Detecting chaotic dynamics of insect populations from long-term survey data

1. Estimates of the Lyapunov exponent, a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions, are used to characterize several sets of insect time series.
2. A new method is described to overcome the difficulty of defining the dynamics of an observed, noisy, short ecological time series. This method provides two test statistics for the estimated Lyapunov exponent.
3. This method is applied to forty-six time series comprising six aphid species from five sites and four moth species from six sites. There are few positive Lyapunov exponents and none is sufficiently large to characterize its time series as chaotic.
4. Two methods to estimate the Lyapunov exponent are compared; that based on logarithmically transformed counts yields less variable estimates for highly variable insect data than that based on untransformed counts.     

Predictability of human EEG: a dynamical approach

The electroencephalogram recordings from human scalp are analysed in the framework of recent methods of nonlinear dynamics. Three stages of brain activity are considered: the alpha waves (eyes closed), the deep sleep (stage four) and the Creutzfeld-Jakob coma. Two dynamical parameters of the attractors are evaluated. These are the Lyapunov exponents, which measure the divergence or convergence of trajectories in phase space and the Kolmogorov or metric entropy, whose inverse gives the mean predicting time of a given EEG signal. In all the stages considered, the results reveal the presence of at least two positive Lyapunov exponents, which are the footprints of chaos. This number increases to three positive exponents in the case of alpha waves, indicating that although for very short episodes the alpha waves seem extremely coherent, the variability of the brain increases markedly over larger periods of activity. The degree of entropy/chaos increases from coma to deep sleep and then to alpha waves. The large predicting time observed for deep sleep suggests that these waves are related to a slow rate of information processing. The predicting time of the alpha waves is much smaller, indicating a rapid loss of information. Finally, with the help of the Lyapunov exponents, the attractor's dimensions are evaluated using two different conjectures and compared to values obtained previously by the Grassberger-Procaccia algorithm.     

黑龙江省2010～2020年猩红热发病与气象因素的关联性研究

分析黑龙江省气象因素与猩红热发病的关系,建立时间序列模型,为今后制定更科学有效的猩红热防控策略提供参考依据。收集黑龙江省2010～2020年猩红热月发病数据以及同期气温、气压等气象资料,应用广义相加模型分析气象因素与猩红热发病之间的关联程度和形式。结果发现: 猩红热全年均有发病而且呈现出较为典型的双峰型特征,在春季的4～5月份和冬季的11～12月份发病数达到高峰;月平均气压、月平均相对湿度、月日照时数和月平均风速的P值均小于0.05,表明具有统计学意义。同时,RR(相对危险度Risk Ratio)值均小于1,即猩红热发病与四个气象因素呈负相关。黑龙江省猩红热发病每年存在两个流行高峰,主要以冬季为主,发病数随着月平均相对湿度、月日照时数、月平均风速与月平均气压的升高而降低。     

Quasicycles revisited: apparent sensitivity to initial conditions

Environmental noise is known to sustain cycles by perturbing a deterministic approach to equilibrium that is itself oscillatory. Quasicycles produced in this way display a regular period but varied amplitude. They were proposed by Nisbet and Gurney (Nature 263 (1976) 319) as one possible explanation for population fluctuations in nature. Here, we revisit quasicyclic dynamics from the perspective of nonlinear time series analysis. Time series are generated with a predator-prey model whose prey's growth rate is driven by environmental noise. A method for the analysis of short and noisy data provides evidence for sensitivity to initial conditions, with a global Lyapunov exponent often close to zero characteristic of populations 'at the edge of chaos'. Results with methods restricted to long time series are consistent with a finite-dimensional attractor on which dynamics are sensitive to initial conditions. These results are compared with those previously obtained for quasicycles in an individual-based model with heterogeneous spatial distributions. Patterns of sensitivity to initial conditions are shown to differentiate phase-forgetting from phase-remembering quasicycles involving a periodic driver. The previously reported mode at zero of Lyapunov exponents in field and laboratory populations may reflect, in part, quasicyclic dynamics.     

Nonlinear dynamics of the blood flow studied by Lyapunov exponents

In order to gain an insight into the dynamics of the cardiovascular system throughout which the blood circulates, the signals measured from peripheral blood flow in humans were analyzed by calculating the Lyapunov exponents. Over a wide range of algorithm parameters, paired values of both the global and the local Lyapunov exponents were obtained, and at least one exponent equaled zero within the calculation error. This may be an indication of the deterministic nature and finite number of degrees of freedom of the cardiovascular system governing the blood-flow dynamics on a time scale of minutes. A difference was observed in the Lyapunov dimension of controls and athletes.     

荒漠植物红砂叶片元素含量与气候因子的关系

 通过测定中国境内红砂(Reaumuria soongorica)主要分布区21个自然种群407个植株叶片氮(N)、磷(P)、钾(K)含量、叶片含水量和稳 定碳同位素组成等叶片特征, 分析不同自然种群红砂叶片特征与环境气候因子之间的关系。研究结果表明, 随着年平均最低温度的升高, 红砂 叶片N、P含量、叶片含水量和稳定碳同位素值显著升高。年平均温度和红砂叶片含水量、年平均最高温度和红砂叶片稳定碳同位素值显著正相 关。不同生长区年平均降雨量和平均湿度对红砂叶片特征的影响一致, 与红砂叶片P、K含量和叶片稳定碳同位素值显著负相关, 与叶片N含量和 叶片含水量显著正相关。不同生长区平均日照时数和蒸发量对红砂叶片特征的影响一致, 与红砂叶片P、K含量和叶片稳定碳同位素值显著正相 关, 与叶片含水量显著负相关。说明不同自然种群中红砂叶片特征受气候条件的影响显著, 不同气候因子对红砂叶片特征的贡献显著不同。不 同种群间红砂叶片N含量的变化是各气象因子均衡作用的结果, 年平均湿度是影响红砂叶片K含量和稳定碳同位素值的主要限制因子, 蒸发量是 影响红砂叶片P含量的关键因子, 平均日照时数是影响红砂叶片含水量的关键因子。红砂叶片特征对不同环境条件下气候因子的这种响应模式在 一定程度上反映和指示了以红砂为建群种荒漠生态系统的环境状况和稳定程度。     

栓皮栎人工林树干液流对不同时间尺度气象因子及水面蒸发的响应

于2006-2008年主要生长季节,利用热扩散技术连续测算得到了华北土石山区30年生栓皮栎人工林液流量(SF),并结合同步测定的太阳辐射(Ra)、空气温度(Ta)、饱和水汽压亏缺(VPD)、风速(V)和降雨量(P)等气象因子、水面蒸发(EV0)及叶面积指数(LAI)等因子,分析了栓皮栎液流对不同时间尺度气象因子及水面蒸发的响应规律,探索建立长时间尺度水面蒸发与树干液流之间的关系模型。试验结果表明:(1)在主要生长季(4—9月份)期间,栓皮栎单株液流与同期测定的Ra、Ta、VPD和V等气象因子间均存在着较强的相关性。时间尺度为10min、1h、d、旬、月时,决定系数分别为0.388、0.482、0.539、0.654和0.812。说明随着时间尺度的增加,相关性越强;在不同时间尺度下,影响SF的最主要气象因子均为Ra。月SF与月Ra变化趋势的同步性尤为明显。(2)日尺度和月尺度上EV0与SF之间具有很好的线性关系,决定系数分别为0.578和0.876,比同时期、相等样本数条件下SF与Ra、Ta、VPD、V多元线性拟合的决定系数分别高3.6%和3.9%。(3)2006、2007、2008年生长季节降雨量分别为464.8、393.3mm和315.0mm,栓皮栎单株液流分别为2024.1L、1739.2L和1688.7L,年际间SF变化趋势与降雨量存在一定的一致性。     

Stability and bifurcations in a model of antigenic variation in malaria

We examine the properties of a recently proposed model for antigenic variation in malaria which incorporates multiple epitopes and both long-lasting and transient immune responses. We show that in the case of a vanishing decay rate for the long-lasting immune response, the system exhibits the so-called “bifurcations without parameters” due to the existence of a hypersurface of equilibria in the phase space. When the decay rate of the long-lasting immune response is different from zero, the hypersurface of equilibria degenerates, and a multitude of other steady states are born, many of which are related by a permutation symmetry of the system. The robustness of the fully symmetric state of the system was investigated by means of numerical computation of transverse Lyapunov exponents. The results of this exercise indicate that for a vanishing decay of long-lasting immune response, the fully symmetric state is not robust in the substantial part of the parameter space, and instead all variants develop their own temporal dynamics contributing to the overall time evolution. At the same time, if the decay rate of the long-lasting immune response is increased, the fully symmetric state can become robust provided the growth rate of the long-lasting immune response is rapid. This work was partially supported by the ATRJVVO grant from the James Martin 21st Century School, University of Oxford.     

Short-term effects of meteorological factors on children hand,foot and mouth disease in Guangzhou,China

Hand, foot and mouth disease (HFMD) is a contagious viral illness that commonly affects infants and children. The underlying risk factors have not yet been systematically examined. This study analyzed the short-term effects of meteorological factors on children HFMD in Guangzhou, China. Daily count of HFMD among children younger than 15 years and meteorological variables from 2009 to 2011 were collected to construct the time series. A generalized additive model was applied to estimate the effects of meteorological factors on HFMD occurrence, after adjusting for long-term trend, seasonal trend, day of week, and public holidays. A negative association between temperature and children HFMD occurrence was observed at lag days 1–3, with the relative risk (RR) for a 1 °C increase on lag day 2 being 0.983 (95 % confidence intervals (CI) 0.977 to 0.989); positive effect was found for temperature at lag days 5–9, with the highest effect at lag day 6 (RR?=?1.014, 95 % CI 1.006 to 1.023). Higher humidity was associated with increased HFMD at lag days 3–10, with the highest effect at lag day 8 (RR?=?1.009 for 1 % increase in relative humidity, 95 % CI 1.007 to 1.010). And we also observed significant positive effect for rainfall at lag days 4 and 8 (RR?=?1.001, 95 % CI 1.000 to 1.002) for 1-mm increase. Subgroup analyses showed that the positive effects of temperature were more pronounced among younger children. This study suggests that meteorological factors might be important predictors of children HFMD occurrence in Guangzhou.     

Seasonal oscillation of human infection with influenza A/H5N1 in Egypt and Indonesia

As of June 22, 2011, influenza A/H5N1 has caused a reported 329 deaths and 562 cases in humans, typically attributed to contact with infected poultry. Influenza H5N1 has been described as seasonal. Although several studies have evaluated environmental risk factors for H5N1 in poultry, none have considered seasonality of H5N1 in humans. In addition, temperature and humidity are suspected to drive influenza in temperate regions, but drivers in the tropics are unknown, for H5N1 as well as other influenza viruses. An analysis was conducted to determine whether human H5N1 cases occur seasonally in association with changes in temperature, precipitation and humidity. Data analyzed were H5N1 human cases in Indonesia (n = 135) and Egypt (n = 50), from January 1, 2005 (Indonesia) or 2006 (Egypt) through May 1, 2008 obtained from WHO case reports, and average daily weather conditions obtained from NOAA''s National Climatic Data Center. Fourier time series analysis was used to determine seasonality of cases and associations between weather conditions and human H5N1 incidence. Human H5N1 cases in Indonesia occurred with a period of 1.67 years/cycle (p<0.05) and in Egypt, a period of 1.18 years/cycle (p≅0.10). Human H5N1 incidence in Egypt, but not Indonesia, was strongly associated with meteorological variables (κ²≥0.94) and peaked in Egypt when precipitation was low, and temperature, absolute humidity and relative humidity were moderate compared to the average daily conditions in Egypt. Weather conditions coinciding with peak human H5N1 incidence in Egypt suggest that human infection may be occurring primarily via droplet transmission from close contact with infected poultry.     

Thresholds in transient dynamics of signal transduction pathways

Transient dynamics of signal transduction pathways play an important role in many biological processes, including cell differentiation, apoptosis, metabolism and DNA damage response. Recent examples of quantitative methods to characterize transient signals include transient metabolic control coefficients and finite time Lyapunov exponents. In our work we compare these quantitative methods to characterize transient phenomena and specifically discuss their predictive power for three examples. We focus on the identification of thresholds that separate different transient dynamic behaviors. Our investigation leads to the following results: The spectrum of the finite-time Lyapunov exponents unambiguously and reliably identifies putative thresholds in transient dynamics. Metabolic control coefficients do not reliably detect all thresholds and suffer from false positives.     

An investigation inot the use of multiple site characteristics to predict the presence and infestation level of wireworms (Agriotes sup., Coleoptera: Elateridae) in individual grass fields

Sixty-two grass fields were sampled in England and Wales over a three year period to assess the level of wireworm population present. Data on site-specific variables including soil physical characteristics, grass duration, grass genera diversity and other abiotic factors such as field aspect, altitude, and meteorological parameters were abiotic factors such as field aspect, altitude, and meteorological parameters were collected at each site. Only grass duration and soil bulk density showed any association with wireworm infestation stauts when considered as single variates. Data from a sub-set of 41 fields were used to develop a series of multi-variate discriminant rules to predit wireworm presence/absece in individual fields. These were vaildated using data from the remaining 21 fields. In general, the rules tended to over-estimate the number of wireworm-infested fields by misclassifying uninfested fields as infestes. Multivariate models to predict wireworm populaiton levels in infested fields were also developed using multiple and generalised linear regression. The predictive accuracy of these was poor. Neither the population prediciton models nor the presence/absence rulses accounted fully for the large inte-field variation in wireworm infestation status.     

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model

The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes—the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.     

陕甘宁地区降水同位素云下二次蒸发效应

大气降水过程中,雨滴由云层底部降落至地面经过不饱和空气时发生的蒸发现象,即为云下二次蒸发,这会使得降水同位素组成发生改变。利用氢氧稳定同位素方法研究云下二次蒸发效应的时空变化及其成因,对探讨区域水循环过程具有重要意义。本研究基于陕甘宁地区2018年3月—2019年2月187个气象站逐小时气象数据,采用改进后的Stewart模型,分析了该区域蒸发剩余比(f)与降水过量氘变化量(Δd)的时空变化,并探讨了f以及气象要素与Δd的关系。结果表明: 从小时尺度来看,该区域各省f与Δd最小值均出现在白天,最大值出现在夜晚,即白天云下二次蒸发效应更明显。从月尺度来看,各省f、Δd月变化趋势较为一致,最小值多出现在夏半年,最大值多出现在冬半年,即夏半年云下二次蒸发效应更显著。研究区f、Δd值在季节尺度上的空间变化一致:春季,东、西部地区较大,中部较小;夏季,西北部地区偏小,其他地区偏大;秋季,由南向北减小;冬季,中部、南部较小,西部及东北部较大,研究区不同季节云下二次蒸发效应的空间差异显著。陕甘宁三省(区)f与Δd的线性关系的斜率均小于1‰·%^-1,这可能与该地区干旱半干旱气候具有较大关系。当气温较高,相对湿度、水汽压、降水量和雨滴直径较小时,Δd值较小,云下二次蒸发效应较明显。     

Limbic irritability and chaotic neural response during conflicting stroop task in the patients with unipolar depression

According to recent findings activation of anterior cingulate cortex (ACC) is related to detecting cognitive conflict. This conflict related activation elicits autonomic responses which can be assessed by psychophysiological measures such as heart rate variability calculated as beat to beat R-R intervals (RRI). Recent findings in neuroscience also suggest that cognitive conflict is related to specific nonlinear chaotic changes of the signal generated by neural systems. The present study used Stroop word-color test as an experimental approach to psychophysiological study of cognitive conflict in connection with RRI measurement, psychometric measurement of limbic irritability (LSCL-33), depression (BDI-II) and calculation of largest Lyapunov exponents in nonlinear data analysis of RRI time series. Significant correlation 0.61 between largest Lyapunov exponents and LSCL-33 found in this study indicate that a defect of neural inhibition during conflicting Stroop task is closely related to limbic irritability. Because limbic irritability is probably closely related to epileptiform abnormalities in the temporolimbic structures, this result might represent useful instrument for indication of anticonvulsant treatment in depressive patients who are resistant to antidepressant medication.     

Intermittent instability is widespread in plankton communities

Chaotic dynamics appear to be prevalent in short-lived organisms including plankton and may limit long-term predictability. However, few studies have explored how dynamical stability varies through time, across space and at different taxonomic resolutions. Using plankton time series data from 17 lakes and 4 marine sites, we found seasonal patterns of local instability in many species, that short-term predictability was related to local instability, and that local instability occurred most often in the spring, associated with periods of high growth. Taxonomic aggregates were more stable and more predictable than finer groupings. Across sites, higher latitude locations had higher Lyapunov exponents and greater seasonality in local instability, but only at coarser taxonomic resolution. Overall, these results suggest that prediction accuracy, sensitivity to change and management efficacy may be greater at certain times of year and that prediction will be more feasible for taxonomic aggregates.     

Recovery of meteorological data for the observatory of A Guarda, Spain

We herein describe the recovery of a series of data on temperature, humidity, precipitation, evaporation, wind, and local weather conditions from documentary sources obtained from the Jesuit observatory of A Guarda (Galicia, Spain) for the period 1881-1896. The data were digitized and made available in accessible electronic formats. Comparisons were made with present-day meteorological data obtained from two nearby stations. We further believe that the discovery of some new complementary documentary sources made during the present research could be a basis for future data recovery efforts. Among these new results, early ozone data from the period are of outstanding importance to meteorologists.     

Kinematic variability and local dynamic stability of upper body motions when walking at different speeds

A ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls. Many clinicians assume these patients walk slower to improve their stability, just as healthy people slow down when walking across ice. However, walking slower also leads to greater variability, which is often assumed to imply deteriorated stability. If this were true, then slowing down would be completely antithetical to the goal of maintaining stability. This study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Eleven young healthy subjects walked on a motorized treadmill at five different speeds. Three-dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking. Mean stride-to-stride standard deviations and maximum finite-time Lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability, respectively, of these movements. Quadratic regression analyses of the dependent measures vs. walking speed revealed highly significant U shaped trends for all three mean standard deviations, but highly significant linear trends, with significant or nearly significant quadratic terms, for five of the six finite-time Lyapunov exponents. Subjects exhibited consistently better local dynamic stability at slower speeds for these five measures. These results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability, even at the cost of increased variability.     

Evapotranspiration measurements in Eriophorum vaginatum tussock tundra in Alaska

Evapotranspiration was measured periodically from late June through mid-August 1978 in Eriophorum vaginiatum tussock tundra near Eagle Creek, Alaska. The average evapotranspiration rates from tussock and intertussock areas were 0.8 mm d⁻¹ and 1.3 mm d⁻¹, respectively. Potential evaporation was calculated according to the Penman equation using microclimate data collected at the same time actual evapotranspiration was measured. Actual evapotranspiration was 0.56 ± 0.06 ( X ± SE, N = 10) of the potential evaporation from moss and 0.43 ± 0.08 ( X ± SE, N = 10) of the potential evaporation from E. vaginatum tussocks. Seventy three percent of the variability in the ratio of actual evapotranspiration to potential evaporation from tussocks was accounted for by linear regression on net radiation. Eighty nine percent of the variability in the same ratio for mosses was explained by linear regression on the vapor pressure deficit of the air and net radiation.     

The weak effects of climatic change on Plantago pollen concentration: 17 years of monitoring in Northwestern Spain

Plantago L. species are very common in nitrified areas such as roadsides and their pollen is a major cause of pollinosis in temperate regions. In this study, we sampled airborne pollen grains in the city of León (NW, Spain) from January 1995 to December 2011, by using a Burkard® 7-day-recording trap. The percentage of Plantago pollen compared to the total pollen count ranged from 11 % (1997) to 3 % (2006) in the period under study. Peak pollen concentrations were recorded in May and June. Our 17-year analysis failed to disclose significant changes in the seasonal trend of plantain pollen concentration. In addition, there were no important changes in the start dates of pollen release and the meteorological parameters analyzed did not show significant variations in their usual trends. We analyzed the influence of several meteorological parameters on Plantago pollen concentration to explain the differences in pollen concentration trends during the study. Our results show that temperature, sun hours, evaporation, and relative humidity are the meteorological parameters best correlated to the behavior of Plantago pollen grains. In general, the years with low pollen concentrations correspond to the years with less precipitation or higher temperatures. We calculated the approximate Plantago flowering dates using the cumulative sum of daily maximum temperatures and compared them with the real bloom dates. The differences obtained were 4 days in 2009, 3 days in 2010, and 1 day in 2011 considering the complete period of pollination.