Evolution towards oscillation or stability in a predator–prey system

We studied a prey–predator system in which both species evolve. We discuss here the conditions that result in coevolution towards a stable equilibrium or towards oscillations. First, we show that a stable equilibrium or population oscillations with small amplitude is likely to occur if the prey''s (host''s) defence is effective when compared with the predator''s (parasite''s) attacking ability at equilibrium, whereas large-amplitude oscillations are likely if the predator''s (parasite''s) attacking ability exceeds the prey''s (host''s) defensive ability. Second, a stable equilibrium is more likely if the prey''s defensive trait evolves faster than the predator''s attack trait, whereas population oscillations are likely if the predator''s trait evolves faster than that of the prey. Third, when the adaptation rates of both species are similar, the amplitude of the fluctuations in their abundances is small when the adaptation rate is either very slow or very fast, but at an intermediate rate of adaptation the fluctuations have a large amplitude. We also show the case in which the prey''s abundance and trait fluctuate greatly, while those of the predator remain almost unchanged. Our results predict that populations and traits in host–parasite systems are more likely than those in prey–predator systems to show large-amplitude oscillations.     

Contactless passive diagnosis for brain intracranial applications: A study using dielectric matching materials

A prototype system for passive intracranial monitoring using microwave radiometry is proposed. It comprises an ellipsoidal conductive wall cavity to achieve beamforming and focusing, in conjunction with sensitive multiband receivers for detection. The system has already shown the capability to provide temperature and/or conductivity variations in phantoms and biological tissue. In this article, a variant of the initially constructed modality is theoretically and experimentally investigated. Specifically, dielectric matching materials are used in an effort to improve the system's focusing attributes. The theoretical study investigates the effect of dielectric matching materials on the system's detection depth, whereas measurements with phantoms focus on the investigation of the system's detection level and spatial resolution. The combined results suggest that the dielectric matching layers lead to the improvement of the system's detection depth and temperature detection level. Also, the system's spatial resolution is explored at various experimental setups. Theoretical and experimental results conclude that with the appropriate combination of operation frequencies and dielectric layers, it is possible to monitor areas of interest inside human head models with a variety of detection depths and spatial resolutions. Bioelectromagnetics 31:335–349, 2010. © 2010 Wiley‐Liss, Inc.     

External drive to inhibitory cells induces alternating episodes of high- and low-amplitude oscillations

Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with episodes of low amplitude. Despite the widespread occurrence of amplitude fluctuations in many frequency bands and brain regions, the mechanisms by which they are generated are poorly understood. Here, we show that irregular transitions between sub-second episodes of high- and low-amplitude oscillations in the alpha/beta frequency band occur in a generic neuronal network model consisting of interconnected inhibitory and excitatory cells that are externally driven by sustained cholinergic input and trains of action potentials that activate excitatory synapses. In the model, we identify the action potential drive onto inhibitory cells, which represents input from other brain areas and is shown to desynchronize network activity, to be crucial for the emergence of amplitude fluctuations. We show that the duration distributions of high-amplitude episodes in the model match those observed in rat prefrontal cortex for oscillations induced by the cholinergic agonist carbachol. Furthermore, the mean duration of high-amplitude episodes varies in a bell-shaped manner with carbachol concentration, just as in mouse hippocampus. Our results suggest that amplitude fluctuations are a general property of oscillatory neuronal networks that can arise through background input from areas external to the network.     

UNDAMPED OSCILLATIONS OF PYRIDINE NUCLEOTIDE AND OXYGEN TENSION IN CHEMOSTAT CULTURES OF KLEBSIELLA AEROGENES

Klebsiella aerogenes was grown in chemostat culture with the pH controlled to ±0.01 and temperature to ±0.1°C. The oxygen tension of the culture was regulated by changing the partial pressure of oxygen in the gas phase and recorded by means of an oxygen electrode. Reduced pyridine nucleotide was monitored continuously in the culture by means of direct fluorimetry. On applying an anaerobic shock to the culture, damped oscillations in pyridine nucleotide fluorescence were obtained. Further anaerobic shocks decreased the damping and eventually gave rise to undamped oscillations of a 2–3 min period which continued for several days. These oscillations were paralleled by oscillations of the same frequency in respiration rate. The amplitude of the oscillations in the respiration rate was equivalent to only 1% of the total steady-state respiration, whereas that of pyridine nucleotide oscillations was equivalent to 10% of the total aerobic/anaerobic fluorescence response. The oscillations ceased on interrupting the glucose feed but restarted on adding excess glucose to the culture. Addition of succinate also restarted the oscillations so that they appear not to be of glycolytic origin. The frequency of oscillations varied with growth rate and conditions. Oscillations of much lower frequency were obtained under limited-oxygen and anaerobic conditions than under fully aerobic conditions. Under glucose-limited conditions, fluctuations were found in adenosine triphosphate (ATP) content which were in phase with the pyridine nucleotide oscillations, but under nitrogen-limited growth conditions no such fluctuations in ATP were observed. The primary oscillating pathway could not be identified but the mechanism would appear to be quite different from that involved in oscillations observed in yeast cells. The synchronization of oscillations and observations of negative damping could be explained by a syntalysis effect.     

Natural,Persistent Oscillations in a Spatial Multi-Strain Disease System with Application to Dengue

Many infectious diseases are not maintained in a state of equilibrium but exhibit significant fluctuations in prevalence over time. For pathogens that consist of multiple antigenic types or strains, such as influenza, malaria or dengue, these fluctuations often take on the form of regular or irregular epidemic outbreaks in addition to oscillatory prevalence levels of the constituent strains. To explain the observed temporal dynamics and structuring in pathogen populations, epidemiological multi-strain models have commonly evoked strong immune interactions between strains as the predominant driver. Here, with specific reference to dengue, we show how spatially explicit, multi-strain systems can exhibit all of the described epidemiological dynamics even in the absence of immune competition. Instead, amplification of natural stochastic differences in disease transmission, can give rise to persistent oscillations comprising semi-regular epidemic outbreaks and sequential dominance of dengue''s four serotypes. Not only can this mechanism explain observed differences in serotype and disease distributions between neighbouring geographical areas, it also has important implications for inferring the nature and epidemiological consequences of immune mediated competition in multi-strain pathogen systems.     

Chaos and evolution

There is growing interest in applying nonlinear methods to evolutionary biology. With good reason: the living world is full of nonlinearities, responsible for steady states, regular oscillations, and chaos in biological systems. Evolutionists may find nonlinear dynamics important in studying short-term dynamics of changes in genotype frequency, and in understanding selection and its constraints. More speculatively, dynamical systems theory may be important because nonlinear fluctuations in some traits may sometimes be favored by selection, and because some long-run patterns of evolutionary change could be described using these methods.     

Low-frequency oscillation of instantaneous heart rate in newly hatched chicks

Instantaneous heart rate (IHR) of chickens began to fluctuate on days 13-14 of incubation and heart rate (HR) fluctuations became augmented towards hatching and increased further after hatching. IHR fluctuations of newly hatched chicks have been categorized into three types: type I HR variability (HRV), which is high-frequency oscillation; type II HRV, which is low-frequency oscillation; and type III HR irregularities (HRI), which are irregular HR accelerations. The present experiment was carried out to investigate the origin of type II HR oscillations. Following previous evidence, we assumed that the low-frequency oscillation of HR in newly hatched chicks was related to thermoregulation and changed by environmental temperature. Eventually, type II HRV was produced or augmented by exposure of hatchlings to lowered ambient temperature and was abolished by exposure to elevated environmental temperature. The hatchlings that were exposed to large temperature decreases tended to increase their HR more than those exposed to small temperature decreases, and vice versa. The HR oscillation accompanied by an elevation of HR baseline in response to cooling may be a phenomenon related to thermoregulation in chick hatchlings.     

Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model

Hormone-induced oscillations of the free intracellular calcium concentration are thought to be relevant for frequency encoding of hormone signals. In liver cells, such Ca2+ oscillations occur in response to stimulation by hormones acting via phosphoinositide breakdown. This observation may be explained by cooperative, positive feedback of Ca2+ on its own release from one inositol 1,4,5-trisphosphate-sensitive pool, obviating oscillations of inositol 1,4,5-trisphosphate. The kinetic rate laws of the associated model have a mathematical structure reminiscent of the Brusselator, a hypothetical chemical model involving a rather improbable trimolecular reaction step, thus giving a realistic biological interpretation to this hallmark of dissipative structures. We propose that calmodulin is involved in mediating this cooperativity and positive feedback, as suggested by the presented experiments. For one, hormone-induced calcium oscillations can be inhibited by the (nonphenothiazine) calmodulin antagonists calmidazolium or CGS 9343 B. Alternatively, in cells overstimulated by hormone, as characterized by a non-oscillatory elevated Ca2+ concentration, these antagonists could again restore sustained calcium oscillations. The experimental observations, including modulation of the oscillations by extracellular calcium, were in qualitative agreement with the predictions of our mathematical model.     

Incubation Temperature and Substrate Quality Modulate Sporulation by Aquatic Hyphomycetes

Frequency and amplitude of temperature oscillations can profoundly affect structure and function of ecosystems. Unless the rate of a biological process changes linearly within the range of these fluctuations, the cumulative effect of temperature differs from the effect measured at the average temperature (Jensen's inequality). Here, we measured numbers and types of spores released by aquatic hyphomycetes from oak and alder leaves that had been exposed in a Portuguese stream for between 7 and 94 days. Recovered leaves were incubated at four temperatures between 5 and 20 °C. Over this range, the sporulation response to temperature was decelerating, with an estimated optimum around 12.5 °C. Assuming a linear response, therefore, overestimates spore release from decaying leaves. The calculated discrepancy was more pronounced with recalcitrant oak leaves (greater toughness, phenolics concentration, lower N and P concentration than alder), and reached 26.6 % when temperature was assumed to oscillate between 1 and 9 °C, rather than remaining constant at 5 °C. The maximum fluctuation of water temperature over 48 h during the field experiment was approximately 3 °C, which would result in a discrepancy of up to 6 %. The composition of the fungal community (assessed by species identification of released spores) was significantly influenced by the state of decomposition, but not by leaf species or temperature. When quantifying the potential impact of global change on aquatic fungal communities, the average increase as well as fluctuations of the temperature have to be considered.     

Pom1 gradient buffering through intermolecular auto‐phosphorylation

Concentration gradients provide spatial information for tissue patterning and cell organization, and their robustness under natural fluctuations is an evolutionary advantage. In rod‐shaped Schizosaccharomyces pombe cells, the DYRK‐family kinase Pom1 gradients control cell division timing and placement. Upon dephosphorylation by a Tea4‐phosphatase complex, Pom1 associates with the plasma membrane at cell poles, where it diffuses and detaches upon auto‐phosphorylation. Here, we demonstrate that Pom1 auto‐phosphorylates intermolecularly, both in vitro and in vivo, which confers robustness to the gradient. Quantitative imaging reveals this robustness through two system's properties: The Pom1 gradient amplitude is inversely correlated with its decay length and is buffered against fluctuations in Tea4 levels. A theoretical model of Pom1 gradient formation through intermolecular auto‐phosphorylation predicts both properties qualitatively and quantitatively. This provides a telling example where gradient robustness through super‐linear decay, a principle hypothesized a decade ago, is achieved through autocatalysis. Concentration‐dependent autocatalysis may be a widely used simple feedback to buffer biological activities.     

Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms.

In this paper theoretical and experimental evidence is presented which indicates that oscillations in internal calcium and cyclic AMP concentrations due to an instability in their common control loops are possible and indeed may be widespread. Further, it is demonstrated that fluctuations in various cellular properties, in particular membrane potential, are a direct consequence of these second messenger oscillations. Given the central importance of calcium and cyclic AMP to the regulation of metabolism, these oscillations would influence most metabolic processes especially rhythmic behaviour. We propose that these oscillations form the basis of several biological rhythms including, potential oscillations in cardiac pacemaker cells, neurones and insulin secreting β-cells, the minute rhythm in smooth muscle, cyclic AMP pulses in Dictyostelium, rhythmical cytoplasmic streaming in Physarum and transepitheliel potential oscillations in Calliphora salivary gland. This model makes possible an explanation of the frequency and amplitude effects of hormones.     

The role of the circadian system in fractal neurophysiological control

Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations – similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation.     

Uncertainty and predictability in population dynamics of a bitrophic ecological model: Mixed-mode oscillations,bistability and sensitivity to parameters

We consider a two-trophic ecological model comprising of two predators competing for their common prey. We cast the model into the framework of a singular perturbed system of equations in one fast variable (prey population density) and two slow variables (predator population densities), mimicking the common observation that the per-capita productivity rate decreases from bottom to top along the trophic levels in Nature. We assume that both predators exhibit Holling II functional response with one of the predators (territorial) having a density dependent mortality rate. Depending on the system parameters, the model exhibits small, intermediate and/or large fluctuations in the population densities. The large fluctuations correspond to periodic population outbreaks followed by collapses (commonly known as cycles of “boom and bust”). The small fluctuations arise due to a singular Hopf bifurcation in the system, and are ecologically more desirable. However, more interestingly, the system exhibits mixed-mode oscillations (which are concatenations of the large amplitude oscillations and the small amplitude oscillations) that indicate the adaptability of the species to prolong the time gap between successive cycles of boom and bust. Numerical simulations are carried out to demonstrate the extreme sensitivity of the system to initial conditions (chaos and bistability of limit cycles are observed) as well as to the system parameters (here we only show the sensitivity to the density dependent mortality rate of the territorial predator). This model throws light at the uncertainties in long term behaviors that are associated with a real ecological system. We show that even very small changes in the system parameters due to natural or human-induced causes can lead to a complete different ecological phenomenon, thus affecting the predictability of the density of the prey population. In this paper, we explain the mechanisms behind the irregular fluctuations in the population sizes in an attempt to understand the dynamics occurring in a natural population and also comment on the inherent uncertainties associated with the system.     

Climatic impacts on the vegetation of eastern North America during the past 2000 years

Pollen diagrams from seven lakes with annually laminated sediments sampled at 40-year intervals are analyzed to isolate the climatic effects from other effects on the long-term dynamics of vegetation during the past 1000–2000 years along a transect from Maine to Minnesota. Principal components analysis is used to reduce the dimensionality of the pollen data. The pollen records from all lakes show long-term trends, medium frequency oscillations, and higher frequency fluctuations. The long-term trend is associated with the neoglacial expansion of the boreal forest. The mechanism causing this replacement is a change in frequency of air masses in the area. The medium-frequency oscillations are also associated with climate changes, the most recent of which is the ‘Little Ice Age’. The climate-related mechanism causing the medium-frequency changes may be changes in disturbance frequency. The higher frequency fluctuations may also be related to disturbance. This analysis of pollen diagrams into time scales of variation has enabled the separation of climate from other factors affecting vegetation dynamics. By comparing the principal components across a transect of sites it proved possible to interpret the climatic effects on vegetation at most sites and not only at range boundaries and ‘sensitive’ sites.     

On estimating the probability of aperiodic outbursts of microbial populations from their fluctuating counts

The irregular sequence of counts of a microbial population, in the absence of observable corresponding environmental changes (e.g., temperature), can be regarded as reflecting the interplay of several unknown or random factors that favor or inhibit growth. Since these factors tend to balance one another, the fluctuations usually remain within bounds, and only by a coincidence—when all or most act in unison—does an ‘outburst’ occur. This situation can be represented mathematically as a sequence of independent random variables governed by a probability distribution. The concept was applied to reported microbial counts of ground meat and wastewater. It is found that the lognormal distribution could serve as a model, and that simulations from this model are indistinguishable from actual records. The parameters of the lognormal (or other) distribution can then be used to estimate the probability of a population outburst, i.e., an increase above a given threshold. Direct estimation of the outburst probability based on frequency of occurrence is also possible, but in some situations requires an impractically large number of observations. We compare the efficiency of these two methods of estimation. Such methods enable translation of irregular records of microbial counts into actual probabilities of an outburst of a given magnitude. Thus, if the environment remains ’stable’ or in dynamic equilibrium, the fluctuations should not be regarded merely as noise, but as a source of information and an indicator of potential population outbursts even where obvious signs do not exist.     

The costs of phenotypic adaptation to repeatedly fluctuating temperatures in a soil arthropod

Costs of phenotypic adaptation to changing environments have often been studied in morphological structures. Such structures typically are irreversible for at least some stage in the organism's life. In this study we investigated whether recurrent and reversible adaptation to changes in the thermal environment incurs a cost in terms of some key life-history traits in the collembolan Orchesella cincta. We exposed juvenile O. cincta to two treatments differing in the frequency of temperature fluctuation but with equal total temperature sums. In the high frequency treatment temperature fluctuated daily between 10 and 20 °C, while in the low frequency treatment temperature fluctuated on a weekly schedule. During the treatments we measured juvenile growth rate and juvenile mortality, and after six weeks the animals were transferred to constant 15 °C and adult starvation resistance was assessed. We found no significant differences between the treatments in juvenile growth rate or juvenile survival. Also, adults that had grown up under high frequency temperature fluctuations did not suffer from reduced starvation resistance compared to animals growing under low frequency temperature fluctuations. This finding supports the hypothesis that selection minimizes the production costs of inducible phenotypes and suggests that the development of optimal phenotypes and evolution of temperature reaction norms are not constrained by such costs.     

Analysis of calcium activated chloride current fluctuations in Xenopus laevis oocytes.

Fluctuations of calcium activated chloride currents were investigated in oocytes of Xenopus laevis. The method of noise analysis and the model of chloride channels activation by calcium ions were used to estimate the chloride channels lifetime and the average frequency of current fluctuations, which depends on changes of cytoplasmic calcium concentration. This current fluctuations can be evoked by activation of cholinergic receptors or inhibition by Na3VO4 of plasma membrane Ca(2+)-ATPase. The average opening lifetime of chloride channels was approximately 100 ms. The frequency of fluctuations increased with the increasing extracellular calcium concentrations and external ACh concentrations. Caffeine in 2 mmol/l concentration changed the current fluctuations into oscillations with a period of about 18-20s. Ten mmol/l caffeine fully inhibited the oscillation activity.     

Estimating non-isothermal bacterial growth in foods from isothermal experimental data

AIM: To develop a mathematical method to estimate non-isothermal microbial growth curves in foods from experiments performed under isothermal conditions and demonstrate the method's applicability with published growth data. METHODS AND RESULTS: Published isothermal growth curves of Pseudomonas spp. in refrigerated fish at 0-8 degrees C and Escherichia coli 1952 in a nutritional broth at 27.6-36 degrees C were fitted with two different three-parameter 'primary models' and the temperature dependence of their parameters was fitted by ad hoc empirical 'secondary models'. These were used to generate non-isothermal growth curves by solving, numerically, a differential equation derived on the premise that the momentary non-isothermal growth rate is the isothermal rate at the momentary temperature, at a time that corresponds to the momentary growth level of the population. The predicted non-isothermal growth curves were in agreement with the reported experimental ones and, as expected, the quality of the predictions did not depend on the 'primary model' chosen for the calculation. CONCLUSIONS: A common type of sigmoid growth curve can be adequately described by three-parameter 'primary models'. At least in the two systems examined, these could be used to predict growth patterns under a variety of continuous and discontinuous non-isothermal temperature profiles. SIGNIFICANCE AND IMPACT OF THE STUDY: The described mathematical method whenever validated experimentally will enable the simulation of the microbial quality of stored and transported foods under a large variety of existing or contemplated commercial temperature histories.