How predation and landscape fragmentation affect vole population dynamics

Background: Microtine species in Fennoscandia display a distinct north-south gradient from regular cycles to stable populations. The gradient has often been attributed to changes in the interactions between microtines and their predators. Although the spatial structure of the environment is known to influence predator-prey dynamics of a wide range of species, it has scarcely been considered in relation to the Fennoscandian gradient. Furthermore, the length of microtine breeding season also displays a north-south gradient. However, little consideration has been given to its role in shaping or generating population cycles. Because these factors covary along the gradient it is difficult to distinguish their effects experimentally in the field. The distinction is here attempted using realistic agent-based modelling. Methodology/Principal Findings: By using a spatially explicit computer simulation model based on behavioural and ecological data from the field vole (Microtus agrestis), we generated a number of repeated time series of vole densities whose mean population size and amplitude were measured. Subsequently, these time series were subjected to statistical autoregressive modelling, to investigate the effects on vole population dynamics of making predators more specialised, of altering the breeding season, and increasing the level of habitat fragmentation. We found that fragmentation as well as the presence of specialist predators are necessary for the occurrence of population cycles. Habitat fragmentation and predator assembly jointly determined cycle length and amplitude. Length of vole breeding season had little impact on the oscillations. Significance: There is good agreement between our results and the experimental work from Fennoscandia, but our results allow distinction of causation that is hard to unravel in field experiments. We hope our results will help understand the reasons for cycle gradients observed in other areas. Our results clearly demonstrate the importance of landscape fragmentation for population cycling and we recommend that the degree of fragmentation be more fully considered in future analyses of vole dynamics.

An analysis of long-term trends, seasonality and short-term dynamics in water quality data from Plynlimon, Wales

This paper examines two hydrochemical time-series derived from stream samples taken in the Upper Hafren catchment, Plynlimon, Wales. One time-series comprises data collected at 7-hour intervals over 22 months (Neal et al., submitted, this issue), while the other is based on weekly sampling over 20 years. A subset of determinands: aluminium, calcium, chloride, conductivity, dissolved organic carbon, iron, nitrate, pH, silicon and sulphate are examined within a framework of non-stationary time-series analysis to identify determinand trends, seasonality and short-term dynamics. The results demonstrate that both long-term and high-frequency monitoring provide valuable and unique insights into the hydrochemistry of a catchment. The long-term data allowed analysis of long-termtrends, demonstrating continued increases in DOC concentrations accompanied by declining SO4 concentrations within the stream, and provided new insights into the changing amplitude and phase of the seasonality of the determinands such as DOC and Al. Additionally, these data proved invaluable for placing the short-term variability demonstrated within the high-frequency data within context. The 7-hour data highlighted complex diurnal cycles for NO3, Ca and Fe with cycles displaying changes in phase and amplitude on a seasonal basis. The high-frequency data also demonstrated the need to consider the impact that the time of sample collection can have on the summary statistics of the data and also that sampling during the hours of darkness provides additional hydrochemical information for determinands which exhibit pronounced diurnal variability. Moving forward, this research demonstrates the need for both long-term and high-frequency monitoring to facilitate a full and accurate understanding of catchment hydrochemical dynamics.

Stress field control of eruption dynamics at a rift volcano: Nyamuragira, D.R.Congo

Using the record of 30 flank eruptions over the last 110 years at Nyamuragira, we have tested the relationship between the eruption dynamics and the local stress field. There are two groups of eruptions based on their duration (< 80days >) that are also clustered in space and time. We find that the eruptions fed by dykes parallel to the East African Rift Valley have longer durations (and larger volumes) than those eruptions fed by dykes with other orientations. This is compatible with a model for compressible magma transported through an elastic-walled dyke in a differential stress field from an over-pressured reservoir (Woods et al., 2006). The observed pattern of eruptive fissures is consistent with a local stress field modified by a northwest-trending, right lateral slip fault that is part of the northern transfer zone of the Kivu Basin rift segment. We have also re-tested with new data the stochastic eruption models for Nyamuragira of Burt et al. (1994). The time-predictable, pressure-threshold model remains the best fit and is consistent with the typically observed declining rate of sulphur dioxide emission during the first few days of eruption with lava emission from a depressurising, closed, crustal reservoir. The 2.4-fold increase in long-term eruption rate that occurred after 1977 is confirmed in the new analysis. Since that change, the record has been dominated by short-duration eruptions fed by dykes perpendicular to the Rift. We suggest that the intrusion of a major dyke during the 1977 volcano-tectonic event at neighbouring Nyiragongo volcano inhibited subsequent dyke formation on the southern flanks of Nyamuragira and this may also have resulted in more dykes reaching the surface elsewhere. Thus that sudden change in output was a result of a changed stress field that forced more of the deep magma supply to the surface. Another volcano-tectonic event in 2002 may also have changed the magma output rate at Nyamuragira.

Transputer based real time robot control

A parallel processor architecture based on a communicating sequential processor chip, the transputer, is described. The architecture is easily linearly extensible to enable separate functions to be included in the controller. To demonstrate the power of the resulting controller some experimental results are presented comparing PID and full inverse dynamics on the first three joints of a Puma 560 robot. Also examined are some of the sample rate issues raised by the asynchronous updating of inertial parameters, and the need for full inverse dynamics at every sample interval is questioned.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Reconstruction of gusty wind speed time series from autonomous data logger records

The collection of wind speed time series by means of digital data loggers occurs in many domains, including civil engineering, environmental sciences and wind turbine technology. Since averaging intervals are often significantly larger than typical system time scales, the information lost has to be recovered in order to reconstruct the true dynamics of the system. In the present work we present a simple algorithm capable of generating a real-time wind speed time series from data logger records containing the average, maximum, and minimum values of the wind speed in a fixed interval, as well as the standard deviation. The signal is generated from a generalized random Fourier series. The spectrum can be matched to any desired theoretical or measured frequency distribution. Extreme values are specified through a postprocessing step based on the concept of constrained simulation. Applications of the algorithm to 10-min wind speed records logged at a test site at 60 m height above the ground show that the recorded 10-min values can be reproduced by the simulated time series to a high degree of accuracy.

On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

On variational data assimilation in continuous time

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalization of what is known as weakly constrained four-dimensional variational assimilation (4D-Var) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two-point boundary value problem. For imperfect models, the trade-off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. This trade-off turns out to be trivial if the model is perfect. However, even in this situation, allowing for minute deviations from the perfect model is shown to have positive effects, namely to regularize the problem. The presented formalism is dynamical in character. No statistical assumptions on dynamical or observational noise are imposed.

System dynamics mapping of acute patient flows

Department of Health staff wished to use systems modelling to discuss acute patient flows with groups of NHS staff. The aim was to assess the usefulness of system dynamics (SD) in a healthcare context and to elicit proposals concerning ways of improving patient experience. Since time restrictions excluded simulation modelling, a hybrid approach using stock/flow symbols from SD was created. Initial interviews and hospital site visits generated a series of stock/flow maps. A ‘Conceptual Framework’ was then created to introduce the mapping symbols and to generate a series of questions about different patient paths and what might speed or slow patient flows. These materials formed the centre of three workshops for NHS staff. The participants were able to propose ideas for improving patient flows and the elicited data was subsequently employed to create a finalized suite of maps of a general acute hospital. The maps and ideas were communicated back to the Department of Health and subsequently assisted the work of the Modernization Agency.

Real-time multi-model decadal climate predictions

We present the first climate prediction of the coming decade made with multiple models, initialized with prior observations. This prediction accrues from an international activity to exchange decadal predictions in near real-time, in order to assess differences and similarities, provide a consensus view to prevent over-confidence in forecasts from any single model, and establish current collective capability. We stress that the forecast is experimental, since the skill of the multi-model system is as yet unknown. Nevertheless, the forecast systems used here are based on models that have undergone rigorous evaluation and individually have been evaluated for forecast skill. Moreover, it is important to publish forecasts to enable open evaluation, and to provide a focus on climate change in the coming decade. Initialized forecasts of the year 2011 agree well with observations, with a pattern correlation of 0.62 compared to 0.31 for uninitialized projections. In particular, the forecast correctly predicted La Niña in the Pacific, and warm conditions in the north Atlantic and USA. A similar pattern is predicted for 2012 but with a weaker La Niña. Indices of Atlantic multi-decadal variability and Pacific decadal variability show no signal beyond climatology after 2015, while temperature in the Niño3 region is predicted to warm slightly by about 0.5 °C over the coming decade. However, uncertainties are large for individual years and initialization has little impact beyond the first 4 years in most regions. Relative to uninitialized forecasts, initialized forecasts are significantly warmer in the north Atlantic sub-polar gyre and cooler in the north Pacific throughout the decade. They are also significantly cooler in the global average and over most land and ocean regions out to several years ahead. However, in the absence of volcanic eruptions, global temperature is predicted to continue to rise, with each year from 2013 onwards having a 50 % chance of exceeding the current observed record. Verification of these forecasts will provide an important opportunity to test the performance of models and our understanding and knowledge of the drivers of climate change.

Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.

Temporal dynamics of emotional responding: amygdala recovery predicts emotional traits

An individual’s affective style is influenced by many things, including the manner in which an individual responds to an emotional challenge. Emotional response is composed of a number of factors, two of which are the initial reactivity to an emotional stimulus and the subsequent recovery once the stimulus terminates or ceases to be relevant. However, most neuroimaging studies examining emotional processing in humans focus on the magnitude of initial reactivity to a stimulus rather than the prolonged response. In this study, we use functional magnetic resonance imaging to study the time course of amygdala activity in healthy adults in response to presentation of negative images. We split the amygdala time course into an initial reactivity period and a recovery period beginning after the offset of the stimulus. We find that initial reactivity in the amygdala does not predict trait measures of affective style. Conversely, amygdala recovery shows predictive power such that slower amygdala recovery from negative images predicts greater trait neuroticism, in addition to lower levels of likability of a set of social stimuli (neutral faces). These data underscore the importance of taking into account temporal dynamics when studying affective processing using neuroimaging.

Reconciling observed and modelled phytoplankton dynamics in a major lowland UK river system, the Thames

This study aims to elucidate the key mechanisms controlling phytoplankton growth and decay within the Thames basin through the application of a modified version of an established river-algal model and comparison with observed stream water chlorophyll-a concentrations. The River Thames showed a distinct simulated phytoplankton seasonality and behaviour having high spring, moderate summer and low autumn chlorophyll-a concentrations. Three main sections were identified along the River Thames with different phytoplankton abundance and seasonality: (i) low chlorophyll-a concentrations from source to Newbridge; (ii) steep concentration increase between Newbridge and Sutton; and (iii) high concentrations with a moderate increase in concentration from Sutton to the end of the study area (Maidenhead). However, local hydrologic (e.g. locks) and other conditions (e.g. radiation, water depth, grazer dynamics, etc.) affected the simulated growth and losses. The model achieved good simulation results during both calibration and testing through a range of hydrological and nutrient conditions. Simulated phytoplankton growth was controlled predominantly by residence time, but during medium–low flow periods available light, water temperature and herbivorous grazing defined algal community development. These results challenge the perceived importance of in-stream nutrient concentrations as the perceived primary control on phytoplankton growth and death.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

Testing for significance of phase synchronisation dynamics in the EEG

A number of tests exist to check for statistical significance of phase synchronisation within the Electroencephalogram (EEG); however, the majority suffer from a lack of generality and applicability. They may also fail to account for temporal dynamics in the phase synchronisation, regarding synchronisation as a constant state instead of a dynamical process. Therefore, a novel test is developed for identifying the statistical significance of phase synchronisation based upon a combination of work characterising temporal dynamics of multivariate time-series and Markov modelling. We show how this method is better able to assess the significance of phase synchronisation than a range of commonly used significance tests. We also show how the method may be applied to identify and classify significantly different phase synchronisation dynamics in both univariate and multivariate datasets.