Sailing West: assessing the role of waterways in the Neolithization of Ebro, Po and Rhône basins

doi:10.21203/rs.3.rs-4687033/v1

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Sailing West: assessing the role of waterways in the Neolithization of Ebro, Po and Rhône basins

https://doi.org/10.21203/rs.3.rs-4687033/v1

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An unresolved issue within the debates on Neolithization processes concerns the role played by rivers. It is known that farmers and herders were capable of navigating, even over long distances. Still, the question arises to what extent this ability was applied in penetration processes. This research investigates the relationship of early Neolithic farmers with the Ebro, Rhône, and Po rivers. The question underlying the research is to what extent waterways may have played a facilitating or hindering role in the movement from coastal areas to the inland regions of the basins. Predictive, spatial, cost-based, geostatistical, and statistical analyses were employed to answer this question.

The initial phase of the research focused on studying the composition of the Neolithic groups in motion. The transported livestock consisted of different species, such as ovicaprids, pigs, and cattle with cattle facing the most difficulties. Therefore, it is likely that the pace of the entire group was adjusted to accommodate the movement of bovids. A movement function based on the characteristics of cattle was developed and integrated with different raster grids to create cost maps representing different scenarios where waterways either hindered or facilitated movement. Subsequently, these scenarios were compared and discussed using statistical analyses, which indicated that in the Ebro basin, rivers likely facilitated Neolithic movement and access to inland points. In the Rhône basin, waterways' roles were variable and less clear. In the Po basin, rivers helped Neolithic groups reach the inner Padana plain, albeit less evidently.

Neolithic

Rivers

Ebro

Rhône

Cost-based Analysis

Geostatistical Analysis

Likelihood-based Analysis

Mobility is intrinsic to humans, and migration has played a pivotal role throughout human history, sparking extensive interdisciplinary debates and research projects. Movement lies at the heart of the 'Neolithisation' process. It is widely acknowledged that the spread of Neolithic migrants and innovations from Southwestern Asia followed diverse pathways, influenced by multiple factors, making a precise depiction challenging (Silva & Vander Linden 2017; Manen et al. 2019; Mazzucco et al. 2020). Over time, efforts have been made to describe this process through various models, at times confining intricate human behaviours within rigid or overly simplistic patterns, influenced by factors yet to be fully grasped (Leppard, 2014). These models primarily revolve around several key concepts: demic migration, indigenism, acculturation, and cultural diffusion. More specifically, the debate has long focused on the definition of the main actors of the Neolithisation process—migrant farmers or local foraging communities—and their forms of contact (Childe, 1958; Ammerman and Cavalli-Sforza, 1984; Zvelebil, 2001; Szécsényi-Nagy et al., 2015; Guilaine, 2018; Zilhão, 2000). In both cases, the role of waterways as one of the main vectors of Neolithization for the diffusion of people and ideas has been highlighted as a central element of the process. Waterways favoured the establishment of supra-regional networks and rapid long-distance travel since the Epipaleolithic/Mesolithic period and throughout the Neolithic, as also demonstrated by obsidian circulation in the Aegean and Mediterranean (Leppard, 2014; Isern et al., 2017; Moutsiou, 2018; Reingruber, 2022).

The first maritime voyages were experimented with in the Eastern Mediterranean, where seasonal navigation was practiced during the 11th millennium BCE between Anatolian coasts and the island of Cyprus, evidenced by human presence at Akrotiri-Aetokremnos in the southwestern part (Simmons, 2012). The discovery of Milos obsidian in the Franchthi Cave in Argolis further supports the existence of navigation in the Aegean Sea during that time, presumably involving a gradual journey from one island to another (Broodbank, 2006). Thus, the presence of early traces of life and materials with distant sources on an island constitutes indisputable evidence of a maritime route.

The expansion of the LBK (Linearbandkeramic) horizon, the earliest Neolithic culture in central Europe, was also facilitated by the utilization of watercraft to cover distances. Particularly in the Danube Valley, the advancement rate has been estimated to be considerably higher than terrestrial movements, reaching 4–6 km/year (Biagi et al., 2005; Davison, Dolukhanov, Sarson & Shukurov, 2006).

In the Mediterranean coastal regions, the speed of expansion has been calculated to be even higher, up to 10 km/year. Futhermore, the presence of numerous documented sites along the Western European coastline, coupled with the irregular settlement pattern, suggests a leapfrog colonization pattern by small maritime groups. This model, termed ‘maritime pioneer colonization’ by Zilhão (2000), involves coastal navigation and the establishment of enclave sites. The further progression towards inland territories, inhabited by hunter-gatherer populations, would have facilitated contacts, mixing and interbreeding. Nevertheless, fluvial ways played a great role as a vector for mobility and accelerated the Neolithization of inner areas.

Recent research on the submerged Early Neolithic site of La Marmotta, located in Lake Bracciano in the Central Mediterranean, has unequivocally demonstrated that watercrafts were used not only for coastal maritime navigation, but also for fluvial and lake travel (Fugazzola Delpino & Mineo, 1995; Caruso Fermé et al., 2023). The discovery of five dugout canoes in Lake Bracciano (Italy, Rome), demonstrates the existence of a diversity of watercrafts, including larger canoes up to 10 meters in length, and small ones, possibly adapted for shorter journeys along fluvial and lake waters (Gibaja et al., 2024). The occupation of La Marmotta may exemplify the rapid penetration of Neolithic communities into inland territories through the use of watercrafts and waterways (Mazzucco et al. 2023).

The principal inquiry driving this study pertains to the significance of river routes in facilitating the migration of Neolithic communities from coastal regions towards the hinterlands. For this purpose, three of the major river basins of the Mediterranean have been taken as case studies: the Ebro, Rhône, and Po basins. These basins have been selected over other smaller river basins because they provided more data in terms of sites, ¹⁴C dates, and surface area to model inland expansion. Movement has been analysed in terms of cost functions, traversal speed, and the advantages derived from moving to a specific location (Verhagen, Nuninger & Groenhuijzen, 2019). Four computational models have been designed to test both water as an obstacle and a facilitator of movement. To build such models, an analysis of the composition of the migrating groups that settled at various points along the three river basins was conducted.

The group that arrived on the coasts comprised not only humans but also included various additional elements such as animals, vessels, grains, and tools. This ensemble moved together over time and eventually arrived at the sites under investigation, either by foot or through waterways. Studies such as those conducted by Broodbank and Strasser (1991) on the initial colonization of Crete, along with research on the discovery of a Neolithic canoe in Lake Bracciano (Fugazzola Delpino & Mineo, 1995; Gibaja et al., 2024), offer a more nuanced perspective on the composition and movement of the group. A portion of the cargo carried by Near Eastern farmers included livestock, consisting of domesticated sheep, goats, pigs, and cattle, which undoubtedly demanded the utmost attention. To ensure the likelihood of obtaining a healthy population of animals suitable for ongoing breeding, the transportation of at least ten individuals per species was deemed necessary (Broodbank & Strasser, 1991). This number aimed to mitigate the risk of low genetic variability and address the challenge of potential deaths during the journey. Transporting adult animals posed greater challenges compared to moving young ones, particularly in the case of cattle. This complexity is heightened when considering that a portion of the journey occurred aboard boats. It is highly probable that meticulous management of the number and age of the animals was undertaken. Opting for animals already in their productive age but not yet fully grown was evidently the more advantageous choice. This ensured greater ease in transportation, a lighter cargo, contribution to the group’s dietary needs during travel, and sustenance in the initial months of settlement. Initially, sustenance would have relied on occasional hunting and gathering (Rowley-Conwy, 2011), a portion of the cereals brought along (Broodbank & Strasser, 1991), as well as products derived from the transported animals. The production of dairy products is evidenced even in the early stages of the Neolithic, suggesting that a portion of the ovicaprids provided a source of milk (Rowley-Conwy, 2011). Furthermore, pigs, with a gestation period of four months, capable of having two litters per year, and generally giving birth to three to seven piglets (Lutwyche, 2019), ensured an immediate source of meat.

The type of boat likely utilized bore resemblance to those discovered in Lake Bracciano (Fugazzola Delpino & Mineo, 1995), i.e., a canoe about ten meters long, carved from an oak trunk and propelled by paddlers. Despite successful experimental expeditions like Monoxylon I and II (Tichý, 2016), which demonstrated the feasibility of navigating with a cargo consisting of livestock, grains, and obsidian, some researchers argue that simple canoes were insufficient, necessitating the use of more complex vessels (Broodbank & Strasser, 1991; Vigne et al., 2014). An alternative proposal involves the use of two or more dugout boats joined by platforms, forming a kind of catamaran (Johnstone & McGrail, 1988; Vigne et al., 2014). This latter hypothesis seems reinforced by the recovery inside La Marmotta canoe-1 of several artifacts that may be related to more sophisticated watercraft, such as joining two dugout canoes or furnishing canoes with stabilizers (Caruso Fermé et al., 2023; Gibaja et al., 2024). In the Monoxylon II experimental expedition, utilizing a canoe replicating the features of those found in Bracciano, the average navigation speed with 9–11 paddlers, 100 kg of obsidian, and two linen bags of dinkel was estimated at 4 km/h (Tichý, 2016). Tichý highlights that a catamaran would likely experience a decrease in speed compared to the experimentally measured rate but acknowledges the possibility of utilizing a sail, a more efficient propulsion method (Gregory, 1997), which could consequently increase speed.

The final part of the study involved comparing the different scenarios to ensure a better understanding of the variables implicated. Finally, the degree of likelihood of the models was assessed, and conclusions were drawn. The data suggests that rivers likely played indeed a significant role in the inland penetration of Neolithic communities, particularly in the Ebro and Po basins.

The chronology and site location data used in this study constitute a subsample of the NeoNet dataset (Huet et al., 2022; Huet et al., 2024), an openly accessible dataset designed for investigating radiocarbon dates relevant to the Mesolithic-Neolithic transition in the Central and Western Mediterranean regions. This dataset spans from 9000 BP to 5000 BP (approximately 7000–3500 cal BCE), but for analytical purposes only dates falling within the range of 6950 to 5005 BP were considered. An additional attribute was added to the dataframe: the median of the dates ("MedianBP"), computed using RStudio and the Rcarbon library. This attribute provides an approximation of the uncertainty range to a single date for each site.

Spatial data was obtained from the Copernicus Programme (Copernicus Programme, n.d.), i.e. a European programme for Earth monitoring and developing processed data, which permits any individual or organization to freely use, reproduce, or distribute the information and data provided. Geographical data was specifically extracted from the land thematic area, obtained from the Copernicus Land Monitoring Service (Copernicus Land Monitoring Service, August 09, 2023). Two datasets were acquired from this platform: EU-DEM (v1.0), a digital surface model (DSM) covering EEA39 countries, and EU-Hydro (River Network Database), a comprehensive dataset containing a photo-interpreted river network along with drainage lines, catchments, and nodes.

A significant concern revolves around the reliability of paleo-data, specifically regarding river networks and topography. Obtaining robust paleo-data is complicated, given the extensive and detailed work required for paleo-environmental reconstruction. This inherent complexity and poor verifiability often result in inaccurate data. As a result, present-day data is often used to analyse past contexts. The main challenge in prehistoric modelling is to decide whether to conduct meticulous research for a reconstruction prone to errors, which may accumulate over time, or to rely on accurate present-day data that inevitably fails to fully reflect past realities (Kvamme, 2006). Predominantly contemporary data was used in this research due to the difficulty in obtaining paleo-data for territories as extensive as the three basins under examination.

The NeoNet dataset has multiple dates for most sites, necessitating a crucial filtering step to extract a single date per site. This selection process adhered to specific criteria. Initially, entries within the attribute ‘period’ were filtered to include only those corresponding to the Neolithic. Subsequently, groups of dates relevant to various sites were individually examined and refined based on the 'Material' attribute. In prioritizing the selection of the most reliable available dating, preference was typically given to dates obtained from short-lived samples. The order of preference, in this regard, was as follows: plant seeds, animal bones (especially those with specified "MaterialSpecies" values), human bones, shells, organic materials, and wood charcoal. To ensure a more precise chronological distribution, dates with a wide range of dispersion were excluded, with a general preference for values with a standard deviation ≤ 100. In order to minimize errors and facilitate predictive analyses, such as Kriging, further refinement of dates was undertaken based on spatial criteria. A square grid with sides of 50 km was implemented over the basins to identify sites that, despite close proximity, displayed significantly different dates (Fig. 1). In such instances, the older date was retained, and the more recent one was discarded, aiming to portray an accurate picture of the early Neolithization.

Additionally, the river layer was filtered to account for various types of natural watercourses encompassed by the 'River_Net_l' feature, ranging from small streams to large river channels with their tributaries, exhibiting varying degrees of variability. Specifically, the attributes ‘HYP’ and ‘STRAHLER’ were filtered. ‘HYP’ indicates the degree of water persistence and allows the selection of only perennial rivers. ‘STRAHLER’ indicates the Strahler index, a value assigned to each branch of a network as a result of stream ordering using the Horton-Strahler technique (Dodds & Rothman, 2000). This method enables the differentiation of the nature and, consequently, the significance of watercourses.

The river network obtained from the Copernicus portal had streams with Strahler values ranging from 1 to 8, and it was filtered to create two distinct layers: the first layer encompassing all rivers with Strahler orders between 4 and 8, forming a network of main rivers and their tributaries, and the second layer, further refined by excluding the fourth and fifth orders, exclusively representing the main river channels. Finally, the Digital Elevation Models (DEMs) were clipped to match the boundaries of the river basins and then resampled to 100 meters resolution to reduce the file size.

To ensure adherence to the FAIR principles (Findable, Accessible, Interoperable, and Reusable) (Wilkinson et al., 2016) predominantly open-source and non-proprietary software were utilized.

During the initial data filtering and cleaning phase, Microsoft Excel and the open-source desktop application OpenRefine (OpenRefine, n.d.) were employed. The analyses were primarily conducted using the free and open-source cross-platform desktop geographic information system application QGIS (version 3.28 Firenze). Given that the analysed river basins are situated in three different zones, the utilized coordinate systems were:

IGNF:UTM30W84 (Ebro);
IGNF:UTM31W84 (Rhône);
IGNF:UTM32W84 (Po).

The workflow involved the creation of raster grids containing information about the geomorphology of the basins as well as the characteristics of the Neolithic group in motion. The combination of these datasets allowed for the generation of a map of "traversability", from which, using the r.cost algorithm of the free GIS software GRASS (8.3.0), cumulative cost maps were derived from the oldest sites on the coast towards the inland areas of the basins. Subsequently, the mobility maps produced were statistically compared through correlation, linear regression and BIC model comparison.

Supplementary materials, including R scripts and workflows, are available for reference on the Digital Library repository and the GitHub repository https://github.com/giadapirrone/Sailing-West.git

Settling inland entailed both overland and riverine movement, with humans following the rhythms of animals while simultaneously guiding and being guided by them (Leary & Kador, 2016). To model this movement accurately, it is crucial to consider not only human agency but also that of animals and the environment. Different environments and terrains demand specific skills and modes of movement unique to each species (Leary & Kador, 2016). When considering slope, ovicaprids exhibit adeptness in climbing and traversing even the steepest mountain paths (Castelló, Huffman & Groves, 2016). Pigs also demonstrate adaptability to semi-mountainous landscapes and possess the capability to clamber over rocks, particularly when under one year of age (Lutwyche, 2019). However, cattle's ability to navigate steep slopes is limited (Phillips, 2002), as evidenced by a study that observed different cattle groups in pastures in Oregon (Ganskopp & Vavra, 1987). The mean slope of sites utilized by cattle was found to be 5.8%, with distinct preferences observed:

Slopes ranging from 0 to 9% were favoured.
Cattle exhibited indifference towards slopes ranging from 10 to 19%.
Avoidance behaviour was recorded for slopes exceeding 20%.

Although humans are capable of traversing terrains with slopes exceeding 20%, it is reasonable to assume that they avoided such paths to facilitate the movement of cattle and, consequently, the entire group. The speed of movement was influenced by various factors, with cattle being the least agile and therefore slower than other animals.

Thus, it can be ypothesized that cattle dictated the pace of the group. Accordingly, the speed of cattle could be regarded as the speed of the entire group. In this study, the speed value will be assumed based on an ethnographic study on long-distance livestock movements, specifically seasonal cattle transhumance during the dry season in Cameroon (Motta et al., 2018). Using GPS-tracking technology, 10 cattle herds were closely monitored during their seasonal migration in the Adamawa Region, characterized by an open woodland Guinea savannah ecotype. Data collected over 8 months were processed, resulting in an overall median speed ranging between 0.48 and 1.02 km/hour.

The data collected on the group in motion were utilized to construct cost surfaces, aiding in the identification of preferences regarding movement corridors. Typically, cost maps are represented in terms of time or caloric expenditure required for movement and serve as the foundational step for further analyses, such as the calculation of least cost paths (LCPs) (Herzog, 2020). LCP analyses have been extensively employed to reconstruct ancient routes using algorithms based on calculations derived from one or more raster grids of cost (Herzog, 2014). Implicit in this type of analysis is directionality, aiming to move from point A to point B (or to multiple points) with minimal effort. However, this approach is unsuitable for modelling dispersal processes such as the Neolithic penetration discussed here (Herzog, 2020), as individuals and animals ventured into uncharted territories based on internal group priorities rather than with the sole aim of reaching a specific destination. Consequently, the hypotheses underlying this work will be evaluated by observing and comparing different cumulative cost surfaces, created based on various variables.

Slope stands out as the most commonly utilized factor in cost surface modelling due to its primary role as a constraint to movement and its widespread availability. It can be readily calculated from Digital Elevation Models (DEMs), which are frequently accessible and freely available (Verhagen, Nuninger & Groenhuijzen, 2019). Various functions have been developed to describe walking speed as a function of slope, with many of these functions incorporated into isotropic or anisotropic cost algorithms within certain GIS software packages (cf. Tobler, 1993; Langmuir, 2004; Irmischer & Clarke, 2017). These functions have been formulated based on the physical and behavioural attributes of humans. However, since this study focuses on the movement of cattle, hypothesized to dictate the pace, no existing literature was found regarding the development of a cost function specifically for cattle movement. Therefore, a basic function, referred to as the MOV function (1), was devised to estimate the speed of cattle based on slopes.

Starting with a Gaussian function and relying on the observed values of slope and speed in cattle, the function was formulated as follows:

(1)

$$\:V\left(s\right)=1.02\:e^(-s^2/260)$$

Where V is the speed based on the slope; 1.02 is the value of the maximum average speed of cattle (Motta, et al., 2018), which is the height of the curve's peak; e is the Euler’s number; s is the value of the slope (%); 260 is the double squared value of the standard deviation.

Given the complexity of human and animal group movements, it is necessary to consider numerous factors when attempting to model cost. By conceptual definition, there is no single model that accurately describes how migration occurred. “All models are wrong, but some are useful” (Box & Draper, 1987: 424), and through their comparison, more insights can be gained than from the analysis of individual ones. This encompasses exploring hypothetical scenarios, such as considering a specific element as a barrier rather than a facilitator or selecting one starting point over another.

The creation of a cost surface involves combining a variable number of raster grids with the same extent and resolution (Etherington, 2016). Each grid contains, for every pixel, the value of a variable contributing to the cost of traversing that area. This process is referred to as multi-criteria analysis (MCA) (Verhagen, Nuninger & Groenhuijzen, 2019), wherein each layer provides information regarding an attractive or repulsive factor, each characterized by its unique attributes and units of measurement. As these factors are not inherently comparable, some form of reclassification is necessary to derive a total surface with dimensionless values, wherein different weights are assigned to various variables. Assigning weights to these factors is a complex process, as it is not standardized and can be influenced by subjective decisions. The determination of the weight assigned to a variable can relate to both the variable itself and its comparison to other variables (Verhagen, Nuninger & Groenhuijzen, 2019). In essence, an attribute may undergo reclassification of its values to make it combinable with other attributes, or it can be parameterized to indicate its relative importance compared to others, emphasizing its role as either an obstructive or facilitating factor to movement.

In a first step, the role of waterways as obstacles to movement will be considered, testing the hypothesis that, after arrival at the coast via boats, further penetration may have occurred overland. Next, the scenario in which rivers could potentially act as facilitators and accelerators for the group will be developed. Then, a third type of scenario will be modelled, assuming that the river did not play a specific role; it will be considered neither an aid nor an obstacle.

In the first case, a scenario was modelled where rivers hindered the movement of the penetrating groups. By applying the MOV function (1), the walking speed of the group was calculated. The pace measured in minutes per kilometre was derived as a variable to generate an effort surface for use as a friction map (Posluschny, 2010), representing a variable based on speed but expressed in terms of time. In order to integrate this surface with those of other parameters, the pace values underwent reclassification to obtain dimensionless values ranging from 1 to 10. Initially, the pace value at a 20% slope was calculated, based on Ganskopp and Vavra (1987), representing the limit within which cattle have been observed to move for grazing. Subsequently, the pace values were divided into 5 classes using the Jenks natural breaks classification method, ranging from the minimum to the maximum corresponding to the calculated limit, and values between 1 and 5 were assigned to them in ascending order. Pace values exceeding the calculated limit were assigned a weight of 10 due to cattle exhibiting avoidance behaviour for those slope percentages.

Two additional grids were added to this surface: one related to slope and another considering the presence of rivers. Regarding slope, to underscore its crucial role, a reclassification of cattle preferences was performed, and the following weights were assigned accordingly:

For slopes between 0 and 9%, a weight of 1 was assigned to indicate preference.
Values between 9 and 19% were given a weight of 2, indicating cattle indifference, albeit with a slight preference compared to the first class.
A weight of 3 was assigned to signify avoidance of slopes greater than 20%.

Given the initial assumption that waterways should be treated as barriers, a third surface was created to address this issue. Specifically, a weight of 4 was assigned to the pixels corresponding to the rivers and a buffer zone around the rivers with a distance parameter set at 500 meters. A weight of 1 was given to all the remaining pixels. The decision to incorporate a river buffer stems from the fact that the data used in this work are contemporary and not paleogeographic. Therefore, the weight was attributed to the entire buffer to minimize errors resulting from possible changes in the course of the rivers. Additionally, an extra weight of 1 was assigned to the remaining land areas.

By summing up all the grids, the obtained output is a cost surface (Figs. 2, 3, 4), indicating areas with lower or higher costs to traverse. In the analysis of a migratory process, it is crucial to consider the cumulative cost. Hence, the subsequent step involved computing cumulative cost grids³, storing the costs of movement radiating from the origin to every other cell in the raster grid (Herzog, 2020). Cumulative cost surfaces are derived by applying a spreading function to minimize the cumulative cost from one or multiple cells with an initial value of 0 (Conolly & Lake, 2006).

In each basin, the starting points were selected based on the two sites with the oldest dating near the shores, except for the Ebro basin, where a starting point from the Pyrenees was also considered (Gassiot-Ballbè, 2021). In the case of the Rhône basin the two points on the coast with the oldest dates were initially set as starting points: Pont de Roque-Haute (Median 7840 cal BP) and Caucade (Median 7656 cal BP). The GRASS r.cost algorithm (r.cost, 2023) was then utilized to compute the cumulative cost (Manen et al., 2019). Similarly, for the Ebro basin, the same raster grid was generated, with Guixeres de Vilobi (Median 7528 cal BP) on the coast and Balma Margineda (Median 7548 cal BP) in the Pyrenees selected as starting points (Oms et al., 2018; Manen et al., 2019). The Po basin followed a similar workflow, with the two chosen sites being Riparo Ala Le Corone (Median cal 7512) and Fiorano Modenese (Median cal 7453) (Starnini et al., 2018).

In the second scenario, the role of the river is considered a support rather than an obstacle to movement, offering a quicker and more convenient pathway for the group of humans and animals. Building upon this premise, cost maps were generated, and subsequently, cumulative cost maps were derived in a similar manner.

Initially, movement through the river was regarded as isotropic, without accounting for the potential effects of downstream or upstream navigation on penetration speed. In contrast to the cost map computed in the previous section, a low value of 1 was assigned to the buffer of the river layer in this case, favouring water passage and indicating its supportive role. For the terrestrial areas of the basin, the pace values calculated using the previous workflow were retained. The only additional grid introduced in this scenario was the slope grid reclassified based on cattle preferences. Subsequently, cumulative cost surfaces were computed for the same sites mentioned earlier.

Subsequently, an attempt was made to model fluvial movement by considering space anisotropically (see Supplementary Materials for the workflow). Although this type of analysis yields outputs with greater approximation compared to those computed in an isotropic space, theoretically, they better reflect reality. Indeed, one of the most crucial factors, if not the most significant, when modelling river movement using vessels, is the current of waterways. The latter can influence the effort involved in movement, doubling the navigation speed when moving downstream, namely, in the same direction as the current, and halving it for upstream navigation (Livingood, White & Surface-Evans, 2012).

All functions describing anisotropic movement must take its direction into account; otherwise, they revert to isotropy (Van Leusen, 2002). To incorporate the direction of movement into the calculation of upstream and downstream speeds, the formula (2) developed by Krist (2001a, b) for computing an adjusted slope was employed:

(2)

$$\:Sa\:=\:S\:*\:cos(At\:-\:A)$$

where S and A are the original slope and aspect values, and At is the direction to the starting point (Van Leusen, 2002). The At values have been obtained using the r.cost algorithm. After computing the adjusted slope for the raster grid of rivers with Strahler order greater than 4, a reclassification was conducted to assign different velocity values, specifically:

A speed of 4 km/h, equivalent to the average measured during the Monoxylon II experimental expedition (Tichý, 2016), was considered for sections unaffected by current flow.
Downstream sections were assigned a speed value of 6 km/h.
Upstream navigation was modelled with a speed value of 2 km/h.

Using these velocity values, pace values were derived and added to those already calculated for terrestrial movement, which were given a higher weight in this scenario. Once again, cost surfaces were generated by summing information related to the reclassified slope according to cattle preferences. Finally, cumulative cost maps were computed for the three basins from the same sites.

In the final scenario, rivers were not considered to play any significant role. Cost maps were computed by combining the reclassified layer of pace with the surface containing the values of the reclassified slope. No additional information was included, resulting in a fictional scenario where waterways do not exist.

Although highly improbable, a scenario depicting the complete absence of waterways is useful for simulating the total indifference of Neolithic people towards rivers. Following the workflow described in the preceding sections, cumulative cost maps were obtained.

In the final stage of the research, several statistical calculations were conducted to better understand the outputs of the cost-based analyses and to compare them with the archaeological data. However, due to the scattered nature of the dataset, the most practical approach was to employ a grid of predicted chronological values obtained through Kriging interpolation of the initial ¹⁴C datings. Universal Kriging was used across all three basins, as it employs a distinct model for analysing the first-order pattern associated with the directional trend (Lloyd & Atkinson, 2020; Fort, 2015). This trend corresponds to the migration direction from the coast to the hinterland. The interpolation was calculated on GRASS GIS and resulted in three different chronological maps, one for each basin (Figs. 5, 6, 7).

All statistical analyses were performed using RStudio (for the scripts, refer to the GitHub repository: https://github.com/giadapirrone/Sailing-West.git). The input raster grids included Universal Kriging, the cumulative cost maps with rivers considered as an obstacle to movement, the cumulative cost maps with rivers considered as an aid to movement (both isotropic and anisotropic), and those where rivers are not considered. The first calculations employed the stats package (R Core Team, 2022). At first,correlation was performed between Kriging and each cumulative cost map, aiming to understand whether and how the chronology is correlated with the direction and speed of cost accumulation across the territories. The correlation values obtained are summarized in Table 1.

Table 1 Correlation values.

RHÔNE
Obstacle	Aid Isotropic	Aid Anisotropic	No River
-0.9307318	-0.9300138	-0.9300645	-0.9307632
EBRO
Obstacle	Aid Isotropic	Aid Anisotropic	No River
-0.5786837	-0.5926106	-0.5962887	-0.5724935
PO
Obstacle	Aid Isotropic	Aid Anisotropic	No River
-0.0005386776	-0.5769551	-0.5257057	− 0.0005385455

All results indicate a negative correlation between variables in all cases. Specifically, as the values of the Kriging maps decrease, those of the cumulative cost maps tend to increase, and viceversa. Additionally, there are variations in the strength of correlation, with the Rhône case exhibiting values close to -1, indicating a strong correlation. In contrast, the Ebro and Po basins show lower values but still suggest a relatively robust correlation. Two exceptions are noted in the Cumulative Cost map: the version that considers the Po River as an obstacle, and the version that excludes the river, both displaying coefficients close to zero, suggesting an apparent lack of correlation with the Universal Kriging map.

After confirming the correlation between variables, linear regression was utilized to quantify the relationship, by modelling the associations between variables and determining the best-fitting straight line to the dataset (Hacigüzeller, 2020). Let us consider the linear regression equation$\:\:y\:=\:a\:+\:bx$, where y represents the estimated dependent value (cumulative cost), a is the average value of y when x is zero, b is the average change in y associated with a one-unit increase in x, and x is the predictor variable's value. The focus is on the slope value (b), for it provides quantitative insights into how the cost variable changes in relation to the temporal variable.

In the Rhône basin, significant p-values were observed in all three cases, allowing for the rejection of the null hypothesis of the slope being 0. The slope value for the regression between Kriging and the Cost with the river as an obstacle was − 0.04001, indicating that for every unit decrease in Kriging, there's a 0.04001 increase in the Cost. When considering the river as an aid, the slope value (b) was − 0.05555 in an isotropic environment and − 0.03314 in an anisotropic environment. Finally, when the river was not considered, the slope value was − 0.06474.

For the Ebro basin, significant p-values were observed in all three cases as well. The slope values for the regression between Kriging and the Cost with the river as an obstacle were − 0.02914. When the river aids movement, the slope values were − 0.03895 in an isotropic environment and − 0.02225 in an anisotropic environment. In the fourth case, the slope value was − 0.04391.

In the Po basin, linear regression between Universal Kriging and the cumulative cost map with the river as an obstacle and between Universal Kriging and cumulative cost map without the river were not computed due to their initial lack of correlation. However, in cases where the river aids movement, linear regression was conducted. This resulted in a slope value (b) of -0.03780 in the isotropic case and − 0.02356 in the anisotropic case.

The final statistical analysis conducted on the cost maps entailed a model comparison. The objective of model comparison is to assess the adequacy of the considered models for the data (Kuha, 2004). Various search methods exist for model selection, with common approaches including the computation of AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion). Although AIC and BIC share the goal of evaluating model fit, they differ in their precise definitions of what constitutes a 'good model' (Kuha, 2004): BIC tends to favour simpler models, whereas AIC favours models with greater complexity. For this analysis, a stepwise BIC model-selection approach was employed. It comprises two components: the likelihood term, indicating how well the model fits the data, and the complexity term, penalizing models with high complexity. The model selection is based on the lower BIC, indicating a model that is both efficient and parsimonious (Brandolini & Carrer, 2021). To conduct the selection, the MASS package (Ripley et al., 2013) was utilized, with linear regressions between the various cost maps and the Universal Kriging discussed previously. Additionally, BIC weights were calculated, offering a normalized estimation of the relative performance of the models (Basile & Campus, 2024). A higher weight signifies better model performance.

Tables 2 and 3 present the obtained results, considering all three basins:

model0 represents the linear regression between Universal Kriging and the cost map where the river is regarded as an obstacle.
model1 corresponds to the linear regression between Universal Kriging and the cost map where the river serves as an aid, and the spatial consideration is isotropic.
model2 entails the regression between Universal Kriging and the cost map where the river acts as an aid within an anisotropic spatial context.
model3 denotes the regression computed between Universal Kriging and the cost map where rivers are not taken into consideration.

As shown in Table 2, for the Rhône basin, model3 exhibits the lowest BIC value, for the Ebro basin, model2 has the lowest BIC, and, finally, for the Po basin, it is model1. When examining BIC weights (Table 3), in all three cases, the model with the lowest BIC value demonstrates significantly better performance compared to the other two, displaying a maximum weight of 1, while the weights of the other two are equal to zero.

When delving into the socio-natural dynamics of ancient societies, pinpointing the precise reasons driving human behaviours and decisions becomes an elusive task (Barceló, 2012). Utilizing simulated scenarios offers the best approach to grasp past realities. It is crucial to determine which scenario is the most likely to have occurred rather than insisting on what surely took place. Ultimately «an absolutely identical replication is not required; only a convincing one» (Whitley, 2016). The generated cost maps aimed to model mobility hypotheses within the territory. These maps represent only a fraction of potential scenarios, and the actual circumstances may closely resemble them or deviate significantly, coinciding with other unaccounted possibilities. To ascertain which of the formulated models is the most "convincing", hypothesis testing was carried out through statistical analyses.

Initially, correlation analysis was utilized to evaluate the association between the generated cost models and archaeological data. The Universal Kriging interpolation grid served as the independent variable, representing the archaeological information and showing the chronological variability. To enhance the robustness and diminish bias, employing a cluster of archaeological data not utilized in the initial analyses or hypothesis formulation could have yielded more reliable results, thereby avoiding the introduction of an extra layer of uncertainty (Peeter & Romeijn, 2016).

Starting with the assumption of penetration from the coast to the inland areas of the basins, as suggested by archaeological data, the expected R output was a strong negative correlation between the chronological distribution and the mobility cost maps. Beginning with the premise of a movement from coastal to inland areas within the basins, the anticipated R output indicated a robust negative correlation between the chronological distribution and the mobility cost maps. By selecting the two oldest sites near the shores (except for Balma Margineda in the Pyrenees for the Ebro basin) as starting points, an anticipated rise in cost over time was expected as the movement advanced towards inner territories. Consequently, this would suggest a decline in chronology towards more recent years. The correlation outputs (see Table 1) consistently revealed strong negative values across all cases, validating the aforementioned hypothesis. Particularly noteworthy were the strongest values observed for the Rhône basin, where, across all four cost models (Obstacle, Aid Isotropic, Aid Anisotropic, No River), the correlation was very close to -1. This trend could likely be attributed to the elongated and stretched shape of the basin, distinguishing it from the Po and Ebro basins.

The subsequent phase involved conducting linear regression analysis, a method that quantifies the relationships between variables (Hacigüzeller, 2020). The values obtained for each scenario in every basin represent the slope value (b) in the regression equation y = a + bx, which illustrates how cost accumulates over time. Notably, in the Ebro and Rhône basins, the highest value arises from the scenario where no river is considered (the Po basin displayed a lack of correlation in the first and fourth cases). This implies that, in this case, cost accumulates much faster through the basin because, for every increase in chronology, there is a higher cost value added. This scenario is considered highly unlikely, firstly due to the way it was constructed, as it describes a fictional reality of complete absence of rivers, and secondly, because mobility would be much more challenging compared to the other scenarios. For instance, when the river was perceived as an obstacle, the accumulation of cost values appeared to occur at a slower pace, even slower than when rivers were considered aids in an isotropic space. The way space was conceptualized likely played a pivotal role, as in the isotropic scenario, rivers facilitated movement, yet when following the direction dictated by the chronological distribution, areas with high unidirectional slope resulted in higher cost values. Conversely, the scenario with rivers serving as aids and an anisotropic space yielded the lowest slope value. Here, the varying levels of effort required to navigate diverse geomorphological environments accounted for directionality, simulating a more realistic scenario and alleviating the challenge of traversing high slope areas when they aligned parallel to the direction of movement.

The subsequent analyses sought to evaluate the appropriateness of the models, identifying which one best matched the archaeological data represented by the predicted chronological values and, consequently, depicted the most plausible scenario. To accomplish this goal, a likelihood-based method was employed, specifically utilizing stepwise BIC model selection. Four models were compared, and BIC values and weights were generated for each model across the three basins (refer to Tables 2, 3 for values).

Initially, BIC was computed by comparing only three cases, excluding the scenario without rivers. In the Rhône basin, the lowest BIC value was initially obtained for model1, which corresponds to the case where rivers are considered as obstacles. This suggested the potential for a simultaneous dual penetration, considering that the major axis of the Rhône divides the basin into two parts, with the two starting points located on opposite sides. However, after introducing model3, it exhibited the lowest BIC value. Interpreting these results is complex. Among the three basins, visually, the Rhône basin shows a more temporally dispersed distribution of sites (see Fig. 5). While the gradient appears gradual on one side, there are areas on the other side that remain empty until the final phase of the chronological range considered, such as the most southwestern tip, the north, and the central west. Figure 8 illustrates the percentage of sites belonging to each chronological class for each basin. The classes, derived through Jenks Natural Breaks, consist of five categories ranging from older to more recent datings. In the Rhône basin, besides having the highest number of sites, datings are distributed more evenly within the classes; the percentages are quite similar for all classes. The most recent class proportionally exhibits a greater number of sites than in the other two basins, and the class with the lowest number of sites is the oldest. Considering this, one possible reason why the Rhône basin shows the lowest BIC for model3 could be the sampling strategy employed and, therefore, the sites considered for the analyses. To validate this hypothesis, it would be necessary to repeat the filtering process, for instance, using a grid with different dimensions or further narrowing the chronological window. However, it is not entirely dismissible that Neolithic groups in motion were entirely indifferent to waterways. It is plausible that waterways played a significant role in traversing certain areas of the basin, and thus, the groups might have partly followed and partly avoided them. Nonetheless, due to the structural constraints of this study, it only allows an analysis of macro-trends and does not provide insights into microvariability.

The BIC stepwise selection for the Ebro basin allowed to discard model0, model1, and model3, confirming model2 as the best fit. This selection corresponds to the scenario where waterways facilitate movement, and space is considered anisotropic, indicating variations in properties or characteristics in different directions. The discussion regarding this outcome will primarily address the nature of space and subsequently explore the role of rivers. Among the two scenarios where the Ebro is deemed an aid, the anisotropic setting exhibited the highest BIC value. Initially, it was hypothesized that this outcome might be influenced by the positioning of the starting points. Specifically, to model a scenario consistent with literature and archaeological findings, two sites were chosen: Guixeres de Vilobi on the coast and Balma Margineda in the Pyrenees. Starting from the latter, given its position, the cost accumulates towards the rest of the basin by traversing many areas with high slope. When space is considered isotropic, the cost escalates rapidly. However, in the context of anisotropic space, where the slope direction aligns with movement, the cost is notably reduced. Initially, it was conjectured that selecting Balma Margineda as one of the starting points might introduce bias into the analysis, potentially influencing the observed outcome. To investigate this possibility, four additional cost maps for the Ebro were generated, using Guixeres de Vilobi as the sole starting point. Subsequently, BIC values were recalculated for the linear regression models between these new raster grids and the Universal Kriging dataset.

Tables 4 and 5 show the output. Once again, the anisotropic aid model demonstrated the lowest BIC. After testing and excluding the influence of Balma Margineda, it was proposed that the slope percentages of sites might have impacted the selection of anisotropic space.

This hypothesis stemmed from the fact that despite constructing cost maps without specifying any ending points, kriging interpolation was conducted on all sites, thereby retaining information about their positions in the regression. To assess the significance of this factor, a detailed examination of the slope distribution among the sites was undertaken. Figure 9 illustrates that in the case of the Ebro basin, 36% of the sites exhibit a slope value exceeding 19%, corroborating the hypothesis. The analysis indicates that the waterways facilitated movement across the basin. This supports the possibility of a rapid penetration from the coast to the western extremity of the Ebro basin, demonstrated by the presence of ancient and nearly contemporaneous dating, and evident from the Kriging grid (see Fig. 6). An example is the Neolithic site of Los Cascajos (Gazólaz et al., 2012), highly relevant as it demonstrates novelties in lithic technology, funerary behaviours, and settlement patterns compared to what is attested for the dense network of Mesolithic sites in the area (Arias, 2007). As previously specified for the Rhône, it is essential to reiterate that the internal variability within the basin is so high that the resulting picture is a generalization of a reality that undoubtedly encompassed numerous and diverse scenarios.

Tables 2 and 3 illustrate that for the Po basin, the model exhibiting the highest likelihood is model1, wherein the river acts as a facilitator in an isotropic environment. The prevalence of isotropy in this context can be elucidated by examining the distribution of slope percentages among the considered sites. Figure 9 reveals that a significant portion, 66%, of the sites are situated in areas characterized by very low slopes. Notably, a closer inspection of the distribution indicates that the majority of sites are concentrated within the Padana plain. The stepwise BIC selection suggests a supportive role played by the Po river and its tributaries, particularly in facilitating diffusion from the coast to the interior of the basin. Among the three basins, the Po basin posed the most significant challenges for analysis due to several factors. Firstly, the limited sample size of examined sites, especially when compared to the other two cases (Fig. 10), results in reduced statistical reliability and complicates the observation of less apparent phenomena or patterns. Additionally, the movement wave examined in this study is embedded in an underlying overland penetration with a south-north direction. This has certainly influenced the situation and consequently the spatiotemporal distribution of the sites.

The models of territorial mobility outlined above provide a comprehensive understanding of the archaeological context, offering insights that align well with the available evidence, or at the very least, offer better explanatory power than alternative models. However, it is crucial to acknowledge the potential issue of equifinality, which suggests that the conducted simulations could hypothetically replicate the evidence without accurately reflecting reality (Murphy, 2012). It is conceivable that similar conclusions could have been reached using different variables or alternative methodologies. Modelling the infinite variability of reality presents a formidable challenge. In this study, two distinct yet equally intricate attempts at reconstruction were undertaken: one focused specifically on investigating the movements of Neolithic groups, and the other took a broader approach, examining mobility patterns.

In both cases, the range of factors that could be considered is vast and diverse. Certainty regarding whether the variables investigated are truly the most significant or have played a role, even if minor, remains elusive. Uncertainty not only stems from analysing a limited number of variables but also from the necessity of expressing qualitative information in mathematical terms, thereby transforming it into quantitative or ranked data (Whitley, 2016). This process introduces bias and consequently increases uncertainty, particularly concerning cultural factors. These types of uncertainties are challenging to lower; therefore, an approach that could prove useful in addressing them is to use modelling not as a faithful description of reality but more as a support, a "tool for thought" (Van der Leeuw, 2016).

The research questions underlying this work are part of a lively debate around the Neolithization process. Specifically, the objective was to delve into the modes of movement and explore the potential significance of fluvial navigation in the migration from coastal regions to inland territories. The same workflow was applied to three different river basins to test its robustness and also the geographical variability. The goal was not to meticulously reconstruct past events, but rather to model diverse scenarios and evaluate their respective plausibility. The methodology encompassed a range of digital techniques, including predictive modelling, geostatistical analysis, cost-based analysis, likelihood-based analysis, and statistical analysis.

In-depth bibliographical research allowed to gather pertinent data concerning the westward movement of Neolithic groups. This encompassed information pertaining to the people involved, the pottery vessels utilized, and the livestock accompanying the journey. Notably, the livestock component was recognized as pivotal, as it presented an opportunity for settlement and the establishment of sustainable breeding practices. Of particular interest were three imported animal species: ovicaprids, pigs, and cattle. Given the challenges faced by cattle during long-distance mobility, particular attention was directed towards developing a walking function tailored to their characteristics and preferences, resulting in the formulation of the MOV function. Using this function and the reconstruction of fluvial navigation characteristics, cost analyses were conducted. To align as closely as possible with archaeological evidence, cost maps were generated with specified starting points but without designated endpoints. This approach facilitated the simulation of a migration directed from the coast towards the interior of the basin, with groups moving without a predefined destination. While the Least Cost Path method has been foundational in numerous studies of ancient mobility, it was deliberately omitted in this research. Instead, the focus was on obtaining models of territorial mobility rather than specific routes that may have been taken. The undertaken workflow effectively allowed to produce cumulative cost maps, identifying potential corridors where movement was deemed easier.

The final phase of the work focused on the statistical testing of the obtained outputs. Through these analyses, the importance of geomorphological variability was highlighted by obtaining three different outputs for the three basins:

For the Ebro basin, it is likely that the rivers and their tributaries played a significant role in the initial Neolithic penetration, facilitating movement and enabling easier access to certain inland points.
In the Rhône basin, on the other hand, the role of waterways was likely variable and challenging to interpret. It is possible that their use did not result in such a pronounced aid. Further analyses could help refine the interpretation.
In the Po basin, although less evident, rivers served as a useful passage for Neolithic farmers to penetrate the inner areas of the Padana plain.

The main constraints encountered are related to the impossibility of modelling every paleo-variable that might have been relevant during the Neolithization process. Such limitations contribute to increased uncertainty, which poses challenges in validation and hypothesis discussion. Dealing with a prehistoric scenario further complicates matters, as interpretations remain unverifiable. Future studies are anticipated to contribute valuable data for analysis, including evidence from archaeological excavations and paleo-environmental reconstructions. This will aid in reducing errors and enhancing the reliability and accuracy of findings.

The developed MOV function, tailored to capture Neolithic movement patterns, and the corresponding cost maps delineating favourable migration corridors, offer a methodological framework adaptable for subsequent studies. Furthermore, the conclusions drawn from statistical analyses in the current study can function as interpretative tools, providing insights for understanding the broader implications of Neolithic movements and adaptations in the studied regions.

Author Contribution

G.P. was responsible for the conceptualization, data curation, formal analysis, investigation, and methodology, and also wrote the original draft. A.C. contributed to the methodology, formal analysis, and investigation, and assisted with the review and editing of the manuscript. G.G. provided supervision, project administration, resources, and contributed to the methodology and the review and editing of the manuscript. N.M. offered supervision and conceptualization, managed the project, provided resources and data curation, carried out the investigation, and co-wrote the original draft.

Acknowledgement

This research has been made possible by the support of the following research projects: "Connecting South Europe during the Neolithic – NeoNet," funded by Acciones de dinamización “Redes de Investigación” (RED2022-134436-T) (Principal Investigator: M. Cubas Morera, University of Alcalá), and "CHRONOS – The Obsidian Route in the Central Mediterranean: Diachronic Pathways and Cultural Connections," funded by PRIN2022 (Principal Investigator: E. Starnini, University of Pisa).

Data Availability

https://github.com/giadapirrone/Sailing-West.git

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Sailing West: assessing the role of waterways in the Neolithization of Ebro, Po and Rhône basins

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