact of climate change on the profitability of vineyards, olive groves, and grain farms in Southern Gaul, which were the main source of wealth in the roman period. This ABM simulates an agroecosystem model which processes potential agricultural yield values from paleoclimatic data. The model calculates the revenues made by agricultural exploitations from the sale of crops whose annual volumes vary according to climate and market prices. The potential profits made by the different agricultural exploitations are calculated by deducting from the income the operating and transportation costs. We conclude that the warm and wet climate of the Roman period may have had an extremely beneficial effect on the profitability of wine and olive farms between the 2nd century BCE and the 3rd century CE, but a more modest effect on grain production. Subsequently, there is a significant decrease in the potential profitability of farms during the Late Antique Little Ice Age (4th-7th century CE). Comparing the results of our model with archaeological data enables us to discuss the impact of these climatic fluctuations on the agricultural and economic growth, and then their subsequent recession in Southern Gaul from the beginning to the end of antiquity.

## Introduction

The evidence of a warming climate between the 3rd century BCE and the 2nd century CE based on various continental and oceanic paleoclimate proxies [1–3] has led to questions about its
GitHub https://github.com/Bernigaud2021/ROMCLIM

**Funding:** JG and his team has received funding from Excellence Initiative of Aix-498 Marseille University - A*MIDEX, a French "Investissements d'Avenir" programme, through the 499 RDMed project and Labex OT-Med project (project ANR-11- LABEX-0061). This work was also supported by the ANR Project MICA (dir. L. Bouby & N. Bernigaud), funded by the French National Research Agency (Agence Nationale de la Recherche) [grant number ANR-22-CE27-0026]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

**Competing interests:** The authors have declared that no competing interests exist.

impact on ancient societies. While the beneficial role of this Roman Climate Optimum (RCO) on agriculture in the Roman Empire has recently been evoked, as well as the negative effect of the Late Antique Little Ice Age [4], it is still difficult to measure with certainty the effects of these climatic fluctuations on agricultural yields and the economy based on textual and archaeological sources alone, which are often very scanty and incomplete or difficult to interpret [5].

The application of agent-based model to archaeology, which provides a new exploratory tool, now makes it possible to overcome these difficulties. It is indeed possible to test multiple hypotheses on the interactions between societies and their environment, independently of the quantity or quality of the data available. In archaeology, this type of modelling has been used for some years to deal with questions related to the demography of ancient societies, agricultural strategies, carrying capacity, and settlement dynamics (details in I, 4).

In this paper, we present our agent-based model, ROMCLIM, which we designed to test the impact of climatic changes between the Iron Age and late antiquity (6th century BCE - 7th century CE) on the potential profitability of farms in Southern Gaul. But this model is also a tool with predictive ability for reconstructing the geography of crops, still partially known by archaeological data. One of the interests of ROMCLIM is to emulate and simplify a complex agro-ecosystemic model (LPJmL) to simulate impact of climate change on crops, which is an important point to understand relationship between climate and ancient societies. The geographical area considered corresponds to most of the ancient Roman province of Gallia Narbonensis, which covered Provence and Languedoc, as well as the middle Rhone valley.

The model can simulate the profits of different types of farms by calculating the average potential agricultural yields for vines, olives, and cereals (wheat/barley), which were the most cultivated crops as of the Roman period. This "Mediterranean triad" was indeed the foundation of agriculture and food in most of the Roman Empire, and therefore its primary source of wealth.

## The study area

The study area corresponds to most of the province of Gallia Narbonensis, conquered by Rome in the 120s BC. Located in Southern France, this area (41°52' N-44°55' N latitude, 2°21' E-7°12' E longitude) encompasses all or part of the current administrative regions of Occitanie, Provence-Alpes-Côte-d'Azur (PACA) and Auvergne-Rhône-Alpes. It is limited to the longitude of Antibes to the east, that of Toulouse to the west and the latitude of Valence to the north. From a geomorphological point of view, this area surrounded by the Alps, the Massif Central and the eastern part of the Pyrenees, is formed by coastal plains and hilly and mountainous hinterland. The Rhone Valley and its delta separate to the west and east the historical regions of Languedoc and Provence.

The Mediterranean climate of this area is characterized by significant annual sunshine (2500-2900 hours/year), high summer temperatures and a low number of frost days (0-40), compared to the rest of France. Precipitation is low in the coastal plains (500-600 mm/year), but much more abundant in the mountain ranges, especially the Cèvennes (1200-1700 mm/year) which receive very intense rainfall in autumn (Fig 1).

## State of the art

### Agricultural production according to historical and archaeological sources

**Vine and olive tree.** According to the Gallo-Roman historian Pompey Trogue, the Greeks taught the Gallic to cultivate vines and olive trees (Justin, *Epitoma historiarum Philippicarum Pompei Trogi*, XLIII, 4, 2). Viticulture was probably introduced to Gaul by the Greeks after the foundation of Marseilles around 600 BCE, as evidenced by the discovery of vine planting pits
GitHub https://github.com/Bernigaud2021/ROMCLIM

**Funding:** JG and his team has received funding from Excellence Initiative of Aix-498 Marseille University - A*MIDEX, a French "Investissements d'Avenir" programme, through the 499 RDMed project and Labex OT-Med project (project ANR-11-LABEX-0061). This work was also supported by the ANR Project MICA (dir. L. Bouby & N. Bernigaud), funded by the French National Research Agency (Agence Nationale de la Recherche) [grant number ANR-22-CE27-0026]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

**Competing interests:** The authors have declared that no competing interests exist.

impact on ancient societies. While the beneficial role of this Roman Climate Optimum (RCO) on agriculture in the Roman Empire has recently been evoked, as well as the negative effect of the Late Antique Little Ice Age [4], it is still difficult to measure with certainty the effects of these climatic fluctuations on agricultural yields and the economy based on textual and archaeological sources alone, which are often very scanty and incomplete or difficult to interpret [5].

The application of agent-based model to archaeology, which provides a new exploratory tool, now makes it possible to overcome these difficulties. It is indeed possible to test multiple hypotheses on the interactions between societies and their environment, independently of the quantity or quality of the data available. In archaeology, this type of modelling has been used for some years to deal with questions related to the demography of ancient societies, agricultural strategies, carrying capacity, and settlement dynamics (details in I, 4).

In this paper, we present our agent-based model, ROMCLIM, which we designed to test the impact of climatic changes between the Iron Age and late antiquity (6th century BCE - 7th century CE) on the potential profitability of farms in Southern Gaul. But this model is also a tool with predictive ability for reconstructing the geography of crops, still partially known by archaeological data. One of the interests of ROMCLIM is to emulate and simplify a complex agro-ecosystemic model (LPJmL) to simulate impact of climate change on crops, which is an important point to understand relationship between climate and ancient societies. The geographical area considered corresponds to most of the ancient Roman province of Gallia Narbonensis, which covered Provence and Languedoc, as well as the middle Rhone valley.

The model can simulate the profits of different types of farms by calculating the average potential agricultural yields for vines, olives, and cereals (wheat/barley), which were the most cultivated crops as of the Roman period. This "Mediterranean triad" was indeed the foundation of agriculture and food in most of the Roman Empire, and therefore its primary source of wealth.

## The study area

The study area corresponds to most of the province of Gallia Narbonensis, conquered by Rome in the 120s BC. Located in Southern France, this area (41°52' N-44°55' N latitude, 2°21' E-7°12' E longitude) encompasses all or part of the current administrative regions of Occitanie, Provence-Alpes-Côte-d'Azur (PACA) and Auvergne-Rhône-Alpes. It is limited to the longitude of Antibes to the east, that of Toulouse to the west and the latitude of Valence to the north. From a geomorphological point of view, this area surrounded by the Alps, the Massif Central and the eastern part of the Pyrenees, is formed by coastal plains and hilly and mountainous hinterland. The Rhone Valley and its delta separate to the west and east the historical regions of Languedoc and Provence.

The Mediterranean climate of this area is characterized by significant annual sunshine (2500-2900 hours/year), high summer temperatures and a low number of frost days (0-40), compared to the rest of France. Precipitation is low in the coastal plains (500-600 mm/year), but much more abundant in the mountain ranges, especially the Cèvennes (1200-1700 mm/year) which receive very intense rainfall in autumn (Fig 1).

## State of the art

### Agricultural production according to historical and archaeological sources

**Vine and olive tree.** According to the Gallo-Roman historian Pompey Trogue, the Greeks taught the Gallic to cultivate vines and olive trees (Justin, *Epitoma historiarum Philippicarum Pompei Trogi*, XLIII, 4, 2). Viticulture was probably introduced to Gaul by the Greeks after the foundation of Marseilles around 600 BCE, as evidenced by the discovery of vine planting pits
<figure><img src="image_3.png" /><figcaption>Fig 1. Location of the study area, physical and climate maps. Annual rainfall and temperature maps were processed with data extracted from ALADIN Model.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g001

on the territory of the Phocean colony [6]. During the Iron Age, Marseille wine was sold in Southern Gaul, as indicated by the discoveries of Massaliot amphorae that contained this wine [7]. Other Etruscan and Greek *emporia* along the Mediterranean coast have certainly also developed viticulture locally. In the protohistoric agglomeration of *Lattara*-Lattes (Hérault) carpological studies and biochemical analyses clearly attest to its intensification from the 3rd century BCE [8, 9]. Despite an importance that appears less and less negligible, this protohistoric viticulture seems to have remained confined during the Iron Age to the Mediterranean coastal strip. The volume of production was obviously insufficient to satisfy the consumption of the rest of Gaul where Italic wine was consumed (as indicated by the discoveries of amphorae of the Dressel 1 type).

After the Roman conquest, viticulture in Gaul experienced a gradual intensification from the 1st century BCE. At the beginning of our era the Greek geographer Strabo (*Geography*, IV, I, 2) described the landscape of this province as like that of Italy because of its crops: vineyards, olive trees and fig trees flourished as far as the Cevennes, before becoming scarce beyond this limit. Archaeological investigations have largely confirmed the importance of viticulture in Languedoc and Provence, as evidenced by the discovery of the remains of wine-growing establishments, wine amphorae workshops, winegrowers' tools, and grape seeds [10–14] (Fig 2).
<figure><img src="image_5.png" /><figcaption>**Fig 1.** Location of the study area, physical and climate maps. Annual rainfall and temperature maps were processed with data extracted from ALADIN Model.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g001

on the territory of the Phocean colony [6]. During the Iron Age, Marseille wine was sold in Southern Gaul, as indicated by the discoveries of Massaliot amphorae that contained this wine [7]. Other Etruscan and Greek *emporia* along the Mediterranean coast have certainly also developed viticulture locally. In the protohistoric agglomeration of *Lattara*-Lattes (Hérault) carpological studies and biochemical analyses clearly attest to its intensification from the 3rd century BCE [8, 9]. Despite an importance that appears less and less negligible, this protohistoric viticulture seems to have remained confined during the Iron Age to the Mediterranean coastal strip. The volume of production was obviously insufficient to satisfy the consumption of the rest of Gaul where Italic wine was consumed (as indicated by the discoveries of amphorae of the Dressel 1 type).

After the Roman conquest, viticulture in Gaul experienced a gradual intensification from the 1st century BCE. At the beginning of our era the Greek geographer Strabo (*Geography*, IV, I, 2) described the landscape of this province as like that of Italy because of its crops: vineyards, olive trees and fig trees flourished as far as the Cevennes, before becoming scarce beyond this limit. Archaeological investigations have largely confirmed the importance of viticulture in Languedoc and Provence, as evidenced by the discovery of the remains of wine-growing establishments, wine amphorae workshops, winegrowers' tools, and grape seeds [10–14] (Fig 2).
<figure><img src="image_4.png" /><figcaption>Fig 2. Map of archaeological data referring to wine and olive oil production in late iron age and roman period (data mainly extracted from Garcia 1992 and Brun 2005).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g002

After reaching its climax in the 2nd century CE, it began to decline in Narbonne from the 3rd century CE but nevertheless continued to spread throughout Gaul [13], as we recently published a paper on this topic with numerous archaeological data [15].

Regarding olive growing, palynological and carpological studies also place towards the end of the 3rd century CE its development in Provence [16, 17]. At the beginning of our era, Strabo evoked his presence in the region of Marseilles (Geography, IV, I, 5) and more broadly in Gallia Narbonensis, as already mentioned. In the 1980s, the first regional archaeological syntheses identified in Provence and Languedoc presses and millstones linked to an olive activity of some importance [13, 18, 19]. However, this interpretation has since been questioned. It was objected that these installations and tools could also have been used to press grapes for viticulture. On the other hand, the strong representation of Betic amphorae on the Gallo-Roman sites of Southern Gaul indicates that olive oil was consumed there, produced in the south of the Iberian Peninsula. These observations therefore led to the conclusion that the importance of ancient olive growing in Narbonne should now be seriously revised downwards [13, 20]. It is now even considered that it should have been of little importance, but the question is not definitively settled. Recently, carpological and anthracological analyses have revealed in Rousillon the existence of olive growing during the High Empire [21]. The progress of
<figure><img src="image_6.png" /><figcaption>Fig 2. Map of archaeological data referring to wine and olive oil production in late iron age and roman period (data mainly extracted from Garcia 1992 and Brun 2005).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g002

After reaching its climax in the 2nd century CE, it began to decline in Narbonne from the 3rd century CE but nevertheless continued to spread throughout Gaul [13], as we recently published a paper on this topic with numerous archaeological data [15].

Regarding olive growing, palynological and carpological studies also place towards the end of the 3rd century CE its development in Provence [16, 17]. At the beginning of our era, Strabo evoked his presence in the region of Marseilles (Geography, IV, I, 5) and more broadly in Gallia Narbonensis, as already mentioned. In the 1980s, the first regional archaeological syntheses identified in Provence and Languedoc presses and millstones linked to an olive activity of some importance [13, 18, 19]. However, this interpretation has since been questioned. It was objected that these installations and tools could also have been used to press grapes for viticulture. On the other hand, the strong representation of Betic amphorae on the Gallo-Roman sites of Southern Gaul indicates that olive oil was consumed there, produced in the south of the Iberian Peninsula. These observations therefore led to the conclusion that the importance of ancient olive growing in Narbonne should now be seriously revised downwards [13, 20]. It is now even considered that it should have been of little importance, but the question is not definitively settled. Recently, carpological and anthracological analyses have revealed in Rousillon the existence of olive growing during the High Empire [21]. The progress of
archaeobotanical studies will undoubtedly lead in the future to reassess (based on less questionable data than those of press installations) its importance in Southern Gaul.

**Grain cultivation.** During the Iron Age, the cultivation of cereals and pulses ensured food production throughout Gaul. Carpological studies have determined that clothed barley was the most important crop. Different varieties of millets and wheats were also grown, such as einkorn, emmer but especially naked wheat, the cultivation of which took on increasing importance during the Second Iron Age [22, 23]. This phenomenon is perhaps related to the probable development of a commercial cereal crop intended to supply the Greek city of Marseilles, whose arid territory was rather suitable for the cultivation of vines and olive trees. Southern Gallic and Phoceans would then have exchanged cereals for wine [24, 25].

In the Gallo-Roman period, the importance of cereal cultivation in Narbonne is still difficult to determine compared to other crops. First, written sources provide little information on this subject. An inscription painted on a small amphora formerly discovered in the port of Marseilles provides, for example, the very punctual testimony of a cargo of barley imported into the Phocean city from the country of Cavares (current department of Vaucluse) [26]. Carpological studies—still few on sites from the Roman period—highlight among the various cereals cultivated, the preponderance of barley and naked wheat, already cultivated before the Roman conquest [23, 27]. Finally, although archaeological investigations conclude that viticulture is omnipresent in Gallia Narbonensis [28], discoveries of Gallo-Roman structures linked to cereal production (granaries, silos, mills, etc.) are still rare [29]. This observation raises the question of whether there is an archaeological bias or whether cereal cultivation had really lost importance in the Roman period, to the benefit of viticulture.

**What rural economy in roman times in Southern Gaul? Autarkic or trade-oriented agriculture?**

The ROMCLIM model presented in this article makes it possible to explore the hypothesis of commercial agriculture spread over the entire study area, but this vision of the rural economy is not shared by all historians and archaeologists. Did the estates of Southern Gaul practice an autarkic agriculture or were they turned towards commercial production? Although the vision of an ancient autarkic economy outlined by the American historian Finley [30] has long been challenged by eminent historians of Roman economics [31–35], Gallo-Roman villae of Southern Gaul (and elsewhere) are still often presented today as areas where polyculture was practiced primarily for the consumption of farmers [36, 37]. Main authors still hesitate to see in these villae rural estates turned towards commercial monocultures, although excavations have revealed in recent decades the existence of large and small vineyards in Languedoc, Provence, and the middle Rhone Valley [10–13, 38, 39].

If the vision of an autarkic Gallo-Roman agriculture is still prominent in the historical and archaeological literature, recent syntheses nevertheless highlight the links between rural settlements and markets throughout the Roman Empire [40–42]. The Latin agronomic treatises also unambiguously describe in Italy rentier's farms clearly specialized in certain types of crops, such as olive grove and winery, of which Cato (De Re Rustica, X-XI) gives for example in the 2nd century BCE a particularly detailed description.

We postulate that agricultural establishments of the Gallo-Roman period practiced cash crops in addition to those intended for food crops. Nevertheless, we consider that the importance given to cash crops should be very variable from a geographical point of view. More was probably grown for markets in the areas closest to the cities than in those furthest from them, on the margins of the ancient cities.
archaeobotanical studies will undoubtedly lead in the future to reassess (based on less questionable data than those of press installations) its importance in Southern Gaul.

**Grain cultivation.** During the Iron Age, the cultivation of cereals and pulses ensured food production throughout Gaul. Carpological studies have determined that clothed barley was the most important crop. Different varieties of millets and wheats were also grown, such as einkorn, emmer but especially naked wheat, the cultivation of which took on increasing importance during the Second Iron Age [22, 23]. This phenomenon is perhaps related to the probable development of a commercial cereal crop intended to supply the Greek city of Marseilles, whose arid territory was rather suitable for the cultivation of vines and olive trees. Southern Gallic and Phoceans would then have exchanged cereals for wine [24, 25].

In the Gallo-Roman period, the importance of cereal cultivation in Narbonne is still difficult to determine compared to other crops. First, written sources provide little information on this subject. An inscription painted on a small amphora formerly discovered in the port of Marseilles provides, for example, the very punctual testimony of a cargo of barley imported into the Phocean city from the country of Cavares (current department of Vaucluse) [26]. Carpological studies—still few on sites from the Roman period—highlight among the various cereals cultivated, the preponderance of barley and naked wheat, already cultivated before the Roman conquest [23, 27]. Finally, although archaeological investigations conclude that viticulture is omnipresent in Gallia Narbonensis [28], discoveries of Gallo-Roman structures linked to cereal production (granaries, silos, mills, etc.) are still rare [29]. This observation raises the question of whether there is an archaeological bias or whether cereal cultivation had really lost importance in the Roman period, to the benefit of viticulture.

**What rural economy in roman times in Southern Gaul? Autarkic or trade-oriented agriculture?**

The ROMCLIM model presented in this article makes it possible to explore the hypothesis of commercial agriculture spread over the entire study area, but this vision of the rural economy is not shared by all historians and archaeologists. Did the estates of Southern Gaul practice an autarkic agriculture or were they turned towards commercial production? Although the vision of an ancient autarkic economy outlined by the American historian Finley [30] has long been challenged by eminent historians of Roman economics [31–35], Gallo-Roman villae of Southern Gaul (and elsewhere) are still often presented today as areas where polyculture was practiced primarily for the consumption of farmers [36, 37]. Main authors still hesitate to see in these villae rural estates turned towards commercial monocultures, although excavations have revealed in recent decades the existence of large and small vineyards in Languedoc, Provence, and the middle Rhone Valley [10–13, 38, 39].

If the vision of an autarkic Gallo-Roman agriculture is still prominent in the historical and archaeological literature, recent syntheses nevertheless highlight the links between rural settlements and markets throughout the Roman Empire [40–42]. The Latin agronomic treatises also unambiguously describe in Italy rentier's farms clearly specialized in certain types of crops, such as olive grove and winery, of which Cato (De Re Rustica, X-XI) gives for example in the 2nd century BCE a particularly detailed description.

We postulate that agricultural establishments of the Gallo-Roman period practiced cash crops in addition to those intended for food crops. Nevertheless, we consider that the importance given to cash crops should be very variable from a geographical point of view. More was probably grown for markets in the areas closest to the cities than in those furthest from them, on the margins of the ancient cities.
In ROMCLIM, we did not try to model agricultural production intended to feed farmers, except in the case of cereal farms where part of the production is consumed on site. While we have no doubt that establishments oriented towards viticulture or olive growing also practiced cereal cultivation to feed farmers, we deliberately limited ourselves to modelling production intended for trade. This choice is explained by the desire to deal solely with the question of the impact of climatic variations on the Roman economy, whose main income was derived from the sale of agricultural products. Consequently, we did not try to consider productions that were not intended to be sold, even if these were of course very important for the food of the populations.

## Impact of climate variation on roman agriculture and economy: The Roman Climate Optimum (RCO) and the Late Antique Little Ice Age (LALIA)

Around the 2nd century BCE, both Latin agronomists Saserna evoked a climate change that would have made it possible to gain for the cultivation of the vine and the olive tree areas of altitude previously too cold (probably in the Apennines) to be able to practice these crops (passage quoted in Columella, *De Re Rustica*, I, 1). The reality of this significant global warming, now called the Roman Climate Optimum (RCO) or Roman Warm Period (RWP) has been highlighted by several paleoclimatic studies [2, 3]. This would have occurred as early as the middle of the 3rd century BCE and may have been particularly important. According to the results of isotopic studies carried out on sedimentary cores, the temperatures of the surface waters of the Mediterranean would have been even during the Roman period 2°C higher than the current one [1]. The precise end of this period of climatic optimum is variably estimated between the 2nd century CE and the 4th century CE according to studies [1–3], before the beginning of the cooling of the Late Antique Little Ice Age (LALIA), paroxysmal in the 6th and 7th centuries CE [43].

Today, we wonder about the impact of these major climatic fluctuations on the societies of antiquity. In a recent book, American historian K. Harper recently argued that the RCO could have been a particularly favourable factor in the economic development of the Roman Empire during the High Empire [4]. On the other hand, it is considered that global cooling may have played a major role in the transformations of agriculture [44, 45] and the many historical and cultural upheavals of late antiquity and early Middle Ages [43].

## Agent-based modelling, archaeology and climate change

Appearing in the 1990s, simulation by agent-based modelling (ABM) is gradually gaining ground in the humanities and social sciences. ABMs are based on the programming of behavioural rules assigned to individual entities (or groups of entities) whose interactions at a micro-scale produce "emergent" phenomena at a higher level of organization (macroscopic scale). Described as a bottom-up approach, agent-based modelling is now used in various fields of fundamental and applied research, including environmental sciences, biology, human sciences (geography, sociology, archaeology), economics and other disciplines interested in the study of human and animal behaviour [46].

Presented by Tim Kohler as a "third way" for archaeology [47], agent-based modelling and the use of simulation began to develop in the 1990s in the social sciences [48]. In the United States, the disciplinary porosity between ecology and the humanities (*Human Ecology*) facilitated the transfer of this approach from one disciplinary field to another. The use of simulation for the study of the behaviour of animal societies has given archaeologists the idea of using it to form virtual human societies [49]. Models that have become iconic, such as SUGARSCAPE
In ROMCLIM, we did not try to model agricultural production intended to feed farmers, except in the case of cereal farms where part of the production is consumed on site. While we have no doubt that establishments oriented towards viticulture or olive growing also practiced cereal cultivation to feed farmers, we deliberately limited ourselves to modelling production intended for trade. This choice is explained by the desire to deal solely with the question of the impact of climatic variations on the Roman economy, whose main income was derived from the sale of agricultural products. Consequently, we did not try to consider productions that were not intended to be sold, even if these were of course very important for the food of the populations.

## Impact of climate variation on roman agriculture and economy: The Roman Climate Optimum (RCO) and the Late Antique Little Ice Age (LALIA)

Around the 2nd century BCE, both Latin agronomists Saserna evoked a climate change that would have made it possible to gain for the cultivation of the vine and the olive tree areas of altitude previously too cold (probably in the Apennines) to be able to practice these crops (passage quoted in Columella, *De Re Rustica*, I, 1). The reality of this significant global warming, now called the Roman Climate Optimum (RCO) or Roman Warm Period (RWP) has been highlighted by several paleoclimatic studies [2, 3]. This would have occurred as early as the middle of the 3rd century BCE and may have been particularly important. According to the results of isotopic studies carried out on sedimentary cores, the temperatures of the surface waters of the Mediterranean would have been even during the Roman period 2°C higher than the current one [1]. The precise end of this period of climatic optimum is variably estimated between the 2nd century CE and the 4th century CE according to studies [1–3], before the beginning of the cooling of the Late Antique Little Ice Age (LALIA), paroxysmal in the 6th and 7th centuries CE [43].

Today, we wonder about the impact of these major climatic fluctuations on the societies of antiquity. In a recent book, American historian K. Harper recently argued that the RCO could have been a particularly favourable factor in the economic development of the Roman Empire during the High Empire [4]. On the other hand, it is considered that global cooling may have played a major role in the transformations of agriculture [44, 45] and the many historical and cultural upheavals of late antiquity and early Middle Ages [43].

## Agent-based modelling, archaeology and climate change

Appearing in the 1990s, simulation by agent-based modelling (ABM) is gradually gaining ground in the humanities and social sciences. ABMs are based on the programming of behavioural rules assigned to individual entities (or groups of entities) whose interactions at a micro-scale produce "emergent" phenomena at a higher level of organization (macroscopic scale). Described as a bottom-up approach, agent-based modelling is now used in various fields of fundamental and applied research, including environmental sciences, biology, human sciences (geography, sociology, archaeology), economics and other disciplines interested in the study of human and animal behaviour [46].

Presented by Tim Kohler as a "third way" for archaeology [47], agent-based modelling and the use of simulation began to develop in the 1990s in the social sciences [48]. In the United States, the disciplinary porosity between ecology and the humanities (*Human Ecology*) facilitated the transfer of this approach from one disciplinary field to another. The use of simulation for the study of the behaviour of animal societies has given archaeologists the idea of using it to form virtual human societies [49]. Models that have become iconic, such as SUGARSCAPE
[50] and ARTIFICIAL ANASAZIS [51, 52] continue to be a source of inspiration in the world of SMAs for more than twenty years.

Over the past ten years, the growing number of pedagogical manuals presenting the principles and expectations of agent-based modelling [53–56] testifies to the strongest interest in this approach in various disciplines [57]. We would like to mention a first book more specifically intended for archaeologists [58], recently published by the *Santa Fe Institute*, which promotes the use of agent-based systems in the field of social sciences and complexity from the United States.

The ability to simulate phenomena produced by interactions between entities and their environment makes ABMs particularly well suited to the study of socio-natural interactions [59]. Also, most Anglo-Saxon archaeological models are part of this paradigm to study the trajectory of ancient societies in relation to their environment, particularly on the American continent (Pueblo, Anasazi, Mayan Indians, ...) [47, 51, 60] and in the Middle East [61]. These models are mostly devoted to a population and its territory in the prehistoric and protohistoric periods. Other rare projects are part of the long-term perspective. This is particularly the case of Medland (Mediterranean Landscape Dynamics), which focuses on the study of society-environment interactions and their impacts on landscape transformations in the Mediterranean, from the Pleistocene to the middle of the Holocene [62].

Despite the early interest of European archaeologists in agent-based models, their concrete use is not detectable in the literature until the end of the 2000s. Early models were variously developed to study salt mining in the Austrian Hallstatt mines in the Bronze Age [63], Ethno-genesis of Patagonian hunter-gatherer societies [64] or demographics, carrying capacity and the agricultural strategies of late Iron Age Celtic societies in the Czech Republic [65–68]. In France, the ANR Obresoc project (2010–2015) stimulated the design of several models to study the diffusion of Early Neolithic agriculture in Western Europe from the Near East and the Balkans [69–71].

While they were initially of interest to prehistorians and protohistorians, ABMs have also been considered in recent years with increasing interest by historians and archaeologists of antiquity in the countries of Northern Europe (Netherlands, Denmark, and England) [72, 73]. Models were thus developed in the field of Roman studies such as MERCURY, dedicated to the study of the tableware trade in the eastern part of the Roman Empire [74–76]. We can also mention ROMFARMS, designed to determine whether the Netherlands had the capacity at the beginning of our era to locally produce enough food to feed the local populations and the Roman army installed on the *Dutch Limes* [77].

Since their inception in the 1990s, ABMs have given rise to debates among modellers about the choice of principles that should govern a model. While the KISS (Keep It Simple Stupid) principle recommends programming agents as simply as possible, KIDS (Keep It Descriptive Stupid) recommend a descriptive approach that takes into account the complexity of the system from the outset [78]. In addition, practices are amended and improved thanks to the self-criticism of agent-based modelling. Opacity of functioning of the early models (« blackbox effect ») encouraged the development of standardised protocols such as Overview, Design concepts, Details (ODD), describing from the most general to the most detailed their expectations and how they work [79, 80].

The increasing complexity of the models, most of which operate stochastically, makes it increasingly difficult to understand the influence of each parameter considered on the outputs. Sensitivity analyses are now frequently used to weigh the relative importance of the various factors involved in the results of these models. A range of methods, from the simplest to the most sophisticated, using Artificial Intelligence, make it possible to better evaluate the functioning of models and their performance [81–83].
[50] and ARTIFICIAL ANASAZIS [51, 52] continue to be a source of inspiration in the world of SMAs for more than twenty years.

Over the past ten years, the growing number of pedagogical manuals presenting the principles and expectations of agent-based modelling [53–56] testifies to the strongest interest in this approach in various disciplines [57]. We would like to mention a first book more specifically intended for archaeologists [58], recently published by the *Santa Fe Institute*, which promotes the use of agent-based systems in the field of social sciences and complexity from the United States.

The ability to simulate phenomena produced by interactions between entities and their environment makes ABMs particularly well suited to the study of socio-natural interactions [59]. Also, most Anglo-Saxon archaeological models are part of this paradigm to study the trajectory of ancient societies in relation to their environment, particularly on the American continent (Pueblo, Anasazi, Mayan Indians, ...) [47, 51, 60] and in the Middle East [61]. These models are mostly devoted to a population and its territory in the prehistoric and protohistoric periods. Other rare projects are part of the long-term perspective. This is particularly the case of Medland (Mediterranean Landscape Dynamics), which focuses on the study of society-environment interactions and their impacts on landscape transformations in the Mediterranean, from the Pleistocene to the middle of the Holocene [62].

Despite the early interest of European archaeologists in agent-based models, their concrete use is not detectable in the literature until the end of the 2000s. Early models were variously developed to study salt mining in the Austrian Hallstatt mines in the Bronze Age [63], Ethno-genesis of Patagonian hunter-gatherer societies [64] or demographics, carrying capacity and the agricultural strategies of late Iron Age Celtic societies in the Czech Republic [65–68]. In France, the ANR Obresoc project (2010–2015) stimulated the design of several models to study the diffusion of Early Neolithic agriculture in Western Europe from the Near East and the Balkans [69–71].

While they were initially of interest to prehistorians and protohistorians, ABMs have also been considered in recent years with increasing interest by historians and archaeologists of antiquity in the countries of Northern Europe (Netherlands, Denmark, and England) [72, 73]. Models were thus developed in the field of Roman studies such as MERCURY, dedicated to the study of the tableware trade in the eastern part of the Roman Empire [74–76]. We can also mention ROMFARMS, designed to determine whether the Netherlands had the capacity at the beginning of our era to locally produce enough food to feed the local populations and the Roman army installed on the *Dutch Limes* [77].

Since their inception in the 1990s, ABMs have given rise to debates among modellers about the choice of principles that should govern a model. While the KISS (Keep It Simple Stupid) principle recommends programming agents as simply as possible, KIDS (Keep It Descriptive Stupid) recommend a descriptive approach that takes into account the complexity of the system from the outset [78]. In addition, practices are amended and improved thanks to the self-criticism of agent-based modelling. Opacity of functioning of the early models (« blackbox effect ») encouraged the development of standardised protocols such as Overview, Design concepts, Details (ODD), describing from the most general to the most detailed their expectations and how they work [79, 80].

The increasing complexity of the models, most of which operate stochastically, makes it increasingly difficult to understand the influence of each parameter considered on the outputs. Sensitivity analyses are now frequently used to weigh the relative importance of the various factors involved in the results of these models. A range of methods, from the simplest to the most sophisticated, using Artificial Intelligence, make it possible to better evaluate the functioning of models and their performance [81–83].
While many conceptual and methodological difficulties have been resolved over the past thirty years, others may not yet have been fully resolved. In particular, it remains difficult to validate or invalidate model outputs by the data [84], especially in archaeology, where they are often quantitatively and qualitatively insufficient. Although it may seem crucial, this final step of validating the outputs is not an absolute necessity to justify the usefulness of the models. Regardless of the significance and relevance of the results they produce, ABMs have great heuristic virtues. For archaeologists interested in phenomena and processes, they require reformulating hypotheses, collating and re-examining datasets, and forging collaborations with other disciplines [85].

It remains difficult to draw up an exhaustive inventory of agent-based models related to archaeology, as not all of them are published or even listed. Of the 1029 designs registered in the CoMSES online bookstore (comses.net)—Across all disciplines, there are currently 30 models that address archaeological issues, representing only 2.9% of the total. This observation leads us to consider that the use of agent-based modelling in archaeology is still timid compared to other disciplines.

An examination of these different models leads us to distinguish some major research themes (which are not exclusive of each other) with in particular the study of:

* Spatial phenomena: how populations, human cultures, consumer products, and epidemics have moved, expanded, and spread (e.g. [71, 86]). For these models, archaeologists favour a realistic representation of space that incorporates GIS layers. These models, known as "Spatial Agent-based models", are the most developed by archaeologists [85].

* Resource exploitation and human strategies: procurement strategies of prehistoric societies (e.g. [87–91]), agricultural strategies (Intensive/Extensive Exploitation) of protohistoric and ancient societies (e.g. [68, 77]). These approaches are strongly inspired by Site Catchment Analysis [92].

* Social phenomena: ethnogenesis, cooperation, competition, collective decision-making (e.g. [64, 93]).

* Dynamics of settlement patterns: clustering of habitats, genesis of the urban phenomenon from protohistory to historical periods (e.g. [61, 94–97]).

* Socio-environmental relations: interaction between societies, the environment and climate (e.g. [98–100]).

In general, the ABMs developed in the United States and Europe respond to various archaeological and historical issues concerning different chrono-cultural periods between Prehistory and late Antiquity, or even the beginning of the Middle Ages. For most of these models, environmental changes do not appear to be considered (perhaps because of a still insufficient involvement of paleoenvironmental specialists in these projects).

Models simulating climate variations and their impact on ancient societies are still few, although agent-based modelling appears particularly well suited for this type of problem, which is part of the complexity of human-environment relations.

## Postulates, materials and methods

### Modelling postulates and explanations

We must warn the reader that ROMCLIM simulates a roman “villa system” during a long period between the 6th c. BC and the 7th c. AD, but this exploitation system does not have historically begun in southern Gaul before the roman conquest (end of the 2nd century BC) for
While many conceptual and methodological difficulties have been resolved over the past thirty years, others may not yet have been fully resolved. In particular, it remains difficult to validate or invalidate model outputs by the data [84], especially in archaeology, where they are often quantitatively and qualitatively insufficient. Although it may seem crucial, this final step of validating the outputs is not an absolute necessity to justify the usefulness of the models. Regardless of the significance and relevance of the results they produce, ABMs have great heuristic virtues. For archaeologists interested in phenomena and processes, they require reformulating hypotheses, collating and re-examining datasets, and forging collaborations with other disciplines [85].

It remains difficult to draw up an exhaustive inventory of agent-based models related to archaeology, as not all of them are published or even listed. Of the 1029 designs registered in the CoMSES online bookstore (comses.net)—Across all disciplines, there are currently 30 models that address archaeological issues, representing only 2.9% of the total. This observation leads us to consider that the use of agent-based modelling in archaeology is still timid compared to other disciplines.

An examination of these different models leads us to distinguish some major research themes (which are not exclusive of each other) with in particular the study of:

* Spatial phenomena: how populations, human cultures, consumer products, and epidemics have moved, expanded, and spread (e.g. [71, 86]). For these models, archaeologists favour a realistic representation of space that incorporates GIS layers. These models, known as "Spatial Agent-based models", are the most developed by archaeologists [85].

* Resource exploitation and human strategies: procurement strategies of prehistoric societies (e.g. [87–91]), agricultural strategies (Intensive/Extensive Exploitation) of protohistoric and ancient societies (e.g. [68, 77]). These approaches are strongly inspired by Site Catchment Analysis [92].

* Social phenomena: ethnogenesis, cooperation, competition, collective decision-making (e.g. [64, 93]).

* Dynamics of settlement patterns: clustering of habitats, genesis of the urban phenomenon from protohistory to historical periods (e.g. [61, 94–97]).

* Socio-environmental relations: interaction between societies, the environment and climate (e.g. [98–100]).

In general, the ABMs developed in the United States and Europe respond to various archaeological and historical issues concerning different chrono-cultural periods between Prehistory and late Antiquity, or even the beginning of the Middle Ages. For most of these models, environmental changes do not appear to be considered (perhaps because of a still insufficient involvement of paleoenvironmental specialists in these projects).

Models simulating climate variations and their impact on ancient societies are still few, although agent-based modelling appears particularly well suited for this type of problem, which is part of the complexity of human-environment relations.

## Postulates, materials and methods

### Modelling postulates and explanations

We must warn the reader that ROMCLIM simulates a roman “villa system” during a long period between the 6th c. BC and the 7th c. AD, but this exploitation system does not have historically begun in southern Gaul before the roman conquest (end of the 2nd century BC) for
collapsing at the end of Antiquity (5th or maybe after). So, our approach is partly ahistorical, mainly for the most part of Iron Age (6th c. - 2nd c. BC), but also for the 6th c. and 7th c. AD.

We do not postulate in this model that socio-economic conditions of Iron Age, Roman period (in all its duration) and Early Middle Age were the same in the area considered. They were clearly different. But we do not try to simulate the real transformations of agricultural exploitations for the different periods considered, due to the big number of uncertainties. This task remains very difficult (but this will be certainly a great challenge for a future model). By this point of view, the model is not realistic, but it's also easier to better isolate the impact of climate change, among other historical and socio-economic parameters. However, it does not mean that we consider there are no other changes driven by these other factors.

Our objective is trying to measure what could have been the profitability of the “villa system” under colder conditions (like beginning of Iron Age and early Middle Ages) than the Roman Climate Optimum (RCO) described in the text. By extending the boundaries of the Roman period to Iron Age and Late Antiquity, our main idea is to try to measure if the so-called RCO could have had (or not) an effect on roman agricultural economy. The interest of such counterfactual simulations is to assess the profits that could have been made by these ancient farms with the climate from other periods and to determine whether they would have been viable.

## Operating principles

The agents used for our ROMCLIM agent-based model (programmed in NetLogo) are family farms and wineries and olive groves. For each century in the chronological sequence explored (6th century BCE - 7th century CE), these three types of agricultural exploitations are generated by each of the cells in the model with 8 km-long sides, which corresponds to the resolution of the input climate data (for an exhaustive presentation of the model see the ODD protocol in S1 Text). Each of these exploitations produces crops annually based on potential yields that vary with the climate. These harvests are sold in the urban markets of the nearest Roman provincial capitals. Our model calculates the profits from these sales by subtracting the production and transport costs from the price paid for the crops. Wineries and olive groves remain viable as long as they are profitable; however, they disappear if their profits are zero or negative. Family farms, which operate differently, disappear when their annual harvest is insufficient to feed the whole family (6 people). Our model also calculates the total amount of potential profits for each type of exploitations according to climatic fluctuations and the values chosen by the user for their characteristics (area, number of employees), the price of the commodities, and the operating and transport costs which are variables. It is thus possible to visualize the changes in the potential profits made by the farms to ultimately discuss the impact of the climate on the agricultural economy.

## Calculation of potential yields with the LPJmL agrosystem model emulator

Potential crop yields for wheat, grapes, and olives are calculated with the ABM based on climate data and using the Lund-Potsdam-Jena managed Land (LPJmL) agroecosystem model [101, 102], which has recently been adapted to compute potential yields in the past [103–105]. Because of the large number of processes described at a daily time step and the mathematical optimization of the representation of water-carbon exchanges, the LPJmL has a high computational time cost, which usually requires the use of a computing cluster in a Linux environment (by SLURM). Therefore, in order to reproduce the functionate of LPJmL with NetLogo, we developed an emulator that simplifies this complex model through a regression equation between yields and climate (see S1 Text for the details and explanations of these equations).
collapsing at the end of Antiquity (5th or maybe after). So, our approach is partly ahistorical, mainly for the most part of Iron Age (6th c. – 2nd c. BC), but also for the 6th c. and 7th c. AD.

We do not postulate in this model that socio-economic conditions of Iron Age, Roman period (in all its duration) and Early Middle Age were the same in the area considered. They were clearly different. But we do not try to simulate the real transformations of agricultural exploitations for the different periods considered, due to the big number of uncertainties. This task remains very difficult (but this will be certainly a great challenge for a future model). By this point of view, the model is not realistic, but it's also easier to better isolate the impact of climate change, among other historical and socio-economic parameters. However, it does not mean that we consider there are no other changes driven by these other factors.

Our objective is trying to measure what could have been the profitability of the “villa system” under colder conditions (like beginning of Iron Age and early Middle Ages) than the Roman Climate Optimum (RCO) described in the text. By extending the boundaries of the Roman period to Iron Age and Late Antiquity, our main idea is to try to measure if the so-called RCO could have had (or not) an effect on roman agricultural economy. The interest of such counterfactual simulations is to assess the profits that could have been made by these ancient farms with the climate from other periods and to determine whether they would have been viable.

## Operating principles

The agents used for our ROMCLIM agent-based model (programmed in NetLogo) are family farms and wineries and olive groves. For each century in the chronological sequence explored (6th century BCE – 7th century CE), these three types of agricultural exploitations are generated by each of the cells in the model with 8 km-long sides, which corresponds to the resolution of the input climate data (for an exhaustive presentation of the model see the ODD protocol in S1 Text). Each of these exploitations produces crops annually based on potential yields that vary with the climate. These harvests are sold in the urban markets of the nearest Roman provincial capitals. Our model calculates the profits from these sales by subtracting the production and transport costs from the price paid for the crops. Wineries and olive groves remain viable as long as they are profitable; however, they disappear if their profits are zero or negative. Family farms, which operate differently, disappear when their annual harvest is insufficient to feed the whole family (6 people). Our model also calculates the total amount of potential profits for each type of exploitations according to climatic fluctuations and the values chosen by the user for their characteristics (area, number of employees), the price of the commodities, and the operating and transport costs which are variables. It is thus possible to visualize the changes in the potential profits made by the farms to ultimately discuss the impact of the climate on the agricultural economy.

## Calculation of potential yields with the LPJmL agrosystem model emulator

Potential crop yields for wheat, grapes, and olives are calculated with the ABM based on climate data and using the Lund-Potsdam-Jena managed Land (LPJmL) agroecosystem model [101, 102], which has recently been adapted to compute potential yields in the past [103–105]. Because of the large number of processes described at a daily time step and the mathematical optimization of the representation of water-carbon exchanges, the LPJmL has a high computational time cost, which usually requires the use of a computing cluster in a Linux environment (by SLURM). Therefore, in order to reproduce the functionate of LPJmL with NetLogo, we developed an emulator that simplifies this complex model through a regression equation between yields and climate (see S1 Text for the details and explanations of these equations).
For each cell of the ABM, monthly temperatures and precipitation, as well as cloud cover, are fed into the emulator, which then calculates potential grape, olive, and wheat yields. The paleoclimatic data needed to simulate yields are derived from a reconstruction performed for the Holocene at the Mediterranean scale [106] (Fig 3). These are time-slices with a 100-year time step and a spatial resolution of 5' latitude and longitude. This resolution was too low for our study, so the data were linearly interpolated at the 8 km scale. We have decided not to work at a finer resolution due to calculations limitations with NetLogo.

## Calculation of agricultural production and its market value

The olive and wine farms were simulated according to the characteristics given by the Latin agronomist Cato (2^nd^ century BCE). In his agronomic treatise, he describes a vineyard of 100 iugera (25 ha) which the exploitation required 16 people, or 1.5 person/ha (*De Agricultura*, XI). He also accurately describes a 240-iugera (60 ha) olive grove for which 13 people were needed (*De Agricultura*, X). The ratio here is 0.21 people/ha, which is seven times less work-force than for a vineyard.

For each century considered, the olive and wine farms produce an average annual harvest of wine and oil based on the area farmed and the potential yields returned by the LPJmL emulator. While for wine, the production is directly calculated in hectoliters by the model, a conversion is applied to the weight of the olives to convert it into liters of oil. The number of kilos of olives needed to produce a liter of oil depends on the varieties grown (5–8 kg), but in our study we used the lowest value of 5 kg/l, the figure most often proposed in the archaeological literature for the Roman period [107].

The market value of the production is then calculated by the model according to a market price selected by the user in a range between 0 and a maximum value, which varies according to the commodity. The Edict of Diocletian (301 CE), which established a maximum price for all agricultural products in the Roman Empire, set prices from 2 to 30 denarii/sextarius for wine (1 sextarius = 1/2 liter) and from 8 to 40 denarii/sextarius for oil, depending on the quality.

Grain farms are operated by a family of 6 people, according to the theoretical model of a family farm of the Roman period [33], which can also be applied to the Iron Age. The area cultivated by these farms is set by the user up to a maximum of 6 ha, which corresponds to the maximum area that a family is capable of farming. The Saserna (2^nd^ century BCE father and son agronomists) argued that a single man could cultivate 8 iugera (2 ha) by hand. If we consider a family composed of 2 adults, 2 elderly people, and 2 children, we can estimate that the "workforce" cannot be based on more than 3 people (i.e., 6 ha).

The farms produce an average annual wheat crop based on the area farmed and the potential yield. Part of this harvest is destined to feed the family, based on an annual ration of 200 kg/person. Another portion is saved to sow the fields the following year at a rate of 5 modius/iugerum (135kg/ha) according to Columella's recommendations (*De Re Rustica*, II, 9). The remaining surplus of grain is sold at a variable market price. Historians generally retain values of 2, 2.5, or 3 sestertii/modius [41, 108]. 100 denarii/modius was the maximum price set by Diocletian's Edict (1 modius = 8.67 liters).

## Production and transport costs, calculating profits

The production costs of vineyards and olive farms are proportional to the number of people employed, at a rate of 140 sestertii/person/year, according to a proposed estimate for the annual cost of a slave or free employee [109]. The cost of transporting goods, also taken into account, is calculated according to the distance separating each farm from the nearest
For each cell of the ABM, monthly temperatures and precipitation, as well as cloud cover, are fed into the emulator, which then calculates potential grape, olive, and wheat yields. The paleoclimatic data needed to simulate yields are derived from a reconstruction performed for the Holocene at the Mediterranean scale [106] (Fig 3). These are time-slices with a 100-year time step and a spatial resolution of 5' latitude and longitude. This resolution was too low for our study, so the data were linearly interpolated at the 8 km scale. We have decided not to work at a finer resolution due to calculations limitations with NetLogo.

## Calculation of agricultural production and its market value

The olive and wine farms were simulated according to the characteristics given by the Latin agronomist Cato (2^nd^ century BCE). In his agronomic treatise, he describes a vineyard of 100 iugera (25 ha) which the exploitation required 16 people, or 1.5 person/ha (*De Agricultura*, XI). He also accurately describes a 240-iugera (60 ha) olive grove for which 13 people were needed (*De Agricultura*, X). The ratio here is 0.21 people/ha, which is seven times less work-force than for a vineyard.

For each century considered, the olive and wine farms produce an average annual harvest of wine and oil based on the area farmed and the potential yields returned by the LPJmL emulator. While for wine, the production is directly calculated in hectoliters by the model, a conversion is applied to the weight of the olives to convert it into liters of oil. The number of kilos of olives needed to produce a liter of oil depends on the varieties grown (5–8 kg), but in our study we used the lowest value of 5 kg/l, the figure most often proposed in the archaeological literature for the Roman period [107].

The market value of the production is then calculated by the model according to a market price selected by the user in a range between 0 and a maximum value, which varies according to the commodity. The Edict of Diocletian (301 CE), which established a maximum price for all agricultural products in the Roman Empire, set prices from 2 to 30 denarii/sextarius for wine (1 sextarius = 1/2 liter) and from 8 to 40 denarii/sextarius for oil, depending on the quality.

Grain farms are operated by a family of 6 people, according to the theoretical model of a family farm of the Roman period [33], which can also be applied to the Iron Age. The area cultivated by these farms is set by the user up to a maximum of 6 ha, which corresponds to the maximum area that a family is capable of farming. The Saserna (2^nd^ century BCE father and son agronomists) argued that a single man could cultivate 8 iugera (2 ha) by hand. If we consider a family composed of 2 adults, 2 elderly people, and 2 children, we can estimate that the "workforce" cannot be based on more than 3 people (i.e., 6 ha).

The farms produce an average annual wheat crop based on the area farmed and the potential yield. Part of this harvest is destined to feed the family, based on an annual ration of 200 kg/person. Another portion is saved to sow the fields the following year at a rate of 5 modius/iugerum (135kg/ha) according to Columella's recommendations (*De Re Rustica*, II, 9). The remaining surplus of grain is sold at a variable market price. Historians generally retain values of 2, 2.5, or 3 sestertii/modius [41, 108]. 100 denarii/modius was the maximum price set by Diocletian's Edict (1 modius = 8.67 liters).

## Production and transport costs, calculating profits

The production costs of vineyards and olive farms are proportional to the number of people employed, at a rate of 140 sestertii/person/year, according to a proposed estimate for the annual cost of a slave or free employee [109]. The cost of transporting goods, also taken into account, is calculated according to the distance separating each farm from the nearest
<figure><img src="image_5.png" /><figcaption>Fig 3. Trend in annual average temperature (red curve) and precipitation (gray bars) anomalies for each century of the last three millennia compared to the present in Southern France (data from Guiot and Kaniewski 2015, point 55). RCO means Roman Climate Optimum LALIA means Late Antique Little Ice Age.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g003

provincial capital and the price of transporting the goods by road. In our model, an agricul-
tural exploitation sells its products at the nearest urban markets, which was not in reality
always the case. For the maximum price of transporting goods by land, we take the rate set by
the Diocletian's Edit of 20 denarii/mile/1200 pounds (i.e., 0.14 sestertii/km/kg).

Finally, the annual profit for each type of farm is calculated by the model by subtracting
production and transportation costs from the market price of the output.

Results

To determine the sensitivity of the outputs of our model to the different parameters consid-
ered, we performed a Sensitivity Analysis with the One-Factor-at-Time (OFAT) method (see
S2 Text). We have thus varied each parameter one by one while keeping the others at constant
value. The results of this analysis show that the different parameters do not have the same
importance for each type of crop. If climatic factors (precipitation, temperatures) are prepon-
derant in the model for viticulture, they appear a little less influential for olive growing. Grain
cultivation, on the other hand, appears to be much more sensitive to economic parameters
(market prices, transport costs) than to climate.

Fig 4 presents the results obtained with the model using the OFAT method used for the Sensitivity Analysis. The graphs show for each parameter and each type of crop the potential benefits calculated by the model. The reference curves (in black) show the results obtained with the median values of the four parameters. Colored envelopes include all the results that can be obtained between the minimum and maximum of the range of values of each of them. Changing the settings of the parameters makes it possible to obtain different potential benefits for each crop and to accentuate more or less the trends of evolution, which nevertheless remain similar.
<figure><img src="image_7.png" /><figcaption>Fig 3. Trend in annual average temperature (red curve) and precipitation (gray bars) anomalies for each century of the last three millennia compared to the present in Southern France (data from Guiot and Kaniewski 2015, point 55). RCO means Roman Climate Optimum LALIA means Late Antique Little Ice Age.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g003

provincial capital and the price of transporting the goods by road. In our model, an agricul-
tural exploitation sells its products at the nearest urban markets, which was not in reality
always the case. For the maximum price of transporting goods by land, we take the rate set by
the Diocletian's Edit of 20 denarii/mile/1200 pounds (i.e., 0.14 sestertii/km/kg).

Finally, the annual profit for each type of farm is calculated by the model by subtracting
production and transportation costs from the market price of the output.

Results

To determine the sensitivity of the outputs of our model to the different parameters consid-
ered, we performed a Sensitivity Analysis with the One-Factor-at-Time (OFAT) method (see
S2 Text). We have thus varied each parameter one by one while keeping the others at constant
value. The results of this analysis show that the different parameters do not have the same
importance for each type of crop. If climatic factors (precipitation, temperatures) are prepon-
derant in the model for viticulture, they appear a little less influential for olive growing. Grain
cultivation, on the other hand, appears to be much more sensitive to economic parameters
(market prices, transport costs) than to climate.

Fig 4 presents the results obtained with the model using the OFAT method used for the Sensitivity Analysis. The graphs show for each parameter and each type of crop the potential benefits calculated by the model. The reference curves (in black) show the results obtained with the median values of the four parameters. Colored envelopes include all the results that can be obtained between the minimum and maximum of the range of values of each of them. Changing the settings of the parameters makes it possible to obtain different potential benefits for each crop and to accentuate more or less the trends of evolution, which nevertheless remain similar.
<figure><img src="image_6.png" /><figcaption>Fig 4. Graphs showing the potential benefits obtained for viticulture, olive growing and cereal cultivation according to the variations in the values of each parameter considered in the model (precipitation, temperatures, market prices and transport costs). The x-axis represents the chronological sequence, and the y-axis represents the potential benefits (in millions of sestertii).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g004

Temporal trend in potential benefits

Fig 4 also shows the trend in the cumulative potential profits by type of farm (olive, wine, grain) for each century in the sequence. We observe that the potential profits generated by the wineries are clearly higher than those of the olive groves, but also of the grain farms, which generate the lowest profits. The profit curves of wineries and olive groves are parallel to each other. Their secular fluctuations are very significant, especially for wine, unlike those of the grain farms, which have a much flatter curve. These results are indirect evidence of the greater sensitivity of vine and olive yields to climatic variations (in the LPJmL model emulator), as compared to wheat.

The curves start at their lowest level in the 6th century BCE, the coldest century according to the paleoclimatic reconstruction used. From this point onwards, a constant secular increase is observed for vineyards and olive farms during the Iron Age until the 2nd century BCE, which marks a first peak before a significant inflection of the curves in the 1st century BCE. Potential profits then reach a high level again during the High Empire (1st-3rd century CE) and then decrease during late antiquity (4th-7th century CE).
<figure><img src="image_8.png" /><figcaption>Fig 4. Graphs showing the potential benefits obtained for viticulture, olive growing and cereal cultivation according to the variations in the values of each parameter considered in the model (precipitation, temperatures, market prices and transport costs). The x-axis represents the chronological sequence, and the y-axis represents the potential benefits (in millions of sestertii).</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g004

Temporal trend in potential benefits

Fig 4 also shows the trend in the cumulative potential profits by type of farm (olive, wine, grain) for each century in the sequence. We observe that the potential profits generated by the wineries are clearly higher than those of the olive groves, but also of the grain farms, which generate the lowest profits. The profit curves of wineries and olive groves are parallel to each other. Their secular fluctuations are very significant, especially for wine, unlike those of the grain farms, which have a much flatter curve. These results are indirect evidence of the greater sensitivity of vine and olive yields to climatic variations (in the LPJmL model emulator), as compared to wheat.

The curves start at their lowest level in the 6th century BCE, the coldest century according to the paleoclimatic reconstruction used. From this point onwards, a constant secular increase is observed for vineyards and olive farms during the Iron Age until the 2nd century BCE, which marks a first peak before a significant inflection of the curves in the 1st century BCE. Potential profits then reach a high level again during the High Empire (1st-3rd century CE) and then decrease during late antiquity (4th-7th century CE).
## Changes in the geography of profitable zones

The potential profit maps produced by the model for the time sequence studied show more or less significant differences according to the centuries considered. For the 6th century BCE (Fig 5), the potential profits generated by viticulture are the most significant in the Languedoc plains, in the middle Rhone valley, and in the Antibes and Fréjus region. Olive growing profits change much more subtly, with higher values to the north-east of Nîmes, in the Var, and in Roussillon, about 20 km southwest of Perpignan. Some regions have no potential for either olive or wine production, such as the hinterland of Languedoc and the High Alps, where only wheat cultivation yields modest profits (Fig 5).

If one compares these results with those produced for the 1st century CE, for example (Fig 6), the profits are much greater for viticulture but also for olive growing, which appears to be extremely profitable in the Languedoc hinterland. This result deserves to be emphasized insofar as this potential was non-existent with the climatic characteristics of the 6th century BCE.

## Discussion

### Strengths and uncertainties of the model

**What real densities of agricultural exploitations? What spatial coverage?** In ROM-CLIM, each cell representing an area of 64 km² is exploited by three agricultural exploitations (a vineyard, an olive farm, a cereal farm). If this density (0.04 exploitations/km²) may seem too low to be realistic, it is nevertheless much higher than those we can calculate from archaeological data. To take the example of the Var department - where research has been particularly intensive - there are 103 olive/wine-growing farms for an area of 5973 km² [110]. The density of 0.01 archaeological sites/km² is here therefore significantly lower than that simulated in the model. Of course, archaeological data represent only a greater or lesser fraction of reality. The densities calculated with these data should be considered minimums. It is still difficult to put forward credible estimates for the density of agricultural settlements in Gallia Narbonensis, but the densities simulated in ROMCLIM - four times higher than those we can apprehend by archaeology - cannot be considered low.

<figure><img src="image_7.png" /><figcaption>Fig 5. Map of potential profitability of villae and farms with climate characteristics of the 6th century BCE. The size of the symbols is proportional to the profitability of the wine (purple squares), olive (green squares), and grain (yellow squares) farms. The red symbols represent the provincial capitals during the Roman period.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g005
## Changes in the geography of profitable zones

The potential profit maps produced by the model for the time sequence studied show more or less significant differences according to the centuries considered. For the 6th century BCE (Fig 5), the potential profits generated by viticulture are the most significant in the Languedoc plains, in the middle Rhone valley, and in the Antibes and Fréjus region. Olive growing profits change much more subtly, with higher values to the north-east of Nîmes, in the Var, and in Roussillon, about 20 km southwest of Perpignan. Some regions have no potential for either olive or wine production, such as the hinterland of Languedoc and the High Alps, where only wheat cultivation yields modest profits (Fig 5).

If one compares these results with those produced for the 1st century CE, for example (Fig 6), the profits are much greater for viticulture but also for olive growing, which appears to be extremely profitable in the Languedoc hinterland. This result deserves to be emphasized insofar as this potential was non-existent with the climatic characteristics of the 6th century BCE.

## Discussion

### Strengths and uncertainties of the model

**What real densities of agricultural exploitations? What spatial coverage?** In ROM-CLIM, each cell representing an area of 64 km² is exploited by three agricultural exploitations (a vineyard, an olive farm, a cereal farm). If this density (0.04 exploitations/km²) may seem too low to be realistic, it is nevertheless much higher than those we can calculate from archaeological data. To take the example of the Var department - where research has been particularly intensive - there are 103 olive/wine-growing farms for an area of 5973 km² [110]. The density of 0.01 archaeological sites/km² is here therefore significantly lower than that simulated in the model. Of course, archaeological data represent only a greater or lesser fraction of reality. The densities calculated with these data should be considered minimums. It is still difficult to put forward credible estimates for the density of agricultural settlements in Gallia Narbonensis, but the densities simulated in ROMCLIM - four times higher than those we can apprehend by archaeology - cannot be considered low.

<figure><img src="image_9.png" /><figcaption>Fig 5. Map of potential profitability of villae and farms with climate characteristics of the 6th century BCE. The size of the symbols is proportional to the profitability of the wine (purple squares), olive (green squares), and grain (yellow squares) farms. The red symbols represent the provincial capitals during the Roman period.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g005
<figure><img src="image_8.png" /><figcaption>**Fig 6.** Map of potential profitability of villae and farm with climate characteristics of the 1st century CE. The size of the symbols is proportional to the profitability of the wine (purple squares), olive (green squares), and grain (yellow squares) farms. The red symbols represent the provincial capitals during the Roman period.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g006

On the other hand, we carried out the simulations with virtual agricultural exploitations evenly distributed throughout the study area. However, archaeological data suggest that these exploitations were concentrated in certain areas (on the outskirts of agglomerations) to leave others vacant. The potential benefits calculated at the output of the model by simulating full exploitation of the study area may therefore be overestimated, considering that commercial agriculture was maybe concentrated in only a few privileged areas.

**Potential predictive value of the outputs.** But by performing "full-gauge" simulations, the model has the advantage of producing results in areas where archaeological data are scarce or absent, which gives the model a potentially predictive power for the location of agricultural exploitations and the geography of crops. If the landowners of antiquity acted with a form of economic rationality (which remains a subject debated among historians) it can indeed be assumed that they sought to optimize their profits by creating or buying their wineries, olive groves and cereal farms in the most favourable places for each of these crops from a geographical, environmental, and climatic point of view, in other words areas defined by our model.

For viticulture, it is observed that the model designates as potentially favourable a geographical area much larger than that identified by archaeology in the middle Rhone Valley. For olive growing, the high potential displayed in the Languedoc hinterland is also not corroborated by archaeological data, but research has been not very intensive in this sector. The results could therefore have a predictive value that could encourage new research (we will develop this point farther).

**Outlooks for improving the calculation of yields for cereals?**

Regarding questions about the vulnerability and resilience of ancient societies to climate change, one of the major interests of the model is to be able to simulate the impact of changes in temperature and precipitation on yields and agricultural productivity using the LPJmL emulator. Simulations show that while the climatic factor is important, it does not have the same impact depending on the type of crop.

The high sensitivity of viticulture and olive growing to variations in rainfall and temperature highlighted by the model supports the hypothesis of a strong impact of climate change on
<figure><img src="image_10.png" /><figcaption>**Fig 6.** Map of potential profitability of villae and farm with climate characteristics of the 1st century CE. The size of the symbols is proportional to the profitability of the wine (purple squares), olive (green squares), and grain (yellow squares) farms. The red symbols represent the provincial capitals during the Roman period.</figcaption></figure>

https://doi.org/10.1371/journal.pone.0298895.g006

On the other hand, we carried out the simulations with virtual agricultural exploitations evenly distributed throughout the study area. However, archaeological data suggest that these exploitations were concentrated in certain areas (on the outskirts of agglomerations) to leave others vacant. The potential benefits calculated at the output of the model by simulating full exploitation of the study area may therefore be overestimated, considering that commercial agriculture was maybe concentrated in only a few privileged areas.

**Potential predictive value of the outputs.** But by performing "full-gauge" simulations, the model has the advantage of producing results in areas where archaeological data are scarce or absent, which gives the model a potentially predictive power for the location of agricultural exploitations and the geography of crops. If the landowners of antiquity acted with a form of economic rationality (which remains a subject debated among historians) it can indeed be assumed that they sought to optimize their profits by creating or buying their wineries, olive groves and cereal farms in the most favourable places for each of these crops from a geographical, environmental, and climatic point of view, in other words areas defined by our model.

For viticulture, it is observed that the model designates as potentially favourable a geographical area much larger than that identified by archaeology in the middle Rhone Valley. For olive growing, the high potential displayed in the Languedoc hinterland is also not corroborated by archaeological data, but research has been not very intensive in this sector. The results could therefore have a predictive value that could encourage new research (we will develop this point farther).

**Outlooks for improving the calculation of yields for cereals?**

Regarding questions about the vulnerability and resilience of ancient societies to climate change, one of the major interests of the model is to be able to simulate the impact of changes in temperature and precipitation on yields and agricultural productivity using the LPJmL emulator. Simulations show that while the climatic factor is important, it does not have the same impact depending on the type of crop.

The high sensitivity of viticulture and olive growing to variations in rainfall and temperature highlighted by the model supports the hypothesis of a strong impact of climate change on
ancient economy, still largely based on agricultural income. The less pronounced effect of these changes on cereal cultivation, on the other hand, suggests a potentially moderate effect on societies and their demography, considering that cereals were the basis of the diet.

In another hand, the importance of grain in Gallia Narbonensis is still certainly underesti-
mated by archaeological and historical sources. If ROMCLIM does not simulate the potential
production of cereal by the villae due to the lack of historical information, the model shows
that wheat produced by farms would be however the only profitable crop in the Alps. In moun-
tain areas that are too cold for wine and olives, wheat would have been the only possible source
of income among the different cash-crops.

However, our model may underestimate these climate effects on grain farming. The cereal
yields calculated are based on a parameterization of LPJmL which groups and averages the bio-
logical and phenological characteristics of barley and naked wheat (the two main cereals
grown in Southern Gaul). It should be noted, however, that different species and varieties of
cereals do not respond to climate change in the same way. But in the future, we plan to develop
new specific parameterizations for barley, naked wheat, and other cultivated cereals in LPJmL
to test the reaction of each of them to changes in precipitation and temperature (ongoing ANR
MICA project). The results obtained could help to qualify our conclusions on the relatively
moderate impact of climate change on grain farming.

Historical questions and models outcomes

In general, the results returned by our model show that the potential profits of the virtual agri-
cultural exploitations gradually rise during the Iron Age, under the effect of a warmer and wet-
ter climate, and reach a maximum during the High Empire, before declining during late
antiquity (Fig 4). Overall, these results are consistent with the hypothesis of a beneficial effect
of the Roman Climate Optimum on the economy of the Roman Empire [4], but also that of
the negative impact of climate on agricultural yields in late antiquity [43, 111]. Our modelling
therefore clearly highlights the role of the climate in fluctuations in yields and agricultural
exploitations profitability, particularly for vine and olive cultivation, while grain farming
appears to be less sensitive to these variations.

**The positive effects of the Roman Climate Optimum (RCO).** Our ROMCLIM model provides a good account of the significant effects of climate change on the potential yields of the crops and the profitability of the agricultural exploitations. The upward slope of the curves in the 3rd century BCE (Fig 4) reflects climatic conditions that were more favourable than in previous centuries for grape and olive yields. However, it is during this same century that the archaeological and archaeobotanical data mentioned above attest to the development of these crops in Southern Gaul [7, 16]. This development could therefore have been favored by warmer but also wetter climatic conditions, which is all the more likely since some studies place the beginning of the RCO as early as 250 BCE [3].

However, one could be surprised that villae were not more widespread in Gallia Narbonen-
sis as of the 1st century BCE, because this territory had been integrated into the Roman empire
and ipso facto into its market economy since the end of the 2nd century BCE. According to the
results produced by ROMCLIM, for the 1st century BCE, there was a clear downturn in the
potential profitability of vineyards and olive groves, which reflects less favourable climatic con-
ditions than in the previous century (Fig 4). Nevertheless, the results obtained remain superior
to those of the 3rd century BCE, which does not allow us to assert that this secular climatic vari-
ation was of sufficient magnitude to delay the development of villae.

The answer to this question could therefore be historical and economic. In the 1st century BCE, Cicero (*De Republica*, III, 6) asserted that the Romans sought to limit the cultivation of
ancient economy, still largely based on agricultural income. The less pronounced effect of these changes on cereal cultivation, on the other hand, suggests a potentially moderate effect on societies and their demography, considering that cereals were the basis of the diet.

In another hand, the importance of grain in Gallia Narbonensis is still certainly underesti-
mated by archaeological and historical sources. If ROMCLIM does not simulate the potential
production of cereal by the villae due to the lack of historical information, the model shows
that wheat produced by farms would be however the only profitable crop in the Alps. In moun-
tain areas that are too cold for wine and olives, wheat would have been the only possible source
of income among the different cash-crops.

However, our model may underestimate these climate effects on grain farming. The cereal
yields calculated are based on a parameterization of LPJmL which groups and averages the bio-
logical and phenological characteristics of barley and naked wheat (the two main cereals
grown in Southern Gaul). It should be noted, however, that different species and varieties of
cereals do not respond to climate change in the same way. But in the future, we plan to develop
new specific parameterizations for barley, naked wheat, and other cultivated cereals in LPJmL
to test the reaction of each of them to changes in precipitation and temperature (ongoing ANR
MICA project). The results obtained could help to qualify our conclusions on the relatively
moderate impact of climate change on grain farming.

Historical questions and models outcomes

In general, the results returned by our model show that the potential profits of the virtual agri-
cultural exploitations gradually rise during the Iron Age, under the effect of a warmer and wet-
ter climate, and reach a maximum during the High Empire, before declining during late
antiquity (Fig 4). Overall, these results are consistent with the hypothesis of a beneficial effect
of the Roman Climate Optimum on the economy of the Roman Empire [4], but also that of
the negative impact of climate on agricultural yields in late antiquity [43, 111]. Our modelling
therefore clearly highlights the role of the climate in fluctuations in yields and agricultural
exploitations profitability, particularly for vine and olive cultivation, while grain farming
appears to be less sensitive to these variations.

**The positive effects of the Roman Climate Optimum (RCO).** Our ROMCLIM model provides a good account of the significant effects of climate change on the potential yields of the crops and the profitability of the agricultural exploitations. The upward slope of the curves in the 3rd century BCE (Fig 4) reflects climatic conditions that were more favourable than in previous centuries for grape and olive yields. However, it is during this same century that the archaeological and archaeobotanical data mentioned above attest to the development of these crops in Southern Gaul [7, 16]. This development could therefore have been favored by warmer but also wetter climatic conditions, which is all the more likely since some studies place the beginning of the RCO as early as 250 BCE [3].

However, one could be surprised that villae were not more widespread in Gallia Narbonen-
sis as of the 1st century BCE, because this territory had been integrated into the Roman empire
and ipso facto into its market economy since the end of the 2nd century BCE. According to the
results produced by ROMCLIM, for the 1st century BCE, there was a clear downturn in the
potential profitability of vineyards and olive groves, which reflects less favourable climatic con-
ditions than in the previous century (Fig 4). Nevertheless, the results obtained remain superior
to those of the 3rd century BCE, which does not allow us to assert that this secular climatic vari-
ation was of sufficient magnitude to delay the development of villae.

The answer to this question could therefore be historical and economic. In the 1st century BCE, Cicero (*De Republica*, III, 6) asserted that the Romans sought to limit the cultivation of
olives and grapevines beyond the Alps to increase the value of their wines and olives. However, the actual existence of Roman protectionist laws remains a controversial topic among historians [17]. The reasons why the cultivation of commercial crops in Southern Gaul in the 1st century BCE was still undeveloped are not yet elucidated.

**The negative impact of the Late Antique Little Ice Age (LALIA).** The decrease in yields and potential profits from grapevine and olive cultivation starting in the 4th century CE indicates a loss of potential profitability of the farms. These results support the hypothesis of a negative impact of LALIA on commercial agriculture and the economy during late antiquity. On the other hand, the potential yields and profits of grain cultivation appear to be only slightly affected. The effects of climatic cooling on a wheat-based diet are therefore less obvious here. While an increase in crop failure under LALIA (AD 450–750) is now being discussed [4, 43, 44], our model results suggest that the effects of late antique climatic cooling may not have had a particularly dramatic effect on agriculture in Southern Gaul. But we have discussed upper of a potential issue with the sensitivity of cereals yields to the climate in the LPJmL model. So, we need further investigations to comfort these conclusions.

**Was olive growing highly developed during antiquity in the Languedoc hinterland?**

If we compare the profitability maps produced by the ROMCLIM model with the archaeological data concerning the grapevine and the olive tree, we notice a certain geographical concordance of the results for the High Empire. The strong potential highlighted by our model in the Languedoc plains, the middle Rhone valley, and Provence for viticulture is supported by the results of archaeological research which have highlighted the importance of this crop [9, 11, 14, 112]. While olive growing at this time has been identified in the Var [13, 112], our model does not show a particularly strong potential in this department. Meanwhile, the potential profitability of olive farms in the Languedoc hinterland was high (Fig 6).

In Languedoc, the profitability map produced by ROMCLIM for the High Empire shows a remarkable similarity with a land-use model proposed thirty years ago [19]. Based on archaeological data, this model contrasted a coastal strip where viticulture was practiced with a hinterland (below the present-day limit of the olive tree) where olives were cultivated. Although the discoveries made by preventive archaeology have largely confirmed the pre-eminence of viticulture in the Languedoc plains, the reality of olive growing at this time in the hilly hinterland has been questioned. The identification of parts of a press that were discovered there as being intended for oil production has been disputed [12]. It is therefore believed today that this activity was only limited compared to Provence [112].

The high potential profitability of olive farms in Gallia Narbonensis, simulated by ROMCLIM, may therefore seem surprising in relation to these arguments. However, if we lend credence to the description by Sidonius Apollinaris (*Epistula* II, 9, 1) of the hills in the Nîmes hinterland planted with grapevines and olive trees, olive growing was more or less developed in this area in the 5th century BCE [13]. However, there is almost no undisputable trace of this activity in today's archaeological data. But, in the hinterland areas, field research (surveys, excavations) is generally more difficult and much less intensive than in the coastal plains, which also benefit from the development of preventive archaeology. The results provided by ROMCLIM could therefore lead to a serious reassessment of the importance of olive growing during the Roman period in the Languedoc hinterland.
olives and grapevines beyond the Alps to increase the value of their wines and olives. However, the actual existence of Roman protectionist laws remains a controversial topic among historians [17]. The reasons why the cultivation of commercial crops in Southern Gaul in the 1st century BCE was still undeveloped are not yet elucidated.

**The negative impact of the Late Antique Little Ice Age (LALIA).** The decrease in yields and potential profits from grapevine and olive cultivation starting in the 4th century CE indicates a loss of potential profitability of the farms. These results support the hypothesis of a negative impact of LALIA on commercial agriculture and the economy during late antiquity. On the other hand, the potential yields and profits of grain cultivation appear to be only slightly affected. The effects of climatic cooling on a wheat-based diet are therefore less obvious here. While an increase in crop failure under LALIA (AD 450–750) is now being discussed [4, 43, 44], our model results suggest that the effects of late antique climatic cooling may not have had a particularly dramatic effect on agriculture in Southern Gaul. But we have discussed upper of a potential issue with the sensitivity of cereals yields to the climate in the LPJmL model. So, we need further investigations to comfort these conclusions.

**Was olive growing highly developed during antiquity in the Languedoc hinterland?**

If we compare the profitability maps produced by the ROMCLIM model with the archaeological data concerning the grapevine and the olive tree, we notice a certain geographical concordance of the results for the High Empire. The strong potential highlighted by our model in the Languedoc plains, the middle Rhone valley, and Provence for viticulture is supported by the results of archaeological research which have highlighted the importance of this crop [9, 11, 14, 112]. While olive growing at this time has been identified in the Var [13, 112], our model does not show a particularly strong potential in this department. Meanwhile, the potential profitability of olive farms in the Languedoc hinterland was high (Fig 6).

In Languedoc, the profitability map produced by ROMCLIM for the High Empire shows a remarkable similarity with a land-use model proposed thirty years ago [19]. Based on archaeological data, this model contrasted a coastal strip where viticulture was practiced with a hinterland (below the present-day limit of the olive tree) where olives were cultivated. Although the discoveries made by preventive archaeology have largely confirmed the pre-eminence of viticulture in the Languedoc plains, the reality of olive growing at this time in the hilly hinterland has been questioned. The identification of parts of a press that were discovered there as being intended for oil production has been disputed [12]. It is therefore believed today that this activity was only limited compared to Provence [112].

The high potential profitability of olive farms in Gallia Narbonensis, simulated by ROMCLIM, may therefore seem surprising in relation to these arguments. However, if we lend credence to the description by Sidonius Apollinaris (*Epistula* II, 9, 1) of the hills in the Nîmes hinterland planted with grapevines and olive trees, olive growing was more or less developed in this area in the 5th century BCE [13]. However, there is almost no undisputable trace of this activity in today's archaeological data. But, in the hinterland areas, field research (surveys, excavations) is generally more difficult and much less intensive than in the coastal plains, which also benefit from the development of preventive archaeology. The results provided by ROMCLIM could therefore lead to a serious reassessment of the importance of olive growing during the Roman period in the Languedoc hinterland.
Conclusion

The results produced by our ROMCLIM agent-based model support the hypothesis of a very positive effect of the Roman Climate Optimum in Southern Gaul on the yields and profitability of agricultural exploitations, which then decline during the Late Antique Little Ice Age (LALIA). For the entire chronological period studied between the middle of the first Iron Age and the early Middle Ages, the highest potential farm incomes calculated by the model are reached during the High Empire (Fig 4). This finding is consistent with the archaeological investigations in Southern Gaul, which have shown that the commercial cultivation of grape-vines, and to a lesser extent the olive tree, reached their peak during this period [112]. Global warming could therefore had seriously boosted the rise of the estate economy within the framework of the villa system developed in our early era. In a pre-industrial society in which most of the wealth still came from the land, a significant increase in the profitability of estates linked to an increase in yields due to a favourable change in climate (to which grapevines and olive trees are particularly sensitive), was certainly more globally a powerful engine for economic growth not only in Gaul but also in the Roman Empire [4].

Yet the effects of the Roman Climate Optimum were probably felt in Southern Gaul well before the beginning of the Roman period, in the middle of the second Iron Age. Our ROM-CLIM simulation clearly shows the beginning of a simulated trend of increasing profits from vineyards and olive farms as early as the 3rd century BCE (Fig 4). While this result is anachronistic and counterfactual (the Roman farms we simulated in our program did not yet exist), it does indirectly indicate a significant increase in potential yields. As already mentioned previously, archaeological and paleoenvironmental surveys conducted in Southern Gaul suggest an increase in olive and wine growing in the second half or towards the end of the 3rd century BCE [7, 16]. While the nature of the socio-economic and historical factors behind this phenomenon has been questioned, an explanation based on the climate should now be considered more seriously given the results of our modelling. Palynological analyses have already concluded that the Roman Warm Period was established as early as 250 BCE in northwest Spain [3]. Roman commercial agriculture could therefore certainly have developed in Gaul rapidly after the Roman conquest in the 120s BCE, at a time when the climate was already favourable for profitable villa farms. The fact that this speculative agriculture apparently did not take off before the end of the 1st century BCE is therefore probably linked to historical or socio-economic factors that are still difficult to identify.

The geographical concordance of the results produced by ROMCLIM and the field data for the different crops studied can be interpreted as proof that our model is quite accurate, at least for the High Empire. However, it is still difficult to fully judge the relevance of our results for the entire geographical area concerned because of the still diffuse nature of the archaeological data from a spatial point of view. In the sectors for which the model indicates a good potential profitability of the farms, but where these concrete data are still rare or absent, we consider that the ROMCLIM results have a potential predictive and heuristic value. The simulated high profitability of olive farms in the Languedoc hinterland during the Roman period could, for example, lead to a reassessment of the controversial question of the importance of olive farming in this area and to additional research.

In general, our model highlights that global warming (with moisture) allowed for strong economic growth as of the moment that commercial agriculture combined with the villa system developed before in Italy [113] was established in Southern Gaul at the beginning of our era. The climatic and socio-economic conditions were then particularly favourable to the profitability and development of viticulture, which was the driving force behind the economic development of Southern Gaul, ahead of olives and wheat. Without this climatic change, it is
Conclusion

The results produced by our ROMCLIM agent-based model support the hypothesis of a very positive effect of the Roman Climate Optimum in Southern Gaul on the yields and profitability of agricultural exploitations, which then decline during the Late Antique Little Ice Age (LALIA). For the entire chronological period studied between the middle of the first Iron Age and the early Middle Ages, the highest potential farm incomes calculated by the model are reached during the High Empire (Fig 4). This finding is consistent with the archaeological investigations in Southern Gaul, which have shown that the commercial cultivation of grape-vines, and to a lesser extent the olive tree, reached their peak during this period [112]. Global warming could therefore had seriously boosted the rise of the estate economy within the framework of the villa system developed in our early era. In a pre-industrial society in which most of the wealth still came from the land, a significant increase in the profitability of estates linked to an increase in yields due to a favourable change in climate (to which grapevines and olive trees are particularly sensitive), was certainly more globally a powerful engine for economic growth not only in Gaul but also in the Roman Empire [4].

Yet the effects of the Roman Climate Optimum were probably felt in Southern Gaul well before the beginning of the Roman period, in the middle of the second Iron Age. Our ROM-CLIM simulation clearly shows the beginning of a simulated trend of increasing profits from vineyards and olive farms as early as the 3rd century BCE (Fig 4). While this result is anachronistic and counterfactual (the Roman farms we simulated in our program did not yet exist), it does indirectly indicate a significant increase in potential yields. As already mentioned previously, archaeological and paleoenvironmental surveys conducted in Southern Gaul suggest an increase in olive and wine growing in the second half or towards the end of the 3rd century BCE [7, 16]. While the nature of the socio-economic and historical factors behind this phenomenon has been questioned, an explanation based on the climate should now be considered more seriously given the results of our modelling. Palynological analyses have already concluded that the Roman Warm Period was established as early as 250 BCE in northwest Spain [3]. Roman commercial agriculture could therefore certainly have developed in Gaul rapidly after the Roman conquest in the 120s BCE, at a time when the climate was already favourable for profitable villa farms. The fact that this speculative agriculture apparently did not take off before the end of the 1st century BCE is therefore probably linked to historical or socio-economic factors that are still difficult to identify.

The geographical concordance of the results produced by ROMCLIM and the field data for the different crops studied can be interpreted as proof that our model is quite accurate, at least for the High Empire. However, it is still difficult to fully judge the relevance of our results for the entire geographical area concerned because of the still diffuse nature of the archaeological data from a spatial point of view. In the sectors for which the model indicates a good potential profitability of the farms, but where these concrete data are still rare or absent, we consider that the ROMCLIM results have a potential predictive and heuristic value. The simulated high profitability of olive farms in the Languedoc hinterland during the Roman period could, for example, lead to a reassessment of the controversial question of the importance of olive farming in this area and to additional research.

In general, our model highlights that global warming (with moisture) allowed for strong economic growth as of the moment that commercial agriculture combined with the villa system developed before in Italy [113] was established in Southern Gaul at the beginning of our era. The climatic and socio-economic conditions were then particularly favourable to the profitability and development of viticulture, which was the driving force behind the economic development of Southern Gaul, ahead of olives and wheat. Without this climatic change, it is
not certain that the Roman Empire's economy would have been able to develop so significantly.

From a methodological point of view, this research shows the potential of such an approach - an agent-based model combined with an agroecosystem model - for other crops and/or other periods and/or other ancient societies.

Even if this approach cannot take in account all the complexity of the socio-ecological processes, it at least allows us to test out various hypotheses. It enables us to shed light on these hypotheses that emerge from the data through mechanistic processes. Such work requires an intrinsically interdisciplinary approach.

On the methodological and heuristic basis of this first work, we could improve this model in the future by taking in account more historical and socio-economic factors and replace for example the regional area considered in a wider system (i.e. Roman Empire), and the commercial interactions with other provinces.

**Supporting information**

**S1 Text. ODD (Overview Design Details) protocol.**

(DOCX)

**S2 Text. Sensitivity analysis.**

(DOCX)

**S3 Text. References for SI.**

(DOCX)

**S1 Table. State variables of agricultural units.**

(DOCX)

**S2 Table. State variables of grid cells.**

(DOCX)

**S3 Table. Seasonal climate variables.**

(DOCX)

**S4 Table. Prices given by the Edict of Diocletian (301 AD).**

(DOCX)

**S5 Table. Minimum, average, and maximum values of each parameter used for the sensitivity analysis (SA).**

(DOCX)

**S1 Fig. Example of January precipitation and temperature fields interpolated for 2500 and 2000 yr BP (VIth and Ist century CE) in the South of France.**

(TIF)

**S2 Fig. XY-plot of yields provides by LPJmL and the emulator.**

(TIF)

**S3 Fig. Tornado diagrams presenting the results of the sensitivity analysis for wine, olive oil and cereal production.** The parameters are ranked from top to bottom from most to least important. The data on the abscissa represent the sum of the benefits (in millions of sestertii) generated by all virtual agricultural exploitations.

(TIF)
not certain that the Roman Empire's economy would have been able to develop so significantly.

From a methodological point of view, this research shows the potential of such an approach - an agent-based model combined with an agroecosystem model - for other crops and/or other periods and/or other ancient societies.

Even if this approach cannot take in account all the complexity of the socio-ecological processes, it at least allows us to test out various hypotheses. It enables us to shed light on these hypotheses that emerge from the data through mechanistic processes. Such work requires an intrinsically interdisciplinary approach.

On the methodological and heuristic basis of this first work, we could improve this model in the future by taking in account more historical and socio-economic factors and replace for example the regional area considered in a wider system (i.e. Roman Empire), and the commercial interactions with other provinces.

**Supporting information**

**S1 Text. ODD (Overview Design Details) protocol.**

(DOCX)

**S2 Text. Sensitivity analysis.**

(DOCX)

**S3 Text. References for SI.**

(DOCX)

**S1 Table. State variables of agricultural units.**

(DOCX)

**S2 Table. State variables of grid cells.**

(DOCX)

**S3 Table. Seasonal climate variables.**

(DOCX)

**S4 Table. Prices given by the Edict of Diocletian (301 AD).**

(DOCX)

**S5 Table. Minimum, average, and maximum values of each parameter used for the sensitivity analysis (SA).**

(DOCX)

**S1 Fig. Example of January precipitation and temperature fields interpolated for 2500 and 2000 yr BP (VIth and Ist century CE) in the South of France.**

(TIF)

**S2 Fig. XY-plot of yields provides by LPJmL and the emulator.**

(TIF)

**S3 Fig. Tornado diagrams presenting the results of the sensitivity analysis for wine, olive oil and cereal production.** The parameters are ranked from top to bottom from most to least important. The data on the abscissa represent the sum of the benefits (in millions of sestertii) generated by all virtual agricultural exploitations.

(TIF)
S1 File. The NetLogo model ROMCLIM with the other files are available in GitHub
https://github.com/Bernigaud2021/ROMCLIM.
(TXT)

## Acknowledgments

We are grateful to Charles La Via for editing the English, and to the two anonymous reviewers. Their remarks and suggestions had led to improve the structuration of the paper and the output analysis of the model.

We acknowledge too the valuable inputs of the RDMed team during numerous upstream discussions: Alan Kirman (CAMS, EHESS, Paris), Sander Van der Leeuw (Arizona State University's School of Sustainability, United States), Sylvain Olivier (University of Nîmes, France), Daniel Contreras (University of Florida, United States), Gül Sürmelihindi (University of Mainz, Germany) and Cees W. Passchier (University of Mainz, Germany).

## Author Contributions

**Conceptualization:** Nicolas Bernigaud.

**Investigation:** Nicolas Bernigaud, Joël Guiot, Philippe Leveau, Delphine Isoardi.

**Methodology:** Nicolas Bernigaud, Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi, Loup Bernard.

**Project administration:** Joël Guiot.

**Supervision:** Joël Guiot.

**Validation:** Nicolas Bernigaud, Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi.

**Writing – original draft:** Nicolas Bernigaud.

**Writing – review & editing:** Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi, Laurent Bouby, Loup Bernard, Delphine Isoardi.

## References

1. Margaritelli G, Cacho I, Català A, Barra M, Bellucci LG, Lubritto C, et al. Persistent warm Mediterranean surface waters during the Roman period. Sci Rep. 2020; 10: 10431. https://doi.org/10.1038/s41598-020-67281-2 PMID: 32591564

2. McCormick M, Büntgen U, Cane MA, Cook ER, Harper K, Huybers P, et al. Climate Change during and after the Roman Empire: Reconstructing the Past from Scientific and Historical Evidence. The Journal of Interdisciplinary History. 2012; 43: 169–220. https://doi.org/10.1162/JINH_a_00379

3. Desprat S, Sánchez Goñi MF, Loutre M-F. Revealing climatic variability of the last three millennia in northwestern Iberia using pollen influx data. Earth and Planetary Science Letters. 2003; 213: 63–78. https://doi.org/10.1016/S0012-821X(03)00292-9

4. Harper K. The Fate of Rome. Princetown; 2017.

5. Harper K, McCormick M. CHAPTER 1. Reconstructing the Roman Climate. In: Scheidel W, editor. The Science of Roman History. Princeton: Princeton University Press; 2018. pp. 11–52. https://doi.org/10.23943/9781400889730-006

6. Boissinot P. Archéologie des vignobles antiques du sud de la Gaule. Gallia. 2001; 58: 45–68. https://doi.org/10.3406/galia.2001.3173

7. Py M, Buxo i Capdevila R. La viticulture en Gaule à l'Âge du Fer. Gallia. 2001; 58: 29–43. https://doi.org/10.3406/galia.2001.3172

8. Rovira N, Alonso N. Crop growing and plant consumption in coastal Languedoc (France) in the Second Iron Age: new data from Pech Maho (Aude), Lattara (Hérault) and Le Cailar (Gard). Veget Hist Archaeobot. 2018; 27: 85–97. https://doi.org/10.1007/s00334-017-0619-x
**S1 File.** The NetLogo model ROMCLIM with the other files are available in GitHub
https://github.com/Bernigaud2021/ROMCLIM.
(TXT)

## Acknowledgments

We are grateful to Charles La Via for editing the English, and to the two anonymous reviewers. Their remarks and suggestions had led to improve the structuration of the paper and the output analysis of the model.

We acknowledge too the valuable inputs of the RDMed team during numerous upstream discussions: Alan Kirman (CAMS, EHESS, Paris), Sander Van der Leeuw (Arizona State University's School of Sustainability, United States), Sylvain Olivier (University of Nîmes, France), Daniel Contreras (University of Florida, United States), Gül Sürmelihindi (University of Mainz, Germany) and Cees W. Passchier (University of Mainz, Germany).

## Author Contributions

**Conceptualization:** Nicolas Bernigaud.

**Investigation:** Nicolas Bernigaud, Joël Guiot, Philippe Leveau, Delphine Isoardi.

**Methodology:** Nicolas Bernigaud, Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi, Loup Bernard.

**Project administration:** Joël Guiot.

**Supervision:** Joël Guiot.

**Validation:** Nicolas Bernigaud, Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi.

**Writing – original draft:** Nicolas Bernigaud.

**Writing – review & editing:** Alberte Bondeau, Joël Guiot, Frédérique Bertoncello, Marie-Jeanne Ouriachi, Laurent Bouby, Loup Bernard, Delphine Isoardi.

## References

1. Margaritelli G, Cacho I, Català A, Barra M, Bellucci LG, Lubritto C, et al. Persistent warm Mediterranean surface waters during the Roman period. Sci Rep. 2020; 10: 10431. https://doi.org/10.1038/s41598-020-67281-2 PMID: 32591564

2. McCormick M, Büntgen U, Cane MA, Cook ER, Harper K, Huybers P, et al. Climate Change during and after the Roman Empire: Reconstructing the Past from Scientific and Historical Evidence. The Journal of Interdisciplinary History. 2012; 43: 169–220. https://doi.org/10.1162/JINH_a_00379

3. Desprat S, Sánchez Goñi MF, Loutre M-F. Revealing climatic variability of the last three millennia in northwestern Iberia using pollen influx data. Earth and Planetary Science Letters. 2003; 213: 63–78. https://doi.org/10.1016/S0012-821X(03)00292-9

4. Harper K. The Fate of Rome. Princetown; 2017.

5. Harper K, McCormick M. CHAPTER 1. Reconstructing the Roman Climate. In: Scheidel W, editor. The Science of Roman History. Princeton: Princeton University Press; 2018. pp. 11–52. https://doi.org/10.23943/9781400889730-006

6. Boissinot P. Archéologie des vignobles antiques du sud de la Gaule. Gallia. 2001; 58: 45–68. https://doi.org/10.3406/galia.2001.3173

7. Py M, Buxo i Capdevila R. La viticulture en Gaule à l'Âge du Fer. Gallia. 2001; 58: 29–43. https://doi.org/10.3406/galia.2001.3172

8. Rovira N, Alonso N. Crop growing and plant consumption in coastal Languedoc (France) in the Second Iron Age: new data from Pech Maho (Aude), Lattara (Hérault) and Le Cailar (Gard). Veget Hist Archaeobot. 2018; 27: 85–97. https://doi.org/10.1007/s00334-017-0619-x
9. McGovern PE, Luley BP, Rovira N, Mirzoian A, Callahan MP, Smith KE, et al. Beginning of viniculture in France. Proceedings of the National Academy of Sciences. 2013; 110: 10147–10152. https://doi.org/10.1073/pnas.1216126110 PMID: 23733937

10. Buffat L, Pellecuer C, Mauné S, Pomarèdes H. La viticulture antique en Languedoc-Roussillon. Gallia. 2001; 58: 91–111. https://doi.org/10.3406/galia.2001.3175

11. Jung C, Odiot T, Berger J-F, Seris D, Bouby L, Lopez Saez J-A, et al. La viticulture antique dans le Tri-castin (moyenne vallée du Rhône). Gallia. 2001; 58: 113–128. https://doi.org/10.3406/galia.2001.3176

12. Mauné S. La villa gallo-romaine de "Vareilles" à Paulhan (Hérault; fouille de l'autoroute A75). Un centre domanial du Haut-Empire spécialisé dans la viticulture? Revue archéologique de Picardie. 2003; 1: 309–337. https://doi.org/10.3406/pica.2003.2375

13. Brun J-P. Archéologie du vin et de l'huile en Gaule romaine. Paris, France: Errance; 2005.

14. Jung C, Pomarèdes H, Compan M, Figueiral I, Martin S, Ginouvez O, et al. Pratiques culturales et système agraire gallo-romain. L'exemple de la vallée de l'Hérault et du Biterrois (Hérault). Revue archéologique de Narbonnaise. 2013; 46: 159–177. https://doi.org/10.3406/ran.2013.1882

15. Bernigaud N, Bondeau A, Guiot J. Understanding the development of viticulture in Roman Gaul during and after the Roman climate optimum: The contribution of spatial analysis and agro-ecosystem modeling. Journal of Archaeological Science: Reports. 2021; 38: 103099. https://doi.org/10.1016/j.jasrep.2021.103099

16. Triat-Laval H, Leveau P, Marinval P, Medus J. L'Olivier et sa culture en Provence. Données historiques, palynologiques et carpologiques. Ecologia Mediterranea. 1990; 16: 427–435. https://doi.org/10.3406/ecmed.1990.1682

17. Leveau P, Heinz C, Laval H, Marinval P, Medus J. Les origines de l'oléiculture en Gaule du Sud. ArchéoSciences, revue d'Archéométrie. 1991; 15: 83–94. https://doi.org/10.3406/arsci.1991.1260

18. Brun J-P. L'Oléiculture antique en Provence d'après les recherches archéologiques récentes. Echos du monde classique: Classical news and views. 1983; 28: 249–262.

19. Garcia D. Les éléments de pressoir de Lattes et l'oléiculture antique en Languedoc. Lattara. 1992; 5: 237–258.

20. Leveau P. L'oléiculture en Gaule Narbonnaise: données archéologiques et paléoenvironnemtales. Présentation - Interprétation. Revue archéologique de Picardie. 2003; 1: 299–308. https://doi.org/10.3406/pica.2003.2374

21. Beauchamp C, Ros J, Cenzon-Salvayre C, Garnier NB, Ruas M-P. De l'olive à l'huile: regards croisés sur la possibilité d'une production d'huile d'olive en Roussillon au Haut Empire. 2017. p. 515. Available: https://shs.hal.science/halshs-01685753

22. Marinval P. Des Gaulois aux Gallo-romains: l'agriculture du midi de la France. Pallas. 2004; 233–242.

23. Bouby L. L'agriculture dans le Bassin du Rhône du Bronze Final à l'Antiquité. Archives d'Écologie Pré-historique. Toulouse; 2014.

24. Garcia D. Observations sur la production et le commerce des céréales en Languedoc méditerranéen durant l'Age du Fer: les formes de stockage des grains. Revue archéologique de Narbonnaise. 1987; 20: 43–98. https://doi.org/10.3406/ran.1987.1306

25. Garcia D, Isoardi D. 2. Variations démographiques et production des céréales en Celtique méditerranéenne: le rôle de Marseille grecque? In: Tréziny H, editor. Grecs et indigènes de la Catalogne à la mer Noire: Actes des rencontres du programme européen Ramses2 (2006–2008). Publications du Centre Camille Jullian; 2020. pp. 403–424. https://doi.org/10.4000/books.pccj.612

26. Liou B, Morel-Deledalle M. L'orge des Cavares: une amphorette à inscription peinte trouvée dans le port antique de Marseille. Revue archéologique de Narbonnaise. 1977; 10: 189–197. https://doi.org/10.3406/ran.1977.1012

27. Ros J. 2000 ans d'agriculture en Roussillon. Productions végétales, pratiques et terroirs protohistoriques, antiques et médiévaux. Editions Mergoil. Montagnac; 2020.

28. Cayn P, Kotarba J, Pellecuer C, Pomarèdes H, Lopez D. Céréaliculture, élevage et viticulture en Languedoc méditerranéen: nouvelles données pour une relecture des systèmes de production en Gaule Narbonnaise. Produire, transformer et stocker dans les campagnes des Gaules Romaines, problèmes d'interprétation fonctionnelle et économique des bâtiments d'exploitation et des structures de production agro-pastorale, actes du XIe colloque de l'Association d'étude du monde rural gallo-romain. Bordeaux: Aquitania; 2017. pp. 21–43.

29. Mauné S, Paillet J-L. Les moulins hydrauliques de Vareilles (Paulhan) et de L'Auribelle-Basse (Pézenas/Hérault). Stockage et transformation des céréales dans l'économie rurale de Gaule Narbonnaise (Ier-IIIe s. ap. J.-C.). In: Anderson P, Cummings L, Schippers T, Simonel B, editors. Le Traitement des récoltes: un regard sur la diversité du Néolithique au présent, Actes des XXIIIe Rencontres internationales d'Archéologie et d'Histoire d'Antibes, 17–19 octobre 2002. Antibes: APDCA; 2003. pp. 295–326.
9. McGovern PE, Luley BP, Rovira N, Mirzoian A, Callahan MP, Smith KE, et al. Beginning of viniculture in France. Proceedings of the National Academy of Sciences. 2013; 110: 10147–10152. https://doi.org/10.1073/pnas.1216126110 PMID: 23733937

10. Buffat L, Pellecuer C, Mauné S, Pomarèdes H. La viticulture antique en Languedoc-Roussillon. Gallia. 2001; 58: 91–111. https://doi.org/10.3406/galia.2001.3175

11. Jung C, Odiot T, Berger J-F, Seris D, Bouby L, Lopez Saez J-A, et al. La viticulture antique dans le Tri-castin (moyenne vallée du Rhône). Gallia. 2001; 58: 113–128. https://doi.org/10.3406/galia.2001.3176

12. Mauné S. La villa gallo-romaine de "Vareilles" à Paulhan (Hérault; fouille de l'autoroute A75). Un centre domanial du Haut-Empire spécialisé dans la viticulture? Revue archéologique de Picardie. 2003; 1: 309–337. https://doi.org/10.3406/pica.2003.2375

13. Brun J-P. Archéologie du vin et de l'huile en Gaule romaine. Paris, France: Errance; 2005.

14. Jung C, Pomarèdes H, Compan M, Figueiral I, Martin S, Ginouvez O, et al. Pratiques culturales et système agraire gallo-romain. L'exemple de la vallée de l'Hérault et du Biterrois (Hérault). Revue archéologique de Narbonnaise. 2013; 46: 159–177. https://doi.org/10.3406/ran.2013.1882

15. Bernigaud N, Bondeau A, Guiot J. Understanding the development of viticulture in Roman Gaul during and after the Roman climate optimum: The contribution of spatial analysis and agro-ecosystem modeling. Journal of Archaeological Science: Reports. 2021; 38: 103099. https://doi.org/10.1016/j.jasrep.2021.103099

16. Triat-Laval H, Leveau P, Marinval P, Medus J. L'Olivier et sa culture en Provence. Données historiques, palynologiques et carpologiques. Ecologia Mediterranea. 1990; 16: 427–435. https://doi.org/10.3406/ecmed.1990.1682

17. Leveau P, Heinz C, Laval H, Marinval P, Medus J. Les origines de l'oléiculture en Gaule du Sud. ArchéoSciences, revue d'Archéométrie. 1991; 15: 83–94. https://doi.org/10.3406/arsci.1991.1260

18. Brun J-P. L'Oléiculture antique en Provence d'après les recherches archéologiques récentes. Echos du monde classique: Classical news and views. 1983; 28: 249–262.

19. Garcia D. Les éléments de pressoir de Lattes et l'oléiculture antique en Languedoc. Lattara. 1992; 5: 237–258.

20. Leveau P. L'oléiculture en Gaule Narbonnaise: données archéologiques et paléoenvironnemtales. Présentation - Interprétation. Revue archéologique de Picardie. 2003; 1: 299–308. https://doi.org/10.3406/pica.2003.2374

21. Beauchamp C, Ros J, Cenzon-Salvayre C, Garnier NB, Ruas M-P. De l'olive à l'huile: regards croisés sur la possibilité d'une production d'huile d'olive en Roussillon au Haut Empire. 2017. p. 515. Available: https://shs.hal.science/halshs-01685753

22. Marinval P. Des Gaulois aux Gallo-romains: l'agriculture du midi de la France. Pallas. 2004; 233–242.

23. Bouby L. L'agriculture dans le Bassin du Rhône du Bronze Final à l'Antiquité. Archives d'Écologie Pré-historique. Toulouse; 2014.

24. Garcia D. Observations sur la production et le commerce des céréales en Languedoc méditerranéen durant l'Age du Fer: les formes de stockage des grains. Revue archéologique de Narbonnaise. 1987; 20: 43–98. https://doi.org/10.3406/ran.1987.1306

25. Garcia D, Isoardi D. 2. Variations démographiques et production des céréales en Celtique méditerranéenne: le rôle de Marseille grecque? In: Tréziny H, editor. Grecs et indigènes de la Catalogne à la mer Noire: Actes des rencontres du programme européen Ramses2 (2006–2008). Publications du Centre Camille Jullian; 2020. pp. 403–424. https://doi.org/10.4000/books.pccj.612

26. Liou B, Morel-Deledalle M. L'orge des Cavares: une amphorette à inscription peinte trouvée dans le port antique de Marseille. Revue archéologique de Narbonnaise. 1977; 10: 189–197. https://doi.org/10.3406/ran.1977.1012

27. Ros J. 2000 ans d'agriculture en Roussillon. Productions végétales, pratiques et terroirs protohistoriques, antiques et médiévaux. Editions Mergoil. Montagnac; 2020.

28. Cayn P, Kotarba J, Pellecuer C, Pomarèdes H, Lopez D. Céréaliculture, élevage et viticulture en Languedoc méditerranéen: nouvelles données pour une relecture des systèmes de production en Gaule Narbonnaise. Produire, transformer et stocker dans les campagnes des Gaules Romaines, problèmes d'interprétation fonctionnelle et économique des bâtiments d'exploitation et des structures de production agro-pastorale, actes du XIe colloque de l'Association d'étude du monde rural gallo-romain. Bordeaux: Aquitania; 2017. pp. 21–43.

29. Mauné S, Paillet J-L. Les moulins hydrauliques de Vareilles (Paulhan) et de L'Auribelle-Basse (Pézenas/Hérault). Stockage et transformation des céréales dans l'économie rurale de Gaule Narbonnaise (Ier-IIIe s. ap. J.-C.). In: Anderson P, Cummings L, Schippers T, Simonel B, editors. Le Traitement des récoltes: un regard sur la diversité du Néolithique au présent, Actes des XXIIIe Rencontres internationales d'Archéologie et d'Histoire d'Antibes, 17–19 octobre 2002. Antibes: APDCA; 2003. pp. 295–326.
30. Finley M. The Ancient Economy. University of California. Oakland; 1973.

31. Duncan-Jones R. The Economy of the Roman Empire: Quantitative Studies. First Edition. Cambridge Eng.: Cambridge University Press; 1974.

32. Greene K. The Archaeology of the Roman Economy. 1990.

33. Ouzoulias P. L'économie agraire de la Gaule: aperçus historiographiques et perspectives archéologiques Texte. Université de Franche-Comté. 2006. Available: https://theses.hal.science/tel-00011567/PDF/Texte.pdf

34. Temin P. The Roman Market Economy. Princeton University Press; 2013.

35. Erdkamp P. How modern was the market economy of the Roman world? Œconomia History, Methodology, Philosophy. 2014; 225-235. https://doi.org/10.4000/oeconomia.399

36. Ferdière A, Matterne V, Méniel P, Nissen-Jaubert A. Histoire de l'agriculture en Gaule. 500 Avant J-C - 1000 après J-C. Paris: Errance; 2006.

37. Buffat L. L'économie domaniale en Gaule Narbonnaise. Montpellier: Monographie d'Archéologie Méditerranéenne; 2011. Available: https://www.librairie-archeologique.com/index.html?produit=42018

38. Mauné S, Durand B, Carrato C, Bourgaut R. La villa de Quintus Iulius Pri(...) à Aspiran (Hérault). Un centre domanial de Gaule Narbonnaise (ier-ve s. apr. J.-C.). Pallas Revue d'études antiques. 2010; 111-143. https://doi.org/10.4000/pallas.3383

39. Carrato C. Le dolium en gaule narbonnaise (Ier s. a.c. IIIe s. p.c.), contribution à l'histoire socio-économique de la méditerranée nord-occidentale. Ausonius. Bordeaux; 2017.

40. Hollander D. Farmers and Agriculture in the Roman Economy. Oxon and New-York; 2019.

41. Bowman A, Wilson A, Bowman A, Wilson A, editors. 1 Introduction: Quantifying Roman Agriculture. The Roman Agricultural Economy: Organisation, Investment, and Production. Oxford University Press; 2013. p. 0. https://doi.org/10.1093/acprof:oso/9780199665723.003.0001

42. Ferdière A. Agriculture in Roman Gaul. A Companion to Ancient Agriculture. John Wiley & Sons, Ltd; 2020. pp. 447-477. https://doi.org/10.1002/9781118970959.ch22

43. Büntgen U, Myglan VS, Ljungqvist FC, McCormick M, Di Cosmo N, Sigl M, et al. Cooling and societal change during the Late Antique Little Ice Age from 536 to around 660 AD. Nature Geosci. 2016; 9: 231-236. https://doi.org/10.1038/ngeo2652

44. Labuhn I, Finné M, Izdebski A, Roberts N, Woodbridge J. Climatic Changes and Their Impacts in the Mediterranean during the First Millennium AD. Environment and Society in the Long Late Antiquity. Brill; 2019. pp. 247-270. https://doi.org/10.1163/9789004392083_017

45. Haldon J. Some Thoughts on Climate Change, Local Environment, and Grain Production in Byzantine Northern Anatolia. Environment and Society in the Long Late Antiquity. Brill; 2019. pp. 200-206. https://doi.org/10.1163/9789004392083_014

46. Macal CM, North MJ. Tutorial on agent-based modelling and simulation. Journal of Simulation. 2010; 4: 151-162. https://doi.org/10.1057/jos.2010.3

47. Kohler TA. Une troisième voie pour l'archéologie: Une modélisation multi-agents dans le Sud-Ouest des États-Unis1. In: Beaune SA de, Francfort H-P, editors. L'archéologie à découvert: Hommes, objets, espaces et temporalités. Paris: CNRS Éditions; 2017. pp. 211-217. Available: http://books.openedition.org/editionscnrs/11291

48. Axelrod R. Advancing the Art of Simulation in the Social Sciences. In: Conte R, Hegselmann R, Terna P, editors. Simulating Social Phenomena. Berlin, Heidelberg: Springer; 1997. pp. 21-40. https://doi.org/10.1007/978-3-662-03366-1_2

49. Kohler TA, Gumerman GG, editors. Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes. 1st edition. New York: Oxford University Press; 2000.

50. Epstein JM, Axtell RL. Growing Artificial Societies: Social Science from the Bottom Up. The MIT Press; 1996. https://doi.org/10.7551/mitpress/3374.001.0001

51. Epstein J, Dean J, Gumerman G, Axtell R. Understanding Anasazi Culture Change Through Agent-Based Modeling. In: Gumerman GJ, Kohler T, editors. Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes. New York: Oxford University Press; 2000. pp. 179-206.

52. Axtell R, Epstein J, Dean J, Gumerman G, Swedlund A, Harburger J, et al. Population Growth and Col lapse in a Multiagent Model of the Kayenta Anasazi in Long House Valley. Proceedings of the National Academy of Sciences of the United States of America. 2002; 99 Suppl 3: 7275-9. https://doi.org/10.1073/pnas.092080799 PMID: 12011406

53. Railsback SF, Grimm V. Agent-Based and Individual-Based Modeling: A Practical Introduction. Prince- ton University Press; 2011. Available: https://www.jstor.org/stable/j.ctt7sns7
30. Finley M. The Ancient Economy. University of California. Oakland; 1973.

31. Duncan-Jones R. The Economy of the Roman Empire: Quantitative Studies. First Edition. Cambridge Eng.: Cambridge University Press; 1974.

32. Greene K. The Archaeology of the Roman Economy. 1990.

33. Ouzoulias P. L'économie agraire de la Gaule: aperçus historiographiques et perspectives archéologiques Texte. Université de Franche-Comté. 2006. Available: https://theses.hal.science/tel-00011567/PDF/Texte.pdf

34. Temin P. The Roman Market Economy. Princeton University Press; 2013.

35. Erdkamp P. How modern was the market economy of the Roman world? Œconomia History, Methodology, Philosophy. 2014; 225-235. https://doi.org/10.4000/oeconomia.399

36. Ferdière A, Matterne V, Méniel P, Nissen-Jaubert A. Histoire de l'agriculture en Gaule. 500 Avant J-C - 1000 après J-C. Paris: Errance; 2006.

37. Buffat L. L'économie domaniale en Gaule Narbonnaise. Montpellier: Monographie d'Archéologie Méditerranéenne; 2011. Available: https://www.librairie-archeologique.com/index.html?produit=42018

38. Mauné S, Durand B, Carrato C, Bourgaut R. La villa de Quintus Iulius Pri(...) à Aspiran (Hérault). Un centre domanial de Gaule Narbonnaise (ier-ve s. apr. J.-C.). Pallas Revue d'études antiques. 2010; 111-143. https://doi.org/10.4000/pallas.3383

39. Carrato C. Le dolium en gaule narbonnaise (Ier s. a.c. IIIe s. p.c.), contribution à l'histoire socio-économique de la méditerranée nord-occidentale. Ausonius. Bordeaux; 2017.

40. Hollander D. Farmers and Agriculture in the Roman Economy. Oxon and New-York; 2019.

41. Bowman A, Wilson A, Bowman A, Wilson A, editors. 1 Introduction: Quantifying Roman Agriculture. The Roman Agricultural Economy: Organisation, Investment, and Production. Oxford University Press; 2013. p. 0. https://doi.org/10.1093/acprof:oso/9780199665723.003.0001

42. Ferdière A. Agriculture in Roman Gaul. A Companion to Ancient Agriculture. John Wiley & Sons, Ltd; 2020. pp. 447-477. https://doi.org/10.1002/9781118970959.ch22

43. Büntgen U, Myglan VS, Ljungqvist FC, McCormick M, Di Cosmo N, Sigl M, et al. Cooling and societal change during the Late Antique Little Ice Age from 536 to around 660 AD. Nature Geosci. 2016; 9: 231-236. https://doi.org/10.1038/ngeo2652

44. Labuhn I, Finné M, Izdebski A, Roberts N, Woodbridge J. Climatic Changes and Their Impacts in the Mediterranean during the First Millennium AD. Environment and Society in the Long Late Antiquity. Brill; 2019. pp. 247-270. https://doi.org/10.1163/9789004392083_017

45. Haldon J. Some Thoughts on Climate Change, Local Environment, and Grain Production in Byzantine Northern Anatolia. Environment and Society in the Long Late Antiquity. Brill; 2019. pp. 200-206. https://doi.org/10.1163/9789004392083_014

46. Macal CM, North MJ. Tutorial on agent-based modelling and simulation. Journal of Simulation. 2010; 4: 151-162. https://doi.org/10.1057/jos.2010.3

47. Kohler TA. Une troisième voie pour l'archéologie: Une modélisation multi-agents dans le Sud-Ouest des États-Unis1. In: Beaune SA de, Francfort H-P, editors. L'archéologie à découvert: Hommes, objets, espaces et temporalités. Paris: CNRS Éditions; 2017. pp. 211-217. Available: http://books.openedition.org/editionscnrs/11291

48. Axelrod R. Advancing the Art of Simulation in the Social Sciences. In: Conte R, Hegselmann R, Terna P, editors. Simulating Social Phenomena. Berlin, Heidelberg: Springer; 1997. pp. 21-40. https://doi.org/10.1007/978-3-662-03366-1_2

49. Kohler TA, Gumerman GG, editors. Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes. 1st edition. New York: Oxford University Press; 2000.

50. Epstein JM, Axtell RL. Growing Artificial Societies: Social Science from the Bottom Up. The MIT Press; 1996. https://doi.org/10.7551/mitpress/3374.001.0001

51. Epstein J, Dean J, Gumerman G, Axtell R. Understanding Anasazi Culture Change Through Agent-Based Modeling. In: Gumerman GJ, Kohler T, editors. Dynamics in Human and Primate Societies: Agent-Based Modeling of Social and Spatial Processes. New York: Oxford University Press; 2000. pp. 179-206.

52. Axtell R, Epstein J, Dean J, Gumerman G, Swedlund A, Harburger J, et al. Population Growth and Col lapse in a Multiagent Model of the Kayenta Anasazi in Long House Valley. Proceedings of the National Academy of Sciences of the United States of America. 2002; 99 Suppl 3: 7275-9. https://doi.org/10.1073/pnas.092080799 PMID: 12011406

53. Railsback SF, Grimm V. Agent-Based and Individual-Based Modeling: A Practical Introduction. Prince- ton University Press; 2011. Available: https://www.jstor.org/stable/j.ctt7sns7
54. Taylor SJE, editor. Agent-Based Modeling and Simulation. London: Palgrave Macmillan UK; 2014.
https://doi.org/10.1057/9781137453648

55. Wilensky U, Rand W. An Introduction to Agent-Based Modeling: Modeling Natural, Social, and Engineered Complex Systems with NetLogo. Illustrated edition. Cambridge, Massachusetts: The MIT Press; 2015.

56. Janssen M. Introduction to Agent-Based Modeling: with applications to social, ecological, and social-ecological systems. 2020.

57. Lake MW. Trends in Archaeological Simulation. J Archaeol Method Theory. 2014; 21: 258-287.
https://doi.org/10.1007/s10816-013-9188-1

58. Romanowska I, Wren C, Crabtree S. [Agent-Based Modeling for Archaeology], Simulating the Complexity of Societies. Santa Fe: Santa Fe Institute Studies in the Sciences of Complexities; 2021.
https://doi.org/10.37911/9781947864382

59. Kohler TA, van der Leeuw SE, editors. The Model-based Archaeology of Socionatural Systems. School for Advanced Research Press; 2007.

60. Heckbert S. MayaSim: An Agent-Based Model of the Ancient Maya Social-Ecological System. JASSS. 2013; 16: 11.

61. Wilkinson TJ, Christiansen JH, Ur J, Widell M, Altaweel M. Urbanization within a Dynamic Environment: Modeling Bronze Age Communities in Upper Mesopotamia. American Anthropologist. 2007; 109: 52-68.

62. Barton CM, Ullah IIT, Bergin SM, Mitasova H, Sarjoughian H. Looking for the future in the past: Long-term change in socioecological systems. Ecological Modelling. 2012; 241: 42-53. https://doi.org/10.1016/j.ecolmodel.2012.02.010

63. Kowarik K, Reschreiter H, Wurzer G, Totschnig R, Rausch A. Mining with Agents - Agent-based Modeling of the Bronze Age Salt Mine of Hallstatt. CD der Stadt Wien, Stadtarchäologie; 2009. pp. 1-19. Available: https://repositum.tuwien.at/handle/20.500.12708/63691

64. Quesada FJM, Barcelo J, Vilà X. Patagonian Ethnogenesis: towards a computational simulation approach. 2010 [cited 7 Feb 2023]. Available: https://www.academia.edu/35409189/Patagonian_Ethnogenesis_towards_a_computational_simulation Approach

65. Olševičová K, Cimler R, Machálek T. Agent-Based Model of Celtic Population Growth: NetLogo and Python. In: Nguyen NT, Trawiński B, Katarzyniak R, Jo G-S, editors. Advanced Methods for Computational Collective Intelligence. Berlin, Heidelberg: Springer; 2013. pp. 135-143. https://doi.org/10.1007/978-3-642-34300-1_13

66. Olševičová K, Cimler R. Agent-based model of carrying capacity of Celtic settlement agglomeration. Proceedings of 3rd World Conference on Information Technology (WCIT-2012). Barcelone; 2013. pp. 862-866.

67. Danielisová A, Hajnalova M. Oppida and agricultural production–state of the art and prospects. Case study from Staré Hradisko oppidum (Czech Republic). Hornung, Sabine. Produktion - Distribution - Ökonomie Siedlungs- und Wirtschaftsmuster der Latènezeit. Hornung, Sabine. Bonn: Habelt Verlag; 2014. pp. 407-428.

68. Danielisová A, Olševičová K, Cimler R, Machálek T. Understanding the Iron Age Economy: Sustainability of Agricultural Practices under Stable Population Growth. In: Wurzer G, Kowarik K, Reschreiter H, editors. Agent-based Modeling and Simulation in Archaeology. Cham: Springer International Publishing; 2015. pp. 183-216. https://doi.org/10.1007/978-3-319-00008-4_9

69. Bocquet-Appel J-P, Dubouloz J, Moussa R, Berger J-F, Tresset A, Ortu E, et al. Multi-agent Modelling of the Trajectory of the LBK Neolithic: A Study in Progress. In: Whittle A, Bickle P, editors. Early Farmers: The View from Archaeology and Science. British Academy; 2014. p. 0. https://doi.org/10.5871/bacad/9780197265758.003.0004

70. Dubouloz J, Bocquet-Appel J-P, Moussa R. Multi-Agent Modelling of the Neolithic LBK. 2014.

71. Zanotti A. Modélisation de type multi-agents en archéologie: l'expansion des premiers agriculteurs Balkaniques: adaptation du modèle OBRESOC: manipulation et exploration des données simulées. Ecole Pratique des Hautes Etudes. 2016.

72. Brughmans T, Hanson JW, Mandich MJ, Romanowska I, Rubio-Campillo X, Carrignon S, et al. Formal Modelling Approaches to Complexity Science in Roman Studies: A Manifesto. Theoretical Roman Archaeology Journal. 2019; 2. https://doi.org/10.16995/traj.367

73. Brughmans T, Wilson A, Brughmans T, Wilson A, editors. Simulating Roman Economies: Theories, Methods, and Computational Models. Oxford, New York: Oxford University Press; 2022.

74. Brughmans T, Poblome J. MERCURY: an Agent-Based Model of Tableware Trade in the Roman East. JASSS. 2016; 19: 3.
54. Taylor SJE, editor. Agent-Based Modeling and Simulation. London: Palgrave Macmillan UK; 2014.
https://doi.org/10.1057/9781137453648

55. Wilensky U, Rand W. An Introduction to Agent-Based Modeling: Modeling Natural, Social, and Engineered Complex Systems with NetLogo. Illustrated edition. Cambridge, Massachusetts: The MIT Press; 2015.

56. Janssen M. Introduction to Agent-Based Modeling: with applications to social, ecological, and social-ecological systems. 2020.

57. Lake MW. Trends in Archaeological Simulation. J Archaeol Method Theory. 2014; 21: 258–287.
https://doi.org/10.1007/s10816-013-9188-1

58. Romanowska I, Wren C, Crabtree S. [Agent-Based Modeling for Archaeology], Simulating the Complexity of Societies. Santa Fe: Santa Fe Institute Studies in the Sciences of Complexities; 2021.
https://doi.org/10.37911/9781947864382

59. Kohler TA, van der Leeuw SE, editors. The Model-based Archaeology of Socionatural Systems. School for Advanced Research Press; 2007.

60. Heckbert S. MayaSim: An Agent-Based Model of the Ancient Maya Social-Ecological System. JASSS. 2013; 16: 11.

61. Wilkinson TJ, Christiansen JH, Ur J, Widell M, Altaweel M. Urbanization within a Dynamic Environment: Modeling Bronze Age Communities in Upper Mesopotamia. American Anthropologist. 2007; 109: 52–68.

62. Barton CM, Ullah IIT, Bergin SM, Mitasova H, Sarjoughian H. Looking for the future in the past: Long-term change in socioecological systems. Ecological Modelling. 2012; 241: 42–53. https://doi.org/10.1016/j.ecolmodel.2012.02.010

63. Kowarik K, Reschreiter H, Wurzer G, Totschnig R, Rausch A. Mining with Agents - Agent-based Modeling of the Bronze Age Salt Mine of Hallstatt. CD der Stadt Wien, Stadtarchäologie; 2009. pp. 1–19. Available: https://repositum.tuwien.at/handle/20.500.12708/63691

64. Quesada FJM, Barcelo J, Vilà X. Patagonian Ethnogenesis: towards a computational simulation approach. 2010 [cited 7 Feb 2023]. Available: https://www.academia.edu/35409189/Patagonian_Ethnogenesis_towards_a_computational_simulation Approach

65. Olševičová K, Cimler R, Machálek T. Agent-Based Model of Celtic Population Growth: NetLogo and Python. In: Nguyen NT, Trawiński B, Katarzyniak R, Jo G-S, editors. Advanced Methods for Computational Collective Intelligence. Berlin, Heidelberg: Springer; 2013. pp. 135–143. https://doi.org/10.1007/978-3-642-34300-1_13

66. Olševičová K, Cimler R. Agent-based model of carrying capacity of Celtic settlement agglomeration. Proceedings of 3rd World Conference on Information Technology (WCIT-2012). Barcelone; 2013. pp. 862–866.

67. Danielisová A, Hajnalova M. Oppida and agricultural production–state of the art and prospects. Case study from Staré Hradisko oppidum (Czech Republic). Hornung, Sabine. Produktion - Distribution - Ökonomie Siedlungs- und Wirtschaftsmuster der Latènezeit. Hornung, Sabine. Bonn: Habelt Verlag; 2014. pp. 407–428.

68. Danielisová A, Olševičová K, Cimler R, Machálek T. Understanding the Iron Age Economy: Sustainability of Agricultural Practices under Stable Population Growth. In: Wurzer G, Kowarik K, Reschreiter H, editors. Agent-based Modeling and Simulation in Archaeology. Cham: Springer International Publishing; 2015. pp. 183–216. https://doi.org/10.1007/978-3-319-00008-4_9

69. Bocquet-Appel J-P, Dubouloz J, Moussa R, Berger J-F, Tresset A, Ortu E, et al. Multi-agent Modelling of the Trajectory of the LBK Neolithic: A Study in Progress. In: Whittle A, Bickle P, editors. Early Farmers: The View from Archaeology and Science. British Academy; 2014. p. 0. https://doi.org/10.5871/bacad/9780197265758.003.0004

70. Dubouloz J, Bocquet-Appel J-P, Moussa R. Multi-Agent Modelling of the Neolithic LBK. 2014.

71. Zanotti A. Modélisation de type multi-agents en archéologie: l'expansion des premiers agriculteurs Balkaniques: adaptation du modèle OBRESOC: manipulation et exploration des données simulées. Ecole Pratique des Hautes Etudes. 2016.

72. Brughmans T, Hanson JW, Mandich MJ, Romanowska I, Rubio-Campillo X, Carrignon S, et al. Formal Modelling Approaches to Complexity Science in Roman Studies: A Manifesto. Theoretical Roman Archaeology Journal. 2019; 2. https://doi.org/10.16995/traj.367

73. Brughmans T, Wilson A, Brughmans T, Wilson A, editors. Simulating Roman Economies: Theories, Methods, and Computational Models. Oxford, New York: Oxford University Press; 2022.

74. Brughmans T, Poblome J. MERCURY: an Agent-Based Model of Tableware Trade in the Roman East. JASSS. 2016; 19: 3.
75. Carrignon S, Brughmans T, Romanowska I. Tableware trade in the Roman East: Exploring cultural and economic transmission with agent-based modelling and approximate Bayesian computation. PLOS ONE. 2020; 15: e0240414. https://doi.org/10.1371/journal.pone.0240414 PMID: 33237902

76. Carrignon S, Brughmans T, Romanowska I. Copying of Economic Strategies in Eastern Mediterranean Inter-regional Tableware Trade. In: Brughmans T, Wilson A, editors. Simulating Roman Economies: Theories, Methods, and Computational Models. Oxford University Press; 2022. p. 0. https://doi.org/10.1093/oso/9780192857828.003.0005

77. Joyce J. Modelling Agricultural Strategies in the Dutch Roman Limes via Agent-Based Modelling (ROMFARMS). In: Verhagen P, Joyce J, Groenhuijzen MR, editors. Finding the Limits of the Limes: Modelling Demography, Economy and Transport on the Edge of the Roman Empire. Cham: Springer International Publishing; 2019. pp. 109–127. https://doi.org/10.1007/978-3-030-04576-0_7

78. Edmonds B, Moss S. From KISS to KIDS–An ‘Anti-simplistic’ Modelling Approach. In: Davidsson P, Logan B, Takadama K, editors. Multi-Agent and Multi-Agent-Based Simulation. Berlin, Heidelberg: Springer; 2005. pp. 130–144. https://doi.org/10.1007/978-3-540-32243-6_11

79. Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, et al. A standard protocol for describing individual-based and agent-based models. Ecological Modelling. 2006; 198: 115–126. https://doi.org/10.1016/j.ecolmodel.2006.04.023

80. Grimm V, Railsback SF, Vincenot CE, Berger U, Gallagher C, DeAngelis DL, et al. The ODD Protocol for Describing Agent-Based and Other Simulation Models: A Second Update to Improve Clarity, Replication, and Structural Realism. JASSS. 2020; 23: 7. https://doi.org/10.18564/jasss.4259

81. Brouwer Burg M, Peeters H, Lovis WA, editors. Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling. Cham: Springer International Publishing; 2016. https://doi.org/10.1007/978-3-319-27833-9

82. Niida A, Hasegawa T, Miyano S. Sensitivity analysis of agent-based simulation utilizing massively parallel computation and interactive data visualization. PLOS ONE. 2019; 14: e0210678. https://doi.org/10.1371/journal.pone.0210678 PMID: 30835730

83. Borgonovo E, Pangallo M, Rivkin J, Rizzo L, Siggelkow N. Sensitivity analysis of agent-based models: a new protocol. Comput Math Organ Theory. 2022; 28: 52–94. https://doi.org/10.1007/s10588-021-09358-5

84. Fagiolo G, Moneta A, Windrum P. A Critical Guide to Empirical Validation of Agent-Based Models in Economics: Methodologies, Procedures, and Open Problems. Comput Econ. 2007; 30: 195–226. https://doi.org/10.1007/s10614-007-9104-4

85. Lake M. Spatial Agent-Based Modelling. In: Gillings M, Hacigüzeller P, Lock G, editors. Archaeological Spatial Analysis. Londres: Routledge; 2020.

86. Vlach M. The Antonine Plague: Evaluation of its Impact through Epidemiological Modelling. In: Brughmans T, Wilson A, editors. Simulating Roman Economies: Theories, Methods, and Computational Models. Oxford University Press; 2022. pp. 69–108. https://doi.org/10.1093/oso/9780192857828.003.0003

87. Lake MW. MAGICAL computer simulation of Mesolithic foraging. Dynamics in human and primate societies: agent-based modelling of social and spatial processes. 2000; 107–143.

88. Brantingham PJ. A Neutral Model of Stone Raw Material Procurement. American Antiquity. 2003; 68: 487–509. https://doi.org/10.2307/3557105

89. Premo LS. Agent-based models as behavioral laboratories for evolutionary anthropological research. Arizona Anthropologist. 2006; 17. Available: http://journals.librarypublishing.arizona.edu/arizanthro/article/id/413/

90. Wren CD, Botha S, De Vynck J, Janssen MA, Hill K, Shook E, et al. The foraging potential of the Holocene Cape south coast of South Africa without the Palaeo-Agulhas Plain. Quaternary Science Reviews. 2020; 235: 105789. https://doi.org/10.1016/j.quascirev.2019.06.012

91. Thomas LS, Wickham-Jones CR, Heppenstall AJ. Combining Agent-Based Modelling and Geographical Information Systems to Create a New Approach for Modelling Movement Dynamics: A Case Study of Mesolithic Orkney. Open Archaeology. 2022; 8: 987–1009. https://doi.org/10.1515/opar-2022-0257

92. Vita-Finzi C, Higgs ES, Sturdy D, Harriss J, Legge AJ, Tippett H. Prehistoric Economy in the Mount Carmel Area of Palestine: Site Catchment Analysis. Proceedings of the Prehistoric Society. 1970; 36: 1–37. https://doi.org/10.1017/S0079497X00013074

93. Phan D. Chapitre 7. La modélisation à base d'agents et la simulation par systèmes multi-agents de sociétés d'agents intentionnels. Modéliser & simuler–Tome 2. Éditions Matériologiques; 2014. pp. 193–244. Available: https://www.cairn-sciences.info/modeliser-et-simuler-tome-2-9782919694730-page-193.htm
75. Carrignon S, Brughmans T, Romanowska I. Tableware trade in the Roman East: Exploring cultural and economic transmission with agent-based modelling and approximate Bayesian computation. PLOS ONE. 2020; 15: e0240414. https://doi.org/10.1371/journal.pone.0240414 PMID: 33237902

76. Carrignon S, Brughmans T, Romanowska I. Copying of Economic Strategies in Eastern Mediterranean Inter-regional Tableware Trade. In: Brughmans T, Wilson A, editors. Simulating Roman Economies: Theories, Methods, and Computational Models. Oxford University Press; 2022. p. 0. https://doi.org/10.1093/oso/9780192857828.003.0005

77. Joyce J. Modelling Agricultural Strategies in the Dutch Roman Limes via Agent-Based Modelling (ROMFARMS). In: Verhagen P, Joyce J, Groenhuijzen MR, editors. Finding the Limits of the Limes: Modelling Demography, Economy and Transport on the Edge of the Roman Empire. Cham: Springer International Publishing; 2019. pp. 109–127. https://doi.org/10.1007/978-3-030-04576-0_7

78. Edmonds B, Moss S. From KISS to KIDS–An ‘Anti-simplistic’ Modelling Approach. In: Davidsson P, Logan B, Takadama K, editors. Multi-Agent and Multi-Agent-Based Simulation. Berlin, Heidelberg: Springer; 2005. pp. 130–144. https://doi.org/10.1007/978-3-540-32243-6_11

79. Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, et al. A standard protocol for describing individual-based and agent-based models. Ecological Modelling. 2006; 198: 115–126. https://doi.org/10.1016/j.ecolmodel.2006.04.023

80. Grimm V, Railsback SF, Vincenot CE, Berger U, Gallagher C, DeAngelis DL, et al. The ODD Protocol for Describing Agent-Based and Other Simulation Models: A Second Update to Improve Clarity, Replication, and Structural Realism. JASSS. 2020; 23: 7. https://doi.org/10.18564/jasss.4259

81. Brouwer Burg M, Peeters H, Lovis WA, editors. Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling. Cham: Springer International Publishing; 2016. https://doi.org/10.1007/978-3-319-27833-9

82. Niida A, Hasegawa T, Miyano S. Sensitivity analysis of agent-based simulation utilizing massively parallel computation and interactive data visualization. PLOS ONE. 2019; 14: e0210678. https://doi.org/10.1371/journal.pone.0210678 PMID: 30835730

83. Borgonovo E, Pangallo M, Rivkin J, Rizzo L, Siggelkow N. Sensitivity analysis of agent-based models: a new protocol. Comput Math Organ Theory. 2022; 28: 52–94. https://doi.org/10.1007/s10588-021-09358-5

84. Fagiolo G, Moneta A, Windrum P. A Critical Guide to Empirical Validation of Agent-Based Models in Economics: Methodologies, Procedures, and Open Problems. Comput Econ. 2007; 30: 195–226. https://doi.org/10.1007/s10614-007-9104-4

85. Lake M. Spatial Agent-Based Modelling. In: Gillings M, Hacigüzeller P, Lock G, editors. Archaeological Spatial Analysis. Londres: Routledge; 2020.

86. Vlach M. The Antonine Plague: Evaluation of its Impact through Epidemiological Modelling. In: Brughmans T, Wilson A, editors. Simulating Roman Economies: Theories, Methods, and Computational Models. Oxford University Press; 2022. pp. 69–108. https://doi.org/10.1093/oso/9780192857828.003.0003

87. Lake MW. MAGICAL computer simulation of Mesolithic foraging. Dynamics in human and primate societies: agent-based modelling of social and spatial processes. 2000; 107–143.

88. Brantingham PJ. A Neutral Model of Stone Raw Material Procurement. American Antiquity. 2003; 68: 487–509. https://doi.org/10.2307/3557105

89. Premo LS. Agent-based models as behavioral laboratories for evolutionary anthropological research. Arizona Anthropologist. 2006; 17. Available: http://journals.librarypublishing.arizona.edu/arizanthro/article/id/413/

90. Wren CD, Botha S, De Vynck J, Janssen MA, Hill K, Shook E, et al. The foraging potential of the Holocene Cape south coast of South Africa without the Palaeo-Agulhas Plain. Quaternary Science Reviews. 2020; 235: 105789. https://doi.org/10.1016/j.quascirev.2019.06.012

91. Thomas LS, Wickham-Jones CR, Heppenstall AJ. Combining Agent-Based Modelling and Geographical Information Systems to Create a New Approach for Modelling Movement Dynamics: A Case Study of Mesolithic Orkney. Open Archaeology. 2022; 8: 987–1009. https://doi.org/10.1515/opar-2022-0257

92. Vita-Finzi C, Higgs ES, Sturdy D, Harriss J, Legge AJ, Tippett H. Prehistoric Economy in the Mount Carmel Area of Palestine: Site Catchment Analysis. Proceedings of the Prehistoric Society. 1970; 36: 1–37. https://doi.org/10.1017/S0079497X00013074

93. Phan D. Chapitre 7. La modélisation à base d'agents et la simulation par systèmes multi-agents de sociétés d'agents intentionnels. Modéliser & simuler–Tome 2. Éditions Matériologiques; 2014. pp. 193–244. Available: https://www.cairn-sciences.info/modeliser-et-simuler-tome-2-9782919694730-page-193.htm
94. Sanders L, Pumain D, Mathian H, Guérin-Page F, Bura S. Simulation de l'évolution du peuplement par les systèmes multi-agents (Simulation of a settlement system evolution by a multi-agent system). Bulletin de l'Association de Géographes Français. 1997; 74: 385-396. https://doi.org/10.3406/bagf.1997.1998

95. Tannier C, Cura R, Leturcq S, Zadora-Rio E. An agent-based model for exploring the combined effects of social and demographic changes on the concentration and hierarchy of rural settlement patterns in North-Western Europe during the Middle Ages (800-1200 CE). Journal of Anthropological Archaeology. 2020; 59: 101204. https://doi.org/10.1016/j.jaa.2020.101204

96. Crema ER. A Simulation Model of Fission-Fusion Dynamics and Long-Term Settlement Change. J Archaeol Method Theory. 2014; 21: 385-404. https://doi.org/10.1007/s10816-013-9185-4

97. Bertoncello F, Ouriachi M-J, Pereira C da C, Tettamanzi A, Purdue L, Contreras D, et al. Modelling complex systems in Archaeology: general issues and first insights from the ModelAnSet project. Université Côte d'Azur; 2018. p. 145. Available: https://hal.science/hal-02014645

98. Vidal-Cordasco M, Nuevo-López A. Resilience and vulnerability to climate change in the Greek Dark Ages. Journal of Anthropological Archaeology. 2021; 61: 101239. https://doi.org/10.1016/j.jaa.2020.101239

99. Angourakis A, Bates J, Baudouin J-P, Giesche A, Walker JR, Ustunkaya MC, et al. Weather, Land and Crops in the Indus Village Model: A Simulation Framework for Crop Dynamics under Environmental Variability and Climate Change in the Indus Civilisation. Quaternary. 2022; 5: 25. https://doi.org/10.3390/quat5020025

100. Bernigaud N, Bertoncello F, Ouriachi M-J, Guiot J, Bondeau A. Simulation et Systèmes Multi-Agents (SMA), Bilan et perspectives pour l'archéologie du peuplement, des paysages et de l'environnement. In: Bertoncello F, Ouriachi M-J, Nuninger L, Favory F, editors. Settlement, territory and landscape dynamics: Assessment and prospects in spatial archaeology, tribute to Jean-Luc Fiches 42es rencontres internationales d'archéologie et d'histoire-Nice Côte d'Azur. Nice: APDCA; 2023. pp. 225-238.

101. Bondeau A, Smith PC, Zaehle S, Schaphoff S, Lucht W, Cramer W, et al. Modelling the role of agriculture for the 20th century global terrestrial carbon balance. Global Change Biology. 2007; 13: 679-706. https://doi.org/10.1111/j.1365-2486.2006.01305.x

102. Schaphoff S, von Bloh W, Rammig A, Thonicke K, Biemans H, Forkel M, et al. LPJmL4-a dynamic global vegetation model with managed land-Part 1: Model description. Geoscientific Model Development. 2018; 11: 1343-1375. https://doi.org/10.5194/gmd-11-1343-2018

103. Contreras DA, Hiriart E, Bondeau A, Kirman A, Guiot J, Bernard L, et al. Regional paleoclimates and local consequences: Integrating GIS analysis of diachronic settlement patterns and process-based agroecosystem modeling of potential agricultural productivity in Provence (France). PLOS ONE. 2018; 13: e0207622. https://doi.org/10.1371/journal.pone.0207622 PMID: 30540786

104. Contreras DA, Bondeau A, Guiot J, Kirman A, Hiriart E, Bernard L, et al. From paleoclimate variables to prehistoric agriculture: Using a process-based agro-ecosystem model to simulate the impacts of Holocene climate change on potential agricultural productivity in Provence, France. Quaternary International. 2019; 501: 303-316. https://doi.org/10.1016/j.quaint.2018.02.019

105. Contreras D, Guiot J, Suarez R, Kirman A. Reaching the human scale: A spatial and temporal down-scaling approach to the archaeological implications of paleoclimate data. Journal of Archaeological Science. 2018; 93: 54-67. https://doi.org/10.1016/j.jas.2018.02.013

106. Guiot J, Kaniewski D. The Mediterranean Basin and Southern Europe in a warmer world: what can we learn from the past? Frontiers in Earth Science. 2015; 3. https://doi.org/10.3389/feart.2015.00028

107. Mattingly DJ. Regional variation in Roman oleoculture: some problems of comparability. Landuse in the Roman Empire. Rome: L'Erma di Bretschneider; 1994. pp. 91-106.

108. Scheidel W, Friesen SJ. The Size of the Economy and the Distribution of Income in the Roman Empire. The Journal of Roman Studies. 2009; 99: 61-91.

109. Étienne R. La comptabilité de Columelle. Publications de l'École Française de Rome. 1980; 37: 121-128.

110. Brun J-P. Oleiculture antique en provence: les huileries du département du Var. Paris, France: CNRS Éditions; 1986. Available: https://www.librairiemartelle.com/livre/9782222037194-oleiculture-antique-en-provence-huileries-departement-var-suppl-revue-archeologique/

111. Peregrine PN. Climate and social change at the start of the Late Antique Little Ice Age. The Holocene. 2020; 30: 1643-1648. https://doi.org/10.1177/0959683620941079

112. Brun J-P. 15. Viticulture et oléiculture en Gaule. Comment les Gaules devinrent romaines. Paris: La Découverte; 2010. pp. 231-253. https://doi.org/10.3917/dec.ouzou.2010.01.0231

113. Marzano A. Country villas in Roman central Italy: reassessing the evidence. In: Aubert J-J, Várhelyi Z, editors. Munchen: K G Saur Verlag Gmbh & Co; 2005. pp. 241-262. Available: http://www.degruyter.com/cont/fb/ge/detailEn.cfm?id=IS-9783598778285-1
94. Sanders L, Pumain D, Mathian H, Guérin-Page F, Bura S. Simulation de l'évolution du peuplement par les systèmes multi-agents (Simulation of a settlement system evolution by a multi-agent system). Bulletin de l'Association de Géographes Français. 1997; 74: 385-396. https://doi.org/10.3406/bagf.1997.1998

95. Tannier C, Cura R, Leturcq S, Zadora-Rio E. An agent-based model for exploring the combined effects of social and demographic changes on the concentration and hierarchy of rural settlement patterns in North-Western Europe during the Middle Ages (800-1200 CE). Journal of Anthropological Archaeology. 2020; 59: 101204. https://doi.org/10.1016/j.jaa.2020.101204

96. Crema ER. A Simulation Model of Fission-Fusion Dynamics and Long-Term Settlement Change. J Archaeol Method Theory. 2014; 21: 385-404. https://doi.org/10.1007/s10816-013-9185-4

97. Bertoncello F, Ouriachi M-J, Pereira C da C, Tettamanzi A, Purdue L, Contreras D, et al. Modelling complex systems in Archaeology: general issues and first insights from the ModelAnSet project. Université Côte d'Azur; 2018. p. 145. Available: https://hal.science/hal-02014645

98. Vidal-Cordasco M, Nuevo-López A. Resilience and vulnerability to climate change in the Greek Dark Ages. Journal of Anthropological Archaeology. 2021; 61: 101239. https://doi.org/10.1016/j.jaa.2020.101239

99. Angourakis A, Bates J, Baudouin J-P, Giesche A, Walker JR, Ustunkaya MC, et al. Weather, Land and Crops in the Indus Village Model: A Simulation Framework for Crop Dynamics under Environmental Variability and Climate Change in the Indus Civilisation. Quaternary. 2022; 5: 25. https://doi.org/10.3390/quat5020025

100. Bernigaud N, Bertoncello F, Ouriachi M-J, Guiot J, Bondeau A. Simulation et Systèmes Multi-Agents (SMA), Bilan et perspectives pour l'archéologie du peuplement, des paysages et de l'environnement. In: Bertoncello F, Ouriachi M-J, Nuninger L, Favory F, editors. Settlement, territory and landscape dynamics: Assessment and prospects in spatial archaeology, tribute to Jean-Luc Fiches 42es rencontres internationales d'archéologie et d'histoire-Nice Côte d'Azur. Nice: APDCA; 2023. pp. 225-238.

101. Bondeau A, Smith PC, Zaehle S, Schaphoff S, Lucht W, Cramer W, et al. Modelling the role of agriculture for the 20th century global terrestrial carbon balance. Global Change Biology. 2007; 13: 679-706. https://doi.org/10.1111/j.1365-2486.2006.01305.x

102. Schaphoff S, von Bloh W, Rammig A, Thonicke K, Biemans H, Forkel M, et al. LPJmL4-a dynamic global vegetation model with managed land-Part 1: Model description. Geoscientific Model Development. 2018; 11: 1343-1375. https://doi.org/10.5194/gmd-11-1343-2018

103. Contreras DA, Hiriart E, Bondeau A, Kirman A, Guiot J, Bernard L, et al. Regional paleoclimates and local consequences: Integrating GIS analysis of diachronic settlement patterns and process-based agroecosystem modeling of potential agricultural productivity in Provence (France). PLOS ONE. 2018; 13: e0207622. https://doi.org/10.1371/journal.pone.0207622 PMID: 30540786

104. Contreras DA, Bondeau A, Guiot J, Kirman A, Hiriart E, Bernard L, et al. From paleoclimate variables to prehistoric agriculture: Using a process-based agro-ecosystem model to simulate the impacts of Holocene climate change on potential agricultural productivity in Provence, France. Quaternary International. 2019; 501: 303-316. https://doi.org/10.1016/j.quaint.2018.02.019

105. Contreras D, Guiot J, Suarez R, Kirman A. Reaching the human scale: A spatial and temporal down-scaling approach to the archaeological implications of paleoclimate data. Journal of Archaeological Science. 2018; 93: 54-67. https://doi.org/10.1016/j.jas.2018.02.013

106. Guiot J, Kaniewski D. The Mediterranean Basin and Southern Europe in a warmer world: what can we learn from the past? Frontiers in Earth Science. 2015; 3. https://doi.org/10.3389/feart.2015.00028

107. Mattingly DJ. Regional variation in Roman oleoculture: some problems of comparability. Landuse in the Roman Empire. Rome: L'Erma di Bretschneider; 1994. pp. 91-106.

108. Scheidel W, Friesen SJ. The Size of the Economy and the Distribution of Income in the Roman Empire. The Journal of Roman Studies. 2009; 99: 61-91.

109. Étienne R. La comptabilité de Columelle. Publications de l'École Française de Rome. 1980; 37: 121-128.

110. Brun J-P. Oleiculture antique en provence: les huileries du département du Var. Paris, France: CNRS Éditions; 1986. Available: https://www.librairiemartelle.com/livre/9782222037194-oleiculture-antique-en-provence-huileries-departement-var-suppl-revue-archeologique/

111. Peregrine PN. Climate and social change at the start of the Late Antique Little Ice Age. The Holocene. 2020; 30: 1643-1648. https://doi.org/10.1177/0959683620941079

112. Brun J-P. 15. Viticulture et oléiculture en Gaule. Comment les Gaules devinrent romaines. Paris: La Découverte; 2010. pp. 231-253. https://doi.org/10.3917/dec.ouzou.2010.01.0231

113. Marzano A. Country villas in Roman central Italy: reassessing the evidence. In: Aubert J-J, Várhelyi Z, editors. Munchen: K G Saur Verlag Gmbh & Co; 2005. pp. 241-262. Available: http://www.degruyter.com/cont/fb/ge/detailEn.cfm?id=IS-9783598778285-1