Introduction

1The question of the emergence of feudal society in the West is at the heart of a long-standing historical debate. Since the eighteenth century, scholars have been seeking to understand how medieval society functioned and identify its fundamental elements. The archives are being continually explored in an effort to understand, individually and with precision, the multiple factors at work in the processes that caused a society called ‘feudal’ to emerge over the tenth and eleventh centuries. Such understanding, however, runs up against the exceeding complexity of these processes, which may vary chronologically but also present infinite nuances according to the regions being studied. These difficulties are further amplified by issues of access to data, which is highly variable according to the state of the documentation, which is subject to the hazards of preservation; in general, historians of feudal times work on rare and fragmentary documents, traces of a society fundamentally transmitted orally. New illuminations, however, have appeared to renew and enrich these debates, starting about forty years ago, thanks to the massive inflow of archaeological records stemming from preventive archaeology. Textual sources, which shed a more or less normative light on the society, can from now on be confronted with material sources capable of better assessing its practical dimensions. Nevertheless, this complementarity of textual and material approaches, far from simplifying interrogations concerning feudal society, has rendered them still more complex by highlighting anthropological aspects and geographical differences hitherto underestimated. The debate has found itself reinvigorated as a result, focussing now on the question of the use of space, considered as an effective marker of social transformations. The fragmentation and dissemination of powers to which the proliferation of castles (seignorial fiefs) bears witness takes place concomitantly with a highly structured religious network (parochialisation of the society), while a settlement system based on a village network is definitively established, the heart of an active communal life. It is therefore with the inter-connections among these three fundamental elements of feudal society (castles, parish churches, villages) that analyses and theories are concerned today. The establishment, concentration and hierarchisation of centres of settlement are now the large social processes being examined through a magnifying glass in approaching medieval society. Medieval historians analyse the ‘encellulement’ of the society2, tracing, on the one hand, the spatial attractiveness of castles (the phenomenon of incastellamento3) and parish churches, together with their cemetery, considered as rallying points of peasant populations, and, on the other hand, the ways in which populations collectively organise the spaces of production (village land) to assure the balanced distribution of resources. In this context, the period 800-1200 is usually considered to be one of transition, during which feudal society developed its structure, with certain scholars evoking the ‘révolution de l’an Mil’ (revolution of the year 1000)4, while others qualify this by speaking of the ‘révélation [revelation] de l’an Mil’5 (‘revelation’ by way of the quantity and quality of the textual documentation). The hypotheses, then, are numerous, and it is difficult to come down in favour of one or the other, so complex is the juncture of social, political, institutional, economic and cultural factors.

2Within the framework of the ANR research project TransMonDyn, the objective, for the transition of the years 800-1200, is to study the processes at work in the dynamic of establishment, clustering and hierarchisation of rural habitat. The approach is resolutely geographic; it is the spatial implications of the social changes that are at the heart of the study. The modelling does not deal with the political and social transformations themselves, but with their impact on the settlement system. The central interrogation consists in examining the combination of factors which permitted, between 800 and 1200, the formation of aggregates of peasant households in a hierarchised and durable form, attracted by the castles or the churches. The idea is to analyse, by means of modelling and computer simulation, the conditions in which the village network emerged.

Setting time limits for the transition

Regime 1

3Regime R1 corresponds to a situation observable at the time of the rise of the Carolingian empire. Around the year 800 CE, that Empire reached its greatest territorial extent, covering a large swathe of Europe from the Ebro to the Elbe. Power was centralised: the sovereign assured himself of the loyalty of the great aristocrats by distributing lands taken from across the whole empire, political offices and riches (gold, silver, slaves…) acquired in the course of annual raids against pagan peoples bordering the territories of the Franks.

4Regionally, settlement patterns were a mix of small scattered villages (loose clusters of a few houses) and isolated farmsteads. Villages and farms were impermanent, and their location often shifted by a few tens of metres or up to several hundred metres every one or two centuries. In this period, towns were civitas capitals inherited from Antiquity. Some served a central function as episcopal sees, but their economic and administrative role was minor.

Regime 2

5Regime 2 is dated from around 1200, at a period when royal authority was in decline and the territory over which it was concretely manifested was reduced to the extent of a province. The reality of political power was in the hands of county dynasties arrogating the prerogatives of public government (justice, military service, taxation). Kings, for practical purposes, intervened scarcely at all in the domains of their great vassals, who themselves constituted their own networks of loyal adherents. These aristocratic houses could not increase their power except by despoiling their neighbours: these rivalries led to a widespread militarisation of society. The costs imposed by this (construction of castles, expenses for armaments, maintenance of knights…) meant that the lords exercised great pressure through taxation on the peasants.

6Because of the imposition of ecclesiastical power, the religious constraints on lay society were very strong.

7The towns that had existed in 800 CE had grown much larger, having developed productive and commercial activities, and new nuclei had formed around suburban monasteries. Many small towns had emerged around castles or rural monasteries ringed by their own precinct walls. This spatial configuration of peopling corresponding to Regime 2 remained in place until the French Revolution and even after, the hierarchical conditions established in the settlement system becoming stronger until that event.

Transformations between 800 and 1200

8In the course of the transition, notable changes occurred at different spatial levels.

At the level of north-western Europe in its entirety

9Under the influence of different factors, especially in combination (crises of succession, pressure resulting from Viking, but also Saracen, raids, the end of Christendom’s territorial expansion …), the empire repeatedly fragmented, first into kingdoms, then into principalities. The Carolingian economic model, based principally on military conquest and an economy of plunder (tributes, slaves) was transformed. The drying up of this source of revenues entailed a reduction in the rewards that the central authority was able to grant.

Within the regional sub-units (provinces, principalities)

10In reaction to the loss of power of the central authority, competition for land and resources increased, stirring up a climate of violence and confrontations that produced defensive structures and a search for protection. Thus, one witnessed the first appearance of castles, which multiplied and covered the space under study.

11At the same time, the religious structure around populations was reinforced at the local level with the creation of a network of parishes, organised according to dispersed ecclesiastic centres, each consisting of a parish church and its cemetery. The privileges attached to churches, of a fiscal nature (tithes) or a religious one (the obligation to attend Sunday services, to receive the sacraments and to be buried in the adjoining cemetery), determined the formation of parochial territories. In the process, Europe became covered by its ‘blanc manteau d’églises’ (white mantle of churches), according to the famous expression of Raoul Glaber at the beginning of the eleventh century. The cost of these new buildings and of maintaining the clergy charged with directing them was cushioned by the increasingly substantial gifts of secular lords (in material form – priories, lands – and immaterial – rights of use, rights of justice) and by increasing levies on parishioners (tithes in particular). The clergy thus succeeded in attracting around parish churches the faithful who brought them social control and revenues.

12These political and social changes had a significant impact on the settlement system. One witnessed the establishment of a new territorial network (parochial and signorial) and a clustering of settlement around places of power (churches, castles), entailing the emergence of new attraction centres (small towns, villages). These phenomena of attraction, more or less important, depending on the attractors, led to a hierarchisation of the settlement system among small towns, villages, small hamlets. This attraction was reinforced by a structuring into communities of peasant society. These village communities, founded on a principle of solidarity, organised not only the exploitation of the food-producing territory, especially of pasture resources, but also their relationship with the signorial lords. The peasants thereby acquired an economic interest in the rationalisation of agricultural practices (for example, crop rotation and common pasturage…), but also a counter-weight in the power-relations that opposed them to their lords, secular or ecclesiastic.

The area of study

13Modelling the general movement of fixing and clustering settlement between 800 and 11606 entails representing the attractiveness of the parish churches and the castles. To do this, the study area has to be large enough to enable us to observe the increasing coverage of space with parishes and castles – on the order of a diocese, for example. Our reference case study is the diocese of Tours, whose settlement dynamics during the Middles Ages have been closely analysed7. A series of quantitative indexes has been derived from archaeological records and historical texts and can be used to calibrate the model and assess the simulation results.

First step in the modelling

Identification of the entities involved in the transition

14The first step in modelling this transition was to identify and describe the spatial entities involved. This task was supported by a geographical reading grid that permits observation of a settlement system according to three levels of analysis present in the transition 800-1200:

• fundamental spatial entities:

  • the agricultural holding, which includes a central unit (living space and annexes), as well as the lands depending on it;

  • the signorial space, which is the territory where the lord exercises his power (a river, a mill, a territory more or less extensive...) and may include different sub-divisions, with a single tenant or several;

  • the catchment area of parish churches, territory over which the church exercises dominion, and which is an emergent spatial entity in the course of the transition.

• mesoscopic spatial entities:

  • villages which consist of a more or less loose cluster of agricultural holdings. They may or may not be the site of a market or fair, and may or may not include a castle, a church or a monastery;

  • towns which include several parishes, signorial courts, merchants, artisans and peasants.

• a macroscopic spatial entity, any region of north-west Christian Europe in 800.

15To describe the processes at work in the course of the transition, it is also necessary to identify the social entities which are agents of changes; these are divided into seven categories:

• the peasant households (families) have the use of an agricultural holding, in which they exercise multiple agricultural activities;

• the households of artisan-merchants sell their home-crafted production in markets or fairs; they may be located in a town or a village;

• the merchants’ centres of activity have the particularity of being located exclusively in towns;

• the secular lords and their entourages (knights, etc.), each entity corresponding to an aristocratic family, its clients and its seat of justice;

• the ecclesiastical lords, each entity corresponding to a religious community, its clients (who may be secular) and its seat of justice;

• the bishop, representative of the Holy See at the diocesan level;

• finally, the central authority (king or emperor).

16In an earlier publication, we have identified and characterised the structural relations between the different spatial and social entities (see Cécile Tannier et al.8, figure 13.1, page 295).

Identification of the processes at work in the transition

17In order to describe as clearly as possible the processes at work in the course of the tradition, we have chosen to multiply the points of view by means of different graphic representations: arrow diagrams and flow charts. Figure 1 is an example. It describes the actions performed by different social entities, represented in the form of rectangles with rounded corners. These actions involve the modification of the attributes of other entities, which may be either social or spatial (represented in the figure in the form of simple rectangles). These modifications themselves entail (directly or indirectly) a change in the settlement pattern: appearance of churches, of priories and of castles, change of location of peasant households.

Establishing rules of behaviour for each social entity

18Establishing rules of behaviour for the social entities consists in identifying stylised facts representing certain aspects of the transition being studied. Table 1 describes these, presenting the objectives of each social entity with the corresponding actions it might undertake to attain them. Certain of these actions directly influence the spatial configuration of the settlement system: creation of castles, priories, parishes; relocation of peasant households. Other actions permit the growth in power of the entities involved, hence the attractiveness of the seats of power (castles, priories, abbeys) or, instead, of villages, when they possess a powerful village community. These actions have an indirect spatial impact.

19Other entities were identified during the first steps of modelling as having a major role in the transition. The decision was made to set aside those that had no direct spatial influence (the mercantile world) or no spatial representation on a regional scale – the case, notably, of the central authority (king or emperor) and of the Holy See.

Figure 1: Actions of different social and spatial entities having a direct or indirect impact on the spatial configuration of regional settlement in north-west Europe between 800 and 1200.

Towards a multi-agent model of transition simulation

20Following this methodological and conceptual procedure, it has been possible to represent some of the processes at work in the form of a simulation model entitled SimFeodal. The objective of this model was to simulate, not the political and social transformations themselves, but their impact on the settlement system at the level of regional analysis. The regional organisations of settlement are very diverse in north-western Europe during the period studied, but they present common features which the model aims at reproducing. It must therefore be sufficiently generic to adapt itself to different regional contexts by way of the modification, by the user, of the parameters and the entries of the model without touching the behavioural rules of the agents. On this basis, the purpose was to find, by means of an exploration through simulation, the values of variables and parameters permitting the reproduction of the dynamics observed in Touraine, the model and its parameter settings thereby becoming candidates for explaining these dynamics.

21The model SimFeodal must be easy to understand and lend itself to discussion: this is why we have chosen to adopt agent-based modelling, in which the behaviour of the entities modelled are represented explicitly. The space modelled reproduces in stylised fashion the frameworks of a principality of the period termed feudal. Each step in the simulation represents 20 years. The model has been created using the GAMA platform.9,10

General architecture of the SimFeodal model¹¹

22Since the transition is being studied from the point of view of the spatial modifications it produced, the agents of the model are either spatial or socio-spatial. From their interactions in the course of a simulation must emerge those transformations of the regional settlement system described earlier.

23The agents represented in the model were defined on the basis of research on Touraine carried out through archaeological records and historical texts extant for the period12. Archaeological surveys and excavations yield a rich database concerning the dynamics of the occupation of the land for the period 800-1200 (vestiges of isolated forms, of hamlets, of villages, of the sites of castles and monasteries…). The basic material, then, is by nature spatial. The textual sources, for their part, take the form of narrative sources (chronicles, annals, histories) and practical records (charters et notices), which give a picture of events, transactions and decisions capable of affecting the occupation of the land from the point of view of the powerful – secular and ecclesiastic lords. Combining the textual and material sources enriches understanding of the behaviour of each agent, but also of the interaction between the agents.

The agents of the model

24The peasants – the majority of the population – are represented by means of agents ‘Peasant Households’ (table 2). The peasant households have a spatial representation corresponding to the location of their farms. This is an abstraction, if only because the peasant households are considered as enduring for the entire span of the transition – something more like the lifetime of the building than that of its inhabitants. Their behaviour in the model represents only the processes which impel them to modify their location.

25In the same way, and with a similar level of abstraction, those holding power are modelled by way of the agents ‘Lords’. These cut across the entire period and so tend to be representative of the functions they discharge rather than of individuals, strictly speaking, in particular when it comes to ecclesiastical lords. The minor lords are situated within the modelled space and have a limited radius of action around their location, whereas the overlords are not situated in one point within the modelled space and can intervene everywhere. The actions of the lords correspond to the creation of spatial entities dependent on them. These are ‘Taxation areas’, spatial representations of the logic of collecting payments and obligations, and instruments of the constitution of their power. The taxation zones are circular in form and have a highly variable radius (from a few dozen metres to many kilometres). The rates of taxation associated with them are likewise variable. Three types of collected fees are involved: rents (farmed lands), rights of high justice (crimes of blood…), other rights (low and middle justice, litigation, communal rights (use of mills, ovens).

26The ‘attractor’ agents created by the lords (‘churches’ and ‘castles’) are specific local spatial entities. When the churches are parochial, they exert an attraction on the peasant households.

27The agents ‘Population clusters’ are generic spatial entities including villages and towns.

28Each category of agents has different characteristics and modes of behaviour. The spatial agents are located in the space modelled. The social (or socio-spatial) agents represent social entities on the historical level. The active agents move (this is the case with the agents ‘peasant households’), or instead create or modify other agents (the agents ‘lords’ can create agents ‘castles’ and ‘taxation areas’; the agents ‘parish churches’ can modify the contour of the parochial influence (i.e., the catchment area) of their neighbours).

Dynamics modelled

29Within the framework of this simulation experiment, seeking to analyse the free-play of the agents submitted to simple rules, we have suppressed every deus ex machina usually invoked as a factor explaining the dynamics observed. Thus, we postulate no hypothesis of crisis or economic growth (no increase or decrease of production, no allowance for a possible improvement of productivity or yields). We also eliminate the hypothesis of demographic growth. Finally, environmental dynamics, such as, for instance, the most positive possible climatic situation, have not been taken into account.

30The emergence of a climate of internal violence in the region modelled (figure 2), resulting from the growing conflictual tendency of lords in the course of the tenth century, is represented in the model by the apparition, then the increase, of a need for protection of the peasant households. The latter then sought to locate as close as possible to a castle in order to benefit from its protection. The increase in religious obligations, resulting notably from the development of pastoral care, manifested itself, for its part, through the increasing attractiveness of parish churches for the peasant household, which pressed the latter to change location in order to get closer to them.

31The peasant households have the possibility of moving (i.e., of modifying the location of their farms) at every step of the model. Their displacements take place towards the most attractive poles situated nearby or, more rarely, at longer distances. The serfs, who did not have the right to leave the lands of their lords13, are represented here in the form of a fraction of peasant households that are able to move only locally.

32The castles and parochial churches are much more limited in number that the peasant households. In approaching these poles, the peasant households thereby constitute population clusters. These clusters may be endowed with a village community, which increases the satisfaction of the peasant households located in such a cluster. Thus, the model indirectly represents the fact that the communities are taken to favour the growth in yields of the farms (especially by communal crop rotation) and diminish the weight of the local lord with respect to the balance of forces.

33Lords collect fees from peasant households, construct castles and, in a competitive process of arrogating powers, attempt to increase their military capacities by assuring the loyalty of a growing number of warriors by turning over rights or lands to them. The basic mechanism is to collect fees from all peasant households located within their tax area, considered as belonging to the lords which create them. In the model, throughout the simulation, new fees are added to existing ones, and new zones of taxation appear, superimposed wholly or partially upon others. This corresponds historically to the flood of dismantling of royal rights (including justice), or again to the creation of new equipment (ovens, mills, wine-presses). These stimulate the formation of taxation zones for the associated communal rights. Besides these mechanisms for creating rights, the lords assure their influence and the loyalty of their vassals by the assignment of rights over their taxation zones or their equipment. For example, when a lord constructs a castle, he can entrust the guarding of it, with all or part of the associated revenues, to a lord of lesser rank who from that point becomes his vassal. By an extension of this logic, and in order to reproduce in the model the parcelling out of signorial powers (especially on the local level), it is assumed that the lords can give all or part of the taxation zones belonging to them to other lords, who are already, or who become, their vassals. A lord who assigns part of his rights to a vassal gains more power than by exercising them himself.

34Throughout the simulation, peasant households disappear and appear, castles are constructed and churches erected. The taxation zones created and possessed by the lords proliferate, increasing the fiscal pressure on the peasant households. Clusters of peasant households appear, become larger or disappear.

Figure 2: The historical processes observed in Touraine and their introduction into the model in the form of exogenous events¹⁴.

The initial state of the model

35The model aims to reproduce the common features of the great diversity of spatial structures over the period studied in north-western Europe. To do this, it includes numerous parameters, which should make it possible, by their variation, to represent the particularities of each of the regional subsections of the area under study. The data and knowledge available for Touraine, which is the reference point chosen to construct an initial version of the model, have allowed us to quantify a certain number of parameters (table 3). Subsequent variation of the parameters and the initial situations will permit simulation of the dynamics at work in other regions of north-western Europe between 800 and 1200.

The space modelled: a Touraine very much stylised

36The space modelled is a zone of 80 kilometres on each side, representing in simplified fashion a diocese of north-west Europe, following the example of Tours. The space modelled is considered as homogeneous, that is, no natural element is represented capable of influencing the dynamics of settlement, whether high ground, water courses, shore-line areas, vegetal covering or deposits of resources. The point is to eliminate any potential source of interference with the processes that are the intended object of the experiment.

37Roman small towns are present at the point of initialisation, as well as twenty or so villages (table 3). The fact that a secondary agglomeration, even a village, also includes artisans (and undoubtedly priests, magistrates, merchants…) is not part of the model. In addition, no major city – here, namely, the city of Tours – is represented, for a number of reasons. In the first place, in the stylised geographic framework defined for modelling, the historical data show that there existed only one city of this kind, so that the problematic of spatial competition between urban centres, or again networks of cities, does not apply. Next, on the scale of analysis of the model, it is not possible to deal with the question of the production of specifically inter-urban spaces. Finally, we know nothing about the attractiveness of Tours at a moment when, certainly, the city was growing, but so were the villages and secondary agglomerations.

Population clusters

38A population cluster (village or small town) is defined as a group of at least five peasant households with space between them of at least 100 m, that distance being a parameter modifiable to adapt to different regional contexts. By convention, each small city consists of about 30 peasant households.

39Each population cluster may contain a village community. By default, no cluster contains a community when created, but with each temporal increment, there is a certain probability (0.2 by default) that one will be seen to emerge. Once a cluster has a community, the latter cannot be lost. When a cluster possesses a community, all of the peasant households in the cluster are considered to form part of that community. A community may be more or less powerful, having a strong influence, or not, on the satisfaction of the peasant households which compose it. The degree of power is variable from one simulation to another, but identical for all the communities in a given simulation.

The peasant households

40Not wishing to represent a demographic evolution about which we are uncertain, we start from the principle that, in 800 as in 1200, the number of peasant households, arbitrarily fixed at 40,000, remains stable. These households comprise groups of from five to six persons, which constitute a space containing between 160,000 and 200,000 inhabitants, that is, an average density of from about 25 to 30 inhabitants per km². In 800, the majority of peasant households are dispersed randomly within the space modelled (table 3).

41We consider that the population partially renews itself in the course of a simulation, that is, with each time-step, a portion (5% by default) of the peasant households disappear and an equal number of peasant households come into existence. This makes it possible to represent departures from the system, whether the peasant households have changed their region or have not had descendants. The peasant households appearing in the course of simulation are placed in a cluster randomly selected, weighted by the number of peasant households present in each cluster. The result is that the peasant households concerned have a greater chance of being located in a cluster of large size than in a small one.

The lords

42At initialisation of the model, two types of lords coexist: the first, whom we call ‘overlords’, have a superior range of action, possessing power and rights which place them far ahead of the other lords in terms of both economic and military strength, so that they rate as war-lords. Their number is variable from one region to another, as is their relative power. In the example of Touraine, two are so designated (the counts of Anjou and of Blois). These lords, unlike those of lesser importance, are able to intervene throughout the territory, whether to construct castles or to levy taxes and fees.

43By contrast, the ‘minor lords’ are more numerous (table 3) but have much less power. They collect some taxes and fees, most often from application of communal rights, and possess some lands. Their range of action is local: their activity is limited to the environs of their residence, within villages or small cities. New minor lords appear little by little in the course of simulation and are added to those initially present. These minor lords only rarely receive rents from property but may obtain other rights in the course of the simulation: this entails a simplification of the model in comparison with a far more complex historical reality.

Churches

44In 800, numerous churches are presented (table 3), distributed randomly in the space of the model. Certain enjoy baptismal rights and are therefore considered parish churches. The non-parochial churches constitute a reserve of buildings which may see themselves endowed with parochial rights in the course of the simulation.

Detailed description of the behaviour of agents

45Each type of active agents enjoys a different degree of initiative and pursues objectives that are likewise different. The ‘peasant household’ agents move within the modelled space as a function of the modifications of their environment. Locally, these modifications consist of the creation of parishes, changes in parochial circumscriptions, an increase in the burden of feudal levies and the appearance of castles. The global modifications of the environment consist, of the advent and development of a climate of violence, as well as the growth of religious obligations. The ‘lord’ agents aim, for their part, to increase their power by creating zones of taxation and castles, and by developing their network of loyal followers. Finally, the agents ‘parish churches’ multiply and modify their catchment areas with the goal of satisfying the greatest possible number of the faithful.

46Interactions among the different types of agents take place uniquely by way of spatial entities: zones of taxation for the interactions between peasant households and lords, parochial catchment areas for the interactions between peasant households and parish churches.

Lords (see Table 4)

Acquisition and exercise of signorial rights

47The collection of signorial fees and rights occurs within a taxation zone, whose attributes are the holder (the lord who has created it), its radius and the rate of taxation.

48Collection of property rights (figure 3). Some of the minor lords appearing in the course of simulation benefit, at the point of their creation, from a taxation zone for property rights, according to a probability of 0.1. The rate of taxation is fixed, by random selection, at between 5% and 25%. The radius is selected at random between 1000 et 5000m. When a lord (minor lord or overlord) obtains a property taxation zone (whether or not linked to a castle), he consequently ‘withdraws’ from one of the overlords a portion of the peasant households taxed by that overlord outside any taxation area. Thus, as the simulation advances, the overlords progressively lose a part of the property rights which they collected from the peasant households initially located outside the taxation zone and which, in greater and greater numbers, are situated within the taxation zones, since these cover more and more of the territory being modelled. Nevertheless, since the largest taxation zones for property rights which emerge in the course of simulation are linked to castles (see above), and most of the castles are held by overlords, the latter do not lose revenues.

Figure 3: Collections of property taxes (rents) by the lords.¹⁹

49Collection of rights of high justice. From 900 on, overlords are able to acquire rights of high justice (figure 2), which are exercised over all the peasant households from which they collect property fees (outside the taxation area or instead by way of the taxation areas associated with the castle, or castles, which they possess). Once an overlord has acquired rights of high justice, all the castles which he creates or already possesses see a high justice taxation zone attributed to them. From 1000 on, the minor lords possessing a castle (as owners or guardians) also have a certain probability of acquiring rights of high justice (default value 0.2). This probability is assigned only at the moment of construction of a castle.

50Collection of other rights. Starting in 800, minor lords can create taxation zones for other rights. Thus, from the outset of the simulation, lords begin to arrogate new rights to themselves, or to appropriate public rights, but this process takes a certain time to be of notable importance.

Construction of castles

51Beginning in 940, and progressively over the simulation, castles are created by lords. Each newly created castle must be, by default, at least 3000 m. distant from existing castles. At each simulation step, a certain probability exists (0.5 by default) that one of the minor lords among these who has power superior to 0 will create a castle. If this probability is realised, the minor lord who constructs the castle is chosen according to a lottery mechanism weighted by the relative strength of each minor lord. The overlords have a greater chance than the minor lords of creating a castle at each simulation step. For each overlord, this probability is calculated as follows:

proba_creer_chateau = puissance_du_seigneur / Σ (puissances_grand_seigneurs)    (1)²⁰

52This probability is determined for each overlord independent of the others. If it is realised, the overlord concerned by the draw constructs a castle. This probability is put to the test several times in succession (3 times by default). The overlords can create castles anywhere in the space of the model, whereas the minor lords create them in their neighbourhoods, whose default radius is 5000 m. Each castle is created in a cluster with a probability of 0.5. At the moment of the creation of a castle, two taxation zones are automatically created with the same radius, one for the collection of property rights, the other for the collection of other rights. These two taxation zones are created at the simulation step following the construction of the castle. Between 940 and 1040 inclusive, certain castles belonging to a pole may become major castles (figure 2), according to a probability, by default, of 0.8.

Cession of signorial rights

53From about 880, the creation of vassalage networks is institutionalised (figure 2). In the feudal relationship, the lord protects his vassal and the vassal contributes to the armed strength of the lord. The lords can pass on some of their rights to other less powerful lords in exchange for their loyalty.

54In the SimFeodal model, minor lords can cede their rights to other minor lords in each of their taxation zones (property fees and other rights, apart from castles), independently of the others. This cession is effected according to a default probability of 0.33. The cession is most often made in favour of a lord located in the neighbourhood of the donor. At the time of a cession, the totality of rights over the taxation zone is ceded. The cession of rights by overlords to minor lords takes place only by means of the grant of castles in guardianship: from 960 on, at each simulation step, an overlord can give each of his castles in be guarded by a minor lord, according to a probability of 0.5 by default. When a castle is given in guardianship, all of the rights are ceded to the lord who receives the gift.

Amount of fees collected

55For each peasant household subject to taxation by him, the lord receives:

• rights of high justice: 2 and 2.5 when the rights have been ceded to another lord.

• property rights: 1 and 1.25 when the rights have been ceded to another lord.

• other rights: 0.25 and 0.35 when the rights have been ceded to another lord

Power of lords

56The power of a lord is calculated by the model at each simulation step. It is presented in two forms:

• Power derived from fees received: the sum of the fees received. This form of power represents the wealth and influence of a lord. Since the peasant households do not remunerate, strictly speaking, the overlords of their local lords, this indicator of power also represents a quantifiable form of influence or visibility, since it is considered that the gift of a castle or of rights directly benefits him who has made it.

• Armed strength of a lord: total number of peasant households which are subject to him (whatever the rights concerned and whether he is donor or recipient of the taxation zone from which they derive). Armed strength permits representation of the capacity of military mobilisation of an influential lord, who can request troops from his vassals.

Peasant households

57The peasant households are characterised by a group of measures of ‘satisfaction’ which impel them to relocate if the measures are too low. These movements take place according to particular modalities determined by the situations but systematically aim at an augmentation of ‘overall satisfaction’.

Satisfaction of peasant households

58Overall satisfaction level of a peasant household (variable titled Satisfaction) is a synthesis of three measures of satisfaction (material, religious, and degree of protection against forms of violence), which are understood as not compensating each other mutually: if one of the measures of satisfaction is low, overall satisfaction will also be so (cf. equation 1 of table 5).

59Satisfaction of material needs (variable S_materielle) is a function of the fees which the peasant household must pay (variable S_redevances – the more fees the peasant household must pay, the less the satisfaction) and of its belonging or not to a village community (parameter puissance_communaute: a peasant household is more satisfied when it belongs to a community, and the more satisfied insofar as the community to which it belongs is powerful). The amount of feudal charges which each peasant household must pay (variable redevances_acquittees) is the sum of the fees of the different lords on whom the peasant household depends (cf. equation 2 table 5).

60Ease of fulfilling religious obligations (variable S_religieuse) corresponds to the relative facility of attending liturgical services: getting to the church and assuring the salvation of one’s soul. This is a function of the distance to travel to reach the nearest parish church (distance_eglise). Evaluation of this distance varies over the course of time and reflects an increased frequentation by the peasant households (cf. equation 3 of table 5).

61Satisfaction of the need for protection (variable S_protection) is a function of the distance between the peasant household and the nearest castle (parameter distance_chateau) and of the need for protection perceived by the peasant household (parameter besoin_protection). This figures from 960 and corresponds to the advent and development of conflicts between local lords resulting from the loss of influence of the central power (cf. equation 4 of table 5).

Table 5: Formalisation of the behaviour of peasant households.

Migration of peasant households

62At every simulation step, the peasant household has a certain probability of migrating locally, within a radius inferior or equal to 2500 m. by default21. If the probability of local migration is realised, a random selection weighted by the respective attractiveness of the poles of attraction determines where the peasant household will be implanted. A pole of attraction is comprised of one or a number of focal points (i.e., attractors) close to each other (less than 200 m.) (cf. table 6). The attractiveness value of a pole corresponds to the sum of attractiveness values of the focal points composing it, so as to express the important differentiation of the attraction of poles entailed by the number of focal points present (cf. Zadora-Rio 2008,22 table 13, page 96). If no pole of attraction exists within a radius of at most 2500 m. around the peasant household, the latter does not relocate.

63If no local migration takes place, and it is able to undertake a long-distance migration, a peasant household has a certain probability of making a long-distance relocation, that is, to a distance superior to 2500 m. from its actual location23. The possible destinations of a distant migration are (exclusively) the poles located within or close to a cluster. If the probability of distant migration is realised, a random selection weighted by the respective attractiveness of the distant poles of attraction determines where the peasant household will be implanted.

Churches

64New churches, constructed by secular lords or religious communities, are added to those that existed before 800 (table 3), and their role as attractors is reinforced with the installation, in the course of the transition, of the parochial system, over which the bishops exercise increasing control. The parish churches, which serve as a focus of cultural and social practices, become central places on the local scale. They determine catchment areas by which their territorialisation is progressively affirmed. Thiessen’s polygons24 permit partition of the space of the model, so that each parish church may be at the centre of a zone defined as its catchment area. At each simulation step, new parish churches appear within, or in proximity to, clusters of peasant households with the implementation of a random selection, according to a probability equal to:

(1  /   ponderation_creation_paroisse_agregat) × (nb_fp_agregat  / nb_paroisses_agregat)

65where:

• nb_fp_agregat is the number of peasant households in the cluster,

• nb_paroisses_agregat is the number of parish areas included in, or intersecting with, the cluster surrounded by a buffer zone 200 m. wide,

• ponderation_creation_paroisse_agregat is fixed by default at 2000.

66Once these new parish churches have been created, the space of the model undergoes a new partition in order to update the contours of the parish areas. Subsequently, within each parish area, the religious satisfaction of each peasant household is calculated. If the number of peasant households with a religious satisfaction of 0 exceeds a stipulated number of unsatisfied peasant households (equal to 20 by default), a new parish is created25 (cf. figure 4). The space of the model then undergoes a new division in order to update the contours of the parish areas and to take account of the new parishes when calculating the religious satisfaction of the peasant households.

Some simulation results

67The objective of the first simulations was to verify that the model furnished plausible results for Touraine as the region was modelled. SimFeodal involves a series of random selections, e.g., to determine whether a peasant household relocates locally or a long distance away, or to determine whether a castle becomes a major castle, or even to determine whether a parish church is to be built within a population cluster. Consequently, for multiple simulations of the same scenario (i.e., a given set of parameter values), simulation results may vary. Considering this, the simulation results provided take into account 20 computational repetitions.

Figure 4: Creation of new parishes and modification of existing parishes²⁶.

68Table 7 shows that the results obtained are often fairly close to the expected levels. Only the number of parishes is higher. The model also reproduces well the process of hierarchisation of the settlement system (figure 5). The number of clusters of peasant households actually grows during the entire period of simulation, given that the number of inhabitants remains constant throughout. From 800 to 1000, the number of clusters varies little, whereas cluster size changes considerably. The smallest clusters grow slightly, ranging from 5 to 25 peasant households in 820, from 5 to 100 peasant households in 900, and from 5 to 150 peasant households in 1000. The intermediate clusters grow considerably. The biggest clusters grow slightly but regularly, from around 250 peasant households in 820 to around 400-550 peasant households in 1200. Their size range is greater in 1200 than in 820. From 1080–1100, the shape of the rank-size distribution becomes convex because medium and large clusters have increased more than small clusters.

Figure 5: Rank-size distributions of population clusters obtained with the default values of variables and parameters established for the diocese of Tours (Touraine region).

69This hierarchisation, as well as the process of clustering, is visible in the space of the model (figure 6)27. It is evident that the population, dispersed at the outset of the simulation, evolves towards a heavy concentration around several major poles at the end of the period. This tendency is accompanied by the development and structuring of the network of parish churches.

Figure 6: Parish churches created by simulation and number of peasant households in their catchment area. Example of one replication among the 20 simulated.

Conclusion

70The study presented here is an instance of the application of modelling and simulation in an interdisciplinary context. We have sought to elicit stylised facts preserving a level of complexity acceptable to, and accepted by, experts in the field. Every modelling procedure pre-supposes simplification, but we do not wish to arrive at a simplistic vision of the processes considered. To this end, we have moved gradually from a literary description of phenomena to their representation in more abstract forms, so as finally to arrive at the definition of entities (objects) engaged in a multi-agent model, namely SimFeodal.

71In a companion paper28, we have simulated a series of 15 scenarios with SimFeodal in order better to understand how certain social and demographic parameters influence the level of concentration and hierarchy emerging in rural regional settlement patterns in North-Western Europe during the Middle Ages. In this way, we have used agent-based modelling to facilitate our understanding of past changes rather than as a mechanism for simply recreating the known past. In time, multiplying such computer-based experiments based on explicit spatial simulations should help researchers to identify and formalize general laws for determining the concentration and dispersion of human settlements. This should also facilitate the identification of specific local features emerging in various social, cultural and political contexts.