Anisotropic dispersion, space competition, and the slowdown of the Neolithic transition

The front speed of the Neolithic (farmer) spread in Europe decreased as it reached Northern latitudes, where the Mesolithic (huntergatherer) population density was higher. Here, we describe a reaction diffusion model with (i) an anisotropic dispersion kernel depending on the Mesolithicpopulation density gradient and (ii) a modified population growth equation. Both effects are related to the space available for the Neolithic population. The model is able to explain the slowdown of the Neolithic front as observed from archaeological data

Time-Delayed Theory of the Neolithic Transition in Europe

The classical wave-of-advance model of the neolithic transition (i.e., the shift from hunter-gatherer to agricultural economies) is based on Fisher's reaction-diffusion equation. Here we present an extension of Einstein's approach to Fickian diffusion, incorporating reaction terms. On this basis we show that second-order terms in the reaction-diffusion equation, which have been neglected up to now, are not in fact negligible but can lead to important corrections. The resulting time-delayed model agrees quite well with observations

Space Competition and Time Delays in Human Range Expansions. Application to the Neolithic Transition

Space competition effects are well-known in many microbiological and ecological systems. Here we analyze such an effectin human populations. The Neolithic transition (change from foraging to farming) was mainly the outcome of a demographic process that spread gradually throughout Europe from the Near East. In Northern Europe, archaeological data show a slowdown on the Neolithic rate of spread that can be related to a high indigenous (Mesolithic) population density hindering the advance as a result of the space competition between the two populations. We measure this slowdown from a database of 902 Early Neolithic sites and develop a time-delayed reaction-diffusion model with space competition between Neolithic and Mesolithic populations, to predict the observed speeds. The comparison of the predicted speed with the observations and with a previous non-delayed model show that both effects, the time delay effect due to the generation lag and the space competition between populations, are crucial in order to understand the observations

Multidelayed random walks: Theory and application to the neolithic transition in Europe

We present a model in which particles (or individuals of a biological population) disperse with a rest time between consecutive motions (or migrations) which may take several possible values from a discrete set. Particles (or individuals) may also react (or reproduce). We derive a new equation for the effective rest time T˜ of the random walk. Application to the neolithic transition in Europe makes it possible to derive more realistic theoretical values for its wavefront speed than those following from the single-delayed framework presented previously [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)]. The new results are consistent with the archaeological observations of this important historical process

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) 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 migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) 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%)

Ancient DNA analysis of 8000 B.C. near eastern farmers supports an early neolithic pioneer maritime colonization of Mainland Europe through Cyprus and the Aegean Islands

The genetic impact associated to the Neolithic spread in Europe has been widely debated over the last 20 years. Within this context, ancient DNA studies have provided a more reliable picture by directly analyzing the protagonist populations at different regions in Europe. However, the lack of available data from the original Near Eastern farmers has limited the achieved conclusions, preventing the formulation of continental models of Neolithic expansion. Here we address this issue by presenting mitochondrial DNA data of the original Near-Eastern Neolithic communities with the aim of providing the adequate background for the interpretation of Neolithic genetic data from European samples. Sixty-three skeletons from the Pre Pottery Neolithic B (PPNB) sites of Tell Halula, Tell Ramad and Dja'de El Mughara dating between 8,700-6,600 cal. B.C. were analyzed, and 15 validated mitochondrial DNA profiles were recovered. In order to estimate the demographic contribution of the first farmers to both Central European and Western Mediterranean Neolithic cultures, haplotype and haplogroup diversities in the PPNB sample were compared using phylogeographic and population genetic analyses to available ancient DNA data from human remains belonging to the Linearbandkeramik-Alföldi Vonaldiszes Kerámia and Cardial/Epicardial cultures. We also searched for possible signatures of the original Neolithic expansion over the modern Near Eastern and South European genetic pools, and tried to infer possible routes of expansion by comparing the obtained results to a database of 60 modern populations from both regions. Comparisons performed among the 3 ancient datasets allowed us to identify K and N-derived mitochondrial DNA haplogroups as potential markers of the Neolithic expansion, whose genetic signature would have reached both the Iberian coasts and the Central European plain. Moreover, the observed genetic affinities between the PPNB samples and the modern populations of Cyprus and Crete seem to suggest that the Neolithic was first introduced into Europe through pioneer seafaring colonization.

Cultural Diffusion Was the Main Driving Mechanism of the Neolithic Transition in Southern Africa

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)

Cohabitation effect on the slowdown of the Neolithic expansion

We introduce the effect of cohabitation between generations to a previous model on the slowdown of the Neolithic transition in Europe. This effect consists on the fact that human beings do not leave their children alone when they migrate, but on the contrary they cohabit until their children reach adulthood. We also use archaeological data to estimate the variation of the Mesolithic population density with distance, and use this information to predict the slowdown of the Neolithic front speed. The new equation leads to a substantial correction, up to 37%, relative to previous results. The new model is able to provide a satisfactory explanation not only to the relative speed but also to the absolute speed of the Neolithic front obtained from archaeological data

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

It is shown that Lotka-Volterra interaction terms are not appropriate to describe vertical cultural transmission. Appropriate interaction terms are derived and used to compute the effect of vertical cultural transmission on demic front propagation. They are also applied to a specific example, the Neolithic transition in Europe. In this example, it is found that the effect of vertical cultural transmission can be important (about 30%). On the other hand, simple models based on differential equations can lead to large errors (above 50%). Further physical, biophysical, and cross-disciplinary applications are outlined

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

En torno a un hallazgo del Neolítico Antiguo en la Valldany (Oliana, comarca del Urgellet, Lérida)

Hablar con unos esquemas rígidos de una unidad cultural neolítica en Cataluña es menospreciar el papel que representa el marco geográfico de este país, desconocer los tres grandes conjuntos geológicos regionales: la costa, el llano y la montaña; cada uno de ellos aporta su nota de originalidad; sin embargo, tampoco cada uno de éstos va a representar una uniformidad monótona, sin~o que se escinden formando un rompecabezas complicado, donde sus piezas, con características propias, son las comarcas.

Evolución de la dentición en la transición Mesolítico-Neolítico de la Península Ibérica: un modelo de sustitución poblacional

Se han medido las variables métricas de la dentición del yacimiento de época mesolítica (7500-6500 a.C.), procedentes del yacimiento de La Oliva (Valencia) y se han comparado con las de otras poblaciones prehistóricas. Estas variables permiten situar esta población en el contexto europeo y extrapolar, mediante el análisis de árboles filogenéticos, los movimientos y relaciones poblacionales del Neolítico en Europa. De esta forma se observa que La Oliva forma parte de un antiguo grupo poblacional ancestral, bastante distanciado de las poblaciones mesolíticas contemporáneas del resto de Europa y de las poblaciones neolíticas posteriores. Parece, a su vez, que estas poblaciones neolíticas las substituirían casi completamente sin mestizaje aparente. Estos resultados se han contrastado y contrastado mediante análisis de variables métricas craneales.

Progress in front propagation research

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined