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.

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.

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.

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).

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.

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.

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.

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).

Language extinction and linguistic fronts.

Language diversity has become greatly endangered in the past centuries owing to processes of language shift from indigenous languages to other languages that are seen as socially and economically more advantageous, resulting in the death or doom of minority languages. In this paper, we define a new language competition model that can describe the historical decline of minority languages in competition with more advantageous languages. We then implement this non-spatial model as an interaction term in a reaction-diffusion system to model the evolution of the two competing languages. We use the results to estimate the speed at which the more advantageous language spreads geographically, resulting in the shrinkage of the area of dominance of the minority language. We compare the results from our model with the observed retreat in the area of influence of the Welsh language in the UK, obtaining a good agreement between the model and the observed data.

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 effect in 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.

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.

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.

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.

Effects of punishment in a mobile population playing the prisoner's dilemma game.

We deal with a system of prisoner's dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation.

Virus infection speeds: theory versus experiment.

In order to explain the speed of Vesicular Stomatitis Virus (VSV) infections, we develop a simple model that improves previous approaches to the propagation of virus infections. For VSV infections, we find that the delay time elapsed between the adsorption of a viral particle into a cell and the release of its progeny has a very important effect. Moreover, this delay time makes the adsorption rate essentially irrelevant in order to predict VSV infection speeds. Numerical simulations are in agreement with the analytical results. Our model satisfactorily explains the experimentally measured speeds of VSV infections.

Fronts from two-dimensional dispersal kernels: Beyond the nonoverlapping-generations model.

Most integrodifference models of biological invasions are based on the nonoverlapping-generations approximation. However, the effect of multiple reproduction events (overlapping generations) on the front speed can be very important (especially for species with a long life spam). Only in one-dimensional space has this approximation been relaxed previously, although almost all biological invasions take place in two dimensions. Here we present a model that takes into account the overlapping generations effect (or, more generally, the stage structure of the population), and we analyze the main differences with the corresponding nonoverlapping-generations results.