Population bottlenecks in quasispecies dynamics.

The characteristics of natural populations result from different stochastic and deterministic processes that include reproduction with error, selection, and genetic drift. In particular, population fluctuations constitute a stochastic process that may play a very relevant role in shaping the structure of populations. For example, it is expected that small asexual populations will accumulate mutations at a higher rate than larger ones. As a consequence, in any population the fixation of mutations is accelerated when environmental conditions cause population bottlenecks. Bottlenecks have been relatively frequent in the history of life and it is generally accepted that they are highly relevant for speciation. Although population bottlenecks can occur in any species, their effects are more noticeable in organisms that form large and heterogeneous populations, such as RNA viral quasispecies. Bottlenecks can also positively select and isolate particles that still keep the ability to infect cells from a disorganized population created by crossing the error threshold.

Foot-and-mouth disease virus evolution: exploring pathways towards virus extinction.

Foot-and-mouth disease virus (FMDV) is genetically and phenotypically variable. As a typical RNA virus, FMDV follows a quasispecies dynamics, with the many biological implications of such a dynamics. Mutant spectra provide a reservoir of FMDV variants, and minority subpopulations may become dominant in response to environmental demands or as a result of statistical fluctuations in population size. Accumulation of mutations in the FMDV genome occurs upon subjecting viral populations to repeated bottleneck events and upon viral replication in the presence of mutagenic base or nucleoside analogs. During serial bottleneck passages, FMDV survive during extended rounds of replication maintaining low average relative fitness, despite linear accumulation of mutations in the consensus genomic sequence. The critical event is the occurrence of a low frequency of compensatory mutations. In contrast, upon replication in the presence of mutagens, the complexity of mutant spectra increases, apparently no compensatory mutations can express their fitness-enhancing potential, and the virus can cross an error threshold for maintenance of genetic information, resulting in virus extinction. Low relative fitness and low viral load favor FMDV extinction in cell culture. The comparison of the molecular basis of resistance to extinction upon bottleneck passage and extinction by enhanced mutagenesis is providing new insights in the understanding of quasispecies dynamics. Such a comparison is contributing to the development of new antiviral strategies based on the transition of viral replication into error catastrophe.

Stochastic multiplicative processes with reset events.

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behavior. In the boundary between them, the mean value of the relevant variable is time independent, and the exponent of the stationary distribution equals -2. The addition of diffusion to the system modifies in a nontrivial way the profile of the stationary distribution. Numerical and analytical results are presented.

Mutual synchronization and clustering in randomly coupled chaotic dynamical networks.

We introduce and study systems of randomly coupled maps where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally coupled maps) until a certain critical threshold for the connectivity is reached. We further show that not only the average connectivity, but also the architecture of the couplings is responsible for the cluster structure observed. We analyze the different phases of the system and use various correlation measures in order to detect ordered nonsynchronized states. Finally, it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs.

On the genealogy of a population of biparental individuals.

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number G(c) approximately log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after G(c)generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.

Shape of ecological networks.

We study the statistics of ecosystems with a variable number of coevolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly through successful adaptations and speciations. They are treated as quenched random variables. These interactions determine long-term topological features of the species network, which are found to agree with those of biological systems.

Diversity patterns from ecological models at dynamical equilibrium.

We study a dynamic model of ecosystems where an immigration flux assembles the species community and maintains its biodiversity. This framework is particularly relevant for insular ecosystems. Population dynamics is represented either as an individual-based model or as a set of deterministic equations for population abundances. Local extinctions and immigrations balance at a statistically stationary state where biodiversity fluctuates around a constant mean value. We find a number of scaling laws characterizing this stationary state. In particular, the number of species increases as a power law of the immigration rate. With additional assumptions on the immigration flux, we obtain species-area relationships in agreement with observations for archipelagos. We also find power-law distributions for species abundances and lifetimes.