Estimating malaria transmission from humans to mosquitoes in a noisy landscape

A basic quantitative understanding of malaria transmission requires measuring the probability a mosquito becomes infected after feeding on a human. Parasite prevalence in mosquitoes is highly age-dependent, and the unknown age-structure of fluctuating mosquito populations impedes estimation. Here, we simulate mosquito infection dynamics, where mosquito recruitment is modelled seasonally with fractional Brownian noise, and we develop methods for estimating mosquito infection rates. We find that noise introduces bias, but the magnitude of the bias depends on the ‘colour' of the noise. Some of these problems can be overcome by increasing the sampling frequency, but estimates of transmission rates (and estimated reductions in transmission) are most accurate and precise if they combine parity, oocyst rates and sporozoite rates. These studies provide a basis for evaluating the adequacy of various entomological sampling procedures for measuring malaria parasite transmission from humans to mosquitoes and for evaluating the direct transmission-blocking effects of a vaccine.

Populations embedded in trophic communities respond differently to coloured environmental noise

Noise in environmental variables is often described as 'coloured', where colour describes the exponent beta of the scaling relationship between the amplitude of variability and its frequency of occurrence (1/f(beta)). Different environments are known to have different colours and models have shown that colour can have important impacts upon population persistence and dynamics. This study advances current knowledge about the impact of environmental colour using a trophic model (consumer-resource) experiencing environmental noise (temperature) in a biologically realistic manner--derived mechanistically from metabolic scaling theory. The model demonstrates that the variability of consumers and resources can respond differently to changing environmental colour, depending upon (i) their relative ability to track and over or undercompensate for environmental changes and (ii) the relative sensitivity of their equilibria to environmental changes. These results form the basis with which to interpret differences and facilitate comparisons of the variability of ecological communities across gradients of environmental colour.

Entropy of seismic electric signals: analysis in natural time under time reversal

Electric signals have been recently recorded at the Earth's surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that of a "uniform" distribution. The same holds for their entropy upon time reversal. Such a behavior, which is also found by numerical simulations in fractional Brownian motion time series and in an on-off intermittency model, stems from infinitely ranged long range temporal correlations and hence these signals are probably seismic electric signal activities (critical dynamics). This classification is strikingly confirmed since three strong nearby earthquakes occurred (which is an extremely unusual fact) after the original submission of the present paper. The entropy fluctuations are found to increase upon approaching bursting, which is reminiscent of the behavior identifying sudden cardiac death individuals when analyzing their electrocardiograms.

The impact of environmental fluctuations on structured discrete time population models: Resonance, synchrony and threshold behaviour

External forcing of a discrete time ecological system does not just add variation to existing dynamics but can change the dynamics. We study the mechanisms that can bring this about, focusing on the key concepts of excitation and suppression which emerge when analysing the power spectra of the system in linear approximation. Excitation, through resonance between the system dynamics and the external forcing, is the greater the closer the system is to the boundary of the stability region. This amplification means that the extinction of populations becomes possible sooner than expected and, conversely, invasion can be significantly delayed. Suppression and the consequent redistribution of power within the spectrum proves to be a function both of the connectivity of the network graph of the system and the way that external forcing is applied to the system. It is also established that colour in stochastic forcing can have a major impact, by enhancing resonance and by greater redistribution of power. This can mean a higher risk of extinction through larger fluctuations in population numbers and a higher degree of synchrony between populations. The implications of external forcing for stage-structured species, for populations in competition and for trophic web systems are studied using the tools and concepts developed in the paper.

Signature of on-off intermittency in measured signals

On-off intermittency is a phase-space mechanism that allows dynamical systems to undergo bursting. As its name suggests, bursting is a phenomenon in which episodes of high activity are alternated with periods of inactivity. Here we attempt to see whether we can tell from the output of a signal when an observed bursting behavior is caused by the presence of on-off intermittency, using the example of a forced logistic map. The results of our study indicate that on-off intermittency can be readily distinguished from other mechanisms for bursting we know of, except for one. Many statistical properties of finite-length signals generated by on-off intermittency can in fact be mimicked by the output of a nonlinearly filtered, linear autoregressive random process.

Data estimation and the colour of time series

There has been a long debate on the source of temporal fluctuations in natural population densities. The difficulty is that unpredictable irregularities might be attributed either to external environmental factors or to chaotic dynamics of populations, or even to the interaction of these two factors. Some years ago Cohen (1995) pointed out that real time series follow redshifted Fourier power spectra, while the simplest chaotic population dynamical models are mostly blueshifted. Since then, the controversy has focused on comparisons of Fourier spectra originating from different models and data. Here, we show experimentally that estimation process by human observers shifts power spectra to the red. This result implies that because of estimation distortion, real population data must be less redshifted than many recorded time series suggest.