Documenta Praehistorica XLII (2015) The origins of agriculture in Iberia: a computational model Salvador Pardo Gordó1, Joan Bernabeu Aubán2, Oreto García Puchol3, C. Michael Barton 4 and Sean M. Bergin5 1 Departament de Prehistoria i Arqueologia, Universität de Valencia, ES salvador.pardo@uv.es 2 Departament de Prehistoria i Arqueologia, Universitat de Valencia, ES jbauban@uv.es 3 Investigadora Ramón y Cajal/Departament de Prehistoria i Arqueologia, Universitat de Valencia, ES oreto.garcia@uv.es 4 Center for Social Dynamics and Complexity, Arizona State University, USA michael.barton@asu.edu 5 School of Human Evolution and Social Change, Arizona State University, USA sean.bergin@asu.edu ABSTRACT - Here we discuss the importance of using the rich and growing database of high-precision, audited radiocarbon dates for high-resolution bottom-up modelling to focus on problems concerning the spread of the Neolithic in the Iberia. We also compare the spread of the Late Mesolithic (so-called Geometric) and the Early Neolithic using our modelling environment. Our results suggest that the source of radiocarbon data used to evaluate alternative hypotheses plays an important role in the results and open up new lines of research for the future. IZVLEČEK - V članku poudarjamo pomen bogate in še vedno rastoče podatkovne zbirke natančnih in revidiranih radioakarbonskih datumov pri pojasnjevanju širjenja neolitika na Iberskem polotoku s pomočjo 'visoko ločljivega modeliranja od spodaj navzgor'. Z njegovo pomočjo primerjamo tudi širitev poznega mezolitika (to je 'geometričnega' mezolitika) in zgodnjega neolitika. Rezultati kažejo, da izvor radioakarbonskih datumov, ki jih uporabljamo pri vrednotenju alternativnih hipotez, vpliva na rezultate in odpira nove možnosti raziskav v prihodnosti. KEY WORDS - simulation; Neolithic; Iberian Peninsula; radiocarbon; agent-based model Introduction: the computational approach to testing the spread of the Neolithic The absence of local wild ancestors for the earliest domestic plants and animals, and recent DNA analyses of domestic animals confirm that they were introduced into Europe from the Near East and Anatolia in the early to mid-Holocene. For Europe, then, the origins of agricultural society involved the geographic and temporal spread of domestic species, technologies, and social practices. Considerable debate continues, however, over the mechanisms by which agriculture spread across Europe. Did this involve the movement of farming peoples who displac- ed or mixed with indigenous hunter-gathers, or was it the transmission of information and materials and knowledge of their use (i.e. the 'Neolithic Package') that brought this new way of life to Europe? The latter is sometimes referred to as cultural, and the former as demic, diffusion. The mechanisms that drove this process (e.g., demographic pressure or climatic events) are also debated. To respond to these questions, new methods and theoretical approaches have been recently applied DOI> 10.4312\dp.42.7 117 Salvador Pardo Gordó, Joan Bernabeu Aubán, Oreto García Puchol, C. Michael Barton and Sean M. Bergin in research on the spread of agriculture. In this context, computer simulation has become one of the techniques most frequently used to explore the space/time of Neolithic dispersal and its subsequent evolution. The introduction of computer applications in archaeological research can be dated roughly to the 1950s. The first work focusing on simulation per se was Do-ran's short essay on cybernetics and its application as a useful tool for generating explanations of the archaeological record (Doran 1970.296-298). Subsequently, computer simulation applied to the problem of the dispersal of the Neolithic can been found throughout the archaeological literature for over 40 years. The first and most influential work was framed by Albert J. Ammerman and Luigi L. Cavalli-Sfor-za (1971; 1973; 1979; 1984), which was based on an adaptation of Fisher's reaction-diffusion model applied to the spread of agricultural groups driven by constant population pressure, so-called logistic growth. They evaluated this model for the diffusion of agriculture across different areas of western Eurasia (1984.134-135) by comparing the timing of the initial arrival of agriculture predicted by their model with then-available radiocarbon dates from the archaeological record. They concluded that the predictions of their model and the archaeological information strongly correlated (R~0.8). They also suggested a southeast-northwest gradient for the spread of agriculture across Europe, validating the theory of a Near Eastern origin for the Neolithic as promulgated by Grahame Clark (1965). Although we are discussing the Neolithic expansion in Europe here, other simulation work has focused on the spread of rice in Asia (Silva et al. 2015), and the expansion of Paleolithic populations (Fort et al. 2004) or languages, such as Bantu (e.g., Grollemund et al. 2015; Russell et al. 2014). expanded radiocarbon database has led to a number of studies revisiting the empirical comparisons and demic diffusion models of Ammerman and Ca-valli-Sforza, using different approaches such as time-delay, the role of waterways, effects of boundaries and cultural practices (e.g., Ackland et al. 2007; Davison et al. 2006; Fort et al. 2012; Fort, Méndez 1999). In other research, we conducted a detailed review of some of the most notable such work (e.g. Bocquet-Appel et al. 2009; Davison et al. 2009; Gkiasta et al. 2003; Pinhasi et al. 2005), concluding that new radiometric information from the Iberian peninsula has not yet been fully utilised in computer models for Neolithic dispersal at continental scales (Pardo Gordó et al. in press). This large body of new radiocarbon dates only has been used in local spreading models (Bernabeu et al. 2015; Isern et al. 2014). Since the 2000s we are now in a position to highlight the growing interest in examining different theoretical frameworks by means of archaeological simulation, and the corresponding increase in the number of papers focused on modelling work (Co-stopoulos 2010; Lake 2014). Computational modelling has become a more common and sophisticated tool in the archaeological analytic toolbox (Barton 2013a; 2013b), although the use of computers to support social theory more generally is hardly actu- In the past 15 years, the availability of inexpensive, high-speed computer processing and a greatly Fig. 1. Map of the Iberian Peninsula with Early Neolithic sites with radiocarbon dates used for the model evaluation. 118 The origins of agriculture in Iberia: a computational model ally a new concept (Hagerstrand 1965). In this paper, we investigate the spread of agriculture in Iberia using by means of simulation methods, and compare results with the preliminary models for the spread of the Late Mesolithic, the so-called Geometric Mesolithic. We focus on the Iberian Peninsula because it is a particularly good region in which to study the process of agricultural dispersal. It has evidence of populations of foragers during the final Mesolithic, post quem 6000 BC (Bernabeu et al. 2014). It is situated at the western extreme of the Mediterranean Basin and serves as a bridge between Africa and Europe. For these reasons, Iberia can be considered a sub-continent where it is possible to examine a number of processes related to the Neolithic transition. For example, this area is the best place to evaluate the possibility of duel expansion routes (South-eastern France and Northern Africa) of the first groups of farmers. This has become a topic of interest recently, although there are different views on its impact on the process of Neolithic expansion (see Cortés Sánches et al. 2012; García Borja et al. 2014; Zilhao 2014 for references). Computational model We use computer simulation models, more specifically in Agent-based Model (ABM), to investigate the spread of agriculture in Iberia. This methodological approach is one of the most active applications of simulation in archaeology (Lake 2015) despite its lack of use in studies of the spread of farming (Pa-risi et al. 2008). Briefly, ABM is a kind of computational model with agents that are discrete and autonomous entities that differ from others in space and time, and usually interact with others or with their environment locally (Bonabeau 2002; Railsback, Grimm 2012). experiment" (Bankes et al. 2002) as this allows us to use computational model environments to explore the effects of different variables and compare hypotheses to existing datasets (Grimm et al. 2005). Virtual world Currently, the emphasis on the importance of environmental conditions is a triggering factor for the dispersal of Neolithic groups (Gronenborn 2009; 2010). Although it is widely recognised that ecological contexts are more or less suitable for early Neolithic agriculture, this has not been considered explicitly - with a few exceptions - in the modeling work (e.g., Ackland et al. 2007; Banks et al. 2013). We classified landscape cells based on their suitability for cereal agriculture, using a combination of terrain and climate parameters1 (Bevan, Conolly 2004; Lopez Bellido 1991). We focused on wheat, because it has the most stringent climatic requirements of the different species of early Eurasian cereals. Maps for minimum temperatures for March, maximum temperatures for the spring months of March through May, and total precipitation for spring months were combined to create an index map of suitability for cereal agriculture; these are summarised in Table 1. A combined ecological suitability index was created by summing the three climate index maps and slope index map. The resulting map was scaled to a 5 x 5km resolution and uploaded to NetLogo. Each patch in the models then has a suitability index value based on a combination of the variables described above. Our spread model (Bergin et al. 2015) was implemented the Netlogo modeling platform (Wilensky 1999) because it allows us to import and use geo-referenced datasets within the modelling environment, including radiocarbon dates and other kinds of information (in our case, ecological). For this reason, our model takes the form of a spatially explicit cellular automaton in a gridded landscape in which agriculture can spread on the basis of rules of dispersal. Our approach is based on "modelling as Parameter Values Index Value Slope 160-1000 1 110-150 2 60-1o0 3 °0-50 4 cell is ocean NULL Mean Maximum Spring Temperature (degrees C for March, April, and May) < 180 or > 300 0 250-3o0 1 180-240 2 Minimum March Temperature < 00 NULL o0-40 1 a 50 2 Total Spring Precipitation (mm for March, April, and May) < 100mm or > 600mm 0 100mm-149mm 1 301mm-6oomm 1 150mm-300mm 2 Tab. 1. Environmental parameters used to calculate Ecological Suitability Index. 1 Climate parameters were derived from the WorldClim database (http://www.worldclim.org) (Hijmans et al. 2005). 119 Salvador Pardo Gordó, Joan Bernabeu Aubán, Oreto García Puchol, C. Michael Barton and Sean M. Bergin Spread movement, demographic effects and starting points for agriculture dispersal The three modes of Neolithic dispersal tested in our model are neighbourhood, leapfrog and the Ideal Despotic Distribution (IDD) model (Fig. 2). The first corresponds to the classical wave-of-advance movement promulgated by Fischer (1937) and applied to population expansion by many researchers (see Steele 2009 for references). The model is straightforward: agriculture spreads from one cell to neighbouring cells that lack agriculture as long as they are suitable for it (i.e. have a sufficiently high ecological suitability index value). The second corresponds to the leapfrog model described by Tjeerd Van Andel and Curtis Runnels (1995). This algorithm simulates the dispersal of agriculture from any cell that has agriculture to another randomly selected cell within a given distance (specified by the user) which does not yet have agriculture and that is suitable. This punctuated spread is also the kind of movement proposed in the maritime pioneers models (e.g., Dawson 2011; Zilhao 2001). Two related types are "neighbourhood with no ecological constraints" and "leapfrog with no ecological constraints". These work like the constrained versions already described, but without taking into account the suitability of cells for agriculture. The third process is the IDD model from Human Behavior Ecology (Kennett, Winterhal-der 2006; Smith 1992; Smith, Winterhaider 2003), it was implemented as a follow-up on suggestions by Stephen Shennan (2008) and Sarah B. McClure et al. (2006) about the potential impacts of socially mediated access to re- sources during the Neolithic. In this case, agriculture spreads to the neighbouring cells with the highest suitability values, but this suitability is affected by the number of farmers already occupying the cell. That is, values decline whenever agriculture 'spreads' to a cell in which it is already present, and agriculture will spread only to neighbouring cells with the highest suitability values. Finally, in this model, we explored 17 different potential starting points for the spread of the Neolithic Fig. 2. Examples of spread models in action. A: shows wave-of-advance dispersal; B: shows the IDD spread algorithm; C: shows leapfrog dispersal with the maximum leap distance set to 5 cells. On the maps, an 'X' murks the starting point for the spread; yellow dots show the locations of Neolithic sites. The colours indicate the relative time of arrival of agriculture: the darkest red is the oldest arrival time, and lightest pink the most recent arrival time. Underlying green shades show the ecological suitability of cereal farming. 120 The origins of agriculture in Iberia: a computational model across Iberia. We chose the mouths of various rivers or areas near of them (e.g., Málaga and Gibraltar) around the perimeter of the Iberian Peninsula, with one of them in the centre as a null case (Madrid). Previous results To estimate a chronological range sufficient to encompass the spread of agriculture over much of the Peninsula, we first identified the oldest acceptable unquestionable date for the use of domesticates: a date of 7569±48 calBP (all dates used here are expressed as calibrated years BP.) We then extended this range up to 6000 calBP to encompass the earliest evidence for agro-pastoral systems across the Peninsula. This range permits us to cover a total time span of between 7800-6000 calBP, with the last 500 years for sites located only in northern Spain. For any region in the Iberian Peninsula, we selected sites representing the earliest dated evidence for domestic plants and/or animals. The radiocarbon dataset (Bernabeu et al. 2015.Tab. 2 SI) includes only dates clearly associated with archaeological remains of domestic taxa (plants or animals). In total, we have 134 radiocarbon dates associated with 115 archaeological sites. Their distribution can be seen in Figure 1. In total, 53 refer to long-lived taxa, 39 to shortlived taxa and 42 to domestic taxa (Fig. 3). We grouped this radiocarbon information into four subsets (the mean radiocarbon age is used in all groups): O Best: includes a mix of dates made on domestic taxa where available, non-domestic short-lived taxa when directly dated domestic taxa are not available, and non-domestic long-lived taxa when this is the only kind of radiocarbon sample available. In other words, this is the best radiocarbon date for each site. © Oldest: the oldest date for each site regardless of the kind of sample. © Short-lived: dates are limited to those from animals (domestic and non-domestic) and human bones, shrubs (like rosemary), grasses and herbs, and domestic and non-domestic fruits O Domestic: dates are limited to radiocarbon dates of domestic plant and animal remains. Before reviewing previous results (Bernabeu et al. 2015; Pardo Gordo et al. in press), we first describe how we compare the model results with the archaeological information. This involves establishing a tem- porary equivalence between the model and the empirical record. In our case, this was not problematic because calculating the Pearson correlation coefficient between model time arrival (ticks) and the average of the calibrated radiocarbon dates (agents) is sufficient to evaluate different modelled scenarios. Since we are comparing simulation time-steps, which increase through time, and radiocarbon dates, which decrease in value from oldest to youngest, negative correlations indicate good results. Our first work (Bernabeu et al. 2015) focused on exploring the radiometric dating sample, points of origin for the Iberian Neolithic and exploration of parameters such as movement, distance, ecology and occupation costs. In the first experiment, we evaluated archaeological samples and initial expansion points, keeping the values of movement, distance and cost of occupation fixed (Bernabeu et al. 2015.Tab. 1). The results show that the samples used influence the results, and the best starting points are systematically located in eastern Spain, confirming the Mediterranean origin of the Neolithic. In the second experiment, we evaluated whether the fit between the model and the empirical data improves with multiple origin points instead of a single origin point. This experiment allowed us to test a possible double entry route for the Iberian Neolithic. The results of this experiment allowed us to discard the idea that simply increasing the number of origin points increases the correlation results. We concluded that 9 of the 10 strongest correlations are associated with a dual entry route of the Neolithic into Iberia (one of them located in the northeast Radiocarbon sample information by type M Fig. 3. Bar chart with the number of radiocarbon dates made on long-lived taxa, short-lived taxa and direct taxa. See the online version to identify the colours of each category. 121 Salvador Pardo Gordó, Joan Bernabeu Aubán, Oreto García Puchol, C. Michael Barton and Sean M. Bergin and the other in the southeast) and a complex, multi-spreading process. Finally, using the best correlations of the previous experiments, we explore movement, distance, ecology threshold and the costs of existing occupation by farming groups. We observed the best correlations are associated with leapfrog dispersal, with a distance between 25-50km, medium-high impacts of prior agricultural occupation (demographic aspects) and a preference for places with high potential cereal productivity (ecological threshold between 5 and 6). This allowed us to conclude that the expansion of Neolithic into Iberia can be characterised by pioneer colonisation, whereby farmers travelled relatively long distances looking for places with no or few people already farming, and an attractive environment for wheat. Finally, in other work (Pardo Gordo et al. in press), we explored in more detail the radiocarbon data and its influence on our model results with several experiments. The first compared different groups (above) from the radiocarbon dataset, with a single origin point, and more specifically the best and oldest sub-sets. We observed that that 15 of the 20 strongest correlations are associated with the best sub-set, suggesting that different selections of the radiocarbon information can produce quite different results. Next, we compared the best sub-set with short-lived dates. Again, we looked at the 20 strongest correlations, with unexpected results. The more 'reliable' short-lived radiocarbon dataset generated correlation coefficients considerably worse than the larger, mixed best dates set. Why? We conducted a sub-experiment to test whether dated shell that had potentially been affected by the reservoir effect (Ascough et al. 2005; Soares, Dias 2006) could have had an impact on the results. We again selected one starting point (the Segura River, eastern Iberia) for each of the 5 configurations and removed those dates for shells in the short-lived data set. Removing shell dates from this sub-set significantly improved its match with model results. It is worth remembering that the use of samples made on shells can be problematic when used to evaluate model results if the reservoir effect is not taken into consideration. In the last experiment, we compared the short-lived dates with the smaller group of dates from domestic taxa. Of the 25 best correlations, better Pearson correlations coefficient were produced from the more reliable dates of domestic taxa only dates than the larger short-lived dataset, even without dates for shell. In short, our previous work suggests that the quality of the radiocarbon information used needs to be considered carefully when using a body of dates to evaluate the results of computational modelling of the spread of farming (empirical evidence for this new economy). The importance of using careful and rigorous criteria for the selection of radiocarbon dates noted by other archaeologists (e.g., Bernabeu 2006; Zilhao 2001; 1993; 2011; Bernabeu et al. 2001; Bernabeu, Marti 2014; Rojo et al. 2008) is firmly reflected in the results of our modelling experiments. Nevertheless, the poor results obtained from samples made on short-lived taxa associated with domestication economies were surprising. New experiments Auditing radiocarbon problems, new modelling results As we observed in the section above, the best correlations obtained from previous experiments made on remains of domestic and dates on short taxa (including domestic and non-domestic plants and animals), generated Pearson correlation coefficients considerably worse than other subsets including the oldest and the best. We suggested that these poor correlations could relate to the reservoir effect (on shells and bones). Consequently, we need to calculate the reservoir effect and its impact on spatio-temporal variations (for details see Ascough et al. 2005). As we pointed out (Bernabeu et al. 2014), these problems are especially visible in Portugal, where a significant number of dates derive from shells and human bones. Also, as recently pointed out by Rachel Wood (2015) and Karl-Goran Sjogren (2011), problems linked with the sampling criteria can also affect different treatment procedures in the laboratory. At the same time, the ratio of nitrogen to carbon in bone collagen has been proposed as a good indicator for testing the quality of radiocarbon results (Van Klinken 1999). Unfortunately, the details of the N/C ratio are not usually available for the published radiocarbon dates, adding uncertainty about the possible importance that this kind of problem in radiocarbon assays of bones. Finally, Haide Martins and colleagues (2015) demonstrated that distinguishing some domestic taxa in animal bones (especially Ovis sp. in the Iberian Peninsula) can be difficult, with consequences for dating the beginning of farming. Bearing in mind the potential effect in the radiocarbon outputs, we designed a new experiment that considers only charred samples such as seeds, fruits and char- 122 The origins of agriculture in Iberia: a computational model coals identified as short taxa (shrubs) and we add domestic bones only when the N/C ratio is known and adequate for dating. A total of 34 radiocarbon dates meet these criteria and were used for the experiments reported here (Tab. 2). Figure 4 shows a comparison of our previous results obtained with domestic taxa (for details see Bernabeu et al. 2015. Tab. 1) and the results using the same model parameters obtained using the new audited radiocarbon data set. As shown in the graph, the correlation obtained increases significantly. To further illustrate this point, if we look at the results associated with the point of origin set to the Rio Segura and using the wave-of-advance spread algorithm with ecology considered, the use of domestic taxa shows only a value of R = -0.39, while the use of a database with the filtered information increases its correlation to R = -0.50. In sum, these results suggest again that the radiocarbon samples used have significant effects on the correlations obtained, and consequently on the evaluation of different model scenarios. If we want to be sure about the evaluation of our models (including mathematical, agent-based or cellular automata) to analyse Neolithic dispersals (and, of course, other similar phenomena) using radiocarbon dates, then we need to carefully audit the samples, a task on which we are working now in order to reexamine our previous conclusions (Bernabeu et al. 2015; Pardo Gordo et al. in press). Geometric spread as a null hypothesis Mesolithic bladelet technology, including trapezoidal forms appeared in the 9th millennium calBP as a European phenomenon which included the appearance of new techniques and tools in lithic industries. A millennium later, agriculture expanded around Western Europe. The Mesolithic dispersal has been considered by several authors, such as Clark (1958), who compares this expansion with the posterior Neolithic advance. Despite an interest in exploring the mechanisms behind this dispersal (demic versus cultural), only a few works have highlighted this potential line of research, without developing it further (Binder et al. 2012). Instead, most authors focus on the geographical origin of the Mesolithic, arguing over the different potential starting points (Biagi, Kiosak 2010; Binder et al. 2012; Marchand, Perrin 2015). Although there is broad spatial variability in Mesolithic technology across Europe, it is generally thought to indicate a major shift in blade technology and the production of compound arrowheads (geometric tools). This involves knapping techniques to obtain regular blades and bladelets using indirect percussion or pressure as a distinctive characteristic in order to make regular blades for geometric forms (trapezes) with symmetric or asymmetric shapes (Binder et al. 2012). Other tools, such as notched blades, are also common, and were probably used for processing plant materials (Gassin et al. 2013). In the Western Mediterranean, this cultural complex is known as the Tardenosien tradition, or referred to as the Late Mesolithic. This encompasses the re- Correlation coefficient with p value < 0.05 from single origin point [Comparative approach] Ter-Tajo-Llobregat -Ebro -Guadiana Guadalquivir -° Gibraltar -Malaga -Millares -Almanzora -Xúquer-Segura- Neolithic audited Neolithic no audited O 00 B) OD - CXfiD BO C œoc asc O (¡D GO CE ra 0 Experiment Leapfrog Leapfrog ecol Neighbor Neighbor ecol O I I I I I I I I I I I I I I I I I I I I 1 I -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.60 -0.55-0.50 -0.45 -0.40-0.35 -0.30 -0.25 -0.20 -0.15 -0.10 R Fig. 4. Correlation coefficients for the results of the Neolithic audited and not audited for individual starting points for agricultural dispersals. The colours indicate the different strategies employed by agents. Positive correlations and models are excluded. 123 Salvador Pardo Gordó, Joan Bernabeu Aubán, Oreto García Puchol, C. Michael Barton and Sean M. Bergin gionally named industries of the Castel-novien Complex (or Second Mesolithic in France and Italy), the Upper Capsian in North Africa (Rahmani 2003) and Geometric Mesolithic in Mediterranean Iberia and Portugal (Fortea 1973; Utril-la, Montes 2009). With some regional particularities, this Mesolithic phenomenon has been considered to have across spread Europe in some kind or diffusion process (Kozlowski 2009). Building on our prior work, we selected radiocarbon dates corresponding to the first Geometric Mesolithic in order to compare some parameters related to Mesolithic and Neolithic dispersals. Current information shows that the Late Mesolithic is well documented in eastern Iberia and the Ebro valley (Mediterranean region), and central and southern Portugal (Atlantic coast). While several authors consider some settlements in the Cantabrian region as Mesolithic with geometrics (Arias, Fano 2009), these settlements did do not include all of the technological elements of the well-defined Late Mesolithic of the Castelno-vien tradition, so they were eliminated from our database for this preliminary assessment. Other areas (northeastern Iberia in Catalonia and the inner territories of the Meseta) lack archaeological data on this period. We compiled a total of 21 dates associated with Me-solithic contexts, considering only audited short-lived samples as described above (Tab. 2). The criteria followed the protocols used in our previous work (Bernabeu et al. 2015), considering the most ancient date for each site provided by short-lived samples and comparing them with the modeling results. A particularity in relation to the nature of the samples affects Portuguese Mesolithic contexts, where human skeletons constitute the main material dated. For this, we used the radiocarbon dates compiled by Antonio Faustino Carvalho (2010). In this experiment, we compare different starting points for the spread of the geometric tools around the perimeter of Iberia and evaluate the modelling results against radiocarbon dates made on shortlived taxa. The parameters for this experiment were set as follows: threshold for ecological suitability (i.e. for wheat cultivation) 0 and 3, costs of prior occupation 5% and leapfrog radius distance of 5 cells Fig. 5. Correlation coefficients for the results of the Late Meso-lithic for individual starting points for agricultural dispersals. The colours indicate the different strategies employed by agents. A red circle indicates negative correlations. (25km). As we can see in Figure 5 that the best correlation between the model result and dated Late Mesolithic sites occurs when the ecological threshold is limited to 0 with R = -0.32 in the best case. Regarding the best correlations (those that have negative values), we note several results. First, most of the points of origin with negative correlations (except Bilbao) are located on the Mediterranean coast of the Iberian Peninsula. These results parallel the proposed expansion of the Mesolithic complex throughout Europe (e.g., Clark 1958). The best fitting spread algorithm in all cases is the wave-of-advance (spreading to neighbouring cells only), and when ecological suitability is not considered. However, are there any similarities between these results and those related to the first groups of farmers? Figure 6 shows the comparison between the Me-solithic and Neolithic (using only dates from domestic taxa). The graph shows that the correlations associated with the Neolithic are higher than those for the Mesolithic, and that the best Neolithic correlations (R > -0.3) are associated with scenarios where ecological suitability is taken into consideration. These results do not seem unreasonable, because the base map used was drafted following ecological parameters for cultivating wheat (see section 2.1), which should not be relevant to Mesolithic foragers. Nevertheless, this first attempt to model the 124 The origins of agriculture in Iberia: a computational model Correlation coefficient with p value < 0.05 between Mesolithic and Neolithic from mediterranean origin points Llobregat-Ter •S Almanzora-Ebro-Millares' Segura -Xúquer ■ Mesolithic Neolithic OD ®o CO QD 03D CXBO 3> e @o e c D © C OO O ® e< Experiment O Leapfrog O Leapfrog ecol O Neighbor O Neighbor ecol -0.4 -0.3 -0.2 -0.1 0.0 0.1 -0.4 R -0.3 -0.2 -0.1 0.0 0.1 Fig. 6. Correlation coefficients for the results of Late Mesolithic and Neolithic results (only dates on domestic taxa used for comparison) for individual starting points for agricultural dispersals. The colours indicate the different strategies employed by agents. A red line indicates negative correlations > -0.3. spread of the Mesolithic in the Iberian Peninsula is interesting, as we can detect the Mediterranean character of this expansion. It demonstrates the potential for a new direction of research in which modelling can be a useful tool for understanding the emergence and expansion of pan-European phenomena in general. Concluding remarks In this paper, we illustrate the potential of bottom-up modelling for investigating the dispersal of agropastoral economies and life ways in Europe, focusing on the Iberian Peninsula as a case study. Additionally, we use computational modelling approach as a method of formalising and testing multiple (and complex) hypotheses about local-scale decision rules, rather than as a means of quantitatively characterising agricultural dispersals at the continental scale (so-called top-down models). Agent-based models and mathematical models are complementary approaches to formalising hypotheses about the dynamics of human societies. Top-down modelling allows us to describe general trends and to aggregate be-haviour(s) in societies at large scales and over extended periods. On the other hand, bottom-up modelling is particularly well suited to understanding individual behaviour and its interactions with others and its environment, which generated the general trends observed. We believe that the formalisation in both kinds of modelling approaches is an essential step for the ability to systematically compare and test hypotheses about spatiotemporal dynamics of past human societies against a poor, fragmentary and incomplete archaeological record. In short, this paper is a good example of methods useful for understanding a complex problem (the Neolithic spread) with a promising new approach (agent-based models). Finally, this work demonstrates the importance of carefully auditing the radiocarbon information used to evaluate quantitative models of Neolithic (and others) dispersals. This is essential if we aim to test the reliability of models of human dynamics against the empirical record. 125 Salvador Pardo Gordó, Joan Bernabeu Aubán, Oreto García Puchol, C. 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Sites and radiocarbon dates used to evaluate model experiment results. All dates are given as calibrated BP. N: Neolithic; M: Mesolithic; S: short taxa; D: domestic taxa. ** Radiocarbon dates used in the audited experiment in this work. Site Period Code lab Type Sample Level BP SD CalBP smean Reference Abric de la Falguera** N Betai42289 D Seed (Tritucum) UE 2051b 6510 80 7407 Bernabeu et al 2015 Almonda N OXA9288 S Bone (Stag) I 6445 45 7373 Bernabeu et al 2015 Alto de Rodilla N CSIC1967 S Bone (Human) II 6171 55 7082 Bernabeu et al 2015 Arenaza N OXA7157 D Bone (60s taurus) IC2 6040 75 6889 Bernabeu et al 2015 Atxoste N GrA9789 S Bone III b 6220 60 7132 Bernabeu et al 2015 Balma Margineda** N Beta35268i S Fruit (Hazelnut) III b 6630 80 7518 Martins et al. 2015 Benamer N CNA539 S Pollen II 6575 50 7491 Bernabeu et al 2015 Ca l'Estrada N Pozi039i S Bone (human) SF501 5740 40 6555 Bernabeu et al. 2015 Cabranosa N Saci32i S Shell (Mytilus) fireplace 6550 70 7490 Bernabeu et al. 2015 Caldeirao N OXA1035 D Bone (Ovis) NA II 6330 80 7290 Bernabeu et al. 2015 Camp Colomer de Juberri** N Beta325686 D Seed (Hordeum) Pit FS 29 5630 40 6409 Martins et al. 2015 Can Roqueta N CR S Bone CRII-173 6400 50 7345 Bernabeu et al. 2015 Can Sadurní ** N OXA15488 D Seed (Tritucum) Layer 18 6421 34 7367 Bernabeu et al. 2015 Cariguela N Pta9i63 S Bone (Human) CIV II 2 6260 20 7207 Bernabeu et al. 2015 Carrascal N Beta27640i D Bone (60s taurus) NA level 6280 40 7214 Bernabeu et al. 2015 Casa da Moura N TO953 S Bone (Human) Ia 5990 60 6820 Bernabeu et al. 2015 Casa Montero N Beta295i52 D Bone (Ovis) Pit 15267 6200 40 7093 Bernabeu et al. 2015 Castelo Belinho N Sac2031 S Bone (Human) Structure 1 5790 70 6582 Bernabeu et al. 2015 Cerro Virtud N OXA6714 S Bone (Human) Lev. 6 (B3.30) 6030 55 6870 Bernabeu et al. 2015 Chaves N GrA38o22 D Bone (Ovis) Ib 6580 35 7468 Bernabeu et al. 2015 Chaves ** N GrA2834i S Fruit (Acorn) Ib 6380 40 7315 Baldellou 2011 Cingle del Mas Cremat ** N Beta232340 S Seed (Sorbus sp.) IIIb 6020 50 6862 Bernabeu et al. 2015 Codella N Beta22i900 D Bone (Ovis) - 5720 60 6530 Bernabeu et al. 2015 2001. Radiocarbon evidence for maritime pioneer colonization at the origins of farming in west Mediterranean Europe. Proceedings of the National Academy of Sciences 98(24): 14180-14185. 2011. Time Is On My Side. In A. Hadjikoumis E. Robinson and S. Viner (eds.), The dynamics of neolithisa-tion in Europe. Studies in honour of Andrew Sher-ratt. Oxbow Books. Oxford: 46-65. 2014. Early prehistoric navigation in the Western Mediterranean: Implications for the Neolithic transition in Iberia and the Maghreb. Eurasian Prehistory 11(1-2): 185-200. 129 Salvador Pardo Gordó, Joan Bernabeu Aubán, Oreto García Puchol, C. Michael Barton and Sean M. Bergin Site Period Code lab Type Sample Level BP SD CalBP smean Reference Costamar N OxA23578 D Bone (Bos) UE 40102 5995 38 6838 Bernabeu et al. 2015 Costamar ** N UCIAMS60738 D Seed (Tritucum) UE 13002 5965 25 6792 Flors 2009 Cova Avellaner N UBAR109 S Bone (Human) 3A 5830 100 6622 Bernabeu et al. 2015 Cova Colomera ** N OxA-23634 D Seed (Tritucum) CE 14 6170 30 7086 Bernabeu et al. 2015 Cova de la Sarsa ** N OxA26076 D Bone (Ovis) 6506 32 7402 Bernabeu et al. 2015 Cova de les Cendres N Beta239377 D Bone (Ovis) H19 6510 40 7406 Bernabeu et al. 2015 Cova de les Cendres ** N GifAioi36o D Seed (Tritucum) H19 6490 90 7396 Bernbabeu, Molina 2009 Cova de l''Or N UCIAMS66316 D Bone (Ovis) VI a 6475 25 7381 Bernabeu et al. 2015 Cova de l''Or ** N OXA10191 D Seed (Tritucum) VI a 6310 70 7239 Martí 2011 Cova de Sant Lloren^ ** N Beta299597 D Seed (Tritucum) II 6160 40 7067 Oms 2014 Cova del Toll ** N OxA26070 D Bone (Ovis) lib 6425 35 7368 Bernabeu et al. 2015 Cova dels Trocs ** N OxA26070 D Seed (Tritucum) I 6080 40 6942 Rojo et al. 2013 Cova den Pardo N Beta23i879 D Bone (Ovis-Capra) VIII 6610 40 7513 Bernabeu et al. 2015 Cova Font Major N Beta3i7705 D Bone (Ovis) lg 6310 40 7224 Bernabeu et al. 2015 Cova Foradada N Beta248524 D Bone (Ovis) Ic 6200 40 7093 Bernabeu et al. 2015 Cova Fosca d'Ebo ** N OxA26047 D Bone (Ovis) II z 6413 33 7364 Bernabeu et al. 2015 Cova Gran ** N Beta265982 S Seed (acorn) E9 6020 50 6862 Bernabeu et al. 2015 Cova Sant Martí N Beta166467 S Bone (Human) UE206 5740 40 6555 Bernabeu et al. 2015 Cueva del Toro ** N Beta341132 D Seed (Tritucum) IV 6150 30 7063 Socas, Camalich 2013 Cueva de la Higuera N Betai66230 S Bone II 6250 60 7144 Bernabeu et al. 2015 Cueva de los Mármoles **N Wk25i7i D Seed (Hordeum) Ni D2 6198 31 7094 Bernabeu et al. 2015 C. Murciélagos (Alb.) ** N CSIC1133 S Charcoal (Stipa) - 6086 45 7013 Bernabeu et al. 2015 C. Murciélagos (Zuh.) ** N GrN6639 D Seed (Cereal sp.) C 6025 45 6865 Bernabeu et al. 2015 Cueva de Nerja N Betai3i577 D Bone (Ovis) IV 6590 40 7496 Bernabeu et al. 2015 El Barranquet N Beta221431 D Bone (Ovis) UE 79 6510 50 7406 Bernabeu et al. 2015 El Cavet ** N OxA26061 D Seed (Triticum) UE 2014 6536 36 7451 Oms 2014 El Congosto N KIA27582 S Bone (Human) - 6015 50 6860 Bernabeu et al. 2015 El Mirador ** N Beta2o8i34 D Seed (Triticum) MIR 23 6300 50 7220 Bernabeu et al. 2015 El Mirón ** N GX309010 D Seed (Cereal sp.) Trench 303.3 5550 40 6348 Bernabeu et al. 2015 El Tonto N Beta3i725i D Bone (Ovis) - 6230 30 7138 Bernabeu et al. 2015 Fuente Celada N UGA75665 S Bone (Human) H62-UE622 6120 30 7048 Bernabeu et al. 2015 Gruta do Correio-Mor N Sac1717 S Bone (Human) - 6330 60 7246 Bernabeu et al. 2015 Hostal Guadalupe N Wk25i67 D Bone (Ovis-Capra) - 6249 30 7205 Bernabeu et al. 2015 Hostal Guadalupe N Wk25i69 S Bone (Human) - 6298 30 7220 Bernabeu et al. 2015 Kobaederra ** N AA29110 D Seed (Cereal sp.) IV 5375 90 6150 Bernabeu et al. 2015 La Draga N Beta278255 D Bone (Ovis-Capra) I 6270 40 7210 Bernabeu et al. 2015 La Draga ** N OxA20233 D Seed (Triticum) I 6179 33 7080 Bosh, Tarrús 2011 La Lampara ** N UtC13346 D Seed (Triticum) Structure 1 6280 50 7214 Bernabeu et al. 2015 La Lampara N KIA21347 S Bone Structure 18 6407 34 7360 Bernabeu et al. 2015 La Paleta N Beta223091 D Bone (Ovis) Structure 175 5850 40 6685 Bernabeu et al. 2015 La Paleta N Beta223092 D Seed (Cerealia) Structure 219 6660 60 7535 Bernabeu et al. 2015 La Revilla del Campo N KIA21356 D Bone (Ovis-Capra) Structure 4 6355 30 7286 Bernabeu et al. 2015 La Revilla del Campo N KIA21358 S Bone Structure 14 6365 36 7333 Bernabeu et al. 2015 La Revilla del Campo ** N UtC13295 D Seed (Triticum) Structure 12 6313 48 7242 Rojo et al. 2008 La Vaquera ** N GrA824i S Fruit (acorn) UE 98 6080 70 6976 Bernabeu et al. 2015 Les Guixeres ** N OxA26068 D Bone (Ovis) A 6655 45 7538 Bernabeu et al. 2015 Los Cascajos ** N Ua24427 D Seed (Cereal sp.) Structure 516 6250 50 7145 Bernabeu et al. 2015 Los Castillejos ** N Ua362i5 D Seed (Cereal sp.) I 6310 45 7223 Bernabeu et al. 2015 Los Gitanos N AA29113 S Bone A3 5945 55 6764 Bernabeu et al. 2015 Los Husos I N Betai6ii82 S Bone XVI 6240 60 7141 Bernabeu et al. 2015 130 The origins of agriculture in Iberia: a computational model Site Perioc Code lab Type Sample Level BP SD CalBP smean Reference Los Husos II N Beta22i640 S Bone VII 6050 40 6878 Bernabeu et al. 2015 Marizulo N Ua-4818 S Bone (Human) I 5285 65 6067 Bernabeu et al. 2015 Mas d'Is ** N Beta162092 D Seed (Hordeum) House 2 6600 50 7500 Bernabeu et al. 2015 Molino de Arriba N KIA41450 S Bone (Human) UE 202 6120 30 7048 Bernabeu et al. 2015 Peña Larga N Beta242783 D Bone (Ovis/Capra) IV 6720 40 7570 Bernabeu et al. 2015 Pico Ramos ** N Ua3051 D Seed (Hordeum) IV 5370 40 6151 Bernabeu et al. 2015 Plaza Vila de Madrid N Beta18271 S Bone (Human) - 6440 40 7373 Bernabeu et al. 2015 Portalón N Beta222339 S Bone N9 north 6100 50 7021 Bernabeu et al. 2015 Prazo N GrN26404 S Charcoal (Arbustus u.) SVII-UE 3 5630 25 6400 Bernabeu et al. 2015 Roca Chica N Wk27462 D Bone (Ovis) - 6234 30 7140 Bernabeu et al. 2015 Sant Pau del Camp N Beta236174 S Bone Trench 1 6290 50 7216 Bernabeu et al. 2015 Senhora das Lapas N ICEN805 S Bone (Human) Layer 3 6100 70 7020 Bernabeu et al. 2015 Serrat del Pont N Betai7252i S Bone (Sus scrofa) III 6470 40 7379 Bernabeu et al. 2015 Tossal de les Basses N Beta232484 D Seed UE34 5950 50 6787 Bernabeu et al. 2015 Vale Boi N OxAi3445 D Bone (Ovis-Capra) C II 6042 34 6875 Bernabeu et al. 2015 Vale Boi N Wki7842 S Bone (wildlife) C II 6095 40 7016 Bernabeu et al. 2015 Ventana N Betai66232 D Bone (Ovis) II lower 6350 40 7328 Bernabeu et al. 2015 Abric de la Falguera M AA59519 S Charcoal (bract) VIII 7526 44 8352 Martí et al. 2009 Aizpea M GrNi6620 S Bone I (b base) 7790 70 8571 Utrilla et al. 2009 Atxoste M GrAi3469 S Bone IV 7480 50 8299 Utrilla et al. 2009 Benámer M CNA680 S Pollen UE2213 7490 50 8310 Torregrosa et al. 2011 Botiquería dels Moros M GrAi3265 S Bone (Cervus elaphus) 2 7600 50 8403 Utrilla et al. 2009 Cabero da Amoreira M TO11819R S Bone (Human) Burial CAM 00 01 7300 80 8113 Bicho et al. 2011 Cabero da Arruda M Betai2745i S Bone (Human) Skeleton 6 7550 100 8355 Carvalho 2010 Cabero das Amoreiras M Betai25iio S Bone (Human) Skeleton 5 7230 40 8042 Carvalho 2010 Costa do Pereiro M Wk17026 S Bone (Deer) cib 7327 42 8118 Carvalho 2010 Cpva da On$a M Betai27448 S Bone (Human) - 7140 40 7966 Carvalho 2010 Cueva de la Cocina M UCIAMS145348 S Bone (Capra pyrenaica) Sector 1941 ci6 7905 40 8720 In this work Cueva de Nerja M GifAi020i0 S Seed (pine nut) NV3 (IIIc) 7610 90 8417 Aura et al. 2013 Esplugón M Beta306725 S Bone Prof 189 7860 40 8645 Utrilla, Domingo 2012 Mendandia M GrN22743 S Bone III inferior 7620 50 8418 Utrilla et al. 2009 Forcas II M Beta250944 S Bone II 7150 40 7973 Utrilla et al. 2009 Casa Corona M OxAV239292 S Bone (Human) Burial 2 7116 32 7949 Fernández López de Pablo et al. 2011 Moita da Sebastiao M TO131 S Bone (Human) Skeleton 22 7240 70 8066 Carvalho 2010 Rambla Legunova M GrA6i768 S Bone 2 7260 45 8085 Montes et al. 2015 Tossal de la Roca M Gif6898 S Bone I ext. 7660 80 8464 Martí et al. 2009 Vale Boi M TO12197 S Bone (Human) Layer 2 (base) 7500 90 8307 Carvalho et al. 2010 Valcervera M GrA45763 S Bone b 7035 45 7875 Montes et al. 2015 back to contents 131