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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.

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We introduce a population dynamics model, where individual genomes are represented by bit strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die, keeping the population constant. An offspring has the same genome as its (randomly chosen) parent, except for a small amount of (also random) mutations. Chance may thus generate a newborn with a genome that is better than that of its parent, and the newborn will have a smaller death probability. When this happens, this individual is a would-be founder of a new lineage. A new lineage is considered created if the number of its live descendants grows above a certain previously defined threshold. The time evolution of populations evolving under these rules is followed by computer simulations and the probability densities of lineage duration and size, among others, are computed. These densities show a scale-free behavior, in accordance with some conjectures in paleoevolution, and suggesting a simple mechanism as explanation for the ubiquity of these power laws.

Using the Finite Size Scaling Renormalisation Group we obtain the two-dimensional flow diagram of the Blume-Capel model, for S = 1 and S = 3/2. In the first case our results are similar to those of Mean Field Theory, which predicts the existence of first and second order transitions whith a tricritical point.In the second case, however, our results are different. While we obtain, in the S = 1 case, a phase diagram presenting a multicritical point, the Mean Field approach predicts only a second order transition and a critical end point.Work partially supported by Brazilian agencies FINEP, CNPq, CAPES and FAPEMIG.

The bit-string model of biological aging is used to simulate the catastrophic senescence of Paci c Salmon. We have shown that reproduction occuring only once and at a xed age is the only ingredient needed to explain the catastrophic senescence according the mutation accumulation theory. Several results are presented, some of them with up to 10 8 shes, showing how the survival rates in catastrophic senescence are a ected by changes in the parameters of the model. PACS number(s): 05.50.+q; 89.60.+x; 07.05.Tp Senescence, or aging, is a process occuring in all higher organisms and it is related to a decrease in functional abilities. Several factors seems to be important to aging: the environment, metabolism, genetic factors and so forth 1,2]. Senescence can be characterized as the decrease in the survival probabilities with the age. At least two theories for the senescence are based on evolution 3]: the antagonistic pleiotropy (an optimality theory based on life strategy of increasing tness by increasing early performance at expense of late) and mutation accumulation (based on a greater mutation load on the later than the earlier ages). These theories, besides providing explanation for several aspects of senescence, also allow the use of methods of statistical physics (see ref. 4] for a review on earlier models). A dramatic manifestation of aging is the so-called catastrophic senescence of Paci c salmon, whereby they pass from sexual maturity to death in a few weeks. Semelparous individuals, which breed only once, usually present this feature 1{3], while for iteroparous individuals, which breed repeatedly, the senescence is more gradual. Jan 5] has shown how to introduce the catastrophic senescence in the PartridgeBarton model, but without taking into account explicitly the number of breeding attempts. In this work we show that, according to a model based on the mutation accumulation theory, this ingredient (semelparity) is the only responsible one for the catastrophic senescence.The bit-string model of life history, recently introduced 6], makes use of a balance between hereditary mutations and evolutionary selection pressure to simulate aging in a population. In this model, each individual of an initial population N (t = 0) is characterized by a string of 32 bits (\genome"), which contains the information when the e ect of a mutation will be present during the life of the individuum. The time is a discrete variable running from 1 to 32 steps (\years"). If at time (t = i) of the individuum lifetime, the i-th bit in the genome is set to one, it will su er the e ects of a deleterious mutation in that and all following years. At each year one bit of the genome is read, and the total number of mutations (bits 1) is computed; if it reaches a value greater than a threshold T, the individuum dies. At every year beyond the minimum reproduction age R the individuum produces b o springs. The genome of each baby differs from that of the parent by one randomly selected bit, toggled at birth. This mutation can be regarded as...

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This paper presents computer simulations of language populations and the development of language families, showing how a simple model can lead to distributions similar to those observed empirically by Wichmann (2005) and others. The model combines features of two models used in earlier work for the simulation of competition among languages : the 'Viviane ' model for the migration of peoples and the propagation of languages, and the 'Schulze ' model, which uses bit-strings as a way of characterising structural features of languages. ). The authors are grateful to JL's anonymous referees for their comments on the original submission and subsequent revisions.