Related papers: Utterance Selection Model of Language Change
The Becker-D\"oring equations are an infinite dimensional system of ordinary differntial equations describing coagulation/fragmentation processes of species of integer sizes. Formal Taylor expansions motivate that its solution should be…
Is it possible to develop a `physics of language' which can explain the spatial, temporal and social patterns we see, and which can predict future change like we forecast the weather? Such a theory is likely to involve ideas from…
This paper introduces new methods based on exponential families for modeling the correlations between words in text and speech. While previous work assumed the effects of word co-occurrence statistics to be constant over a window of several…
The understanding of language competition helps us to predict extinction and survival of languages spoken by minorities. A simple agent-based model of a sexual population, based on the Penna model, is built in order to find out under which…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
We study a system of Fokker-Planck equations recently introduced to describe the temporal evolution of statistical distributions of population densities with predator-prey interactions. At the macroscopic level, the system recovers a…
The word-stock of a language is a complex dynamical system in which words can be created, evolve, and become extinct. Even more dynamic are the short-term fluctuations in word usage by individuals in a population. Building on the recent…
Motivated by the dynamics of cultural change and diversity, we generalize the three-species constrained voter model on a complete graph introduced in [J. Phys. A 37, 8479 (2004)]. In this opinion dynamics model, a population of size N is…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
Natural languages display a trade-off among different strategies to convey syntactic structure, such as word order or inflection. This trade-off, however, has not appeared in recent simulations of iterated language learning with neural…
The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
Taylor's law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor's law has been applied in many natural and social…
Languages and genes are both transmitted from generation to generation, with opportunity for differential reproduction and survivorship of forms. Here we apply a rigorous inference framework, drawn from population genetics, to distinguish…
The neutral theory of genetic and linguistic evolution holds that the relative frequencies of variants evolve by random drift. Neutral evolution remains a plausible null model of language change. In this paper we provide evidence against…
The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the…
The similarity of the evolution of human languages (or alphabets, bird songs, >...) to biological evolution of species is utilized to study with up to $10^9$ people the rise and fall of languages either by macroscopic differential equations…
Populations have often been perceived as a structuring component for language to emerge and evolve: the larger the population, the more structured the language. While this observation is widespread in the sociolinguistic literature, it has…
Increasing evidence demonstrates that in many places language coexistence has become ubiquitous and essential for supporting language and cultural diversity and associated with its financial and economic benefits. The competitive evolution…
It is argued that the present log-normal distribution of language sizes is, to a large extent, a consequence of demographic dynamics within the population of speakers of each language. A two-parameter stochastic multiplicative process is…