Critical slowing down as an indicator of transitions in two-species models

Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems.     

On pathlength and energy straggling of megavoltage electrons slowing down

Purposeto elucidate the effects of multiple scattering and energy-loss straggling on electron beams slowing down in materials.MethodsEGSnrc Monte Carlo simulations are done using a purpose-written user-code.ResultsPlots are presented of the primary electron’s energy as a function of pathlength for 20 MeV electrons incident on water and tantalum as are plots of the overall distribution of pathlengths as the 20 MeV electrons slow down under various Monte Carlo scenarios in water and tantalum. The distributions range from 1 % to 135 % of the CSDA range in water and from 1 % to 186 % in tantalum. The effects of energy-loss straggling on energy spectra at depth and electron fluence at depth are also presented.ConclusionsThe role of energy-loss straggling and multiple scattering are shown to play a significant role in the range straggling which determines the dose fall-off region in electron beam dose vs depth curves and a significant role in the energy distributions as a function of depth.     

Critical slowing down as an early warning of transitions in episodes of bipolar disorder: A simulation study based on a computational model of circadian activity rhythms

Bipolar disorder is characterized by repeated episodes of mania and depression, and can be understood as pathological complex system behaviour involving cognitive, affective and psychomotor disturbance. Accurate prediction of episode transitions in the long-term pattern of mood changes in bipolar disorder could improve the management of the disorder by providing an objective early warning of relapse. In particular, circadian activity changes measured via actigraphy may contain clinically relevant signals of imminent systemic dysregulation. In this study, we propose a mathematical index to investigate the correlation between apparently irregular circadian activity rhythms and critical transitions in episodes of bipolar disorder. Not only does the proposed index illuminate the effects of pharmacological and psychological therapies in control over the state, but it also provides a framework to understand the dynamic (or state-dependent) control strategies. Modelling analyses using our new approach suggest that key clinical goals are minimizing side effects of mood stabilizers as well as increasing the efficiency of other therapeutic strategies.     

用心率变异功率谱研究出生后心率变慢的机理

目的 :探讨神经机制及心源性因素在出生后心率变慢中的作用。方法 :运用心率变异性的频域和时域分析方法 ,主要为功率谱分析方法 ,以不同年龄组的人和家兔为实验对象 ,对出生后心脏的自主神经调控进行初步探讨 ;并通过观察不同年龄组离体灌流兔心 (无神经体液因素影响 )自律性的变化 ,探讨心脏本身因素是否参与出生后心率变慢的调控。结果 :人和家兔迷走交感对心率的调控作用比在各年龄组之间有显著差异 ,且随年龄增长逐渐升高 ;家兔离体心脏的自主心率在各年龄组之间有显著差异 ,且随年龄增长逐渐降低。结论 :出生后心率减慢与神经机制有关 ,也有心脏本身因素的参与     

Spectral analysis of stereo-electroencephalograms: preictal slowing in partial epilepsies

A substantial challenge in epileptology consists of reliable seizure anticipation ahead in time (minutes). We propose a procedure which derives from our demonstrating here that seizure outbreak shares the pretransitional behaviour characterizing nonequilibrium phase transitions with instabilities found in a number of domains. We investigated stereo-electroencephalograms, using chronically implanted cerebral electrodes, and found preictal (that is, preseizure) slowing. The method employed rests on reconstructing a high-dimensional phase orbit, projecting the orbit back to a scalar time series, namely Lerner's density function which is shown here to play the role of an order parameter, and Fourier-transforming the latter. This reduces the problem to comparing spectral characteristics of interictal and preictal states. The preictal states behaved alike for temporal-lobe and frontal-lobe partial seizures, as well as for the one subclinical temporal-lobe seizure studied. These signs of universality are in accordance with nonequilibrium phase-transitions being in essence the amplification up to a macroscopic size of fluctuations, which may be conjectured here to consist of synchronized neuronal assemblies. Received: 10 January 2000 / Accepted in revised form: 8 May 2000     

Speciation slowing down in widespread and long-living tree taxa: insights from the tropical timber tree genus Milicia (Moraceae)

The long generation time and large effective size of widespread forest tree species can result in slow evolutionary rate and incomplete lineage sorting, complicating species delimitation. We addressed this issue with the African timber tree genus Milicia that comprises two morphologically similar and often confounded species: M. excelsa, widespread from West to East Africa, and M. regia, endemic to West Africa. We combined information from nuclear microsatellites (nSSRs), nuclear and plastid DNA sequences, and morphological systematics to identify significant evolutionary units and infer their evolutionary and biogeographical history. We detected five geographically coherent genetic clusters using nSSRs and three levels of genetic differentiation. First, one West African cluster matched perfectly with the morphospecies M. regia that formed a monophyletic clade at both DNA sequences. Second, a West African M. excelsa cluster formed a monophyletic group at plastid DNA and was more related to M. regia than to Central African M. excelsa, but shared many haplotypes with the latter at nuclear DNA. Third, three Central African clusters appeared little differentiated and shared most of their haplotypes. Although gene tree paraphyly could suggest a single species in Milicia following the phylogenetic species concept, the existence of mutual haplotypic exclusivity and nonadmixed genetic clusters in the contact area of the two taxa indicate strong reproductive isolation and, thus, two species following the biological species concept. Molecular dating of the first divergence events showed that speciation in Milicia is ancient (Tertiary), indicating that long-living tree taxa exhibiting genetic speciation may remain similar morphologically.     

出生后心率变慢的窦房结调控机制

用离体兔心灌流、窦房结细胞动作电位记录、膜片钳实验和放射免疫分析细胞内cAMP含量等方法,研究不同周龄组兔心自律性变慢的心脏内源性因素。实验结果提示,离体心脏和窦房结标本在没有神经体液因素影响的情况下也有随周龄增长而自律性变慢的现象。进一步的实验提示,这可能是由于窦房结细胞内cAMP含量下降,使起搏离子流If的阈电位向负方向移位,造成窦房结细胞4期自动除极速率降低,最后导致心率变慢。上述结果表明,成长过程中的心率变慢,除有神经体液因素影响外,窦房结细胞本身自律性的改变也起了一定作用。     

Inverse bifurcation analysis: application to simple gene systems

Background  

Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties.     

Pyruvate dehydrogenase kinase isoform 2 activity limited and further inhibited by slowing down the rate of dissociation of ADP

Pyruvate dehydrogenase kinase 2 (PDK2) activity is enhanced by the dihydrolipoyl acetyltransferase core (E2 60mer) that binds PDK2 and a large number of its pyruvate dehydrogenase (E1) substrate. With E2-activated PDK2, K(+) at approximately 90 mM and Cl(-) at approximately 60 mM decreased the K(m) of PDK2 for ATP and competitive K(i) for ADP by approximately 3-fold and enhanced pyruvate inhibition. Comparing PDK2 catalysis +/- E2, E2 increased the K(m) of PDK2 for ATP by nearly 8-fold (from 5 to 39 microM), increased k(cat) by approximately 4-fold, and decreased the requirement for E1 by at least 400-fold. ATP binding, measured by a cold-trapping technique, occurred at two active sites with a K(d) of 5 microM, which equals the K(m) and K(d) of PDK2 for ATP measured in the absence of E2. During E2-aided catalysis, PDK2 had approximately 3 times more ADP than ATP bound at its active site, and the pyruvate analogue, dichloroacetate, led to 16-fold more ADP than ATP being bound (no added ADP). Pyruvate functioned as an uncompetitive inhibitor versus ATP, and inclusion of ADP transformed pyruvate inhibition to noncompetitive. At high pyruvate levels, pyruvate was a partial inhibitor but also induced substrate inhibition at high ATP levels. Our results indicate that, at physiological salt levels, ADP dissociation is a limiting step in E2-activated PDK2 catalysis, that PDK2.[ADP or ATP].pyruvate complexes form, and that PDK2.ATP.pyruvate.E1 reacts with PDK2.ADP.pyruvate accumulating.     

基于临界慢化模型和长时间序列叶面积指数的植被及其恢复力遥感监测研究——以三峡库区为例

基于临界慢化模型,利用长时间序列叶面积指数(GLASS LAI)数据,进行时间序列分解后,计算了LAI及其时间自相关指数作为指标,对三峡库区植被及其恢复力进行监测,通过案例模型对临界慢化模型精度进行了验证,分析了三峡库区植被及其植被恢复力的时空分布特征,探索基于临界慢化模型的植被恢复力遥感定量估算方法的适用性。结果表明：(1)2000—2018年三峡库区LAI平均值为3.4,重庆段LAI较低,湖北段LAI较高;三峡库区LAI整体呈上升趋势,重庆段LAI呈现降低趋势,显著下降区域占重庆段面积的21.75%,湖北段LAI呈现升高趋势,显著上升区域占湖北段面积的21.22%;(2)2000—2018年三峡库区重庆市北碚区、大渡口区、渝北区植被恢复力较低,宜昌市兴山县、夷陵区、点军区植被恢复力较高;(3)模型精度方面,在两个地质灾害扰动事件中案例模型结果与临界慢化模型结果呈现较高的一致性。本文对三峡库区2000—2018年的植被恢复力进行了定量估算,同时通过案例模型对临界慢化模型在恢复力监测上的有效性进行了验证,为三峡库区制定相应生态环境管理决策提供理论基础,为保障西南地区生态安全提供决策依据...     

Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis

We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL₁ in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.     

Formation of a regular dissipative structure: a bifurcation and non-linear analysis.

A non-linear reaction diffusion model of a negative feedback epigenetic control system is presented. The model involves synthesis of the mitotic inducing and inhibiting proteins, simultaneously with intercellular self-diffusion and cross-diffusion of the latter only. The importance of negative cross-diffusion for creating a regular dissipative structure is shown. A bifurcation analysis of the non-linear diffusive system has been performed and it is concluded that bifurcation is supercritical. Lastly, using Liapunov's direct method, it is shown that the pattern evolved by the system is globally asymptotically stable.     

Diatom flora in Mediterranean streams: flow intermittency threatens endangered species

In the context of global environmental changes, Mediterranean rivers are considered highly endangered. Temporal and spatial increases of the dry stretches during the summer lead to the loss of river tridimensional connectivity, which represents a major threat for freshwater biodiversity. In this study, we aimed at exploring the response of diatom communities to summer droughts by analyzing taxonomical composition, specific ecological requirements, ecological guilds and percentages of endangered species. The evolution of diatom communities was monitored under both intermediate and intermittent flows, with traditional and innovative sampling procedures, i.e. collecting diatoms from transects and microhabitats, respectively. Microhabitats differed in terms of water velocity, substrate, isolation and presence of macrophytes. Diatom flora was mainly composed of β-mesasoprobous taxa. We highlighted an increase of species considered as aerophilous and planktonic in sites characterized by intermittent flow. In general, ecological guilds did not respond to hydrological disturbance as expected. Statistical models identified the maintenance of a minimum of 0.20 m/s flow velocity as the main factor influencing the abundance of endangered species. Conversely, flow instability, lentification and habitat fragmentation represented the major threats for endangered species. In conclusion, diatoms can provide useful information to improve river management practices when faced with an increasing water scarcity scenario. Water stability and river habitat heterogeneity strongly favor the presence of endangered diatom species. In the absence of these conditions, isolated pools surrounded by dry riverbed are very important habitats to be preserved, representing the only refugia for benthic diatom communities during summer.     

Transduction in photoreceptors with bistable pigments: Intermediate processes

The prolonged depolarizing after potential (PDA) in the R1–6 receptors of the fly was used to isolate intermediate processes in phototransduction which are not manifested directly in the voltage response. It is first demonstrated that a pigment shift by light from metarhodopsin to rhodopsin in four species of the flies: Drosophila, Calliphora, Chrysomya and Musca induces an independent antagonistic process to the PDA, which is manifested in a strong inhibitory effect on PDA induction and is called the anti-PDA.By using mutants of Drosophila the existence of processes underlying the PDA were examined. The norpA ^H52and the trp mutant were used in which the voltage response of the photoreceptors could be reversibly abolished by elavated temperature and long intense light respectively. It is shown that the excitatory process underlying the PDA could be induced and depressed in conditions that block the voltage response of the photoreceptors, thus indicating the existance of intermediate processes which link the pigment activation by light to the PDA voltage response.Based on material presented at the European Neurosciences Meeting, Florence, September 1978     

Joint effects of mitosis and intracellular delay on viral dynamics: two-parameter bifurcation analysis

To understand joint effects of logistic growth in target cells and intracellular delay on viral dynamics in vivo, we carry out two-parameter bifurcation analysis of an in-host model that describes infections of many viruses including HIV-I, HBV and HTLV-I. The bifurcation parameters are the mitosis rate r of the target cells and an intracellular delay τ in the incidence of viral infection. We describe the stability region of the chronic-infection equilibrium E* in the two-dimensional (r, τ) parameter space, as well as the global Hopf bifurcation curves as each of τ and r varies. Our analysis shows that, while both τ and r can destabilize E* and cause Hopf bifurcations, they do behave differently. The intracellular delay τ can cause Hopf bifurcations only when r is positive and sufficiently large, while r can cause Hopf bifurcations even when τ = 0. Intracellular delay τ can cause stability switches in E* while r does not.