Fronts from integrodifference equations and persistence effects on the Neolithic transition

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.

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.

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.

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

The Neolithic transition is the shift from hunting–gathering 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.

Front propagation speeds of T7 virus mutants

We propose a new reaction-diffusion model with an eclipse time to study the spread of viruses on bacterial populations. This new model is both biologically and physically sound, unlike previous ones. We determine important parameter values from experimental data, such as the one-step growth. We verify the proposed model by comparing theoretical and experimental data of the front propagation speed for several T7 virus strains.

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.

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.

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.

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.

Stochastic model for population migration and the growth of human settlements during the Neolithic transition

We present a stochastic two-population model that describes the migration and growth of semisedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea is that random migration and transition from a sedentary to a foraging way of life, and backwards, is strongly coupled with the local crop production and associated degradation of land. We derive a nonlinear integral equation for the population density coupled with the equations for the density of soil nutrients and crop production. Our model provides a description of the formation of human settlements along the river valley. The numerical results show that the individual farmers have a tendency for aggregation and clustering. We show that the large-scale pattern is a transient phenomenon which eventually disappears due to land degradation.