1. Introduction
This comment concerns the recent article in Radiocarbon entitled “The Neolithic Transition in the Western Mediterranean: a complex and non-linear diffusion process—the radiocarbon record revisited” (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019). While the new high-quality dates for the sites of Pont de Roque-Haute and Peiro Signado in the region of Languedoc in Southern France are welcome additions to the literature, this cannot be said for the opening and closing sections of their article. In my view, both sections include a number of misunderstandings of the work that I have done on the Neolithic transition in Europe over the years. In trying to build a case for their position, the authors make a number of errors in scholarship, as explained in the next six sections. The plan is to keep my comments short and not to digress on other issues raised by the article. It is worth mentioning, by way of introduction, that in 2020 I wrote a chapter called “The Neolithic Transition in Europe at 50 Years,” which traces the evolution of my research on this question and related research topics, starting with our initial work on “Measuring the rate of spread of early farming in Europe” (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971) and running through our most recent publication called “Modeling the role of voyaging in the coastal spread of the early Neolithic in the West Mediterranean” (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017). My plan was to fly from New York to Italy in March to continue my research projects there. But the outbreak of the coronavirus meant that I had to shelter in place at home (Hamilton in Upstate New York), which meant that there was now the unexpected chance to write the chapter as a first step toward a memoir on my archaeological projects in Rome, Venice, Paestum, Athens and on the island of Cyprus (where we worked on the origins of seafaring in the Eastern Mediterranean in the time before the Neolithic; Ammerman Reference Ammerman, Anderson, Barret and Boyle2010, Reference Ammerman, Bailey, Galanidou, Peeters, Jons and Mennenga2019; Ammerman and Davis Reference Ammerman and Davis2013–2014). When the manuscript had reached an advanced stage, I sent a copy of it to several colleagues for their comments, and one of the replies drew my attention to the new article by Manen and coauthors in Radiocarbon. The chapter that I wrote in March and April 2020 and that will eventually appear in the Festschrift in honor of Ryszard Grygiel and Peter Bogucki, two leading scholars in Neolithic studies who have worked in collaboration in Poland for years, provides historical background on the comments offered here (a preprint of the chapter can be found online at Ammerman Reference Ammerman2020).
Here the focus will be on three points: (1) to set the record straight with regard to misinformation in the article written by Manen et al. (Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019), (2) to clarify several misconceptions that have persisted in the literature for some time, and (3) to comment on the convergence between our own regional modeling of the spread of first farmers along the north coast of the West Mediterranean (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017) and the position currently held by Manen and coauthors, who insist, of course, that the opposite is the case. As we shall see in the last two sections, there was previously a shortage of high-quality dates at early Neolithic sites in the southern part of Languedoc. The new determinations reported in the article now fill in this gap, and they also lend support to the argument put forward in our article in PNAS at the end of 2017.
2. Measuring the rate of spread of early farming in Europe
This was the title that we gave to our first publication on the Neolithic transition (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971). At the time, archaeologists were just beginning to take a more quantitative approach to their investigations. No previous attempt had been made to measure such a rate. In short, what we were trying to do 50 years ago was not a routine piece of research. Furthermore, what we were starting to learn about the spread in this way was put forward as a first approximation—one that could be improved as more early Neolithic sites with radiocarbon dates became available. Thus, the article concentrated on how one goes about measuring such a rate and on presenting the new results obtained. In the 1971 article, no attempt is made to discuss at any length the model of “the wave of advance” except to introduce it briefly on the last page and say that it would be the subject of a forthcoming publication. Here it is worth noting, by the way, that this article just happens to be the only one of our publications on the Neolithic transition that Manen and coauthors cite in their article (even though they comment at various points about the wave of advance model; for some of our other publications on the subject, see Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973; Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984; several chapters in Ammerman and Biagi Reference Ammerman and Biagi2003). This is rather strange behavior. It too involves a misunderstanding on their part when it comes to scholarship on the Neolithic transition in Europe.
Looking back, it will be recalled that there were in the 1970s two main lines of explanation for the spread of early agro-pastoralism in the case of Europe: cultural diffusion on the one hand and what we now called demic diffusion on the other hand. In our view, the two should not be taken as mutually exclusive, but they merited being clearly distinguished at the conceptual level (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: 686). Since both of us were working on hunters-gatherers at the time (see the Ammerman Reference Ammerman2020 preprint chapter), we were initially inclined to favor the cultural side. However, upon further thought, we began to realize that the demic hypothesis deserved more serious attention than it had received in the previous literature. In any event, by measuring the rate of spread, there was the chance to gain a better understanding of the problem and perhaps even move toward sorting out these two modes of explanation on the basis of the rates observed. The analysis itself involved three main steps. To begin with, one would like the diffusionary process under consideration to take the basic form of a linear advance—otherwise attempts at modeling the process will become complex in mathematical terms. Accordingly, the first step was to visualize four possible patterns of the data (based on graphs where time was plotted against distance from the start of the diffusionary process; Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: fig. 1). They would serve as a frame of reference in terms of where we stood when it came to producing graphs of the actual data. They were respectively: (1) a pattern of widely dispersed points with no clear trend over time, (2) a pattern showing an increasing rate over time, (3) a pattern showing a decreasing rate over time, and (4) a pattern showing a linear trend over time. This step was undertaken in visual terms since most archaeologists at the time did not have the mathematic training to conduct it in more formal terms.
The second step was to plot the actual data (53 Neolithic sites in Europe with radiocarbon dates) drawing on several selected “centers” (early sites) in the Near East and see where their respective patterns fell in the context of the four different patterns. There was the good fortune that each of the observed graphs fits fairly well with the fourth pattern (e.g., Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: fig. 2). In turn, this meant that use could be made of classical methods of regression analysis in statistics, where the correlation coefficient measures how consistent the data are with respect to a strictly linear pattern and the slope of the regression line measures the average rate of the spread. Somehow the authors have their own ideas about the latter measurement and reinterpret it to mean a constant rate of spread (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 532; “the result is a constant diffusion speed in time and space”). What we actually say is the following: “The slope of the straight line can supply a good estimate of the average rate of diffusion” (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: 681). In short, due allowance is made for variability in time and space when the rate of spread is measured in this way. The plan is to return to this misconception on the part of the authors in section 5, which is entitled “the heart of the matter.”
In the third step of the analysis, we then went on to measure several regional rates in the spread of early farming, including the Linear Bandkeramik (LBK), the Balkans and the Western Mediterranean (Ammerman and Cavalli Reference Ammerman and Cavalli-Sforza1971: table 2). For one reason or another, the authors do not mention the third step in the analysis. Indeed, even with the limited data available at that time, it was possible to recognize some degree of variation in the average rate of spread from one region of Europe to the next. For instance, the LBK and the Western Mediterranean both yielded faster average rates than the one for Europe as a whole. In other words, it makes no sense to claim that one is dealing with just one fixed rate of spread that holds for all times and places in Europe. Remarkably, the authors advance the further claim that no attempt is made in the 1971 article to take into account regional or spatial variation in the rate of spread (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 532; “it does not take into consideration the spatial dispersal of radiocarbon data”). But this happens to be just what we were doing, in an initial way, at the third step. Of course, we did not have the data and the analytical tools to work with 50 years ago that are available today. In sum, what we find here is yet another misreading of our work.
As in the other historical sciences, one works by steps of approximation in archaeology. The data, the methods, the models and the working hypotheses can all change as time’s arrow moves forward. For our present purposes, this can be illustrated by mentioning two examples. One of them involved using a larger database and displaying the pattern of the spread by placing computer generated isochron lines on the map of Europe (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: fig. 4.6). Such a treatment is in better accord with the idea that the origins of agriculture in the Southwest Asia did not happen at just a single place or “center” but at multiple ones over an area of fair size. The second example is linked with the growth over the years in the number of early farming sites with radiocarbon dates. By 2005, the sample size had increased to 735 dated sites, and the decision was made to repeat, with appropriate refinements, the regression analysis done in 1971. Much the same results were obtained with the value for the average rate of spread over Europe being close to 1 km per year again (Pinhasi et al. Reference Pinhasi, Fort and Ammerman2005).
3. A population model for the diffusion of early farming in Europe
This is the title of our chapter on the wave of advance model that came out two years later (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973). There was a good deal to cover on the model—its history, its formula, how to conceptualize its three variables, a computer simulation of “the wave of advance” and it implications for human population genetics—in the limited space available in The Explanation of Culture Change. Here it is worth adding that a fuller account of the model is given in the fifth chapter of The Neolithic Transition and the Genetics of Populations in Europe (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984). The wave of advance model was first put forward by the British geneticist R. A. Fisher (Reference Fisher1937) to predict the diffusion of an advantageous gene in a linear habitat. The ecologist J. G. Skellam (Reference Skellam1951) then used the model in his study of the spread of the muskrat after its introduction as a new species in central Europe at the start of the 20th century (see the next section).
In Fisher’s formulation, the model has three variables, and each of them has the potential to be measured. The first one is called a or the initial growth rate of the population, and growth is taken to occur according to a logistic form (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973: figs. 2–3): that is, it is actively taking place only at the wave front and growth then progressively slows down in a given place as the wave front moves forward. In other words, population growth does not take place according to an exponential form; instead, it is self-regulating: in effect, little or no population growth is happening in those places located behind the wave front. In the case of human populations, we know that the fastest rate of growth is about 3% per year or a doubling time of 23 years. The second variable involves a quantitative expression that provides a summary of “the migratory activity” of a population. In the case of the first farmers, processes involving the movement of people are considered to take place essentially in the context of the relocation of households and settlements on the landscape. Without going into the details here, this variable, which is identified as m in Fisher’s equation, is measured as the mean square root of movement per unit time. Working in combination, these two variables generate the rate of advance of the diffusionary process or the variable r as Fisher calls it. In fact, it takes some heavy lifting in mathematics to fully appreciate how Fisher managed to bring these three variables together in a concise formula. And this is even more so when it comes to the extension of his model by Fort and Mendez (Reference Fort and Mendez1999) to include time-delay theory, which takes into better account the discrete character of the relocation of households and settlements.
We have reached a good point to turn to one of the authors’ comments on the wave of advance model (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 532): “The ‘wave of advance’ explains the Neolithic transition by a regular movement of populations as a result of an ever-increasing demography contributing to the segmentation of groups.” This sentence is quite misleading. To begin with, our primary aim is to explain the spread of early farming in terms of demic diffusion. The wave of advance model is just a tool that is used in attempting to evaluate this hypothesis (more on this below). According to the model, population growth, as mentioned above, occurs in a logistic form: that is, with growth actively taking place only at the wave front (and not behind it) and not according to “an ever increasing” or exponential form, as the authors seem to imply. Moreover, in contrast with their claim, we have never written a word about “the segmentation of groups.” This is something that they have advanced in an attempt to attack what is a bête noir for them: the wave of advance model. The question that needs to be asked at this point is a basic one: What is a model? Here it is worth quoting at length what I wrote in the opening chapter of The Widening Harvest (Ammerman Reference Ammerman, Ammerman and Biagi2003: 8). “A model is a tool for thinking – a framework for addressing a problem. The value of a model, as the economic historian David Landes (Reference Landes1969: 540) notes, is accordingly heuristic; it does not tell us what happened in the past; it helps us to discover and to understand what may have happened. I would like to add here that the wave of advance model is not to be confused, as is often done in the literature, with the demic hypothesis.” Again, the latter constitutes our primary interest; the former is simply a means toward that end. And like all models in the sciences, the wave of advance model can be refined and extended over the course of time (e.g., Fort and Mendes Reference Fort and Mendez1999; Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017).
4. The introduction of the muskrat in Central Europe
For most archaeologists, the best way to see how the model of the wave of advance can be applied is by turning to the case study of the spread of the muskrat (Skellam Reference Skellam1951). The following is a short version of what is presented in chapter 5 of our 1984 book (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: 69–71). The muskrat, whose fur is of industrial importance, occurs naturally only in North America. It was thus exported to Europe where a few muskrats escaped from captivity in the area to the north of Vienna and found its plains to their liking. They multiplied freely and soon established themselves as a feral species in Central Europe. Through growth and dispersal, the muskrats covered each year a wider and wider area. By using a map that shows the spatial distribution of the expansion for a sequence of years between 1905 and 1927, Skellam, an ecologist, was able to estimate the area covered in a given year and found that the square root of the area when plotted against time yielded a close fit to a straight line, whose slope gave the average rate of advance of the “wave front” (for the map and also Skellam’s graph, see Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: fig. 5.3). Thus, Skellam found just what Fisher’s model predicted. It is worth adding here that the contour lines for the respective years can be quite irregular in shape, as one might expect in the case of an animal spreading through a heterogeneous environment. “But if the law of averages is given a chance to operate, regularities emerge” (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: 70). This is what we had in mind when we began working on the question of the spread of early farming in 1970. We did not expect absolute regularity; there was room for variability in space as we began to learn from the measurement of regional rates as mentioned before (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: table 2). Once the rates had been estimated, we also drew a map where the date for each site was put in its respective place there, and this made it possible to see in two dimensions that the pattern as a whole had its basic regularity and that the spread was faster in both Central Europe and the Western Mediterranean, as we indicated on the map itself (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: fig. 6). Again, this map should be seen today as a first approximation, based on the limited data that was available 50 years ago.
5. The heart of the matter
In light of what is presented above, I believe it is fair to say that the authors lack a good understanding of our 1971 article and also the chapter on the model of the wave of advance published in 1973. They seem to have no idea that we measured not only the average rate of spread for Europe as a whole but several regional rates as well. In addition, they appear not to appreciate the difference between what is taking place on the ground and its treatment in Fisher’s model, as shown by Skellam’s study of the introduction of the muskrat in Central Europe (cited in the 1971 article). In addition, they make no mention of the map (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973: fig. 6), which goes against their claim that we made no allowance for regional variation in Reference Ammerman and Cavalli-Sforza1971. Furthermore, they bring confusion in the literature when they speak of an average rate (measured on the ground) as if it were a constant rate (with a fixed value at all times and places). In short, to use French words again, this is the idée fixe of the authors—the primary source of their misunderstanding of our research on the Neolithic transition. This is not a minor point but one at the very heart of the matter. To make certain that this issue and its implications are well understood, it is useful to illustrate the problem by means of an example from the modern world. Suppose that one is interested in studying the economy of the United States and would like to measure the rate of growth in GDP per year during the time of the Obama administration (2008–2016). By plotting on a graph the values of GDP against time for each of eight years, there are ways to estimate (using quantitative methods perhaps more refined than the ones that we use in archaeology) the average rate of growth in GDP per year for this time span. What one should not do, however, is to turn around and then say that this average rate holds as the one fixed rate of growth for each of the individual eight years. To do this sort of thing over and over would be to turn economics into a static field of study.
Returning to the Neolithic world, this misconception on the authors’ part may well stem from two quite different meanings of the word constant in the dictionary. In its common and older usage, what it means is to be consistent or to stand firm (the Latin root of the word). When Fisher or Cavalli-Sforza uses the term to describe the character of a variable in an equation, it is being used in this sense: to emphasize that it stands firm in a linear form, which makes everything simpler from the standpoint of mathematics. It is not being used in the second and more technical sense of the term (as a noun that goes back only to 1832 in both British and American usage): that is, as a constant such as the Greek letter π in the equation for the area of a circle. Here it is important to remember that “the wave of advance” is a model that began its life in the field of population biology. For those in the biological sciences, there is the understanding that what is taking place on the ground is usually messier and more irregular than what is held to occur in a formal model. This is a perspective shared by the model-building economist as well. Indeed, this way of thinking should not be so foreign to the authors. Given their current interest in irregularity and discontinuity on the ground, it will take modeling of one kind or another to sort out and try to explain what is happening in such a complex world. Where the authors go off course is by taking regularity in the sense of its representation in the domain of a formal model and somehow then projecting it back as a “constant” on the ground (a different domain, a place with variability in time and space where an average rate can be measured).
The value of a model, as a heuristic tool, is connected with the predictions that it makes and the chance to test them. In other words, the proof (test) of the pudding (model) is in the eating (its predictions). The wave of advance model has clear implications for human population genetics. When our book came out in 1984, the genes of early farmers could not be studied in a direct way (see the preprint chapter Ammerman Reference Ammerman2020), and so modern proxies had to be used instead to evaluate the model’s genetic predictions. In the last 20 years, it has become possible to analyze DNA recovered from human bones of early Neolithic age. The results of a fair number of studies, without going into the details here, now provide direct support for the hypothesis of demic diffusion (Bramante et al. Reference Bramanti2009; Haak et al. Reference Haak2010; Fu et al. Reference Fu, Rudan, Pääbo and Krause2012; Szécsényi-Nagy et al. Reference Szécsényi-Nagy, Keeri, Jakucs, Brandt, Banffy, Alt, Whittle and Bickle2014; Mathieson et al. Reference Mathieson2015; Hofmanova et al. Reference Hofmanova2016; Olalde et al. Reference Olalde2019; Brunel et al. Reference Brunel2020; see Section 4 of Ammerman Reference Ammerman2020). In sum, it is widely accepted today that the spread of agro-pastoralism over Europe involved a diffusionary process and more specifically that the spread of first farming is to a large extent the consequence of demic diffusion. The wave of advance model is thus on target in terms of its genetic predictions. At the same time, we have long held that local hunter and gatherers also played a role in the story (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973: 353; Reference Ammerman and Cavalli-Sforza1984: 116–119; Ammerman Reference Ammerman, Ammerman and Biagi2003: 8). Recently, we have incorporated hunter-gatherers in a direct and interactive way (for instance, in mating and as guides to local knowledge at the wave front) in the modeling of the rapid coastal spread in the West Mediterranean (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017: 4–5).
6. The seven high-quality dates from Pont de Roque-Haute and Peiro Signado in Languedoc
Only a few brief words will be said here about the single most important result in the article of interest (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019). Both of the sites are open-air settlements, and all seven of the dates were made on seeds of emmer (Triticum dicoccum). In the case of Pont de Roque-Haute, the artifacts recovered by the excavations include obsidian from Palmarola. Obsidian from the same island source in the Tyrrhenian Sea has also been recovered from early Neolithic levels at Arene Candide in Liguria, which indicates that things were moving over considerable distances at the time in the context of early voyaging (e.g., Ammerman Reference Ammerman, Anderson, Barret and Boyle2010: fig. 7.3). All seven of the dates tend to cluster around 5800 cal. BCE with a range on the order of ±100 years. These are now the earliest high-quality dates for the Neolithic in Southern France. This number of dates is just large enough to make this new result convincing. The claim by the authors that emphasis should be placed on short-life samples in radiocarbon dating is not something new. This position has been around for some time (e.g., Zilhão Reference Zilhäo, Hadjikoumis, Robinson and Viner2011), and it has finally been achieved at two sites in the south of France (both of which were excavated more than 20 years ago).
Modeling the role of voyaging in the coastal spread of the Early Neolithic in the West Mediterranean
This is the title of our regional study published three years ago (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017). As mentioned before, the modeling of the diffusionary process now includes voyaging and local hunters-gatherers. In the discussion at the end of their article, Manen et al. (Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 561) raise a straw man with regard to studies done at a continental scale citing our 1971 article again. They believe that their new results diverge from previous studies and that no other group of scholars has yet to undertake a regional study in the Western Mediterranean. Of course, this is incorrect: we recently published just such a study in PNAS, as mentioned before. And to compound the disorder in this case, our modeling exercise in 2017 actually entails an extension of the wave of advance model: that is, a new treatment of the component of “migratory activity,” which draws on our recent work on early voyaging in the Mediterranean (e.g., Ammerman and Davis Reference Ammerman and Davis2013–2014). Be that as it may, it is worth noting that we mention the shortage of high-quality dates for Languedoc at the time: “the only major geographical gap in our dataset concerning an area with a well-known and rather dense network of Early Neolithic sites is the French Languedoc, as is apparent in Fig. 1. The lack of quality dates means that there is at present time little than can be done to remedy the situation” (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017: SI p. 2). If the seven dates mentioned in Section 6 had been available at the time, we would have used them to fill in this gap on the map. In other words, this new data would have contributed positively to our argument, and, in this sense, there is convergence between our respective regional studies in the West Mediterranean. The irony here is that, all along, we have been doing research and writing papers that the authors have not read carefully, and this has led, in turn, to one misunderstanding after the next. Finally, as an archaeologist who has lived and worked in Italy for the last 50 years, it is premature, in my view, to take the Early Neolithic dates that are currently available there simply at face value. For instance, the high-quality dates for the oldest Neolithic settlement in the heel of Southern Italy may one day go back to around 6200 cal. BCE. Again, we work by steps of approximation in archaeology, and, to my knowledge, there has yet to be in Southern Italy an advanced project such as PROCOME. Ten years ago, Southern France was in much the same boat, since it too had at that time comparatively few good seed dates and there was a gap in the chronology of Languedoc.
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1. Introduction
This comment concerns the recent article in Radiocarbon entitled “The Neolithic Transition in the Western Mediterranean: a complex and non-linear diffusion process—the radiocarbon record revisited” (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019). While the new high-quality dates for the sites of Pont de Roque-Haute and Peiro Signado in the region of Languedoc in Southern France are welcome additions to the literature, this cannot be said for the opening and closing sections of their article. In my view, both sections include a number of misunderstandings of the work that I have done on the Neolithic transition in Europe over the years. In trying to build a case for their position, the authors make a number of errors in scholarship, as explained in the next six sections. The plan is to keep my comments short and not to digress on other issues raised by the article. It is worth mentioning, by way of introduction, that in 2020 I wrote a chapter called “The Neolithic Transition in Europe at 50 Years,” which traces the evolution of my research on this question and related research topics, starting with our initial work on “Measuring the rate of spread of early farming in Europe” (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971) and running through our most recent publication called “Modeling the role of voyaging in the coastal spread of the early Neolithic in the West Mediterranean” (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017). My plan was to fly from New York to Italy in March to continue my research projects there. But the outbreak of the coronavirus meant that I had to shelter in place at home (Hamilton in Upstate New York), which meant that there was now the unexpected chance to write the chapter as a first step toward a memoir on my archaeological projects in Rome, Venice, Paestum, Athens and on the island of Cyprus (where we worked on the origins of seafaring in the Eastern Mediterranean in the time before the Neolithic; Ammerman Reference Ammerman, Anderson, Barret and Boyle2010, Reference Ammerman, Bailey, Galanidou, Peeters, Jons and Mennenga2019; Ammerman and Davis Reference Ammerman and Davis2013–2014). When the manuscript had reached an advanced stage, I sent a copy of it to several colleagues for their comments, and one of the replies drew my attention to the new article by Manen and coauthors in Radiocarbon. The chapter that I wrote in March and April 2020 and that will eventually appear in the Festschrift in honor of Ryszard Grygiel and Peter Bogucki, two leading scholars in Neolithic studies who have worked in collaboration in Poland for years, provides historical background on the comments offered here (a preprint of the chapter can be found online at Ammerman Reference Ammerman2020).
Here the focus will be on three points: (1) to set the record straight with regard to misinformation in the article written by Manen et al. (Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019), (2) to clarify several misconceptions that have persisted in the literature for some time, and (3) to comment on the convergence between our own regional modeling of the spread of first farmers along the north coast of the West Mediterranean (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017) and the position currently held by Manen and coauthors, who insist, of course, that the opposite is the case. As we shall see in the last two sections, there was previously a shortage of high-quality dates at early Neolithic sites in the southern part of Languedoc. The new determinations reported in the article now fill in this gap, and they also lend support to the argument put forward in our article in PNAS at the end of 2017.
2. Measuring the rate of spread of early farming in Europe
This was the title that we gave to our first publication on the Neolithic transition (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971). At the time, archaeologists were just beginning to take a more quantitative approach to their investigations. No previous attempt had been made to measure such a rate. In short, what we were trying to do 50 years ago was not a routine piece of research. Furthermore, what we were starting to learn about the spread in this way was put forward as a first approximation—one that could be improved as more early Neolithic sites with radiocarbon dates became available. Thus, the article concentrated on how one goes about measuring such a rate and on presenting the new results obtained. In the 1971 article, no attempt is made to discuss at any length the model of “the wave of advance” except to introduce it briefly on the last page and say that it would be the subject of a forthcoming publication. Here it is worth noting, by the way, that this article just happens to be the only one of our publications on the Neolithic transition that Manen and coauthors cite in their article (even though they comment at various points about the wave of advance model; for some of our other publications on the subject, see Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973; Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984; several chapters in Ammerman and Biagi Reference Ammerman and Biagi2003). This is rather strange behavior. It too involves a misunderstanding on their part when it comes to scholarship on the Neolithic transition in Europe.
Looking back, it will be recalled that there were in the 1970s two main lines of explanation for the spread of early agro-pastoralism in the case of Europe: cultural diffusion on the one hand and what we now called demic diffusion on the other hand. In our view, the two should not be taken as mutually exclusive, but they merited being clearly distinguished at the conceptual level (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: 686). Since both of us were working on hunters-gatherers at the time (see the Ammerman Reference Ammerman2020 preprint chapter), we were initially inclined to favor the cultural side. However, upon further thought, we began to realize that the demic hypothesis deserved more serious attention than it had received in the previous literature. In any event, by measuring the rate of spread, there was the chance to gain a better understanding of the problem and perhaps even move toward sorting out these two modes of explanation on the basis of the rates observed. The analysis itself involved three main steps. To begin with, one would like the diffusionary process under consideration to take the basic form of a linear advance—otherwise attempts at modeling the process will become complex in mathematical terms. Accordingly, the first step was to visualize four possible patterns of the data (based on graphs where time was plotted against distance from the start of the diffusionary process; Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: fig. 1). They would serve as a frame of reference in terms of where we stood when it came to producing graphs of the actual data. They were respectively: (1) a pattern of widely dispersed points with no clear trend over time, (2) a pattern showing an increasing rate over time, (3) a pattern showing a decreasing rate over time, and (4) a pattern showing a linear trend over time. This step was undertaken in visual terms since most archaeologists at the time did not have the mathematic training to conduct it in more formal terms.
The second step was to plot the actual data (53 Neolithic sites in Europe with radiocarbon dates) drawing on several selected “centers” (early sites) in the Near East and see where their respective patterns fell in the context of the four different patterns. There was the good fortune that each of the observed graphs fits fairly well with the fourth pattern (e.g., Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: fig. 2). In turn, this meant that use could be made of classical methods of regression analysis in statistics, where the correlation coefficient measures how consistent the data are with respect to a strictly linear pattern and the slope of the regression line measures the average rate of the spread. Somehow the authors have their own ideas about the latter measurement and reinterpret it to mean a constant rate of spread (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 532; “the result is a constant diffusion speed in time and space”). What we actually say is the following: “The slope of the straight line can supply a good estimate of the average rate of diffusion” (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: 681). In short, due allowance is made for variability in time and space when the rate of spread is measured in this way. The plan is to return to this misconception on the part of the authors in section 5, which is entitled “the heart of the matter.”
In the third step of the analysis, we then went on to measure several regional rates in the spread of early farming, including the Linear Bandkeramik (LBK), the Balkans and the Western Mediterranean (Ammerman and Cavalli Reference Ammerman and Cavalli-Sforza1971: table 2). For one reason or another, the authors do not mention the third step in the analysis. Indeed, even with the limited data available at that time, it was possible to recognize some degree of variation in the average rate of spread from one region of Europe to the next. For instance, the LBK and the Western Mediterranean both yielded faster average rates than the one for Europe as a whole. In other words, it makes no sense to claim that one is dealing with just one fixed rate of spread that holds for all times and places in Europe. Remarkably, the authors advance the further claim that no attempt is made in the 1971 article to take into account regional or spatial variation in the rate of spread (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 532; “it does not take into consideration the spatial dispersal of radiocarbon data”). But this happens to be just what we were doing, in an initial way, at the third step. Of course, we did not have the data and the analytical tools to work with 50 years ago that are available today. In sum, what we find here is yet another misreading of our work.
As in the other historical sciences, one works by steps of approximation in archaeology. The data, the methods, the models and the working hypotheses can all change as time’s arrow moves forward. For our present purposes, this can be illustrated by mentioning two examples. One of them involved using a larger database and displaying the pattern of the spread by placing computer generated isochron lines on the map of Europe (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: fig. 4.6). Such a treatment is in better accord with the idea that the origins of agriculture in the Southwest Asia did not happen at just a single place or “center” but at multiple ones over an area of fair size. The second example is linked with the growth over the years in the number of early farming sites with radiocarbon dates. By 2005, the sample size had increased to 735 dated sites, and the decision was made to repeat, with appropriate refinements, the regression analysis done in 1971. Much the same results were obtained with the value for the average rate of spread over Europe being close to 1 km per year again (Pinhasi et al. Reference Pinhasi, Fort and Ammerman2005).
3. A population model for the diffusion of early farming in Europe
This is the title of our chapter on the wave of advance model that came out two years later (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973). There was a good deal to cover on the model—its history, its formula, how to conceptualize its three variables, a computer simulation of “the wave of advance” and it implications for human population genetics—in the limited space available in The Explanation of Culture Change. Here it is worth adding that a fuller account of the model is given in the fifth chapter of The Neolithic Transition and the Genetics of Populations in Europe (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984). The wave of advance model was first put forward by the British geneticist R. A. Fisher (Reference Fisher1937) to predict the diffusion of an advantageous gene in a linear habitat. The ecologist J. G. Skellam (Reference Skellam1951) then used the model in his study of the spread of the muskrat after its introduction as a new species in central Europe at the start of the 20th century (see the next section).
In Fisher’s formulation, the model has three variables, and each of them has the potential to be measured. The first one is called a or the initial growth rate of the population, and growth is taken to occur according to a logistic form (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973: figs. 2–3): that is, it is actively taking place only at the wave front and growth then progressively slows down in a given place as the wave front moves forward. In other words, population growth does not take place according to an exponential form; instead, it is self-regulating: in effect, little or no population growth is happening in those places located behind the wave front. In the case of human populations, we know that the fastest rate of growth is about 3% per year or a doubling time of 23 years. The second variable involves a quantitative expression that provides a summary of “the migratory activity” of a population. In the case of the first farmers, processes involving the movement of people are considered to take place essentially in the context of the relocation of households and settlements on the landscape. Without going into the details here, this variable, which is identified as m in Fisher’s equation, is measured as the mean square root of movement per unit time. Working in combination, these two variables generate the rate of advance of the diffusionary process or the variable r as Fisher calls it. In fact, it takes some heavy lifting in mathematics to fully appreciate how Fisher managed to bring these three variables together in a concise formula. And this is even more so when it comes to the extension of his model by Fort and Mendez (Reference Fort and Mendez1999) to include time-delay theory, which takes into better account the discrete character of the relocation of households and settlements.
We have reached a good point to turn to one of the authors’ comments on the wave of advance model (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 532): “The ‘wave of advance’ explains the Neolithic transition by a regular movement of populations as a result of an ever-increasing demography contributing to the segmentation of groups.” This sentence is quite misleading. To begin with, our primary aim is to explain the spread of early farming in terms of demic diffusion. The wave of advance model is just a tool that is used in attempting to evaluate this hypothesis (more on this below). According to the model, population growth, as mentioned above, occurs in a logistic form: that is, with growth actively taking place only at the wave front (and not behind it) and not according to “an ever increasing” or exponential form, as the authors seem to imply. Moreover, in contrast with their claim, we have never written a word about “the segmentation of groups.” This is something that they have advanced in an attempt to attack what is a bête noir for them: the wave of advance model. The question that needs to be asked at this point is a basic one: What is a model? Here it is worth quoting at length what I wrote in the opening chapter of The Widening Harvest (Ammerman Reference Ammerman, Ammerman and Biagi2003: 8). “A model is a tool for thinking – a framework for addressing a problem. The value of a model, as the economic historian David Landes (Reference Landes1969: 540) notes, is accordingly heuristic; it does not tell us what happened in the past; it helps us to discover and to understand what may have happened. I would like to add here that the wave of advance model is not to be confused, as is often done in the literature, with the demic hypothesis.” Again, the latter constitutes our primary interest; the former is simply a means toward that end. And like all models in the sciences, the wave of advance model can be refined and extended over the course of time (e.g., Fort and Mendes Reference Fort and Mendez1999; Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017).
4. The introduction of the muskrat in Central Europe
For most archaeologists, the best way to see how the model of the wave of advance can be applied is by turning to the case study of the spread of the muskrat (Skellam Reference Skellam1951). The following is a short version of what is presented in chapter 5 of our 1984 book (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: 69–71). The muskrat, whose fur is of industrial importance, occurs naturally only in North America. It was thus exported to Europe where a few muskrats escaped from captivity in the area to the north of Vienna and found its plains to their liking. They multiplied freely and soon established themselves as a feral species in Central Europe. Through growth and dispersal, the muskrats covered each year a wider and wider area. By using a map that shows the spatial distribution of the expansion for a sequence of years between 1905 and 1927, Skellam, an ecologist, was able to estimate the area covered in a given year and found that the square root of the area when plotted against time yielded a close fit to a straight line, whose slope gave the average rate of advance of the “wave front” (for the map and also Skellam’s graph, see Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: fig. 5.3). Thus, Skellam found just what Fisher’s model predicted. It is worth adding here that the contour lines for the respective years can be quite irregular in shape, as one might expect in the case of an animal spreading through a heterogeneous environment. “But if the law of averages is given a chance to operate, regularities emerge” (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1984: 70). This is what we had in mind when we began working on the question of the spread of early farming in 1970. We did not expect absolute regularity; there was room for variability in space as we began to learn from the measurement of regional rates as mentioned before (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: table 2). Once the rates had been estimated, we also drew a map where the date for each site was put in its respective place there, and this made it possible to see in two dimensions that the pattern as a whole had its basic regularity and that the spread was faster in both Central Europe and the Western Mediterranean, as we indicated on the map itself (Ammerman and Cavalli-Sforza Reference Ammerman and Cavalli-Sforza1971: fig. 6). Again, this map should be seen today as a first approximation, based on the limited data that was available 50 years ago.
5. The heart of the matter
In light of what is presented above, I believe it is fair to say that the authors lack a good understanding of our 1971 article and also the chapter on the model of the wave of advance published in 1973. They seem to have no idea that we measured not only the average rate of spread for Europe as a whole but several regional rates as well. In addition, they appear not to appreciate the difference between what is taking place on the ground and its treatment in Fisher’s model, as shown by Skellam’s study of the introduction of the muskrat in Central Europe (cited in the 1971 article). In addition, they make no mention of the map (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973: fig. 6), which goes against their claim that we made no allowance for regional variation in Reference Ammerman and Cavalli-Sforza1971. Furthermore, they bring confusion in the literature when they speak of an average rate (measured on the ground) as if it were a constant rate (with a fixed value at all times and places). In short, to use French words again, this is the idée fixe of the authors—the primary source of their misunderstanding of our research on the Neolithic transition. This is not a minor point but one at the very heart of the matter. To make certain that this issue and its implications are well understood, it is useful to illustrate the problem by means of an example from the modern world. Suppose that one is interested in studying the economy of the United States and would like to measure the rate of growth in GDP per year during the time of the Obama administration (2008–2016). By plotting on a graph the values of GDP against time for each of eight years, there are ways to estimate (using quantitative methods perhaps more refined than the ones that we use in archaeology) the average rate of growth in GDP per year for this time span. What one should not do, however, is to turn around and then say that this average rate holds as the one fixed rate of growth for each of the individual eight years. To do this sort of thing over and over would be to turn economics into a static field of study.
Returning to the Neolithic world, this misconception on the authors’ part may well stem from two quite different meanings of the word constant in the dictionary. In its common and older usage, what it means is to be consistent or to stand firm (the Latin root of the word). When Fisher or Cavalli-Sforza uses the term to describe the character of a variable in an equation, it is being used in this sense: to emphasize that it stands firm in a linear form, which makes everything simpler from the standpoint of mathematics. It is not being used in the second and more technical sense of the term (as a noun that goes back only to 1832 in both British and American usage): that is, as a constant such as the Greek letter π in the equation for the area of a circle. Here it is important to remember that “the wave of advance” is a model that began its life in the field of population biology. For those in the biological sciences, there is the understanding that what is taking place on the ground is usually messier and more irregular than what is held to occur in a formal model. This is a perspective shared by the model-building economist as well. Indeed, this way of thinking should not be so foreign to the authors. Given their current interest in irregularity and discontinuity on the ground, it will take modeling of one kind or another to sort out and try to explain what is happening in such a complex world. Where the authors go off course is by taking regularity in the sense of its representation in the domain of a formal model and somehow then projecting it back as a “constant” on the ground (a different domain, a place with variability in time and space where an average rate can be measured).
The value of a model, as a heuristic tool, is connected with the predictions that it makes and the chance to test them. In other words, the proof (test) of the pudding (model) is in the eating (its predictions). The wave of advance model has clear implications for human population genetics. When our book came out in 1984, the genes of early farmers could not be studied in a direct way (see the preprint chapter Ammerman Reference Ammerman2020), and so modern proxies had to be used instead to evaluate the model’s genetic predictions. In the last 20 years, it has become possible to analyze DNA recovered from human bones of early Neolithic age. The results of a fair number of studies, without going into the details here, now provide direct support for the hypothesis of demic diffusion (Bramante et al. Reference Bramanti2009; Haak et al. Reference Haak2010; Fu et al. Reference Fu, Rudan, Pääbo and Krause2012; Szécsényi-Nagy et al. Reference Szécsényi-Nagy, Keeri, Jakucs, Brandt, Banffy, Alt, Whittle and Bickle2014; Mathieson et al. Reference Mathieson2015; Hofmanova et al. Reference Hofmanova2016; Olalde et al. Reference Olalde2019; Brunel et al. Reference Brunel2020; see Section 4 of Ammerman Reference Ammerman2020). In sum, it is widely accepted today that the spread of agro-pastoralism over Europe involved a diffusionary process and more specifically that the spread of first farming is to a large extent the consequence of demic diffusion. The wave of advance model is thus on target in terms of its genetic predictions. At the same time, we have long held that local hunter and gatherers also played a role in the story (Ammerman and Cavalli-Sforza Reference Ammerman, Cavalli-Sforza and Renfrew1973: 353; Reference Ammerman and Cavalli-Sforza1984: 116–119; Ammerman Reference Ammerman, Ammerman and Biagi2003: 8). Recently, we have incorporated hunter-gatherers in a direct and interactive way (for instance, in mating and as guides to local knowledge at the wave front) in the modeling of the rapid coastal spread in the West Mediterranean (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017: 4–5).
6. The seven high-quality dates from Pont de Roque-Haute and Peiro Signado in Languedoc
Only a few brief words will be said here about the single most important result in the article of interest (Manen et al. Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019). Both of the sites are open-air settlements, and all seven of the dates were made on seeds of emmer (Triticum dicoccum). In the case of Pont de Roque-Haute, the artifacts recovered by the excavations include obsidian from Palmarola. Obsidian from the same island source in the Tyrrhenian Sea has also been recovered from early Neolithic levels at Arene Candide in Liguria, which indicates that things were moving over considerable distances at the time in the context of early voyaging (e.g., Ammerman Reference Ammerman, Anderson, Barret and Boyle2010: fig. 7.3). All seven of the dates tend to cluster around 5800 cal. BCE with a range on the order of ±100 years. These are now the earliest high-quality dates for the Neolithic in Southern France. This number of dates is just large enough to make this new result convincing. The claim by the authors that emphasis should be placed on short-life samples in radiocarbon dating is not something new. This position has been around for some time (e.g., Zilhão Reference Zilhäo, Hadjikoumis, Robinson and Viner2011), and it has finally been achieved at two sites in the south of France (both of which were excavated more than 20 years ago).
Modeling the role of voyaging in the coastal spread of the Early Neolithic in the West Mediterranean
This is the title of our regional study published three years ago (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017). As mentioned before, the modeling of the diffusionary process now includes voyaging and local hunters-gatherers. In the discussion at the end of their article, Manen et al. (Reference Manen, Perrin, Guilaine, Bouby, Bréhard, Briois, Durand, Marinval and Vigne2019: 561) raise a straw man with regard to studies done at a continental scale citing our 1971 article again. They believe that their new results diverge from previous studies and that no other group of scholars has yet to undertake a regional study in the Western Mediterranean. Of course, this is incorrect: we recently published just such a study in PNAS, as mentioned before. And to compound the disorder in this case, our modeling exercise in 2017 actually entails an extension of the wave of advance model: that is, a new treatment of the component of “migratory activity,” which draws on our recent work on early voyaging in the Mediterranean (e.g., Ammerman and Davis Reference Ammerman and Davis2013–2014). Be that as it may, it is worth noting that we mention the shortage of high-quality dates for Languedoc at the time: “the only major geographical gap in our dataset concerning an area with a well-known and rather dense network of Early Neolithic sites is the French Languedoc, as is apparent in Fig. 1. The lack of quality dates means that there is at present time little than can be done to remedy the situation” (Isern et al. Reference Isern, Zilhão, Fort and Ammerman2017: SI p. 2). If the seven dates mentioned in Section 6 had been available at the time, we would have used them to fill in this gap on the map. In other words, this new data would have contributed positively to our argument, and, in this sense, there is convergence between our respective regional studies in the West Mediterranean. The irony here is that, all along, we have been doing research and writing papers that the authors have not read carefully, and this has led, in turn, to one misunderstanding after the next. Finally, as an archaeologist who has lived and worked in Italy for the last 50 years, it is premature, in my view, to take the Early Neolithic dates that are currently available there simply at face value. For instance, the high-quality dates for the oldest Neolithic settlement in the heel of Southern Italy may one day go back to around 6200 cal. BCE. Again, we work by steps of approximation in archaeology, and, to my knowledge, there has yet to be in Southern Italy an advanced project such as PROCOME. Ten years ago, Southern France was in much the same boat, since it too had at that time comparatively few good seed dates and there was a gap in the chronology of Languedoc.