Synchronisation and stability in river metapopulation networks

Spatial structure in landscapes impacts population stability. Two linked components of stability have large consequences for persistence: first, statistical stability as the lack of temporal fluctuations; second, synchronisation as an aspect of dynamic stability, which erodes metapopulation rescue effects. Here, we determine the influence of river network structure on the stability of riverine metapopulations. We introduce an approach that converts river networks to metapopulation networks, and analytically show how fluctuation magnitude is influenced by interaction structure. We show that river metapopulation complexity (in terms of branching prevalence) has nonlinear dampening effects on population fluctuations, and can also buffer against synchronisation. We conclude by showing that river transects generally increase synchronisation, while the spatial scale of interaction has nonlinear effects on synchronised dynamics. Our results indicate that this dual stability – conferred by fluctuation and synchronisation dampening – emerges from interaction structure in rivers, and this may strongly influence the persistence of river metapopulations.     

Perception of odors by a nonlinear model of the olfactory bulb

The behavior of the olfactory bulb is modeled as a network of interconnected cells with nonlinear dynamics. External inputs from sensory neurons are introduced as perturbations to subsets of cells within the network. We describe the attractors of the system and show how they can be classified and ordered according to their varying degrees of symmetry. By studying networks of attractors in the system's phase space, it is shown how different perturbations may evoke specific switches between various patterns of behavior. This ensures that different odors, even if present at extremely low concentrations, are able to evoke a specific spatio-temporal behavior in the olfactory bulb, permitting their unique perception. The model incorporates many of the processes proposed to mediate perception, such as the topographic organisation of sensory systems, destabilization of cortex by sensory input and synchronisation between neurons. It is also consistent with the character of the olfactory electroencephalogram.     

Synchronisation effects on the behavioural performance and information dynamics of a simulated minimally cognitive robotic agent

Oscillatory activity is ubiquitous in nervous systems, with solid evidence that synchronisation mechanisms underpin cognitive processes. Nevertheless, its informational content and relationship with behaviour are still to be fully understood. In addition, cognitive systems cannot be properly appreciated without taking into account brain-body- environment interactions. In this paper, we developed a model based on the Kuramoto Model of coupled phase oscillators to explore the role of neural synchronisation in the performance of a simulated robotic agent in two different minimally cognitive tasks. We show that there is a statistically significant difference in performance and evolvability depending on the synchronisation regime of the network. In both tasks, a combination of information flow and dynamical analyses show that networks with a definite, but not too strong, propensity for synchronisation are more able to reconfigure, to organise themselves functionally and to adapt to different behavioural conditions. The results highlight the asymmetry of information flow and its behavioural correspondence. Importantly, it also shows that neural synchronisation dynamics, when suitably flexible and reconfigurable, can generate minimally cognitive embodied behaviour.     

Statistical analysis of in situ hybridization data: derivation and use of the zmax test.

There are many situations in which grain distributions resulting from in situ hybridization of radioactively labeled probes to unique genes should be subjected to a statistical analysis. However, the problems posed by analysis of in situ hybridization data are not straightforward, and no completely satisfying method is currently available. We have developed a procedure in which the major and any number of minor site(s) of hybridization may be specifically located and the significance of each tested. This zmax procedure first tests the overall distribution for departure from randomness and then identifies significantly overlabeled whole chromosomes (or chromosome arms or other large segments), a process that may be repeated to pinpoint significantly overlabeled regions within these chromosomes. We describe in detail the derivation of the zmax statistic, present tables of significant zmax levels, and show with examples how zmax is used in tests of significance of in situ hybridization data.     

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.     

Potential Mechanisms for Imperfect Synchronization in Parkinsonian Basal Ganglia

Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinson''s disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson''s disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson''s disease.     

Coordination and synchronisation of anti-predation vigilance in two crane species

Much of the previous research on anti-predation vigilance in groups has assumed independent scanning for threats among group members. Alternative patterns that are based on monitoring the vigilance levels of companions can also be adaptive. Coordination of vigilance, in which foragers avoid scanning at the same time as others, should decrease the odds that no group member is alert. Synchronisation of vigilance implies that individuals are more likely to be vigilant when companions are already vigilant. While synchronisation will increase the odds that no one is vigilant, it may allow a better assessment of potential threats. We investigated temporal sequences of vigilance in family flocks consisting of two parents and at most two juveniles in two species of cranes in coastal China. We established whether the observed probability that at least one parent is alert was greater (coordination) or lower (synchronisation) than that predicted under the null hypothesis of independent vigilance. We documented coordination of vigilance in common cranes (Grus grus) foraging in an area with high potential for disturbance by people. We documented synchronisation of vigilance in red-crowned cranes (Grus japonensis) in the less but not in the more disturbed area. Coordination in small flocks leads to high collective vigilance but low foraging rates that may not be suitable in areas with low disturbance. We also argue that synchronisation should break down in areas with high disturbance because periods with low vigilance are riskier. Results highlight the view that temporal patterns of vigilance can take many forms depending on ecological factors.     

Periodic synchronisation of dengue epidemics in Thailand over the last 5 decades driven by temperature and immunity

The spatial distribution of dengue and its vectors (spp. Aedes) may be the widest it has ever been, and projections suggest that climate change may allow the expansion to continue. However, less work has been done to understand how climate variability and change affects dengue in regions where the pathogen is already endemic. In these areas, the waxing and waning of immunity has a large impact on temporal dynamics of cases of dengue haemorrhagic fever. Here, we use 51 years of data across 72 provinces and characterise spatiotemporal patterns of dengue in Thailand, where dengue has caused almost 1.5 million cases over the last 30 years, and examine the roles played by temperature and dynamics of immunity in giving rise to those patterns. We find that timescales of multiannual oscillations in dengue vary in space and time and uncover an interesting spatial phenomenon: Thailand has experienced multiple, periodic synchronisation events. We show that although patterns in synchrony of dengue are similar to those observed in temperature, the relationship between the two is most consistent during synchronous periods, while during asynchronous periods, temperature plays a less prominent role. With simulations from temperature-driven models, we explore how dynamics of immunity interact with temperature to produce the observed patterns in synchrony. The simulations produced patterns in synchrony that were similar to observations, supporting an important role of immunity. We demonstrate that multiannual oscillations produced by immunity can lead to asynchronous dynamics and that synchrony in temperature can then synchronise these dengue dynamics. At higher mean temperatures, immune dynamics can be more predominant, and dengue dynamics more insensitive to multiannual fluctuations in temperature, suggesting that with rising mean temperatures, dengue dynamics may become increasingly asynchronous. These findings can help underpin predictions of disease patterns as global temperatures rise.

This study shows that spatially large-scale shifts in temperature can synchronize dengue dynamics across Thailand; however, as average temperatures rise, dengue dynamics may increasingly be dictated by dynamics of immunity, which may in turn mean fewer synchronous outbreaks in the future.     

Detection of phase shifts in batch fermentation via statistical analysis of the online measurements: a case study with rifamycin B fermentation

Industrial production of antibiotics, biopharmaceuticals and enzymes is typically carried out via a batch or fed-batch fermentation process. These processes go through various phases based on sequential substrate uptake, growth and product formation, which require monitoring due to the potential batch-to-batch variability. The phase shifts can be identified directly by measuring the concentrations of substrates and products or by morphological examinations under microscope. However, such measurements are cumbersome to obtain. We present a method to identify phase transitions in batch fermentation using readily available online measurements. Our approach is based on Dynamic Principal Component Analysis (DPCA), a multivariate statistical approach that can model the dynamics of non-stationary processes. Phase-transitions in fermentation produce distinct patterns in the DPCA scores, which can be identified as singular points. We illustrate the application of the method to detect transitions such as the onset of exponential growth phase, substrate exhaustion and substrate switching for rifamycin B fermentation batches. Further, we analyze the loading vectors of DPCA model to illustrate the mechanism by which the statistical model accounts for process dynamics. The approach can be readily applied to other industrially important processes and may have implications in online monitoring of fermentation batches in a production facility.     

Baseline requirements for assessment of mining impact using biological monitoring

Abstract Biological monitoring programmes for environmental protection should provide for both early detection of possible adverse effects, and assessment of the ecological significance of these effects. Monitoring techniques are required that include responses sensitive to the impact, that can be subjected to rigorous statistical analysis and for which statistical power is high. Such issues in baseline research of‘what and how to measure?’and‘for how long?’have been the focus of a programme being developed to monitor and assess effects of mining operations on the essentially pristine, freshwater ecosystems of the Alligator Rivers Region (ARR) in tropical northern Australia. Application of the BACIP (Before, After, Control, Impact, Paired differences) design, utilizing a form of temporal replication, to univariate (single species) and multivariate (community) data is described. The BACIP design incorporates data from single control and impact sites. We argue for modification of the design for particular studies conducted in streams, to incorporate additional independent control sites from adjacent catchments. Inferential power, by way of (i) more confidently attributing cause to an observed change and (ii) providing information about the ecological significance of the change, will be enhanced using a modified BACIP design. In highly valued environments such as the ARR, monitoring programmes require application of statistical tests with high power to guarantee that an impact no greater than a prescribed amount has gone undetected. A minimum number of baseline years using the BACIP approach would therefore be required in order to achieve some desired level of statistical power. We describe the results of power analyses conducted on 2–5 years (depending upon the technique) of baseline data from streams of the ARR and discuss the implications of these results for management.     

A Comparison of Aggregate P-Value Methods and Multivariate Statistics for Self-Contained Tests of Metabolic Pathway Analysis

For pathway analysis of genomic data, the most common methods involve combining p-values from individual statistical tests. However, there are several multivariate statistical methods that can be used to test whether a pathway has changed. Because of the large number of variables and pathway sizes in genomics data, some of these statistics cannot be computed. However, in metabolomics data, the number of variables and pathway sizes are typically much smaller, making such computations feasible. Of particular interest is being able to detect changes in pathways that may not be detected for the individual variables. We compare the performance of both the p-value methods and multivariate statistics for self-contained tests with an extensive simulation study and a human metabolomics study. Permutation tests, rather than asymptotic results are used to assess the statistical significance of the pathways. Furthermore, both one and two-sided alternatives hypotheses are examined. From the human metabolomic study, many pathways were statistically significant, although the majority of the individual variables in the pathway were not. Overall, the p-value methods perform at least as well as the multivariate statistics for these scenarios.     

Tests for density dependence revisited

We have examined a number of statistical issues associated with methods for evaluating different tests of density dependence. The lack of definitive standards and benchmarks for conducting simulation studies makes it difficult to assess the performance of various tests. The biological researcher has a bewildering choice of statistical tests for testing density dependence and the list is growing. The most recent additions have been based on computationally intensive methods such as permutation tests and boot-strapping. We believe the computational effort and time involved will preclude their widespread adoption until: (1) these methods have been fully explored under a wide range of conditions and shown to be demonstrably superior than other, simpler methods, and (2) general purpose software is made available for performing the calculations. We have advocated the use of Bulmer's (first) test as a de facto standard for comparative studies on the grounds of its simplicity, applicability, and satisfactory performance under a variety of conditions. We show that, in terms of power, Bulmer's test is robust to certain departures from normality although, as noted by other authors, it is affected by temporal trends in the data. We are not convinced that the reported differences in power between Bulmer's test and the randomisation test of Pollard et al. (1987) justifies the adoption of the latter. Nor do we believe a compelling case has been established for the parametric bootstrap likelihood ratio test of Dennis and Taper (1994). Bulmer's test is essentially a test of the serial correlation in the (log) abundance data and is affected by the presence of autocorrelated errors. In such cases the test cannot distinguish between the autoregressive effect in the errors and a true density dependent effect in the time series data. We suspect other tests may be similarly affected, although this is an area for further research. We have also noted that in the presence of autocorrelation, the type I error rates can be substantially different from the assumed level of significance, implying that in such cases the test is based on a faulty significance region. We have indicated both qualitatively and quantitatively how autoregressive error terms can affect the power of Bulmer's test, although we suggest that more work is required in this area. These apparent inadequacies of Bulmer's test should not be interpreted as a failure of the statistical procedure since the test was not intended to be used with autocorrelated error terms.     

Testing quantitative traits for association and linkage in the presence or absence of parental data

Zhu and Elston developed a transmission disequilibrium test for quantitative traits by defining a linear transformation to condition out founder information. The method tests the null hypothesis of no linkage or association and can be applied to general pedigree structures. However, this method requires both genotype and phenotype parental information, which may be difficult to obtain. In this paper, we describe parametric and non-parametric methods to relax this requirement when only nuclear families are sampled. We show that neither method is affected by population stratification in the absence of linkage. The statistical power and validity of the tests are investigated by simulation. A simple simulation method to calculate the power of the nonparametric method is also discussed. In practice, the data may have some families with parental phenotype and genotype information available and some without. We briefly discuss how all the data may be analyzed jointly.     

Phylogenetic ANOVA: Group‐clade aggregation,biological challenges,and a refined permutation procedure

Phylogenetic regression is frequently used in macroevolutionary studies, and its statistical properties have been thoroughly investigated. By contrast, phylogenetic ANOVA has received relatively less attention, and the conditions leading to incorrect statistical and biological inferences when comparing multivariate phenotypes among groups remain underexplored. Here, we propose a refined method of randomizing residuals in a permutation procedure (RRPP) for evaluating phenotypic differences among groups while conditioning the data on the phylogeny. We show that RRPP displays appropriate statistical properties for both phylogenetic ANOVA and regression models, and for univariate and multivariate datasets. For ANOVA, we find that RRPP exhibits higher statistical power than methods utilizing phylogenetic simulation. Additionally, we investigate how group dispersion across the phylogeny affects inferences, and reveal that highly aggregated groups generate strong and significant correlations with the phylogeny, which reduce statistical power and subsequently affect biological interpretations. We discuss the broader implications of this phylogenetic group aggregation, and its relation to challenges encountered with other comparative methods where one or a few transitions in discrete traits are observed on the phylogeny. Finally, we recommend that phylogenetic comparative studies of continuous trait data use RRPP for assessing the significance of indicator variables as sources of trait variation.     

distantia: an open-source toolset to quantify dissimilarity between multivariate ecological time-series

There is a large array of methods to extract knowledge and perform ecological forecasting from ecological time-series. However, in spite of its importance for data-mining, pattern-matching and ecological synthesis, methods to assess their similarity are scarce. We introduce distantia (v1.0.1), an R package providing general toolset to quantify dissimilarity between ecological time-series, independently of their regularity and number of samples. The functions in distantia provide the means to compute dissimilarity scores by time and by shape and assess their significance, evaluate the partial contribution of each variable to dissimilarity, and align or combine sequences by similarity. We evaluate the sensitivity of the dissimilarity metrics implemented in distantia, describe its structure and functionality, and showcase its applications with two examples. Particularly, we evaluate how geographic factors drive the dissimilarity between nine pollen sequences dated to the Last Interglacial, and compare the temporal dynamics of climate and enhanced vegetation index of three stands across the range of the European beech. We expect this package may enhance the capabilities of researchers from different fields to explore dissimilarity patterns between multivariate ecological time-series, and aid in generating and testing new hypotheses on why the temporal dynamics of complex-systems changes over space and time.     

Partitioning the variation among spatial,temporal and environmental components in a multivariate data set

Abstract We propose a method of partitioning the variation in a multivariate set of data according to (i) environmental variables, (ii) variables describing the spatial structure in the data and (iii) temporal variables. This method is an extension of an existing method for partialling out the spatial component of environmental variation, using canonical analysis. Our proposed method extends this approach by including temporal variables in the analysis. Thus, the partitioning of variation for a data matrix of species’abundances or biomass can include, by our methodology, the following components: (1) pure environmental, (2) pure spatial, (3) pure temporal, (4) pure spatial component of environmental, (5) pure temporal component of environmental, (6) pure combined spatial/temporal component, (7) combined spatial/temporal component of environmental and (8) unexplained. In addition, permutation testing accompanying the analyses allows tests of significance for the relationship between the different components and the species data. We illustrate the method with a set of survey data of penaeid species (prawns) obtained on the far northern Great Barrier Reef, Australia. This extension is a useful tool for multivariate analysis of ecological data from surveys, where space, time and environment commonly overlap and are important influences on observed variation.     

Risky Business: Temporal and Spatial Variation in Preindustrial Dryland Agriculture

Traditional dryland agriculture in the Pacific island was often labor-intensive and risky, yet settlement and farming in dry areas played an important role in the development of Polynesian societies. We investigate how temporal and spatial climatic fluctuations shape variation in agricultural production across dryland landscapes. We use a model that couples plant growth, climate, and soil organic matter dynamics, together with data from Kohala, Hawai'i, to understand how temperature, rainfall, nitrogen availability, and cropping activity interact to determine yield dynamics through time and space. Due to these interactions, the statistical characterization of rainfall alone is a poor characterization of agricultural yield. Using a simple linear model of human population dynamics, we show that the observed yield variation can affect long-term population growth substantially. Our approach to analyzing spatial and temporal fluctuations in food supply, and to interpreting the population consequences of these fluctuations, provides a quantitative evaluation of agricultural risk and human carrying capacity in dry regions.     

Temporal coding: the relevance of classical activity, its relation to pattern frequency bands, and a remark on recoding of excitatory drive into phase shifts

We consider an oscillatory network model that is obtained as complex-valued generalization of the classical Cohen-Grossberg-Hopfield (CGH) model. Apart from a synchronizing mechanism, a stronger and/or more coherent input to a unit in the network implies a higher phase velocity of this unit. This constitutes the desynchronizing mechanism, referred to as acceleration. The units' activity of the classical model translates into the amplitudes of the phase model oscillators. This allows to associate classical and temporal coding with amplitude and phase dynamics, respectively. We discuss how the two dynamics act together to achieve the unambiguous pattern recognition that avoids the superposition problem. With respect to coherence, dominating patterns may take coherent states also if only a subset of its units is on-state. The competition for coherence, introduced by acceleration, realizes a kind of feature counting that identifies the dominating pattern as the pattern with the most on-state units. This dominating but possibly only partially active pattern may take a coherent state with a frequency level that is related to the number of on-state units. We also speculate on neurophysiological findings, related to observed phase differences between optimally and suboptimally activated neurons, that may indicate the presence of acceleration.     

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein–Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.     

Evaluating the improvement in diagnostic utility from adding new predictors

Multiple diagnostic tests and risk factors are commonly available for many diseases. This information can be either redundant or complimentary. Combining them may improve the diagnostic/predictive accuracy, but also unnecessarily increase complexity, risks, and/or costs. The improved accuracy gained by including additional variables can be evaluated by the increment of the area under (AUC) the receiver‐operating characteristic curves with and without the new variable(s). In this study, we derive a new test statistic to accurately and efficiently determine the statistical significance of this incremental AUC under a multivariate normality assumption. Our test links AUC difference to a quadratic form of a standardized mean shift in a unit of the inverse covariance matrix through a properly linear transformation of all diagnostic variables. The distribution of the quadratic estimator is related to the multivariate Behrens–Fisher problem. We provide explicit mathematical solutions of the estimator and its approximate non‐central F‐distribution, type I error rate, and sample size formula. We use simulation studies to prove that our new test maintains prespecified type I error rates as well as reasonable statistical power under practical sample sizes. We use data from the Study of Osteoporotic Fractures as an application example to illustrate our method.