Universal Power Laws Govern Intermittent Rarity in Communities of Interacting Species

The temporal dynamics of many populations involve intermittent rarity, that is, the alternation, over variable periods of time, of phases of extremely low abundance, and short outbreaks. In this paper we show that intermittent rarity can arise in simple community models as a result of competitive interactions within and between species. Intermittently rare species are typified as weak invaders in fluctuating communities. Although the dynamics of intermittent rarity are highly irregular, the distribution of time spent in phases of rarity (`rarity times') involves strong regularity. Specifically, intermittent rarity is governed by a well-defined power law. The scaling exponent (-3/2) is a universal feature of intermittent rarity: it does not depend on species demographic parameters; it is insensitive to environmental stochasticity; and the same exponent is found in very different models of nonstructured populations. The distribution of rarity times implies that the dynamics of rarity have no characteristic timescale. Yet in practice the universal scaling law offers a general form of prediction in which one can calculate the frequency of occurrence of rarity phases of any given duration. Data on marine fish communities support the prediction of a -3/2 power law underlying the dynamics of intermittently rare species. The scale-free dynamics reported here place intermittent rarity in the same class as the critical states of other nonlinear dynamical systems in the physical sciences. At a critical state, general laws govern the systems' dynamics irrespective to the specific details of the interactions between constituents

Modélisation d'un système lotique pollué par une charge organique : prise en compte de l'activité des microorganismes benthiques

Les études entreprises depuis 1982 sur un petit cours d'eau pollué par une forte charge organique, ont servi de base au développement d'un modèle mathématique destiné à appréhender le fonctionnement des mécanismes d'auto-épuration.L'écriture du modèle a débuté par la description de l'écoulement du cours d'eau et des mécanismes de transports associés. Deux sous-modèles ont été utilisés dans ce but : un sous-modèle hydrodynamique dérivé du modèle de Saint-Venant et un sous-modèle de transport, constitué par l'équation classique de convection-dispersion. Ces deux sous-modèles sont appliqués à un écoulement monodimensionnel, non uniforme et non stationnaire.Dans les petits cours d'eau le compartiment benthique joue un rôle prépondérant du point de vue de l'ensemble des processus détritiques. Le modèle a donc été appliqué, dans un premier temps, à la simulation de la dynamique du carbone organique dissous et des microorganismes benthiques.Les mécanismes de biodégradation sont modélisés, ici, en utilisant l'analogie entre les processus détritiques et l'activité des biomasses des procédés de traitement des eaux usées. Le modèle de biofilm développé permet, par sa structure, d'englober tous les mécanismes physiques et biologiques qui entrent dans les phénomènes de disparition et de dégradation de la matière organique dissoute.Ce modèle est utilisé, sous sa forme actuelle, en tant qu'outil cognitif destiné à accroître la connaissance des mécanismes d'auto-épuration de la matière organique dissoute dans les petits cours d'eau.Several studies have been performed since 1982 on a small organically polluted stream. Their results have been used to conceive a mathematical model with the purpose of simulating the self-purification mechanisms.The physical part of this model includes a hydrodynamic component derived from Saint-Venant's equations which is coupled with a transport model based on the classical convection-dispersion equation. The model is applied to unidirectional, non-uniform, unsteady flow conditions.As the main detritic processes which occur in small streams take place in the sediment, the model has been applied, first, to simulate the dynamics of both dissolved organic matter and benthic microorganisms.The simulation of the biodegradation mechanisms is based, in this work, on the analogy between the detritic processes in streams and the activity of the microbial biomass in wastewater treatment plants. From the structure of the biofilm model proposed, it was assessed that nearly all mechanisms involved in the removal and degradation of dissolved organic matter may be considered.In these studies, the model is used as a cognitive tool intended to increase the understanding of self-purification mechanisms applied to dissolved organic matter is small streams

Modélisation d'un écosystème lotique pollué par une charge organique : prise en compte de l'hydrodynamique et des mécanismes de transport

L'article décrit la partie hydrophysique d'un modèle écologique de simulation des transferts de carbone organique dans un cours d'eau pollué par le rejet d'une porcherie. Cette partie est constituée d'un modèle hydrodynamique inspiré du modèle de Saint-Venant, couplé à un modèle de transport basé sur l'équation classique de convection-diffusion. Ces modèles sont appliqués à un écoulement unidirectionnel, non uniforme et non stationnaire.Les équations de ces deux modèles sont résolues par une méthode aux différences finies utilisant des schémas implicites. L'ajustement des paramètres est réalisé à partir de résultats d'expériences de traçage à la rhodamine.Appliqués au carbone organique dissous de l'Albenche, les modèles montrent l'extrême étalement des nuages dû aux seuls phénomènes physiques. L'une des interprétations possibles de l'écart entre les valeurs expérimentales et les valeurs calculées au niveau de la station aval, peut être l'importance de la consommation du carbone par les biocoenoses benthiques.A simulation model of organic carbon movement was designed for a river polluted by piggery wastes.The physical dynamics of this model, as described in this paper, include a hydrodynamic component inspired by a Saint Venant's model coupled with a transport model based on the classical advection-diffusion equation. The model is applied to unidirectional, non-uniform, unsteady flow conditions.The equations were solved by a finite difference method using implicit schemes. The parameters of the equation were adjusted to fit flow conditions determined with a rhodamine dye tracer.When applied to the dissolved organic carbon transport in the Albenche river, the model showed that the distribution of organic carbon in space and in time was due to physical processes only. The differences in concentration between the observed and the expected values in the downstream station could represent the consumption of benthic biotic organic carbon

Explaining rapid reinfections in multiple-wave influenza outbreaks: Tristan da Cunha 1971 epidemic as a case study.

Influenza usually spreads through the human population in multiple-wave outbreaks. Successive reinfection of individuals over a short time interval has been explicitly reported during past pandemics. However, the causes of rapid reinfection and the role of reinfection in driving multiple-wave outbreaks remain poorly understood. To investigate these issues, we focus on a two-wave influenza A/H3N2 epidemic that occurred on the remote island of Tristan da Cunha in 1971. Over 59 days, 273 (96%) of 284 islanders experienced at least one attack and 92 (32%) experienced two attacks. We formulate six mathematical models invoking a variety of antigenic and immunological reinfection mechanisms. Using a maximum-likelihood analysis to confront model predictions with the reported incidence time series, we demonstrate that only two mechanisms can be retained: some hosts with either a delayed or deficient humoral immune response to the primary influenza infection were reinfected by the same strain, thus initiating the second epidemic wave. Both mechanisms are supported by previous empirical studies and may arise from a combination of genetic and ecological causes. We advocate that a better understanding and account of heterogeneity in the human immune response are essential to analysis of multiple-wave influenza outbreaks and pandemic planning.Published versio

Quantifying the added value of climate information in a spatio-temporal dengue model

Dengue is the world’s most important vector-borne viral disease. The dengue mosquito and virus are sensitive to climate variability and change. Temperature, humidity and precipitation influence mosquito biology, abundance and habitat, and the virus replication speed. In this study, we develop a modelling procedure to quantify the added value of including climate information in a dengue model for the 76 provinces of Thailand, from 1982–2013. We first developed a seasonal-spatial model, to account for dependency structures from 1 month to the next and between provinces. We then tested precipitation and temperature variables at varying time lags, using linear and nonlinear functional forms, to determine an optimum combination of time lags to describe dengue relative risk. Model parameters were estimated using integrated nested Laplace approximation. This approach provides a novel opportunity to perform model selection in a Bayesian framework, while accounting for underlying spatial and temporal dependency structures and linear or nonlinear functional forms. We quantified the additional variation explained by interannual climate variations, above that provided by the seasonal-spatial model. Overall, an additional 8 % of the variance in dengue relative risk can be explained by accounting for interannual variations in precipitation and temperature in the previous month. The inclusion of nonlinear functions of climate in the model framework improved the model for 79 % of the provinces. Therefore, climate forecast information could significantly contribute to a national dengue early warning system in Thailand

Early-life sexual segregation: ontogeny of isotopic niche differentiation in the Antarctic fur seal

Investigating the ontogeny of niche differentiation enables to determine at which life-stages sexual segregation arises, providing insights into the main factors driving resource partitioning. We investigated the ontogeny of foraging ecology in Antarctic fur seals (Arctocephalus gazella), a highly dimorphic species with contrasting breeding strategies between sexes. Sequential δ(13)C and δ(15)N values of whiskers provided a longitudinal proxy of the foraging niche throughout the whole life of seals, from weaning, when size dimorphism is minimal to the age of 5. Females exhibited an early-life ontogenetic shift, from a total segregation during their first year at-sea, to a similar isotopic niche as breeding females as early as age 2. In contrast, males showed a progressive change in isotopic niche throughout their development such that 5-year-old males did not share the same niche as territorial bulls. Interestingly, males and females segregated straight after weaning with males appearing to feed in more southerly habitats than females. This spatial segregation was of similar amplitude as observed in breeding adults and was maintained throughout development. Such early-life niche differentiation is an unusual pattern and indicates size dimorphism and breeding constraints do not directly drive sexual segregation contrary to what has been assumed in otariid seals

Complex temporal climate signals drive the emergence of human water-borne disease

Predominantly occurring in developing parts of the world, Buruli ulcer is a severely disabling mycobacterium infection which often leads to extensive necrosis of the skin. While the exact route of transmission remains uncertain, like many tropical diseases, associations with climate have been previously observed and could help identify the causative agent's ecological niche. In this paper, links between changes in rainfall and outbreaks of Buruli ulcer in French Guiana, an ultraperipheral European territory in the northeast of South America, were identified using a combination of statistical tests based on singular spectrum analysis, empirical mode decomposition and cross-wavelet coherence analysis. From this, it was possible to postulate for the first time that outbreaks of Buruli ulcer can be triggered by combinations of rainfall patterns occurring on a long (i.e., several years) and short (i.e., seasonal) temporal scale, in addition to stochastic events driven by the El Nino-Southern Oscillation that may disrupt or interact with these patterns. Long-term forecasting of rainfall trends further suggests the possibility of an upcoming outbreak of Buruli ulcer in French Guiana

Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure