Modeling the role of voyaging in the coastal spread of the Early Neolithic in the West Mediterranean.

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.

Modeling Demic and Cultural Diffusion: An Introduction.

Identifying the processes by which human cultures spread across different populations is one of the most topical objectives shared among different fields of study. Seminal works have analyzed a variety of data and attempted to determine whether empirically observed patterns are the result of demic and/or cultural diffusion. This special issue collects articles exploring several themes (from modes of cultural transmission to drivers of dispersal mechanisms) and contexts (from the Neolithic in Europe to the spread of computer programming languages), which offer new insights that will augment the theoretical and empirical basis for the study of demic and cultural diffusion. In this introduction we outline the state of art in the modeling of these processes, briefly discuss the pros and cons of two of the most commonly used frameworks (equation-based models and agent-based models), and summarize the significance of each article in this special issue.

Synthesis between demic and cultural diffusion in the Neolithic transition in Europe.

There is a long-standing controversy between two models of the Neolithic transition. The demic model assumes that the Neolithic range expansion was mainly due to the spread of populations, and the cultural model considers that it was essentially due to the spread of ideas. Here we integrate the demic and cultural models in a unified framework. We show that cultural diffusion explains ∼40% of the spread rate of the Neolithic transition in Europe, as implied by archaeological data. Thus, cultural diffusion cannot be neglected, but demic diffusion was the most important mechanism in this major historical process at the continental scale. This quantitative approach can be useful also in regional analysis, the description of Neolithic transitions in other continents, and models of many human spread phenomena.

Interbreeding between farmers and hunter-gatherers along the inland and Mediterranean routes of Neolithic spread in Europe.

The Neolithic (i.e., farming and stockbreeding) spread from the Near East across Europe since about 9000 years before the common era (BCE) until about 4000 yr BCE. It followed two main routes, namely a sea route along the northern Mediterranean coast and an inland one across the Balkans and central Europe. It is known that the dispersive behavior of farmers depended on geography, with longer movements along the Mediterranean coast than along the inland route. In sharp contrast, here we show that for both routes the percentage of farmers who interbred with hunter-gatherers and/or acculturated one of them was strikingly the same (about 3.6%). Therefore, whereas the dispersive behavior depended on the proximity to the Mediterranean sea, the interaction behavior (incorporation of hunter-gatherers) did not depend on geographical constraints but only on the transition in the subsistence economy (from hunting and gathering to farming) and its associated way of life. These conclusions are reached by analyzing the clines of haplogroup K, which was virtually absent in hunter-gatherers and the most frequent mitochondrial haplogroup in early farmers. Similarly, the most frequent Y-chromosome Neolithic haplogroup (G2a) displays an inland cline that agrees with the percentage of interbreeding reported above.

Front speed of language replacement.

We use two coupled equations to analyze the space/time dynamics of two interacting languages. First, we introduce a cohabitation model, which is more appropriate for human populations than classical (noncohabitation) models. Second, using numerical simulations, we find the front speed of a new language spreading into a region in which another language was previously used. Third, for a special case, we derive an analytical formula that makes it possible to check the validity of our numerical simulations. Finally, as an example, we find that the observed front speed for the spread of the English language into Wales in the period 1961 through 1981 is consistent with the model predictions. We also find that the effects of linguistic parameters are much more important than the effects of parameters related to population dispersal and reproduction. If the initial population densities of both languages are similar, they have no effect on the front speed. We outline the potential of the new model to analyze relationships between language replacement and genetic replacement.

Biased dispersal can explain fast human range expansions.

Some human fronts spread faster than expected by models based on dispersal and reproduction. The only explanation proposed so far assumes that some autochthonous individuals are incorporated by the expanding populations, leading to faster front speeds. Here we show that simple models without this effect are also consistent with the observed speeds of two fronts (a Khoi-khoi expansion of herders and a Bantu expansion of farmers), provided that the dispersal of individuals is biased (i.e., more probable) in directions closer to the front propagation direction. The physical models presented may also be applied to other kinds of social phenomena, including innovation diffusion, rumor propagation, linguistic fronts, epidemic spread, diffusion in economic space and the evolution of cooperation in spatial systems. They can be also adapted to non-human systems with biased dispersal, including biological invasions, cancer tumors and virus treatment of tumors.

Assessing the importance of cultural diffusion in the Bantu spread into southeastern Africa.

The subsistence of Neolithic populations is based on agriculture, whereas that of previous populations was based on hunting and gathering. Neolithic spreads due to dispersal of populations are called demic, and those due to the incorporation of hunter-gatherers are called cultural. It is well-known that, after agriculture appeared in West Africa, it spread across most of subequatorial Africa. It has been proposed that this spread took place alongside with that of Bantu languages. In eastern and southeastern Africa, it is also linked to the Early Iron Age. From the beginning of the last millennium BC, cereal agriculture spread rapidly from the Great Lakes area eastwards to the East African coast, and southwards to northeastern South Africa. Here we show that the southwards spread took place substantially more rapidly (1.50-2.27 km/y) than the eastwards spread (0.59-1.27 km/y). Such a faster southwards spread could be the result of a stronger cultural effect. To assess this possibility, we compare these observed ranges to those obtained from a demic-cultural wave-of-advance model. We find that both spreads were driven by demic diffusion, in agreement with most archaeological, linguistic and genetic results. Nonetheless, the southwards spread seems to have indeed a stronger cultural component, which could lead support to the hypothesis that, at the southern areas, the interaction with pastoralist people may have played a significant role.

Tracing the origin and spread of agriculture in Europe.

The origins of early farming and its spread to Europe have been the subject of major interest for some time. The main controversy today is over the nature of the Neolithic transition in Europe: the extent to which the spread was, for the most part, indigenous and animated by imitation (cultural diffusion) or else was driven by an influx of dispersing populations (demic diffusion). We analyze the spatiotemporal dynamics of the transition using radiocarbon dates from 735 early Neolithic sites in Europe, the Near East, and Anatolia. We compute great-circle and shortest-path distances from each site to 35 possible agricultural centers of origin--ten are based on early sites in the Middle East and 25 are hypothetical locations set at 5 degrees latitude/longitude intervals. We perform a linear fit of distance versus age (and vice versa) for each center. For certain centers, high correlation coefficients (R > 0.8) are obtained. This implies that a steady rate or speed is a good overall approximation for this historical development. The average rate of the Neolithic spread over Europe is 0.6-1.3 km/y (95% confidence interval). This is consistent with the prediction of demic diffusion (0.6-1.1 km/y). An interpolative map of correlation coefficients, obtained by using shortest-path distances, shows that the origins of agriculture were most likely to have occurred in the northern Levantine/Mesopotamian area.

A serial founder effect model of phonemic diversity based on phonemic loss in low-density populations.

It has been observed that the number of phonemes in languages in use today tends to decrease with increasing distance from Africa. A previous formal model has recently reproduced the observed cline, but under two strong assumptions. Here we tackle the question of whether an alternative explanation for the worldwide phonemic cline is possible, by using alternative assumptions. The answer is affirmative. We show this by formalizing a proposal, following Atkinson, that this pattern may be due to a repeated bottleneck effect and phonemic loss. In our simulations, low-density populations lose phonemes during the Out-of-Africa dispersal of modern humans. Our results reproduce the observed global cline for the number of phonemes. In addition, we also detect a cline of phonemic diversity and reproduce it using our simulation model. We suggest how future work could determine whether the previous model or the new one (or even a combination of them) is valid. Simulations also show that the clines can still be present even 300 kyr after the Out-of-Africa dispersal, which is contrary to some previous claims which were not supported by numerical simulations.

Estimating the relative importance of demic and cultural diffusion in the spread of the Neolithic in Scandinavia.

Using a database of early farming sites in Scandinavia, we estimate that the spread rate of the Neolithic was in the range 0.44-0.66 km yr-1 This is substantially slower (by about 50%) than the rate in continental Europe. We interpret this result in the framework of a new mathematical model that includes horizontal cultural transmission (acculturation), vertical cultural transmission (interbreeding) and demic diffusion (reproduction and dispersal of farmers). To parametrize the model, we estimate reproduction rates of early farmers using archaeological data (sum-calibrated probabilities for the dates of early Neolithic Scandinavian sites) and use them in a wave-of-advance model for the first time. Comparing the model with the archaeological data, we find that the percentage of the spread rate due to cultural diffusion is below 50% (except for very extreme parameter values, and even for them it is below 54%). This strongly suggests that the spread of the Neolithic in Scandinavia was driven mainly by demic diffusion. This conclusion, obtained from archaeological data, agrees qualitatively with the implications of ancient genetic data, but the latter are yet too few in Scandinavia to produce any quantitative percentage for the spread rate due to cultural diffusion. We also find that, on average, fewer than eight hunter-gatherers were incorporated in the Neolithic communities by each group of 10 pioneering farmers, via horizontal and/or vertical cultural transmission.

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%).

The ancient cline of haplogroup K implies that the Neolithic transition in Europe was mainly demic.

Using a database with the mitochondrial DNA (mtDNA) of 513 Neolithic individuals, we quantify the space-time variation of the frequency of haplogroup K, previously proposed as a relevant Neolithic marker. We compare these data to simulations, based on a mathematical model in which a Neolithic population spreads from Syria to Anatolia and Europe, possibly interbreeding with Mesolithic individuals (who lack haplogroup K) and/or teaching farming to them. Both the data and the simulations show that the percentage of haplogroup K (%K) decreases with increasing distance from Syria and that, in each region, the %K tends to decrease with increasing time after the arrival of farming. Both the model and the data display a local minimum of the genetic cline, and for the same Neolithic regional culture (Sweden). Comparing the observed ancient cline of haplogroup K to the simulation results reveals that about 98% of farmers were not involved in interbreeding neither acculturation (cultural diffusion). Therefore, cultural diffusion involved only a tiny fraction (about 2%) of farmers and, in this sense, the most relevant process in the spread of the Neolithic in Europe was demic diffusion (i.e., the dispersal of farmers), as opposed to cultural diffusion (i.e., the incorporation of hunter-gatherers).

Can a linguistic serial founder effect originating in Africa explain the worldwide phonemic cline?

It has been proposed that a serial founder effect could have caused the present observed pattern of global phonemic diversity. Here we present a model that simulates the human range expansion out of Africa and the subsequent spatial linguistic dynamics until today. It does not assume copying errors, Darwinian competition, reduced contrastive possibilities or any other specific linguistic mechanism. We show that the decrease of linguistic diversity with distance (from the presumed origin of the expansion) arises under three assumptions, previously introduced by other authors: (i) an accumulation rate for phonemes; (ii) small phonemic inventories for the languages spoken before the out-of-Africa dispersal; (iii) an increase in the phonemic accumulation rate with the number of speakers per unit area. Numerical simulations show that the predictions of the model agree with the observed decrease of linguistic diversity with increasing distance from the most likely origin of the out-of-Africa dispersal. Thus, the proposal that a serial founder effect could have caused the present observed pattern of global phonemic diversity is viable, if three strong assumptions are satisfied.

A mathematical approach to virus therapy of glioblastomas.

BACKGROUND: It 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. RESULTS: We 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. CONCLUSIONS: We 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.

Demic and cultural diffusion propagated the Neolithic transition across different regions of Europe.

The Neolithic transition is the shift from hunting­gathering into farming. About 9000 years ago, the Neolithic transition began to spread from the Near East into Europe, until it reached Northern Europe about 5500 years ago. There are two main models of this spread. The demic model assumes that it was mainly due to the reproduction and dispersal of farmers. The cultural model assumes that European hunter-gatherers become farmers by acquiring domestic plants and animals, as well as knowledge, from neighbouring farmers. Here we use the dates of about 900 archaeological sites to compute a speed map of the spread of the Neolithic transition in Europe. We compare the speed map to the speed ranges predicted by purely demic, demic-cultural and purely cultural models. The comparison indicates that the transition was cultural in Northern Europe, the Alpine region and west of the Black Sea. But demic diffusion was at work in other regions such as the Balkans and Central Europe. Our models can be applied to many other cultural traits. We also propose that genetic data could be gathered and used to measure the demic kernels of Early Neolithic populations. This would lead to an enormous advance in Neolithic spread modelling.

Description of diffusive and propagative behavior on fractals.

The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived.

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.

Dynamical features of reaction-diffusion fronts in fractals.

The speed of front propagation in fractals is studied by using (i) the reduction of the reaction-transport equation into a Hamilton-Jacobi equation and (ii) the local-equilibrium approach. Different equations proposed for describing transport in fractal media, together with logistic reaction kinetics, are considered. Finally, we analyze the main features of wave fronts resulting from this dynamic process, i.e., why they are accelerated and what is the exact form of this acceleration.

Dispersal probability distributions and the wave-front speed problem.

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models.