An approach to the nonlinear dynamics of Russian wheat aphid population growth with the cusp catastrophe model

Many insect field populations, especially aphids, often exhibit irregular and even catastrophic fluctuations. The objective of the present study is to explore whether or not the population intrinsic rates of growth ( r _m) obtained under laboratory conditions can shed some light on the irregular changes of insect field populations. We propose to use the catastrophe theory, one of the earliest nonlinear dynamics theories, to answer the question. To collect the necessary data, we conducted a laboratory experiment to investigate population growth of the Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), in growth chambers. The experiment was designed as the factorial combinations of five temperatures and five host plant-growth stages (25 treatments in total): 1800 newly born RWA nymphs arranged in the 25 treatments (each treatment with 72 repetitions) were observed for their development, reproduction and survival through their entire lifetimes. After obtaining the population intrinsic rates of growth ( r _m) from the experimental data under various environmental conditions, we built a cusp catastrophe model for RWA population growth by utilizing r _m as the system state variable, and temperature and host plant-growth stage as control variables. The cusp catastrophe model suggests that RWA population growth is intrinsically catastrophic , and dramatic jumps from one state to another might occur even if the temperature and plant-growth stage change smoothly . Other basic behaviors of the cusp catastrophe model, such as catastrophic jumps , hystersis and divergence , are also expected in RWA populations. These results suggest that the answer to the previously proposed question should be "yes".     

Anticipatory regulation and avoidance of catastrophe during exercise-induced hyperthermia

Although evidence exists that a critical limiting temperature during exercise leads to premature fatigue secondary to a reduced central nervous system (CNS) drive to skeletal muscle, other thermoregulatory models may provide alternative explanations for limitations to exercise and heat stress in humans. This paper considers a number of mammalian species and their thermoregulatory strategies which deal with physical work and survival in hot environments. The critical limiting temperature hypothesis as the cause of premature fatigue is discussed in relation to the evidence for a CNS down-regulation of skeletal muscle drive. However, recent studies suggest that exercise duration or the point of fatigue is determined by a mechanism of anticipatory regulation for the avoidance of catastrophe. Evidence is offered that premature fatigue in the heat is not limited by a critical limiting temperature per se, but rather the rate at which core temperature rises so that the organism can anticipate the point of termination and avoid a catastrophic outcome.     

基于椭圆脐点突变模型的大熊猫生存状态研究

得益于有力的保护,大熊猫受威胁等级由"濒危"降为"易危"。根据全国大熊猫调查数据,近年来,大熊猫野生种群与栖息地面积总体上均处于持续增加态势;同时,大熊猫栖息地破碎化与局域种群隔离也呈加剧的趋势。两相对比,形成悖论现象,难以正确认知当前大熊猫的生存状态。大熊猫作为高度特化的K对策大型动物,其生存高度依赖于栖息地生态系统,极易受栖息地丧失与破碎化的影响。对大熊猫生存状态的研究,不应局限于栖息地或种群等单项指标的变化,而应基于系统科学的整体视角。结合全国第三、四次大熊猫调查数据,对大熊猫野生种群数量与栖息地及潜在栖息地的面积进行复相关分析,发现大熊猫野生种群数量与栖息地、潜在栖息地的面积之间存在着高度显著正相关,表明三者之间存在着稳定而密切的耦合关系,进而建立了大熊猫种群与栖息地、潜在栖息地之间的耦合函数。突变理论作为一种成熟的系统科学理论,提供了较完备的数学方法,利用系统中少量的关键指标便可实现对系统行为的刻画。基于突变理论,以大熊猫分布区生态系统为研究对象,选取了大熊猫种群数量、栖息地与潜在栖息地的面积为系统关键指标,利用种群与栖息地、潜在栖息地之间的耦合函数,构建了"大熊猫—栖息地"系统椭圆脐点突变模型,对生态系统的稳定性进行研究。发现虽然野生种群数量、栖息地与潜在栖息地的面积均持续增长,但严峻的局域种群生存危机与栖息地的高度破碎化,从总体上削弱了系统的稳定性,大熊猫分布区生态系统的稳定性处于持续下降态势,且濒临系统临界状态,生态系统具有较大的退化压力,大熊猫的生存危机依然严峻。     

害虫种群动态模型的燕尾突变分析

在农田生态系统中,以作物状况、气象因素及天敌分别为3种控制变量,以害虫种群数量动态为状态变量,建立了燕尾突变模型,并用燕尾突变模型的性质分析害虫种群数量动态中产生的突变现象.具体对燕尾突变的分歧点集所分各个控制区域的系统势函数形式和平衡点情况进行了分析,说明了害虫种群数量发生突变的条件和机理,为实际应用提供理论依据.同时利用燕尾突变的性质直观描述了害虫种群数量变化中的突跳和滞后等现象.     

Biological power laws and Darwin's principle

Assuming that the repertoire of responses by living systems to perturbation gives a measure of their Darwinian fitness in a rapidly fluctuating environment, those that fulfill allometries (power laws) are described by means of catastrophes, whose variables and parameters are smooth functions of biological attributes. Using empirical allometries from a given system as input, a method is proposed to construct its associated catastrophe, allowing specific predictions on its susceptibility to perturbation and related properties, based on general results from catastrophe theory. The method is discussed within the macroecological context, and an example is provided by applying it to ecological systems that satisfy the self-thinning rule.     

Catastrophe Theory Enables Moves to be Detected Towards and Away from Self-Organization: The Example of Epileptic Seizure Onset

Macroscopic systems with many interacting subunits, when driven far from equilibrium, exhibit self-organization, for example when a pathological rhythm appears suddenly in an epileptic patient. Sudden changes occurring while conditions vary smoothly have, in cases of interest, underlying mathematics that are the subject of Thom’s catastrophe theory. The assumption made herein that the system’s state variables, akin to order parameters, reduce in practice to only one single real variable, ensures that the system derives from a potential function, and warrants recourse to the catastrophe theory. The order parameter is, furthermore, interpreted as a measure of the electropathophysiological activity in the brain, increasing monotonously with the degree of neuronal synchronism. With two neuronal influences, excitatory and inhibitory, as control parameters, the catastrophe is the archetypal cusp. Implementation of catastrophe theory leads to equations showing that fluctuations in a system’s dynamics may be utilised for signalling steps precursory to oncoming catastrophes. Pre-seizure dynamics in epileptic patients exhibit steps towards and away from catastrophe; the steps away are interpreted in terms of homeostatic feedback, consequent on changing patterns of neuronal activity. A number of characteristics of epileptic seizures of differing types merely follow from the geometry of the cusp equilibrium surface. In particular, types of seizures are distinguished by their angle of final approach to onset in parameter space. The measurable parameters by which approach to catastrophe is characterized, may be of use in investigations of the organism’s plasticity in epileptic patients, and in tests of therapeutic means for preventing seizures. There is no need to resort to a model, in the usual sense of the word, and therefore no differential equation needs to be set up.     

Cellular proteomes have broad distributions of protein stability

Biological cells are extremely sensitive to temperature. What is the mechanism? We compute the thermal stabilities of the whole proteomes of Escherichia coli, yeast, and Caenorhabditis elegans using an analytical model and an extensive database of stabilities of individual proteins. Our results support the hypothesis that a cell''s thermal sensitivities arise from the collective instability of its proteins. This model shows a denaturation catastrophe at temperatures of 49–55°C, roughly the thermal death point of mesophiles. Cells live on the edge of a proteostasis catastrophe. According to the model, it is not that the average protein is problematic; it is the tail of the distribution. About 650 of E. coli''s 4300 proteins are less than 4 kcal mol⁻¹ stable to denaturation. And upshifting by only 4° from 37° to 41°C is estimated to destabilize an average protein by nearly 20%. This model also treats effects of denaturants, osmolytes, and other physical stressors. In addition, it predicts the dependence of cellular growth rates on temperature. This approach may be useful for studying physical forces in biological evolution and the role of climate change on biology.     

A Catastrophe Model for Water Bloom Prediction: A Case Study of China's Lake Chaohu

Using a case study of Lake Chaohu, the fifth largest lake in China, we constructed a cusp model for water bloom prediction that used TP (total phosphorus), T (temperature), Chla (chlorophyll-a), and DO (dissolved oxygen). These four parameters were assumed to be the most important factors in eutrophication and water bloom of the lake. The model was found to be accurate, because its relative error was around 10%. What is more convincing, according to the catastrophe discriminant of the cusp model, it could be judged that a discontinuous jump of the aquatic ecosystem occurred in July 2004, in Lake Chaohu. This conclusion is consistent with the fact that water blooms arose in August 2004. The cusp model also showed satisfactory precision when applied to forecast the eutrophication trend and prediction of water bloom in Lake Chaohu in 2005. The case study found that water bloom brought on by eutrophication can be fit and predicted by a catastrophe model. We suggest that catastrophe models would be a constructive approach to forecast and judge the outbreak of water bloom in lakes. In addition, by constructing and studying such catastrophe models, lake managers would be able to simulate the effects of different protection and mitigation projects and enrich the scientific basis for the optimization of these projects as well.     

水华爆发的突变模型——以巢湖为例

面对湖泊水库富营养化的严峻形势,水华防治是当务之急,而根据富营养化现状对水华进行准确的判定和预报更是重中之重.从水生态系统的角度出发,综合考虑TP、T、Chla和DO等4个对巢湖富营养化乃至水华影响最为突出的因子,构建了巢湖水华突变的尖点模型,通过模型来模拟巢湖富营养化引发水华的情势.在对巢湖2000～2003年时间序列的监测数据进行数据拟合的基础上,发现南淝河入湖区断面处逐月TP、T、Chla和DO数据的演变规律符合突变理论的尖点模型特征.经检验,模型的相对误差控制在10%左右,具有较好的拟合精度.根据模型的突变判别,巢湖的水生态系统2003年7月在南淝河入湖区断面处发生了突变,这一模拟结论与该断面2003年8月爆发水华的实际情况相一致.研究表明,水华突变模型的建立,准确地反映了巢湖富营养化引发水华的实际情况,系统地勾勒出富营养化状态下水生态系统各要素间的动态响应模式,揭示了水华爆发的突变机理.通过水华突变模型的构建,不仅能够对巢湖水华的发生进行判断和预报,还可以对各项防治措施的实施效果进行预测和模拟,进而为综合整治方案的优化和统筹提供科学依据.水华的爆发是多诱因的综合作用结果,是营养物质长期累积、由量变到质变的演化过程,作为目前唯一的一种研究由渐变引起突变的系统理论,突变理论满足水华研究的数理要求,为水华现象的数值模拟提供了可行的解决方案.     

突变级数法在生态适宜度评价中的应用——以镇江新区为例

《开发区区域环境影响评价技术导则》（HJ／T2003）已将生态适宜度评价列为区域环境影响评价的主要内容,并明确提出了三级指标集成的框架要求,但并未推荐具体的技术方法。在当前的环评工作实际中,出现了多种生态适宜度的评价技术,如排列成比较技术、层次分析、模糊评价法等,然而这些方法却普遍存在着权重分配过程中的主观性问题。而对于生态适宜度评价这类多指标集成的问题,无论采用何种技术方法,只有减少权重赋值的主观性才能体现评价结论的科学性。鉴于此,推荐了一种新型的生态适宜度评价方法——突变级数法。通过镇江新区环评的具体案例分析,突变级数法表现出在生态适宜度评价方面较好的适用性。更为重要的是,通过对前述3种方法的数理分析对比,突变级数法表现出主营以下两方面的比较优势：首先该法不使用权重,只需按指标间的内在逻辑关系对指标的重要程度进行排序,很大限度地避免了人为制定权重的主观性;同时,作为定性与定量相结合的技术方法,突变级数法不仅可以对各地块是否适合其利用类型做出评价,还可以运用模型计算出各个地块生态适宜度的具体数值,对不同地块的生态适宜性程度进行定量的对比。诚然,应该客观地指出,在按指标的重要程度排序过程、以及评价指标的量化分级过程中,突变级数法仍然不能完全避免人为主观性,这也需要今后继续探索整合其他技术方法。加以进一步完善。     

Topological Approach of Jungian Psychology

In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom’s topology and the latter is Jung’s psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom’s catastrophe theory to some Jung’s notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious and conscious. Moreover, we have correlated this morphology with Jung’s evolutive processes like individualisation and individuation. These comparisons incited us to think that some morphologies of Thom’s catastrophe theory are the geometrical dealing of Jung’s archetypes.     

Regulation of copy number and stability of phage λ derived pTCλ1 plasmid in the light of the dimer/multimer catastrophe hypothesis

The dimer catastrophe hypothesis has been proposed previously to explain instability of multicopy plasmids whose partitioning is random, contrary to low copy number plasmids which are stably maintained and actively partitioned. Until now, this hypothesis has been investigated using multicopy ColE1 plasmids. However, for more detailed testing of the dimer/multimer catastrophe hypothesis, one should use a plasmid which can be maintained at either low or high copy number and still possesses the same mechanism of replication regulation. Here we used a modified lambda plasmid, pTC lambda 1. The advantage of this plasmid is that it can be maintained at different copy numbers depending on the concentration of an inducer which stimulates the initiation of plasmid replication. Results obtained with this plasmid in recombination proficient and deficient cells generally support the dimer/multimer catastrophe hypothesis, but also suggest some modification in the model.