[en] Glioblastomas are highly diffuse, malignant tumors that have so far evaded clinical treatment. The strongly invasive behavior of cells in these tumors makes them very resistant to treatment, and for this reason both experimental and theoretical efforts have been directed toward understanding the spatiotemporal pattern of tumor spreading. Although usual models assume a standard diffusion behavior, recent experiments with cell cultures indicate that cells tend to move in directions close to that of glioblastoma invasion, thus indicating that a biased random walk model may be much more appropriate. Here we show analytically that, for realistic parameter values, the speeds predicted by biased dispersal are consistent with experimentally measured data. We also find that models beyond reaction–diffusion–advection equations are necessary to capture this substantial effect of biased dispersal on glioblastoma spread. (paper)

[en] We analytically explore the scaling properties of a general class of nested subgraphs in complex networks, which includes the K-core and the K-scaffold, among others. We name such a class of subgraphs K-nested subgraphs since they generate families of subgraphs such that ...S_K+1(G) subset or equal S_K(G) subset or equal S_K-1(G).... Using the so-called configuration model it is shown that any family of nested subgraphs over a network with diverging second moment and finite first moment has infinite elements (i.e. lacking a percolation threshold). Moreover, for a scale-free network with the above properties, we show that any nested family of subgraphs is self-similar by looking at the degree distribution. Both numerical simulations and real data are analyzed and display good agreement with our theoretical predictions

[en] In the present work we study the role of cooperation and parasites on extinction delayed transitions for self-replicating species with catalytic activity. We first use a one-dimensional continuous equation to study the dynamics of both single autocatalytic replicator and symmetric two-member hypercycles, where two well-defined phases involving survival and extinction of replicators are shown to exist. Extinction dynamics is analyzed numerically and analytically and under both deterministic and stochastic scenarios. A ghost is also found for the single autocatalytic replicator and for the asymmetric hypercycle, with an extinction time delay following the square-root scaling law near bifurcation threshold. We find that the extinction delay is longer for the two-member hypercycle than for the single autocatalytic species, indicating that cooperation among replicators might involve to spend a longer time in the bottle-neck region of the ghost. The asymmetry of the network is shown to prolong the extinction time. We also show that an attached parasite decreases the time spent in the bottle-neck region of the ghost, thus accelerating extinction in these systems of replicators. Nevertheless the effect of the parasite is not so important when replicators catalytically cooperate, being the two-member hypercycle less sensitive to the parasite than the autocatalytic species. Here the hypercycle asymmetry can also significantly increase the delaying capacity. These features make the hypercycle to undergo a longer extinction delay, thus increasing the memory effect of the ghost. We finally explore the role of the ghost in fluctuating media, where the extinction delayed transition is shown to increase the survival probability of cooperating catalytic species

[en] In this paper we analyze delayed transition phenomena associated to extinction thresholds in a mean field model for hypercycles composed of three and four units, respectively. Hence, we extend a previous analysis carried out with the two-membered hypercycle [see Sardanyes J, Sole RV. Ghosts in the origins of life? Int J Bifurcation Chaos 2006;16(9), in press]. The models we analyze show that, after the tangent bifurcation, these hypercycles also leave a ghost in phase space. These ghosts, which actually conserve the dynamical properties of the coalesced coexistence fixed point, delay the flows before hypercycle extinction. In contrast with the two-component hypercycle, both ghosts show a plateau in the delay as φ ^→ 0, thus displacing the power-law dependence to higher values of φ, in which the scaling law is now given by τ ∼ φ ^β, with β = -1/3 (where τ is the delay and φ = ε - ε _c, the parametric distance above the extinction bifurcation point). These results suggest that the presence of the ghost is a general property of hypercycles. Such ghosts actually cause a memory effect which might increase hypercycle survival chances in fluctuating environments

[en] We study a continuous time model describing gene-for-gene, host-parasite interactions among self-replicating macromolecules evolving in both neutral and rugged fitness landscapes. Our model considers polymorphic genotypic populations of sequences with 3 bits undergoing mutation and incorporating a 'type II' non-linear functional response in the host-parasite interaction. We show, for both fitness landscapes, a wide range of chaotic coevolutionary dynamics governed by Red Queen strange attractors. The analysis of a rugged fitness landscape for parasite sequences reveals that fittest genotypes achieve lower stationary concentration values, as opposed to the flattest ones, which undergo a higher stationary concentration. Our model also shows that the increase of parasites pressure (higher self-replication and mutation rates) generically involves a simplification of the host-parasite dynamical behavior, involving the transition from a chaotic to an ordered coevolutionary phase. Moreover, the same transition can also be found when hosts 'run' faster through the hypercube. Our results, in agreement with previous studies in host-parasite coevolution, suggest that chaos might be common in coevolutionary dynamics of changing self-replicating entities undergoing a host-parasite ecology

[en] A minimal Lotka-Volterra type predator-prey model describing coevolutionary traits among entities with a strength of interaction influenced by a pair of haploid diallelic loci is studied with a deterministic time continuous model. We show a Hopf bifurcation governing the transition from evolutionary stasis to periodic Red Queen dynamics. If predator genotypes differ in their predation efficiency the more efficient genotype asymptotically achieves lower stationary concentrations