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

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

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

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

Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system

Self-organization in the olfactory system: one shot odor recognition in insects

We show in a model of spiking neurons that synaptic plasticity in the mushroom bodies in combination with the general fan-in, fan-out properties of the early processing layers of the olfactory system might be sufficient to account for its efficient recognition of odors. For a large variety of initial conditions the model system consistently finds a working solution without any fine-tuning, and is, therefore, inherently robust. We demonstrate that gain control through the known feedforward inhibition of lateral horn interneurons increases the capacity of the system but is not essential for its general function. We also predict an upper limit for the number of odor classes Drosophila can discriminate based on the number and connectivity of its olfactory neurons

WAVOS: a MATLAB toolkit for wavelet analysis and visualization of oscillatory systems

<p>Abstract</p> <p>Background</p> <p>Wavelets have proven to be a powerful technique for the analysis of periodic data, such as those that arise in the analysis of circadian oscillators. While many implementations of both continuous and discrete wavelet transforms are available, we are aware of no software that has been designed with the nontechnical end-user in mind. By developing a toolkit that makes these analyses accessible to end users without significant programming experience, we hope to promote the more widespread use of wavelet analysis.</p> <p>Findings</p> <p>We have developed the WAVOS toolkit for wavelet analysis and visualization of oscillatory systems. WAVOS features both the continuous (Morlet) and discrete (Daubechies) wavelet transforms, with a simple, user-friendly graphical user interface within MATLAB. The interface allows for data to be imported from a number of standard file formats, visualized, processed and analyzed, and exported without use of the command line. Our work has been motivated by the challenges of circadian data, thus default settings appropriate to the analysis of such data have been pre-selected in order to minimize the need for fine-tuning. The toolkit is flexible enough to deal with a wide range of oscillatory signals, however, and may be used in more general contexts.</p> <p>Conclusions</p> <p>We have presented WAVOS: a comprehensive wavelet-based MATLAB toolkit that allows for easy visualization, exploration, and analysis of oscillatory data. WAVOS includes both the Morlet continuous wavelet transform and the Daubechies discrete wavelet transform. We have illustrated the use of WAVOS, and demonstrated its utility for the analysis of circadian data on both bioluminesence and wheel-running data. WAVOS is freely available at <url>http://sourceforge.net/projects/wavos/files/</url></p

Multi-Way Multi-Group Segregation and Diversity Indices

Background: How can we compute a segregation or diversity index from a three-way or multi-way contingency table, where each variable can take on an arbitrary finite number of values and where the index takes values between zero and one? Previous methods only exist for two-way contingency tables or dichotomous variables. A prototypical three-way case is the segregation index of a set of industries or departments given multiple explanatory variables of both sex and race. This can be further extended to other variables, such as disability, number of years of education, and former military service. Methodology/Principal Findings: We extend existing segregation indices based on Euclidean distance (square of coefficient of variation) and Boltzmann/Shannon/Theil index from two-way to multi-way contingency tables by including multiple summations. We provide several biological applications, such as indices for age polyethism and linkage disequilibrium. We also provide a new heuristic conceptualization of entropy-based indices. Higher order association measures are often independent of lower order ones, hence an overall segregation or diversity index should be the arithmetic mean of the normalized association measures at all orders. These methods are applicable when individuals selfidentify as multiple races or even multiple sexes and when individuals work part-time in multiple industries. Conclusions/Significance: The policy implications of this work are enormous, allowing people to rigorously test whethe