Turing patterns and apparent competition in predator-prey food webs on networks

Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles in many fields of biology, such as ecology and morphogenesis. In the present study we focus on the role of Turing patterns in describing the abundance distribution of predator and prey species distributed in patches in a scale free network structure. We extend the original model proposed by Nakao and Mikhailov by considering food chains with several interacting pairs of preys and predators. We identify patterns of species distribution displaying high degrees of apparent competition driven by Turing instabilities. Our results provide further indication that differences in abundance distribution among patches may be, at least in part, due to self organized Turing patterns, and not necessarily to intrinsic environmental heterogeneity

Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Coexistence and critical behaviour in a lattice model of competing species

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.Comment: 11 pages, 14 figure

Statistical mechanics and stability of a model eco-system

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct competitive or co-operative interaction between species may occur through a random coupling matrix. We compute the order parameters of the system in a fixed point regime, and identify the onset of instability and compute the phase diagram. We focus on the effects of variability of resources, direct interaction between species, co-operation pressure and dilution on the stability and the diversity of the ecosystem. It is shown that resources can be exploited optimally only in absence of co-operation pressure or direct interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended, references adde

Effects of Noise on Ecological Invasion Processes: Bacteriophage-mediated Competition in Bacteria

Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in nature. Using an experimental system of bacteriophage-mediated competition in bacterial populations and a deterministic model, we have shown in [Joo et al 2005] that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of the initial phage concentration and other phage and host parameters such as the infection-causing contact rate, the spontaneous and infection-induced lysis rates, and the phage burst size. Here we investigate the effects of stochastic fluctuations on bacterial invasion facilitated by bacteriophage, and examine the validity of the deterministic approach. We use both numerical and analytical methods of stochastic processes to identify the source of noise and assess its magnitude. We show that the conclusions obtained from the deterministic model are robust against stochastic fluctuations, yet deviations become prominently large when the phage are more pathological to the invading bacterial strain.Comment: 39 pages, 7 figure

Habitat filtering determines spatial variation of macroinvertebrate community traits in northern headwater streams

Although our knowledge of the spatial distribution of stream organisms has been increasing rapidly in the last decades, there is still little consensus about trait-based variability of macroinvertebrate communities within and between catchments in near-pristine systems. Our aim was to examine the taxonomic and trait based stability vs. variability of stream macroinvertebrates in three high-latitude catchments in Finland. The collected taxa were assigned to unique trait combinations (UTCs) using biological traits. We found that only a single or a highly limited number of taxa formed a single UTC, suggesting a low degree of redundancy. Our analyses revealed significant differences in the environmental conditions of the streams among the three catchments. Linear models, rarefaction curves and beta-diversity measures showed that the catchments differed in both alpha and beta diversity. Taxon- and trait-based multivariate analyses also indicated that the three catchments were significantly different in terms of macroinvertebrate communities. All these findings suggest that habitat filtering, i.e., environmental differences among catchments, determines the variability of macroinvertebrate communities, thereby contributing to the significant biological differences among the catchments. The main implications of our study is that the sensitivity of trait-based analyses to natural environmental variation should be carefully incorporated in the assessment of environmental degradation, and that further studies are needed for a deeper understanding of trait-based community patterns across near-pristine streams

A high-temperature superconducting weak-link defined by ferroelectric field-effect

In all-oxide ferroelectric (FE) - superconductor (S) bilayers, due to the low carrier concentration of oxides compared to transition metals, the FE interfacial polarization charges induce an accumulation (or depletion) of charge carriers in the S. This leads either to an enhancement or a depression of its critical temperature depending on FE polarization direction.Here we exploit this effect at a local scale to define planar weak-links in high-temperature superconducting wires. This is realized in BiFeO3(FE)/YBa2Cu3O7(S)bilayers in which the remnant FE domain structure is written at will by locally applying voltage pulses with a conductive-tip atomic force microscope. In this fashion, the FE domain pattern defines a spatial modulation of superconductivity. This allows us to write a device whose electrical transport shows different temperature regimes and magnetic field matching effects that are characteristic of Josephson coupled weak-links. This illustrates the potential of the ferroelectric approach for the realization of high-temperature superconducting devices

Structure in parasite component communities in wild rodents: predictability, stability, associations and interactions or pure randomness?

Experimental data establish that interactions exist between species of intestinal helminths during concurrent infections in rodents, the strongest effects being mediated through the host’s immune responses. Detecting immune-mediated relationships in wild rodent populations has been fraught with problems and published data do not support a major role for interactions in structuring helminth communities. Helminths in wild rodents show predictable patterns of seasonal, host age-dependent and spatial variation in species richness and in abundance of core species. When these are controlled for, patterns of co-infection compatible with synergistic interactions can be demonstrated. At least one of these, the positive relationship between Heligmosomoides polygyrus and species richness of other helminths has been demonstrated in three totally independent data-sets. Collectively, they explain only a small percentage of the variance/deviance in abundance data and at this level are unlikely to play a major role in structuring helminth communities, although they may be important in the more heavily infected wood mice. Current worm burdens underestimate the possibility that earlier interactions through the immune system have taken place, and therefore interactions may have a greater role to play than is immediately evident from current worm burdens. Longitudinal studies are proposed to resolve this issue

Transplanting the leafy liverwort Herbertus hutchinsiae : A suitable conservation tool to maintain oceanic-montane liverwort-rich heath?

Thanks to the relevant landowners and managers for permission to carry out the experiments, Chris Preston for helping to obtain the liverwort distribution records and the distribution map, Gordon Rothero and Dave Horsfield for advice on choosing experimental sites and Alex Douglas for statistical advice. Juliane Geyer’s help with fieldwork was greatly appreciated. This study was made possible by a NERC PhD studentship and financial support from the Royal Botanic Garden Edinburgh and Scottish Natural Heritage.Peer reviewedPostprin