Acknowledgements to Helene Mathian and François Favory for all collaborative work around this topic and for fruitful discussions.
 1 This work is a part of the project ARCHAEOMEDES (DG12) which is based on a collaboration between : (...)
1This paper describes a part of a research program 1on the long term dynamics of settlement systems. Long term means here about 2000 years, duration which makes it possible to get an insight in the diversity of settlements "life stories ". Some settlements already existed more than 2000 years ago, but most emerged later. Among them, some lasted only a few hundred of years when others grew and maintained until today. The "intercrossing " of these trajectories forms the evolution of the settlement system whose spatial and hierarchical organization changes through time as an expression of the global evolution of society. These long term dynamics are delicate to study because of the lack of precise data for past periods. Two complementary methods have been used in parallel to explore these dynamics. One is more hypotheticodeductive and relies on a simulation framework: assumptions about the main mechanismes which underly the dynamics of a settlement system have been expressed in rules and equations through a model using multiagent systems. These mechanisms and the rôle of inital conditions are then validated by the mean of simulations (Bura et al. 1996, Sanders et al. 1997). Because of the lack of appropriate data, the validation is principally based on information at a global scale and privileging the last centuries. The other approach which will be developed here is more empirical and aims at getting a better insight in past time settlement dynamics at a meso scale. It is also based upon a modelling approach but the model is used here to explore the factors which favour the durability of a settlement, using the empirical data which are available for past settlements.
2The empirical study has been developed for an area of southern France where archeological investigation has been done quite exhaustivly (Favory et al. 1995, Favory et Van der Leeuw 1995, Archaeomedes 1997). Most settlements which have once existed between the roman colonization and the present day have been recorded, what allows for a long term analysis. 2000 years is long enough to observe qualitative change in the settlement pattern and the hierarchical organization. On the one hand, this organization is characterized by a trend of permanence, as a result of the inertia of buildings and roads, which tends to maintain the spatial organization of the settlement system. On the other hand, different kinds of changes which have occured both in the production techniques and in the political framing of the territory, tend to induce modifications in this organization. Some inhabited places loose population and even disappear, others assert their rôle as structuring poles, some new settlements emerge on unoccupied areas. Precise information about the size of a settlement at different periods of time is rarely available at these time scales. Therefore we have chosen to analyse the dynamics of the settlement through the durability of the settlements. The underlying hypothesis is that the ability of a settlement to remain through time gives evidence of a kind of success compared to disappearing ones.
3In the area of study, there are in total 679 settlements, comprising simple agricultural annexes, farms, hamlets, villages and, at the top, the city of Nîmes which had a dominating rôle already before the roman period. About one out of six of these settlements are still inhabited today. These places, the rural settlings as well as the villages, represent the permanences in the settlement system. The question we deal with is following : what factors make some settlements remain through time when others are deserted: chance, an advantageous site, favourable situation, or the result of an accumulation, of a long valorization? and to what degree are these factors interrelated ?
4Using a quite general framework of investigation, we start from the hypothesis that the dynamics of a settlement will depend on a combination of features involving three dimensions (DurandDastès 1990, Péguy 1997):

an " ecological " dimension which refers to the physical and human characteristics of the settlement;

a historical dimension which refers to the past trajectory of the settlement;

a spatial dimension which refers to the interactions between the different settlements.
5As underlined above, the dynamics of the settlement will be measured by its durability. One could use the " life length " of the settlement but we have chosen here to consider the ability of the settlement to maintain inhabited until nowadays. The corresponding variable is simple and dichotomic:
6DURABILITY = 1 if the settlement has remained inhabited until nowadays
7= 0 if the settlement has been deserted
8The ecological, historical and spatial dimensions of the settlements will be defined using informations collected by historians and archeologists who have elaborated a quite homogeneous data base (ArchaeBase, Favory et Girardot 1995) on the settlements of the area. The informations which will be used can be classified into four groups :

archeological indicators: For each part settlement, the atcheologists have estimated the surface of the inhabited area, valued the quality of the materials and of the furnitures, and picked out the traces of a craftmen activity and of the trace of ideological or political functions through the presence of a cemetery, religious remains or fortifications. These variables give an indication of the human features of the settlements and can be used more particularly to hypothesize on their past functional and hierarchical level.

site indicators: soil quality, altitude and topography give an insight of the physical environment in which the first settlers have chosen to establish.

chronological indicators: dates of creation and of disappearance of each settlement, existence or not of previous occupation of corresponding place or surroundings give an idea of the historical context of the place where the settlement established.

situation indicators: two kinds of variables will be used; the first have been collected by historians and refer to the past way network. It concerns the number of ways leading to the settlement and the number of contemporary settlements with which there exist a direct road connection; the second group is calculated: distance to nearest neighbour, level of occupation of surrounding area, and distance to a pole. As these last variables don't make sense outside the context of a given period, they have only been calculated for certain periods. All these variables give an idea of the possibilities of interaction of a settlement with the other ones.
9The model to be used in order to find out the factors which favour the durability of a settlement has then following general form:
10DURABILITY = F(HIERARCHY, SITE, CHRONOLOGY, SITUATION) (1)
11where the two first terms of the function refer to matrices describing the " ecological " dimension of the settlement, and the following two to matrices describing respectivly its historical and spatial dimensions.
12Most of the variables are qualitative and even those that are intrinsically quantitative have been transformed. As a matter of fact, the imprecision of the information makes it more appropriate to consider the surface of the settlements through categories rather than using a very approximative quantitative measure.
13Simple chisquare analyses show that most of the variables described above are strongly related to the ability of a settlement to maintain until nowadays. In order to investigate the degree of redundancy or complementarity between these variables to explain the differences in the durability of the settlements, a multivariate model is necessary. As all the variables are qualitative, an appropriate model is the logit one which could be expressed following way:
where:
p is the probability that a settlement remains inhabited until nowadays,
the X^{GROUP}s are the explanatory variables associated to each subgroup defined in (1) and describing respectivly the hierarchical level, the site, the anteriority and the situation of the settlements,
the ßs are the coefficients of the logit model corresponding to the different variables,
the indexes j and k refer respectivly to the categories of the variable and to the variables of the subgroup.
14The variables have betweeen 2 and 7 categories and a direct application to the empirical data would then be impossible as the number of observations is only of 679 when the number of subpopulations induced by the explanatory variables is far beyond. It is then necessary to develop intermediate steps in order to simplify the model altogether keeping its richness. First the number of categories of the variables have been reduced by simply regrouping neighbouring categories when they had similar durability frequencies. Second it was necessary to reduce also the number of variables. As there are neither theoretical argument or empirical evidence to determine which variables to select in each subgroup, a simplification procedure has been developed using intermediate empirical results. In a first step, the logit model was applied separatly to the four subsets of variables, and depending on the results, two different methods have were applied:

if only one or two variables appear to be significant when they are combined, these are selected as the most representative of the subgroup as concerns durability;

if many variables appear to be significant when they are combined, a synthetic variable is constructed through a combination of the others.
15Thus, by combination and selection, one obtains a small number of indicators representing the different groups of variables which can then be integrated in a global model. Each step gives knowledge about the factors underlying the permanence of a settlements. The final step makes it possible to show the respective rôles of these factors and their eventual interactions according to their ability to maintain through time.
16When the archeological variables are successively introduced in a logit model, they appear to be all significative. The results are convergent and show that the bigger the surface, the higher the type of function and the better the quality of the material and the furniture level of a past establishment, higher is its probability to maintain until nowadays. Meanwhile, the effects of the different variables are not systematically redundant and they act additivly (figure 1). Beside these additive effects there is an interaction between the surface of the settlements and its type of function. Thus, for places where not even a necropolis was found, the frequency to remain until nowadays increases with the size of the settlement when for the settlements, where a kind of function has been identified, the highest frequencies of durability are observed for the medium sized places (figure 2). The curves corresponding to settlements having respectivly a necropolis, a cult place or fortifications, have the same qualitative shape, with a lag of about 25%.
Note : The noted line means that the percentage has been calculated on a number of settlements too low to be a statistical significance. The value is simply illustrative.
 2 the values of the categories of the variables were used as quantitative marks, from 1 for the simpl (...)
17As the results were very coherent, converging towards a ranking effect from the simplest settlements with the lowest probabilities to maintain, to the most sophisticated ones associated to the highest probabilities of " surviving ", a principal component analysis 2has been done in order to take into account the complementarities between the informations contained in the four variables. The first component, representing about 80% of the variance, has been interpreted as measuring the hierarchical level of the settlements. None of the variables is a direct measure of it but they all reflect in some way the past wealth, political power and/or concentration of population of a settlement. The interest of this measure is that it is based on a combination of informations of different kinds. That way, it rubs out the particular cases and gives a more stable image of the hierarchical differences between the settlements than each of the indicators taken separetely. One variable wasn't used to build this global indicator as it wasn't discriminant to explain the differences of durability, that is the existence of a craftmen activity.
 3 the categories were built using leaps in the histogramm of values and the results were then validat (...)
18The hierarchical indicator has been categorized into three classes3: 26 settlements of highest level are interpreted as poles in the settlement system, 251 places are qualified as secundary poles and the following 402 are minor settlements. These minor settlements are clearly the most ephemeral, only 1% of them still exist as inhabited places when that is the case of 85% of the poles. Their creation depended probably on conjunctural factors as for example the agricultural colonization of the territory which had a peak in the 1st century and their disappearance corresponds to a restructuration of the settlement system to the benefit of the biggest places.
19Data about soil quality, topographic features and altitude give an idea on the environmental conditions in which the settlement has developed. These conditions seem more to have discriminated the choice of a place for establishing than the ability of the settlement to maintain through time, one it is settled. This ability seems only to be related to altitude, with an advantage for the locations at intermediate altitudes. A particularly brutal threshold appears at 100m beyond which only 2 settlements out of 75 have maintained until nowadays. The altitude (categorized in 3 levels) and the hierarchical level of the settlements being introduced together in a logit model, both are significative (table 1) and there is no interaction between them. Figure 3 illustrates the additive character of these two variables on the ability of a settlement to remain on the long term.
Table 1: Results of a logit model combining the hierarchical level and the altitude of a settlement
20Independently of what the site variables measure, the past occupation of a place or of its surroundings (defined as an area of 500m around the built up area) gives an idea of the perceived attractivity of a place or a local environment by past societies. As a matter of fact, this attractivity could be due to some specificitic feature of the place but it could also reflect an opportunistic behaviour, the new settlers taking benefit from the anthroposition of the place, through grubbing up or draining for example (Archaeomedes 1997). It appears that if the reoccupation of the surroundings of an already occupied place is discriminant for explaining differences in durability, the reoccupation of the place itself has no influence. In opposition to the relations accounted for above, this relation depends strongly on the period of creation of the settlement: for the most ancient settlements, created before the 4th century, 50% of the durable settlings were established in the surroundings of a former settlement; for the more recent settlements, the result is paradoxal: there are more reestablishment than before, but they give reise to less durable settlements than those which established in completly new surroundings. The criteria of success in the medieval settlement network appear then to be different than those of the preceding galloroman period. In fact, the differences between the periods are so specific as if one combines in a logit model the period of creation (in 3 categories, before the 4th century, 5th to 8th century, after the 9th century) of a settlement and its past occupation, only the former one is significative. It is obvious that the effect of such a chronological variable stands for all the information we do not possess and which intervenes on a settlements'dynamic.
21The situation of a settlement can be characterized by its accessibility and by its position relatively to the other settlements. The number of ways which lead to the settlement gives a first idea of its accessibility. A clear threshold effect appears at the level of three roads, that is a situation of intersection. Thus, the existence of an intersection appears to be fondamental to " explain " the ability of a settlement to maintain through time, but not the importance of this intersection: indeed, 3, 4 or more than 5 ways doesn't make so big difference: about 40% of the settlements with such a location still exist nowadays when that is only the case of less than 5% of the formers. This statistical relationship of course does not recover a simple relation of causality. On the one hand, one can presume that a settlement has bigger chance to maintain when it is at the node of a network, on the other hand, an intersection has greater chance to be created at a place when a settlement has persisted for a long time. The number of contemporary settlements directly accessible by the road is a complementary information which refers to the degree of integration of a settlement in the local network of settlements. A logit model combining these two variables show that they are both significative, and the complementary rôles of these variables can be illustrated by following : for the settlements located at an intersection of many ways, the probability of durability is of 0.60 for those which are directly related to several other contemporary settlements but only of 0.14 for those which have one or less connections.
22There is then a small number of variables representing each group, either obtained by a synthetic construction, either by selection with the logit model (figure 3). They are combined in a global logit model (table 2) which shows that the hierarchical level, the period of creation and both variables measuring accessibility keep their significativity when they are combined. The results underly their complementarities in explaining the differences between the settlements in terms of durability when the effect of altitude is no more discriminant when the other variables are taken into account. No interaction effects appear to be significative in this final model, which shows that the effects are simply additive. The measures of likelihood can be used to get an empirical idea of the goodness of fit of the model. Following Wrigley (1985) one can use for example:
23RO2 = 1  log L(b)/log L(cte)
24where L(b) is the maximised log likelihood value of the fitted model, b being the vector of estimated parameters, and log (cte) that of the model with a constant term. Following values were then obtained :
Figure 3: Towards a global model
Table 2: Estimates of the global logit model
variable: significative at the 1°/ooo level
variable: significative at the 5% level
variable: not significative at the 10% level
25The results let suppose that hierarchical level, situation and period of creation have explanatory powers of almost comparable intensity, part of it refering to redundant information (many poles being located at an intersection for example), part of it refering to independant rôles: whatever the hierarchical level of a settlement, the location at an intersection will increase its probability to maintain and vice versa; whatever hierarchical level and situation, the most recently created settlements will have the greatest probabilities to exist today. This last relation is quite natural in a study where all settlements are considered together independently from the period when they emerged and shows the necessity to go more deeply into the question of time.
26Another limit appears when all settlements are considered together independently of any time consideration. The spatial dimension of the settlement system, that means the relative locations of the settlements according to each other, their spacings, can only be defined for a precise period. As a matter of fact, distance to neighbouring settlement has a meaning only if the two considered settlements have existed simultaneously, at least for some time. Three periods seem to have played a determining rôle in the spatial structure of the settlement system (Archaeomedes 1997), the 1st century, period of diffusion of the settlings with the agricultural colonization of the territory, the 5th century which is a period of contraction and the 11th century with the new medieval bases of development. We will now concentrate successivly on the 359 settlements existing during the 1st century, (5% still occupied nowadays), the 151 settlements existing during the 5th century (17% still occupied nowadays) and the 164 settlements existing during the 11th century (55% still occupied nowadays). The hierarchical level of the settlements has been calculated by applying the same method as above but restricted to the settlements existing at corresponding period. Then distance to nearest neighbour, distance to nearest pole and the number of neighbours in the surroundings at respectivly 1km and 3 km have been calculated for each settlement.
27The statistical analysis shows that more isolated settlements resist more often on the long term. For example, in the 5th century, nearly 30% of the settlements which had only a few neighbours at less than 3km exist nowadays when that is the case for less of 10% of the settlements embedded in a dense local settlement system. At the 11th century the frequencies of durability are higher, of course, but the variation, from 87 to 44% is still important. The differences are even more striking when one just observes the distance to nearest neighbour (table 3). These results illustrate a process of concentration where competition is disadvantaging settlements located too near each other. Most of them disappear to the advantage of the most powerful one. Distance to nearest pole is only discriminant at the 11th c.: it appears then that the settlements which maintain until now and which are not poles themselves are farther from a pole than the settlements which have disappeared.
Table 3: Frequencies of settlement still inhabited nowadays according to their local relative situation
N.B. the categories which have been used to measure the number of settlements and the distance are adapted to each period in order to be comparable. Mean value and standard deviation of each period were used to define them.
28This process of selection leads to an increasing spacing of the settlements at a regional level: average distance to nearest neighbour increased from 0.6km in the 1st century to 1.1 km in the 11th century and the number of settlements located at less than 3 km decreased respectivly from 28 to 6. This trend towards an increasing spacing is significative at the three periods of time even when the spatial pattern of the settlement system has evolved in between. So relations of complementarity and relations of competition between the settlements can both be observed through the data: a higher number of contemporary direct connections increases the probability of maintaining through time but when the neighbours are too close this probability will decrease. The balance of these two tendancies seems to produce progressivly a more regular settlement pattern.
29A last question concerns the role of these variables describing the position of the settlements relatively to their local environment compare to those describing the hierarchical level, the site and the situation of the settlements (table 4). The results show up a strong convergence between the different periods: hierarchical level and intersection situation are the most determinant factors and where they are taken into account, the other effects loose their significativity. In some senses, their explanatory power includes that altitude, anteriority of occupation, proximity to pole, density of occupation of the surroundings. It means that all these variables are statistically redundant with the former ones. As a matter of fact one observes, in the Antiquity, that the categories of " pole " and " intersection situation " appear more often for isolated settlements than for the grouped ones, which illustrates why the variables measuring the degree of isolation of a settlement give no additional information on the durability. On the other hand, the results for the medieval period show a more complex situation: distance to nearest neighbour is then significative, even when hierarchical level and accessibility are taken into account. That means that at equal hierarchical level and situation, there is a process of local selection which tends to disadvantage settlements which are located very near to another one. That process of local selection modified the spatial pattern of the settlement system which took at that period , its definitive shape. This spatial pattern largely maintained until the beginning of this century and constitutes the basis of actual spatial organization of the area.