Effects of confinement on supercooled tetrahedral liquids.

We use molecular dynamics simulations to ascertain the effects of geometrical restriction on glass-forming tetrahedral liquids. Striving for a broad approach, we study families of waterlike and silicalike liquids, for which we systematically scale the partial charges and, hence, the relevance of the tetrahedral networks. The confined liquids and the confining matrices consist of the same type of particles to avoid disruptive interactions and distorted structures at the interfaces. Spatially resolved analyses show that these neutral confinements still impose static mobility gradients and density correlations on the liquids. We quantify the increasing degree and range of the altered properties upon cooling. For both families of models, common relations describe the confinement effects of all systems with tetrahedral order, while deviations occur for systems with lower polarities and different structures. The observations are rationalized by considering the fact that a pinned wall imprints a static energy landscape to a neighboring liquid. We explore the properties of this landscape based on changes in vibrational motion and structural relaxation and find that typical barrier heights amount to two to three times the activation energy of bulk dynamics. Combining the present and previous results, we predict the evolution of confinement effects down to the glass transition temperature for liquids without fragile-to-strong crossover. In addition, it is found for silicalike liquids that the temperature dependence of dynamic and static correlation lengths from confinement studies is not affected when cooling through fragile-to-strong transitions of the bulk materials, casting doubt on the relevance of these length scales for the glassy slowdown.

Effects of the bond polarity on the structural and dynamical properties of silica-like liquids.

Silica is a network-forming liquid that shares many properties with water due to its tetrahedral structure. It undergoes a transition from a fragile to a strong liquid as the temperature is decreased, which is accompanied by a structural change to lower density and higher tetrahedral order. In order to disentangle the effects of Coulomb and van der Waals interactions on the structure and dynamics of liquid silica, we modify the bond polarity by changing the partial charges assigned to each atom. Using molecular dynamics simulations, we show that density, tetrahedral order, and structural relaxation times decrease when reducing bond polarity. Moreover, we find that the density maximum and the fragile-to-strong transition move to lower temperatures until they eventually vanish when the partial charges are decreased below approximately 75% of their regular value. Irrespective of whether strong or fragile behavior exists, structural relaxation is governed by hopping motion at sufficiently low temperatures. As long as there is a strong regime, the energy barrier associated with strong dynamics decreases with decreasing partial charges, but the dependence on the bond polarity differs from that of the activation energy in the Arrhenius regime at high temperatures. We show that the fragile-to-strong transition is associated with structural changes occurring between the first and second coordination shells that lead to a decrease in density and an increase in tetrahedral order. In particular, independent of the value of the partial charges, the distribution of the local structures is the same at this dynamic crossover, but we find no evidence that the effect occurs upon crossing the Widom line. In the fragile regime at intermediate temperatures, the relaxation times are well described by a previously proposed model which decomposes the apparent activation energy into a constant single-particle contribution and a temperature-dependent collective contribution. However, our results for silica-like melts do not obey several common relations of the model parameters reported for molecular glass formers.

The influence of dispersal on a predator-prey system with two habitats.

Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and comprehensive study of the simplest possible system that includes dispersal and local interactions, namely a 2-patch 2-species system. We evaluate the impact of dispersal on stability and on the occurrence of bifurcations, including pattern forming bifurcations that lead to spatial heterogeneity, in 19 different classes of models with the help of the generalized modelling approach. We find that dispersal often destabilizes equilibria, but it can stabilize them if it increases population losses. If dispersal is nonrandom, i.e. if emigration or immigration rates depend on population densities, the correlation of stability with dispersal rates is positive in part of the models. We also find that many systems show all four types of bifurcations and that antisynchronous oscillations occur mostly with nonrandom dispersal.

3D replicon distributions arise from stochastic initiation and domino-like DNA replication progression.

DNA replication dynamics in cells from higher eukaryotes follows very complex but highly efficient mechanisms. However, the principles behind initiation of potential replication origins and emergence of typical patterns of nuclear replication sites remain unclear. Here, we propose a comprehensive model of DNA replication in human cells that is based on stochastic, proximity-induced replication initiation. Critical model features are: spontaneous stochastic firing of individual origins in euchromatin and facultative heterochromatin, inhibition of firing at distances below the size of chromatin loops and a domino-like effect by which replication forks induce firing of nearby origins. The model reproduces the empirical temporal and chromatin-related properties of DNA replication in human cells. We advance the one-dimensional DNA replication model to a spatial model by taking into account chromatin folding in the nucleus, and we are able to reproduce the spatial and temporal characteristics of the replication foci distribution throughout S-phase.

Biodiversity and ecosystem functioning in evolving food webs.

We use computer simulations in order to study the interplay between biodiversity and ecosystem functioning (BEF) during both the formation and the ongoing evolution of large food webs. A species in our model is characterized by its own body mass, its preferred prey body mass and the width of its potential prey body mass spectrum. On an ecological time scale, population dynamics determines which species are viable and which ones go extinct. On an evolutionary time scale, new species emerge as modifications of existing ones. The network structure thus emerges and evolves in a self-organized manner. We analyse the relation between functional diversity and five community level measures of ecosystem functioning. These are the metabolic loss of the predator community, the total biomasses of the basal and the predator community, and the consumption rates on the basal community and within the predator community. Clear BEF relations are observed during the initial build-up of the networks, or when parameters are varied, causing bottom-up or top-down effects. However, ecosystem functioning measures fluctuate only very little during long-term evolution under constant environmental conditions, despite changes in functional diversity. This result supports the hypothesis that trophic cascades are weaker in more complex food webs.

Evolutionary food web model based on body masses gives realistic networks with permanent species turnover.

The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the complexity and stability of such food webs, we developed an eco-evolutionary model in which new species emerge as modifications of existing ones and dynamic ecological interactions determine which species are viable. The food-web structure thereby emerges from the dynamical interplay between speciation and trophic interactions. The proposed model is less abstract than earlier evolutionary food web models in the sense that all three evolving traits have a clear biological meaning, namely the average body mass of the individuals, the preferred prey body mass, and the width of their potential prey body mass spectrum. We observed networks with a wide range of sizes and structures and high similarity to natural food webs. The model networks exhibit a continuous species turnover, but massive extinction waves that affect more than 50% of the network are not observed.

Single generation cycles and delayed feedback cycles are not separate phenomena.

We study a simple model for generation cycles, which are oscillations with a period of one or a few generation times of the species. The model is formulated in terms of a single delay-differential equation for the population density of an adult stage, with recruitment to the adult stage depending on the intensity of competition during the juvenile phase. This model is a simplified version of a group of models proposed by Gurney and Nisbet, who were the first to distinguish between single-generation cycles and delayed-feedback cycles. According to these authors, the two oscillation types are caused by different mechanisms and have periods in different intervals, which are one to two generation times for single-generation cycles and two to four generation times for delayed-feedback cycles. By abolishing the strict coupling between the maturation time and the time delay between competition and its effect on the population dynamics, we find that single-generation cycles and delayed-feedback cycles occur in the same model version, with a gradual transition between the two as the model parameters are varied over a sufficiently large range. Furthermore, cycle periods are not bounded to lie within single octaves. This implies that a clear distinction between different types of generation cycles is not possible. Cycles of all periods and even chaos can be generated by varying the parameters that determine the time during which individuals from different cohorts compete with each other. This suggests that life-cycle features in the juvenile stage and during the transition to the adult stage are important determinants of the dynamics of density limited populations.

The ecological advantage of sexual reproduction in multicellular long-lived organisms.

We present a model for the advantage of sexual reproduction in multicellular long-lived species in a world of structured resources in short supply. The model combines features of the Tangled Bank and the Red Queen hypothesis of sexual reproduction and is of broad applicability. The model is ecologically explicit with the dynamics of resources and consumers being modelled by differential equations. The life history of consumers is shaped by body mass-dependent rates as implemented in the metabolic theory of ecology. We find that over a broad range of parameters, sexual reproduction wins despite the two-fold cost of producing males, due to the advantage of producing offspring that can exploit underutilized resources. The advantage is largest when maturation and production of offspring set in before the resources of the parents become depleted, but not too early, due to the cost of producing males. The model thus leads to the dominance of sexual reproduction in multicellular animals living in complex environments, with resource availability being the most important factor affecting survival and reproduction.

Sexual reproduction prevails in a world of structured resources in short supply.

We present a model for the maintenance of sexual reproduction based on the availability of resources, which is the strongest factor determining the growth of populations. The model compares completely asexual species to species that switch between asexual and sexual reproduction (sexual species). Key features of the model are that sexual reproduction sets in when resources become scarce, and that at a given place only a few genotypes can be present at the same time. We show that under a wide range of conditions the sexual species outcompete the asexual ones. The asexual species win only when survival conditions are harsh and death rates are high, or when resources are so little structured or consumer genotypes are so manifold that all resources are exploited to the same extent. These conditions largely represent the conditions in which sexuals predominate over asexuals in the field.

Properties of attractors of canalyzing random Boolean networks.

We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory leads to an intuitive understanding of the system's dynamics as it demonstrates the analogy between standard random Boolean networks and networks with canalyzing functions only. It reproduces correctly the scaling of the number of nonfrozen nodes with system size. We then investigate numerically attractor lengths and numbers, and explain the findings in terms of the properties of relevant components. In particular we show that canalyzing networks can contain very long attractors, albeit they occur less often than in standard networks.

The influence of predator--prey population dynamics on the long-term evolution of food web structure.

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.

Phase ordering and roughening on growing films.

We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimensions, we find a variety of different scaling behaviors, depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations.

Competitive speciation in quantitative genetic models.

We study sympatric speciation due to competition in an environment with a broad distribution of resources. We assume that the trait under selection is a quantitative trait, and that mating is assortative with respect to this trait. Our model alternates selection according to Lotka-Volterra-type competition equations, with reproduction using the ideas of quantitative genetics. The recurrence relations defined by these equations are studied numerically and analytically. We find that when a population enters a new environment, with a broad distribution of unexploited food sources, the population distribution broadens under a variety of conditions, with peaks at the edge of the distribution indicating the formation of subpopulations. After a long enough time period, the population can split into several subpopulations with little gene flow between them.

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using the Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behavior for large values of the coupling. We have also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For a spin glass in a field the maximum of non-self-averaging follows a line for given system size that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the approach via one-step replica symmetry breaking predicts two transitions, the first transition being dynamic and the second thermodynamic. Our results suggest that in real finite-dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.

Ecological character displacement in quantitative genetic models.

We study, both analytically and numerically, models of ecological character displacement for two species that compete for the same set of food sources. These models include quantitative genetics and Lotka-Volterra type competition and are symmetric with respect to the two species. We allow for various shapes of the carrying capacity and the competition function, and we discuss under what general conditions large character displacement can occur. While some of these conditions, like genetic rigidity, or flat and truncated carrying capacity curves, were known before, we also find that slow dynamics of the genetic variance, steep slopes in the interaction function and carrying capacities that are not truncated can lead to large displacements. We interpret these conditions biologically and also give new insights into models which have been previously investigated.