The earliest dates for the West Mediterranean Neolithic indicate that it expanded across 2,500 km in about 300 y. Such a fast spread is held to be mainly due to a demic process driven by dispersal along coastal routes. Here, we model the Neolithic spread in the region by focusing on the role of voyaging to understand better the core elements that produced the observed pattern of dates. We also explore the effect of cultural interaction with Mesolithic populations living along the coast. The simulation study shows that (i) sea travel is required to obtain reasonable predictions, with a minimum sea-travel range of 300 km per generation; (ii) leapfrog coastal dispersals yield the best results (quantitatively and qualitatively); and (iii) interaction with Mesolithic people can assist the spread, but long-range voyaging is still needed to explain the archaeological pattern.T he Neolithic transition in Europe spread at an average rate of about 1 km·y −1 (1, 2). This process can be modeled by the socalled wave-of-advance model, which describes a progressive land-based expansion due to population growth and short-range migratory activity (3). Ancient DNA studies provide support for a mainly demic expansion in many parts of Europe (4), involving two main pathways: one up the Danube, connected with the spread of the Linearbandkeramic (LBK) culture (5, 6), and the other along the Mediterranean shores (7).Current radiocarbon dates indicate a coastal spread in West Mediterranean Europe taking place at a much faster rate (above 5 km·y −1 ) than one would expect on the basis of the classical wave-of-advance model. An alternative approach is needed to explain this process. The maritime pioneer colonization model (8, also refs. 9, 10) postulates a sea-based expansion that involves voyaging along the coast in the form of cabotage (with the possibility of making a short stop here and there along the way). This model drew upon new and more reliable carbon-14 dates [including accelerator mass spectrometry (AMS) determinations on short-lived samples to avoid the old wood effect], and is consistent with a demic expansion and the observed pattern (alternative approaches to the West Mediterranean spread are discussed in ref. 11). During the past 15 y, quality dates for the Early Neolithic in the West Mediterranean have continued to come in. As a result, the overall pattern is now more refined but remains consistent with the maritime pioneer model.Voyaging during the Early Neolithic is well documented in the Eastern Mediterranean (e.g.,. From the distribution of obsidian artifacts in the Cyprus, Aegean, and Tyrrhenian basins, we know that its quantity tends to fall off with distance from a given source and that long-distance crossing of the open sea between these three basins is extremely rare (15). In short, it is fair to say that early voyaging in the eastern and central parts of the Mediterranean was kept on a comparatively short leash. In the West Mediterranean, obsidian is far less common at Early Neolithic sites; it occurs in small...
We extend a previous model of the Neolithic transition in Europe ͓J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 ͑1999͔͒ by taking two effects into account: ͑i͒ we do not use the diffusion approximation ͑which corresponds to second-order Taylor expansions͒, and ͑ii͒ we take proper care of the fact that parents do not migrate away from their children ͑we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate͒. We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect ͑ii͒ is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important ͑up to 70%͒.
It is well known that the Neolithic transition spread across Europe at a speed of about 1 km/yr. This result has been previously interpreted as a range expansion of the Neolithic driven mainly by demic diffusion (whereas cultural diffusion played a secondary role). However, a long-standing problem is whether this value (1 km/yr) and its interpretation (mainly demic diffusion) are characteristic only of Europe or universal (i.e. intrinsic features of Neolithic transitions all over the world). So far Neolithic spread rates outside Europe have been barely measured, and Neolithic spread rates substantially faster than 1 km/yr have not been previously reported. Here we show that the transition from hunting and gathering into herding in southern Africa spread at a rate of about 2.4 km/yr, i.e. about twice faster than the European Neolithic transition. Thus the value 1 km/yr is not a universal feature of Neolithic transitions in the world. Resorting to a recent demic-cultural wave-of-advance model, we also find that the main mechanism at work in the southern African Neolithic spread was cultural diffusion (whereas demic diffusion played a secondary role). This is in sharp contrast to the European Neolithic. Our results further suggest that Neolithic spread rates could be mainly driven by cultural diffusion in cases where the final state of this transition is herding/pastoralism (such as in southern Africa) rather than farming and stockbreeding (as in Europe).
We develop front spreading models for several jump distance probability distributions (dispersion kernels). We derive expressions for a cohabitation model (cohabitation of parents and children) and a non-cohabitation model, and apply them to the Neolithic using data from real human populations. The speeds that we obtain are consistent with observations of the Neolithic transition. The correction due to the cohabitation effect is up to 38%.
BackgroundIt is widely believed that the treatment of glioblastomas (GBM) could benefit from oncolytic virus therapy. Clinical research has shown that Vesicular Stomatitis Virus (VSV) has strong oncolytic properties. In addition, mathematical models of virus treatment of tumors have been developed in recent years. Some experiments in vitro and in vivo have been done and shown promising results, but have been never compared quantitatively with mathematical models. We use in vitro data of this virus applied to glioblastoma.ResultsWe describe three increasingly realistic mathematical models for the VSV-GBM in vitro experiment with progressive incorporation of time-delay effects. For the virus dynamics, we obtain results consistent with the in vitro experimental speed data only when applying the more complex and comprehensive model, with time-delay effects both in the reactive and diffusive terms. The tumor speed is given by the minimum of a very simple function that nonetheless yields results within the experimental measured range.ConclusionsWe have improved a previous model with new ideas and carefully incorporated concepts from experimental results. We have shown that the delay time τ is the crucial parameter in this kind of models. We have demonstrated that our new model can satisfactorily predict the front speed for the lytic action of oncolytic VSV on glioblastoma observed in vitro. We provide a basis that can be applied in the near future to realistically simulate in vivo virus treatments of several cancers.ReviewersThis article was reviewed by Yang Kuang and Georg Luebeck. For the full reviews, please go to the Reviewers’ comments section.
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