Modelling cultural shift : application to language decline and extinction

Cultural shift is present in many aspects of human history. Here we present a model developed to study the particular case of language shift when a minority language is in competition with another language, which is perceived by the population as being socially and economically more advantageous (Isern and Fort, J. R. Soc. Interface 2014). We show that this model can describe satisfactorily the decline on the fraction of Welsh speakers over the last century. We also apply our language shift model as an interaction term into a reaction-diffusion equation and use it to predict the spread of retreat of the area of prevalence of the Welsh language. We find that the predictions are consistent with observational data

Irreversible thermodynamics of Poisson processes with reaction

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics

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

Do Global String Loops Collapse to Form Black Holes?

Hawking has shown that the emission of gravitational radiation cannot prevent circular loops of gauged cosmic strings from collapsing into black holes. Here we consider the corresponding question for global strings: can Goldstone boson emission prevent circular loops of global cosmic strings from forming black holes? Our results show that for every value of the string tension there is a certain critical size below which the circular loop does not collapse to form a black hole. For GUT scale strings, this critical size is much larger than the current horizon.Comment: 10pp, 3 figures available on request, plain TeX (no macros needed), to be published in Phys. Lett.

Modelling 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 amongst different fields of study. Seminal works have analysed 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 papers 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 modelling of these processes, briefly discuss the pros and cons of two of the most commonly used frameworks (i.e. equation-based models and agent-based models), and summarise the significance of each paper published in this special issue

Reaction-diffusion wave fronts : multigeneration biological species under climate change

A generalization of reaction-diffusion models to multigeneration biological species is presented. It is based on more complex random walks than those in previous approaches. The new model is developed analytically up to infinite order. Our predictions for the speed agree to experimental data for several butterfly species better than existing models. The predicted dependence for the speed on the number of generations per year allows us to explain the change in speed observed for a specific invasion

Population spread and cultural transmission in Neolithic transitions

The classical wave-of-advance model is based on Fisher's equation. However, this approach leads to an unbounded wave-of-advance speed at high reproduction rates. In contrast, an integro-difference model leads to a finite upper bound for the speed, namely the maximum dispersal distance divided by the generation time. Intuitively, this is a very reasonable result. This demic model has been generalized to include cultural transmission (Fort, PNAS 2012). We apply this recent demic-cultural model to determine the percentages of demic and cultural diffusion in the Neolithic transition for two case studies: (i) Europe, and (ii) southern Africa (Jerardino et al., submitted 2014). The similarities and differences between both case studies are interpreted in terms of the three mechanisms at work (population reproduction, dispersal and acculturation)

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