Biology, Sociology, Geology by Computational Physicists

Antivax movement and epidemic spreading in the era of social networks: Nonmonotonic effects, bistability, and network segregation

In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders-rather than favoring-the global disease spreading. Thus our results hint vaccination campaigns should avoid policies that end up segregating excessively antivaccine groups so that they effectively work as echo chambers in which individuals look to confirmation without jeopardizing the safety of the whole population.

Disorder-induced phase transition in an opinion dynamics model: Results in two and three dimensions

We study a model of continuous opinion dynamics with both positive and negative mutual interactions. The model shows a continuous phase transition between a phase with consensus (order) and a phase having no consensus (disorder). The mean field version of the model was already studied. Using extensive numerical simulations, we study the same model in two and three dimensions. The critical points of the phase transitions for various cases and the associated critical exponents have been estimated. The universality class of the phase transitions in the model is found to be same as Ising model in the respective dimensions.

Epigenetic contribution to age distribution of mortality within the Penna model

Some modifications of the simple asexual Penna model, enriched by epigenetic contributions, are presented. The standard bit-string Penna model of biological aging and population evolution is based on an inherited DNA structure which defines the future life of a newly born individuals, when genes are activated by the biological clock, and the predefined genetic death is fully controlled by the number of defected genes. Epigenomes allow to introduce additional mechanism of gene activation or silencing without affecting the DNA genome itself. It may be either inherited or may reflect external, environmental factors. In the presented model, information read from the introduced epigenome may alter gene expression that may be stopped or re-activated. We concentrate on the influence of epigenetics on the age a distribution of genetic mortality m(a). Changes in m(a) are strong for the case of inherited epigenetic contribution with nearly perfect inheritance and 'positive' epigenome that partly ignores the 'bad' mutations. We conclude that the epigenetic contribution may influence population structure m(a) and could be, at least partly, responsible for deviation of m(a) distribution from the Gompertz law. In short, we claim that proposed epigenetic contribution may be seen as a candidate for possible explanation of observed deviation from the Gompertz law, also among senior members of society. A very simple model was used in this paper and many crucial mechanisms of biological aging were omitted. Therefore, further work based on a more realistic models is necessary.

A model for cross-cultural reciprocal interactions through mass media

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod's model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.

Nonequilibrium model on Apollonian networks

We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.

Dynamical model for competing opinions

We propose an opinion model based on agents located at the vertices of a regular lattice. Each agent has an independent opinion (among an arbitrary, but fixed, number of choices) and its own degree of conviction. The latter changes every time two agents which have different opinions interact with each other. The dynamics leads to size distributions of clusters (made up of agents which have the same opinion and are located at contiguous spatial positions) which follow a power law, as long as the range of the interaction between the agents is not too short; i.e., the system self-organizes into a critical state. Short range interactions lead to an exponential cutoff in the size distribution and to spatial correlations which cause agents which have the same opinion to be closely grouped. When the diversity of opinions is restricted to two, a nonconsensus dynamic is observed, with unequal population fractions, whereas consensus is reached if the agents are also allowed to interact with those located far from them. The individual agents' convictions, the preestablished interaction range, and the locality of the interaction between a pair of agents (their neighborhood has no effect on the interaction) are the main characteristics which distinguish our model from previous ones.

Dual modeling of political opinion networks

We present the result of a dual modeling of opinion networks. The model complements the agent-based opinion models by attaching to the social agent (voters) network a political opinion (party) network having its own intrinsic mechanisms of evolution. These two subnetworks form a global network, which can be either isolated from, or dependent on, the external influence. Basically, the evolution of the agent network includes link adding and deleting, with the opinion changes influenced by social validation, the political climate, the attractivity of the parties, and the interaction between them. The opinion network is initially composed of numerous nodes representing opinions or parties that are located on a one dimensional axis according to their political positions. The mechanism of evolution includes union, splitting, change of position, and attractivity, taking into account the pairwise node interaction decaying with node distance in power law. The global evolution ends in a stable distribution of the social agents over a quasistable and fluctuating stationary number of remaining parties. Empirical study on the lifetime distribution of numerous parties and vote results is carried out to verify numerical results.

Modelling survival and allele complementation in the evolution of genomes with polymorphic loci

We have simulated the evolution of sexually reproducing populations composed of individuals represented by diploid genomes. A series of eight bits formed an allele occupying one of 128 loci of one haploid genome (chromosome). The environment required a specific activity of each locus, this being the sum of the activities of both alleles located at the corresponding loci on two chromosomes. This activity is represented by the number of bits set to zero. In a constant environment the best fitted individuals were homozygous with alleles’ activities corresponding to half of the environment requirement for a locus (in diploid genome two alleles at corresponding loci produced a proper activity). Changing the environment under a relatively low recombination rate promotes generation of more polymorphic alleles. In the heterozygous loci, alleles of different activities complement each other fulfilling the environment requirements. Nevertheless, the genetic pool of populations evolves in the direction of a very restricted number of complementing haplotypes and a fast changing environment kills the population. If simulations start with all loci heterozygous, they stay heterozygous for a long time.

Local interaction scale controls the existence of a nontrivial optimal critical mass in opinion spreading

We study a model of opinion formation where the collective decision of a group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a critical mass. We find that there exists a unique nontrivial critical mass giving the most efficient convergence to consensus. In addition, we observe that for small critical masses, the characteristic time scale for the relaxation to consensus splits into two. The shorter time scale corresponds to a direct relaxation and the longer one can be explained by the existence of intermediate metastable states similar to those found in [P. Chen and S. Redner, Phys. Rev. E 71, 036101 (2005)]. This longer time scale is dependent on the precise condition for consensus-with a modification of the condition it can go away.

Numerical solution of the Penna model of biological aging with age-modified mutation rate

In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of a -dependent mutation rate m(a), where a is the parent's age. The mutation rate m(a) is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that m(a) increases with age a. As compared with the reference case of the standard Penna model based on a constant mutation rate m , the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality q(a), a fraction of items eliminated from the population when we go from age (a) to (a+1) in simulated transition from time (t) to next time (t+1). The experimentally observed q(a) dependence essentially follows the Gompertz exponential law for a above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate m with age a discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe et al. [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe et al.

Consequence of reputation in an open-ended naming game

We study a modified version of the naming game, a recently introduced model which describes how shared vocabulary can emerge spontaneously in a population without any central control. In particular, we introduce a mechanism that allows a continuous interchange with the external inventory of words. A playing strategy, influenced by the hierarchical structure that individuals' reputation defines in the community, is implemented. We analyze how these features influence the convergence times, the cognitive efforts of the agents, and the scaling behavior in memory and time.

Coevolutionary dynamics of opinions and networks: from diversity to uniformity

We investigate the coevolutionary dynamics of opinions and networks based upon majority-preference (MP) and minority-avoidance (MA) rules. Under MP, individuals adopt the majority opinion among their neighbors; while in MA individuals can break the link to one holding a minority and different opinion, and rewire either to neighbors of their neighbors with the same opinion or to a random one from the whole population except their nearest neighbors. We study opinion formation as a result of combination of these two competing rules, with a parameter tuning the balance between them. We find that the underlying network can be self-organized into connected communities with like-minded individuals belonging to the same group; thus a broad variety of opinions coexist. Diverse opinions disappear in a population in which all individuals share a uniform opinion, when the model parameter exceeds a critical value. Furthermore, we show that an increasing tendency to redirect to neighbors of neighbors is more likely to result in a consensus of opinion.

The Penna Model of Biological Aging

This review deals with computer simulation of biological aging, particularly with the Penna model of 1995. They are based on the mutation accumulation theory of half a century ago. The results agree well with demographical reality, and also with the seemingly contradictory influence of predators on the aging of prey.

Consensus formation on adaptive networks

The structure of a network can significantly influence the properties of the dynamical processes that take place on them. While many studies have been paid to this influence, much less attention has been devoted to the interplay and feedback mechanisms between dynamical processes and network topology on adaptive networks. Adaptive rewiring of links can happen in real life systems such as acquaintance networks, where people are more likely to maintain a social connection if their views and values are similar. In our study, we consider different variants of a model for consensus formation. Our investigations reveal that the adaptation of the network topology fosters cluster formation by enhancing communication between agents of similar opinion, although it also promotes the division of these clusters. The temporal behavior is also strongly affected by adaptivity: while, on static networks, it is influenced by percolation properties, on adaptive networks, both the early and late time evolutions of the system are determined by the rewiring process. The investigation of a variant of the model reveals that the scenarios of transitions between consensus and polarized states are more robust on adaptive networks.

Why are diploid genomes widespread and dominant mutations rare?

We have used the sexual Penna ageing model to show that the relation between dominance and recessiveness could be a force which optimizes the genome size. While the possibility of complementation of the damaged allele by its functional counterparts (recessiveness) leads to the redundancy of genetic information, the dominant effect of defective genes tends to diminish the number of alleles fulfilling the same function. Playing with the fraction of dominant loci in the genome it is possible to obtain the condition where the diploid state of the genome is optimal. If the status of each bit position as dominant or recessive mutations is changed for each individual randomly and rarely, then after a long time a stationary equilibrium of many recessive and few dominant loci is established in the sexual Penna model. This effect vanishes if the same changing distribution of dominant loci applies to all individuals.

Nonequilibrium phase transition in negotiation dynamics

We introduce a model of negotiation dynamics whose aim is that of mimicking the mechanisms leading to opinion and convention formation in a population of individuals. The negotiation process, as opposed to "herdinglike" or "bounded confidence" driven processes, is based on a microscopic dynamics where memory and feedback play a central role. Our model displays a nonequilibrium phase transition from an absorbing state in which all agents reach a consensus to an active stationary state characterized either by polarization or fragmentation in clusters of agents with different opinions. We show the existence of at least two different universality classes, one for the case with two possible opinions and one for the case with an unlimited number of opinions. The phase transition is studied analytically and numerically for various topologies of the agents' interaction network. In both cases the universality classes do not seem to depend on the specific interaction topology, the only relevant feature being the total number of different opinions ever present in the system.

Sympatric speciation as intrinsic property of the expanding population

Sympatric speciation is still debatable, though some well documented empirical data that support it already exist. Our computer modeling reveals that sympatric speciation is an intrinsic property of the expanding populations with differentiated inbreeding-higher at the edges and lower inside the territory. At the edges of expanding populations, the probability of forming deleterious phenotypes by placing two defective alleles in the corresponding loci is relatively high even with low genetic load. Thus, the winning strategy is to use rather the complementary haplotypes to form zygotes. This strategy leads to a very fast sympatric speciation and specific distribution of recombination activity along the chromosomes-higher at the subtelomeric regions (close to the ends of chromosomes) and lower in the middle of chromosomes, which is also observed in all human chromosomes (excluding Y).

Complex population dynamics as a competition between multiple-time-scale phenomena

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The mean-field level of description allows one to highlight the delicate interplay between the different time-scale processes in the resulting complex dynamics of the system. We clarify the influence of the amplitude and period of the environmental changes on the critical value of the selection pressure corresponding to a phase-transition "extinct-alive" of the population. However, the intrinsic stochasticity and the dynamically-built in correlations among the individuals, as well as the role of the mutation-induced variety in population's evolution are not appropriately accounted for. A more refined level of description, which is an individual-based one, has to be considered. The inherent fluctuations do not destroy the phase transition "extinct-alive," and the mutation amplitude is strongly influencing the value of the critical selection pressure. The phase diagram in the plane of the population's parameters-selection and mutation are discussed as a function of the environmental variation characteristics. The differences between a smooth variation of the environment and an abrupt, catastrophic change are also addressed.

Anomalies and the Eve effect in the asexual Penna model

The Penna model of evolutionary ageing is an influential model of mutation accumulation and selection, where an individual's genomic information is represented by a binary bit string. One key parameter of the model is the death threshold, T, the number of diseases any particular individual is able to endure. We show, by combined computer simulations and analytical formulation, that certain anomalies emerge in the asexual Penna model for T>1, which may lead to the so-called Eve effect. We characterize these anomalies and their associated demographic distributions. We argue that this anomaly is similar in nature to the well known first-passage problem.