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The authors have declared that no competing interests exist.

Christianity emerged as a small and marginal movement in the first century Palestine and throughout the following three centuries it became highly visible in the whole Mediterranean. Little is known about the mechanisms of spreading innovative ideas in past societies. Here we investigate how well the spread of Christianity can be explained as a diffusive process constrained by physical travel in the Roman Empire. First, we combine a previously established model of the transportation network with city population estimates and evaluate to which extent the spatio-temporal pattern of the spread of Christianity can be explained by static factors. Second, we apply a network-theoretical approach to analyze the spreading process utilizing effective distance. We show that the spread of Christianity in the first two centuries closely follows a gravity-guided diffusion, and is substantially accelerated in the third century. Using the effective distance measure, we are able to suggest the probable path of the spread. Our work demonstrates how the spatio-temporal patterns we observe in the data can be explained using only spatial constraints and urbanization structure of the empire. Our findings also provide a methodological framework to be reused for studying other cultural spreading phenomena.

The spread of Christianity through the Roman Empire has been widely studied in the humanities relying especially on close reading of ancient literary sources [

Our work represents an extension of the pioneering work of Rodney Stark [

By Christianization of a city we mean the emergence of the first Christian congregation in that city, counting ca. from a dozen to 200 adherents [

Although it has been recently challenged that Christianity was mainly an urban phenomenon in its early existence and that we should not overlook the evidence for existence of numerous rural Christians [

The congregations from the three periods of interest [

To formalize this, we make use of the gravity model, which is widely used to model mobility flows and economic interactions [

We show that the spread of Christian congregations in the first three centuries follows to a large extent a gravity-guided diffusion model. We compare this model to corresponding static factors and to a simple spatial diffusion and demonstrate that our model is the best one in capturing the spatio-temporal pattern of the Christianization process. Compared to the empirical data, our model systematically overestimates the extent of Christianization in the area of modern Egypt and the neighborhood of the city of Carthage in the first two centuries, which can direct future qualitative research.

In recent years, network analysis has became increasingly popular both in archaeology and history [

In the structure of the transportation network in the ancient Mediterranean we rely on the data from the ORBIS project [

As the precise data on population size of the cities in the ancient Mediterranean are unknown, they have to be derived by means of archaeological proxies. Here we draw on the estimates of the urbanization and city size offered by Wilson [

From Wilson, we were able to map 121 explicitly named cities directly to the nodes of ORBIS. Then, the remaining explicit cities together with the cities not specified by title were assigned to the ORBIS nodes on a by-province basis to conserve the total population estimates for the given province. The population estimates for the cities in the province were assigned from largest to smallest according to the rank of the ORBIS node, which is derived from ORBIS source data on cities [

Despite the fact that there are some more up-to-date publications available [

The data behind the maps are mainly based on information scattered over early Christian literary sources (the archaeological evidence is virtually non-existent before the third century [

From the atlas, we coded three maps: “The Earliest Churches: Recorded Congregations of the First Century”, “The Church in the Second Century”, and “Churches Founded before the Persecution by Diocletian”. On this basis, we formed three point map layers representing Christian congregations claimed to emerge by the year 100 (N = 54), 200 (N = 111) and 304 (N = 594) respectively.

During the coding, wherever possible, we used georeferences from the Barrington Atlas of the Greek and Roman world [

Gravity model has a long history of application to model mobility flows [_{n} and _{m} are the population sizes of the interacting cities and

The framework of effective distances enables us to model the dynamics and arrival times of a spreading process given just the network structure and flux of the carriers of the contagion in the network. It is based on the idea that the small fraction of traffic between two neighboring nodes is effectively equivalent to large distance and vice versa [

Under this representation, the complex spatio-temporal geographical patterns exhibited by the diffusive processes on networks are turned into homogeneous traveling waves, which enables us to represent the dynamics of the spreading process without the need to realize the diffusive network model computationally. This compact representation however still allows one to reason about the origin, arrival times, and the spatio-temporal dynamics.

In our case, the flux _{nm} is equal to the gravity _{nm}. The flux fraction _{nm} derived from the gravity model is a full network with numerous very weak links. To determine the significant links, we follow the procedure of Manitz et al. _{nm} network had a sparsity of 25% (see

The effective distance from _{nm} = 1 − _{nm}, and for path Γ = {_{1}, …, _{k}} the effective length is given by _{nm} = min_{Γ} λ(Γ). The shortest path tree Ψ_{n} then comprises the most probable paths of the spread of a process from the root node

There was a significant negative correlation between the first documented presence of Christian congregations and both the population of the city and the gravity model (

(A) Travel expense to Jerusalem, (B) population size, (C) gravity model with

As can be seen in

However, the evidence on the spatial distribution of Christian congregations in the first two centuries further contains clusters of smaller cities in the neighborhood of these regional centers, which seem to be seeded in advance of the traveling wavefront. These clusters of small cities have small gravity to Jerusalem, and cannot be explained by static gravity with a single point of origin. Therefore, in the next section, we will investigate the possible gravity-guided spreading process that would be able to correctly capture the gradual appearance of new sources of the spread.

The computational models of the network dynamic phenomena can quickly become sophisticated and parameter-rich, which is unsuitable in our case as the knowledge on the mechanisms of the spreading process as well as its empirical trace is not sufficient to inform the construction of such model. Therefore, we opt for the effective distance approach, which enables us to study the spreading processes on mobility networks without having to explicitly build, run and analyze the computational implementation of the model (see

Normally, the effective distance is computed from a mobility network representing the flux of people between cities; however, there are no such historical data available. Therefore we approximate the mobility network by the gravity model.

By computing the shortest effective paths from a single point of origin, we obtain two important things: a) an expected causal tree of the spreading process and b) the effective distance to the point of origin suggesting the relative time of arrival of the spreading process. The shortest effective path tree from Jerusalem as shown in

There was a significant positive correlation between the time of Christianization and the effective distance from Jerusalem (_{s} = 0.43, ^{−6};

(A) the radial distance is equal to the effective distance, colors correspond to the time of Christianization. (B) the distribution of the effective distance against the time of Christianization. The box shows the median and the quartiles, the whiskers extend past the quartiles by 1.5 interquartile range.

The cost of travel from the point of origin explains a large portion of the spatio-temporal variability in the spread of Christianity in the first two centuries (see

We interpret the process in terms of the diffusion of innovations theory [

The spatial dimension of the diffusion of innovations is far less studied than other aspects of the diffusion process [

The combination of the gravity model and the effective distance enabled us to capture the emergence of Christian congregations in distant regional centers and their neighborhood ahead of the geographical wavefront (i.e. the expanding boundary of the area effected by spatially continuous diffusion). However, some of the cities with low effective distance to Jerusalem were Christianized much later than others with the same effective distance. This means that the spread of innovations is not automatic as is the case of disease outbreaks, where, even if an appearance of a remote cluster is possible [

On the other hand, in some instances, the emergence of remote clusters in the model also produces some differences against the available evidence. The case of Egypt and of the neighborhood of Carthage deserves more attention in this respect, as our dataset on Christianization suggests that a considerable increase in the number of congregations occurred in these areas mainly during the third century. Contrary to this, our model, based on the effective distance, predicts many more cities in these areas to have a Christian congregation already in the first or second century. This difference between the model and the available data can mean two things: either (1) the insufficiency of the model itself (a better fit of which would require an implementation of a variable for resistance constraining the diffusion process in some areas, e.g. in the form of a cultural immunological force [

The case of Northern Africa is different. Here we suggest that our findings might be interpreted as being in agreement with the indirect evidence that there has been a well-established spread of Christianity already by 180 CE [

Further, the rapid increase in the number of Christian congregations in the third century could be also related to some external factors that could have accelerated the spread of Christianity. Since religious and magical beliefs flourish especially under the conditions of perceived uncertainty and stress [

Relying on a limited dataset of 31 biggest cities of the empire, Stark supported his hypothesis 3-2 (“The closer a city was to Jerusalem, the sooner a city had a Christian congregation”) by finding a significant correlation between cities having a church by 100 CE and being within 1,000 miles from Jerusalem and his hypothesis 3-4 (“Larger cities had Christian congregations sooner than smaller cities”) by finding a significant correlation between cities having a church by 100 CE and having a population of 75,000 or more [

Stark’s usage of the geographic distance implicitly assumes a crucial role of Jerusalem in the diffusion process. This is a problematic assumption, as it seems that, especially after the destruction of the Temple, the role of Jerusalem was rather marginal [

One of the main limitations of our study is the low reliability and temporal resolution of the data on the spread of Christianity. Since a vast majority of the data on Christianization is based on literary accounts of early Christian authors, they are necessarily tendentious [

Finally, our study demonstrates that the quantitative study of spatial constraints on the diffusion of religious innovations might produce meaningful results even in areas with limited amount of primary data. With slight modifications, our model could be applied to the study of the spread of other cultural innovations in the ancient Mediterranean where we face similar problems. Moreover, with different data on transportation and population structure (such as medieval trade routes [

Cities, roads, rivers and Roman provinces are shown, maritime routes ommited for brevity.

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Edges represent direct cheapest connection in the ORBIS model, nodes are ORBIS sites. Only sites with population estimate available are shown, and colored by the logarithm of population size.

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Edges represent direct cheapest connection in the ORBIS model, nodes are ORBIS sites. Only sites with population estimate available are shown, and colored by the cost of travel from Jerusalem.

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Edges represent direct cheapest connection in the ORBIS model, nodes are ORBIS sites. Only sites with population estimate available are shown, and colored by the logarithm of gravity (

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Color of the edges corresponds to the logarithm of the flux fraction between the nodes.

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Each node is identified by the ORBIS id and annotated with name of the city, geographical location, and a canonical URI within the PLEIADES project

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Source and destination cities (nodes) are identified with unique ORBIS id. Edges are weighted by the default cost estimated by the ORBIS model.

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For every ORBIS city, only a year of the earliest congregation is retained in the

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_{2}/D hypothesis: On the intercity movement of persons