cvaz@inesc-id.ptSupplementary information: Supplementary data are available at Bioinformatics online.

The one-dimensional Sznajd model "united we stand, divided well fall" is generalized to the square lattice with similar fixed points. Only in two of the variants are the distribution of equilibration times roughly log-normal. Probabilistic generalizations destroyed the "dictatorial" fixed points.

The Sznajd model of socio-physics, that only a group of people sharing the same opinion can convince their neighbors, is applied to a scale-free random network modeled by a deterministic graph. We also study a model for elections based on the Sznajd model and the exponent obtained for the distribution of votes during the transient agrees with those obtained for real elections in Brazil and India. Our results are compared to those obtained using a Barabási-Albert scale-free network.

Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter q c , as well as the critical exponents β/ν, γ/ν and 1/ν have been calculated as a function of the connectivity z of the random graph.

No abstract

The Monte Carlo simulation of Bonabeau, Theraulaz and Deneubourg is reinvestigated. The phase transition between an egalitarian and an hierarchical society found was due to an instability when the past fights are not forgotten fast enough. Their model is also changed to include pair-specific memories, which again favor egalitarian societies.

Several cases of the Sznajd model of socio-physics, that only a group of people sharing the same opinion can convince their neighbors, have been simulated on a more realistic network with a stronger clustering. In addition, many opinions, instead of usually only two, and a convincing probability have been also considered. Finally, with minor changes we obtain a vote distribution in good agreement with reality.

One species is simulated to split into two separate species via random mutations, even if both populations live together in the same environment. This speciation is achieved in the Penna bitstring model of biological ageing, with modified Verhulst factors, and in part by additional bitstrings regulating phenotype and mate selection. I IntroductionThe common ancestors of today's humans and today's chimpanzees presumably lived several million years ago. Then, due to genetic mutations and/or changes in the environment, the population split into the ancestors of humans and the ancestors of chimpanzees. Such a separation of one species into two is called "speciation". It is easily explained if the two populations live in separate environments, like one on an island and the other on a continent, making the mating of males from one population with females from the other population impossible. This effect is called allopatric speciation. More difficult to explain is sympatric speciation, where the two populations continue to live in the same environment but nevertheless cease to mate each other [1]. A recent computer model [2] in the physics literature also cites biological examples, serving as a background also for our paper. We concentrate here on models with age-structured populations [3,4,5] and in particular use the Penna bitstring model [6,7], which is the presently most widespread model to simulate biological ageing. We deal only with sexual reproduction where two populations are defined as being different species if the mating from different populations produces no viable offspring.The next section shortly explains this Penna model and then presents the minimal modifications which we found necessary to get sympatric speciation. A more realistic model involving three pairs of bitstrings instead of only one is discussed in the following section. We end with a short summary. II Simple Model II.1 Penna ModelThe Penna bitstring model for biological ageing [6,7] simulates the mutation accumulation by storing bad mutations (= hereditary diseases) in a string of (usually) 32 bits. The position of the bit corresponds to the age of the individual; its value corresponds to health (zero) or sickness (one). Sick bits act from the age to which their positions belong up to the death of the individual. Three active sicknesses kill the animal; in addition all animals are killed at each time step t = 1, 2, . . . with the Verhulst probability V (t) = N (t)/N max where N (t) is the current population and N max is often called the carrying capacity describing the limitation of food and space. After reaching an age of eight "years" (= bit positions or iterations), each individual gives birth to one child per year until its death; the child inherits the same bitstring as the mother except for one possible mutation at a randomly selected position where the mutated bit is set to one irrespective of its previous value. Initially, all bit strings are zero.For the sexual Penna model used here, each individual has two bitstrings inherited f...