Institute of Linguistics, Department of Applied Logic

We study a lattice model of a prey–predator system. Mean-field approximation predicts that the active phase, i.e., one with a finite fraction of preys and predators, is a generic phase of this model. Moreover, within this approximation the model exhibits quasi-oscillations resembling Lotka–Volterra systems. However, Monte Carlo simulations for a one-, two-, and three-dimensional versions of this model do not support this scenario and predict that at a certain value of some parameter the model enters the absorbing state, i.e., a state where the entire population of predators dies out and the model is invaded by preys. Simulations for the one-dimensional version indicate that the transition into the absorbing state belongs to the directed percolation universality class.

We examine an evolutionary naming-game model where communicating agents are equipped with an evolutionarily selected learning ability. Such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of a model control parameter a poorly communicating group of linguistically unskilled agents transforms into almost perfectly communicating group with large learning abilities. When learning ability is kept fixed, the transition appears to be continuous. Genetic imprinting of the learning abilities proceeds via Baldwin effect: initially unskilled communicating agents learn a language and that creates a niche in which there is an evolutionary pressure for the increase of learning ability.Our model suggests that when linguistic (or cultural) processes became intensive enough, a transition took place where both linguistic performance and biological endowment of our species experienced an abrupt change that perhaps triggered the rapid expansion of human civilization.

Computational modelling with multi-agent systems is becoming an important technique of studying language evolution. We present a brief introduction into this rapidly developing field, as well as our own contributions that include an analysis of the evolutionary naming-game model. In this model communicating agents, that try to establish a common vocabulary, are equipped with an evolutionarily selected learning ability. Such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of the model control parameter a poorly communicating group of linguistically unskilled agents transforms into almost perfectly communicating group with large learning abilities. Genetic imprinting of the learning abilities proceeds via Baldwin effect: initially unskilled communicating agents learn a language and that creates a niche in which there is an evolutionary pressure for the increase of learning ability. Under the assumption that communication intensity increases continuously with finite speed, the transition is split into several transition-like changes. It shows that the speed of cultural changes, that sets an additional characteristic timescale, might be yet another factor affecting the evolution of language. In our opinion, this model shows that linguistic and biological processes have a strong influence on each other and this effect certainly has contributed to an explosive development of our species.

We examine a weighted-network multiagent model with preferential selection such that agents choose partners with probability p(w), where w is the number of their past selections. When p(w) increases sublinearly with the number of past selections [p(w)∼w(α),α<1], agents develop a uniform preference for all other agents. At α=1, this state loses stability and more complex structures form. For a superlinear increase (α>1), strong heterogeneities emerge and agents make selections mainly within small and sometimes asymmetric clusters. Even in a few-agent case, the formation of such clusters resembles phase transitions with spontaneous symmetry breaking.

We examine a community structure in random graphs of size n and link probability p/n determined with the Newman greedy optimization of modularity. Calculations show that for p<1 communities are nearly identical with clusters. For p=1 the average sizes of a community s(av) and of the giant community s(g) show a power-law increase s(av)∼n(α') and s(g)∼n(α). From numerical results we estimate α'≈0.26(1) and α≈0.50(1) and using the probability distribution of sizes of communities we suggest that α'=α/2 should hold. For p>1 the community structure remains critical: (i) s(av) and s(g) have a power-law increase with α'≈α<1 and (ii) the probability distribution of sizes of communities is very broad and nearly flat for all sizes up to s(g). For large p the modularity Q decays as Q∼p(-0.55), which is intermediate between some previous estimations. To check the validity of the results, we also determine the community structure using another method, namely, a nongreedy ...