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We have investigated the rate of substitution of advantageous mutations in populations of haploid organisms where the rate of recombination can be controlled. We have verified that in all the situations recombination speeds up adaptation through recombination of beneficial mutations from distinct lineages in a single individual, and so reducing the intensity of clonal interference. The advantage of sex for adaptation is even stronger when deleterious mutations occur since now recombination can also restore genetic background free of deleterious mutations. However, our simulation results demonstrate that evidence of clonal interference, as increased mean selective effect of fixed mutations and reduced likelihood of fixation of small-effect mutations, are also present in sexual populations. What we see is that this evidence is delayed when compared to asexual populations.

The understanding of the central mechanisms favoring sex and recombination in real populations is one of the fundamental issues in evolutionary biology. Based on a previous stochastic formulation for the study of sex, here we aim to investigate the conditions under which epistasis favors the fixation of the sexual mode of reproduction in a given population. In addition, we try to identify the evolutionary forces which contribute to this process. One considers a finite population model which assumes the existence of a recombination modifier allele that can activate the recombination mechanism. We have found that sex is very little favored in a scenario of antagonistic epistasis, and this advantage only occurs in a narrow range of values of the selection coefficient s_{d} . On the other hand, synergistic epistasis favors recombination in a very broad domain. However, the major mechanism contributing to the spreading of the modifier allele depends on the range of values of s_{d} . At large s_{d} , background selection favors recombination since it increases the efficacy of selection, while at low s_{d} Muller's ratchet is the leading mechanism.

We investigate by means of a simple theoretical model the emergence of prime numbers as life cycles, as those seen for some species of cicadas. The cicadas, more precisely the Magicicadas, spend most of their lives below the ground and then emerge and die in a short period of time. The Magicicadas display an uncommon behavior: their emergence is synchronized and these periods are usually prime numbers. In the current work, we develop a spatially extended model at which preys and predators coexist and can change their evolutionary dynamics through the occurrence of mutations. We verified that prime numbers as life cycles emerge as a result of the evolution of the population. Our results seem to be a first step in order to prove that the development of such strategy is selectively advantageous, especially for those organisms that are highly vulnerable to attacks of predators.

We investigate the majority-vote model on small-world networks by rewiring the two-dimensional square lattice. We observe that the introduction of long-range interactions does not remove the critical character of the model, that is, the system still exhibits a well-defined phase transition. However, we find that now the critical point is a monotonically increasing function of the rewiring probability. Moreover, we find that small-world effects change the class of universality of the model.

Complementarity among species with different traits is one of the basic processes affecting biodiversity, defined as the number of species in the ecosystem. We present here a soluble model of microbial-based ecosystems in which the species are characterized by binary traits and their pairwise interactions follow a complementarity principle. Manipulation of the species composition, and so the study of its effects on the species diversity, is achieved through the introduction of a bias parameter favoring one of the traits. Using statistical mechanics tools we find explicit expressions for the allowed values of the equilibrium species concentrations in terms of the control parameters of the model.

The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interactions are studied analytically with tools of equilibrium statistical mechanics of disordered systems. Emphasis is given to the effects of externally induced extinction of a fixed fraction of species at the outset of the evolutionary process. The manner the ecosystem copes with the initial extinction event depends on the degree of competition among the species as well as on the strength of that event. For instance, in the regime of high competition the ecosystem diversity, given by the fraction of surviving species, is practically insensitive to the strength of the initial extinction provided it is not too large, while in the less competitive regime the diversity decreases linearly with the size of the event. In the case of large extinction events we find that no further biotic extinctions take place and, furthermore, that rare species become very unlikely to be found in the ecosystem at equilibrium. In addition, we show that the reciprocal of the Edwards-Anderson order parameter yields a good measure of the diversity of the model ecosystem.

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.