拟环纹狼蛛对褐飞虱的捕食作用及其模拟模型的研究Ⅱ.单种捕食者-单种猎物系统的模拟模型及其稳定性分析

本文提出了描述单种捕食者-单种猎物系统的模拟模型。在拟环纹狼蛛对褐飞虱功能反应实验的基础上,分析了模型中备个参数对模型局部稳定性的影响以及拟环纹狼蛛-褐飞虱系统的局部稳定性。     

草间小黑蛛对棉铃虫幼虫的捕食作用及其模拟模型的研究——Ⅲ.模拟模型的进一步研究

根据实验室实验的结果,李超等(1982a、b)分别提出了草间小黑蛛-棉铃虫作用系统和草间小黑蛛-棉铃虫-棉蚜作用系统的模拟模型。本文通过大田中进行的笼罩实验结果,进一步完善了功能反应参数的修正方法,使模型的行为更接近于实际情形。在此基础上,对描述草间小黑蛛-棉铃虫-棉蚜作用系统的四种可能的模拟模型的行为,通过数值模拟的结果来进行初步的探讨。     

生态系统模拟模型的研究进展

从四个方面概述了生态系统模拟模型的发展现状：1)个体及种群,种群动态模型主要模拟在一个生境中单个种的动、植物个体出生或发芽、成长及其死亡过程,还有种内竞争和种间相互作用,主要分析生境中生物之间的相互作用。主要概述了林窗模型和土壤一植物一大气系统模型。2)群落与生态系统,概述了生态系统生产力模型、生物地球化学循环模型及演替模型。主要模拟植物种类在整个生态系统发展过程中的变化,以及植被类型的转变和相关的生物地球化学循环过程的改变,从而反映生物群落对气候变化的响应。3)景观生态系统,景观动态研究包含了时空两个方面的动态变化,一般可分为随机景观模型和基于过程的景观模型。随机模型用于模拟群落格局在演替过程中的动态变化等,基于过程的景观模型深入研究组成景观的各生态系统的空间结构。4)生物圈与地球生态系统,基于过程的陆地生物地球化学模式被用来研究自然生态系统中碳和其它矿物营养物质的潜在通量和蓄积量,较为流行的模式有陆地生态系统模式TEM、CENTURY、法兰克福生物圈模式FBM、Biome-BGC、卡内基-埃姆斯-斯坦福方法CASA等。这些模式己被用于估算自然生态系统对大气CO2加倍及相关气候变化在区域和全球尺度的平衡响应。最后,结合实际工作展望了生态系统模拟模型在各方面的发展方向。     

湿地植物生长模型的改进及其动态的计算机模拟分析

湿地植被的恢复与人工调控是恢复生态学研究的热点问题之一,建立湿地大型植物生长的控制模型。能为此提供一种理论模式。在湿地植物群落中,植物种间的相互作用关系较为复杂,在植物生长的不同阶段显现为互利、竞争或相互独立。基于此我们对Shukla提出的湿地植物生长模型进行了改进．建立了一种能够反映种间复杂作用机制(包括互利与竞争)的新模型。以植物的生物量为描述变量,用统计方法确定了模型参数,对实例进行了计算机模拟与数值分析．并研究了植物生长系统的稳定性。结果表明：①新模型能有效地描述湿地植物种间互利或竞争作用．优于只考虑种间竞争作用的Shukla模型;②对植物生长过程的计算机模拟结果和图像显示,在较低生物量水平上．种间显现互利关系;在较高生物量水平上．种间发生竞争作用,竞争的结局为一种植物占优势,而另一种植物趋于灭亡．这些与实际观测结果是一致的;③对系统进行了稳定性分析;④根据数值模拟结果,提出了湿地恢复的人工调控对策与建议。     

城市生态系统的模拟方法：灵敏度模型及其改进

评估城市生态系统的持续发展能力,探讨其持续发展对策是一个复杂的动态问题,需要运用动态的模拟方法进行。由德国著名生态控制论专家Ｆ．Ｖｅｓｔｅｒ和Ａ．Ｖ．Ｈｅｓｌｅｒ教授提出的“灵敏度模型”方法,将系统科学思想、生态控制论方法及城市规划融为一体,解释、模拟、评价和规划城市复杂的系统关系,是模拟城市生态系统很好的方法。本文对该方法进行了改进。改进后的“灵敏度模型”为评价城市持续发展能力、探讨其持续发展对策提供了新的思路。     

日光温室黄瓜生长发育模拟模型

实现日光温室黄瓜生长发育动态模拟预测,可为日光温室黄瓜智慧生产管理提供技术支撑.本研究依据黄瓜生长发育的光温反应特性,以‘津优35’为试验品种,利用2年4茬分期播种试验观测数据建立基于钟模型的温室黄瓜发育模拟模型.依据温室黄瓜叶片生长与关键气象因子(温度和辐射)的关系,以辐热积(TEP)为自变量构建了黄瓜叶面积指数(LAI)模拟模型;依据单位叶面积光合作用对叶面积指数和日长的二重积分,结合黄瓜不同器官的呼吸消耗,构建了黄瓜干重生产分配模拟模型,结合器官含水量,构建了黄瓜器官鲜重模拟模块.基于各子模块构建了温室黄瓜生长发育模拟模型,确定了模型品种参数并进行检验.结果表明: 日光温室黄瓜移栽期-伸蔓期、移栽期-初花期、移栽期-采收初期和移栽期-拉秧期的模拟值与观测值的均方根误差(RMSE)在3.9～10.5 d,归一化均方根标准误差(nRMSE)在6.5%～28.6%,符合度指数(D)在0.79～0.97.LAI与TEP呈S型曲线变化关系,LAI模拟值与实际观测值的RMSE为0.19,nRMSE为17.2%,D值为0.90.根、茎、叶、花和果干重模拟值与实际观测值的RMSE在0.39～8.94 g·m^-2,nRMSE在10.9%～17.7%,D值均为0.98以上.表明模型能够较准确地模拟黄瓜关键发育期、叶面积和各器官干鲜重,定量化日光温室黄瓜生长发育过程.     

食物链种群模型的格子Boltzmann方法模拟

用格子Boltzmann方法求解用反应一扩散方程组描述的食物链种群模型．我们用一维和二维方程组进行数值实验,模拟结果与现有的数值实验结果很好地吻合,反映了格子Boltzmann方法的高效性和稳定性,并就二维格子、Boltzmann格式,通过其等价的差分格式,由极值原理证明了该格式的稳定性．     

土壤氮素循环模型及其模拟研究进展

N既是植物必需的营养元素,又是造成环境污染的重要元素.正确模拟土壤中N循环已经成为科学家共同关注的热点问题.简述了土壤N循环的基本过程,重点介绍了13种土壤N循环模型和6个土壤N循环过程的模拟,并讨论了模拟中存在的参数化问题.     

害虫综合治理模型及其最优控制

针对最优害虫综合治理问题,首先建立农作物药效模型,与害虫-天敌动态模型结合起来,建立喷洒杀虫剂和释放天敌的脉冲控制模型,并分析周期解的稳定性.然后利用最优控制理论,求出最适杀虫剂药量和喷洒时间间隔,使得杀虫剂药量在农作物的残留最少,同时使害虫数量控制在经济危害阈值以下,给出一个利用杀虫剂控制农业害虫的最佳方案.最后,通过数值模拟解释这一方案的执行.     

斑块生境中具有捕食风险的动力系统模型及其数值模拟研究

从生物的捕食系统出发．提出了一种斑块生境中具有异质捕食风险的新机制．并构造了一个动力系统模型。在此模型之上,首先研究了扩散对系统稳定性的作用．并对系统进行了计算机模拟。研究发现：具有不同捕食风险的斑块生境之间的扩散(无论是只有食饵的扩散．还是食饵和捕食者共同的扩散)对整个捕食系统所起的作用主要取决于扩散的速率——只有在适中的扩散速率下系统才会稳定．如果扩散速率过快,则引起系统的强烈振荡。当只有食饵发生扩散时,参数f的值越小(f代表高捕食风险生境斑块体积占整个系统体积的比例)．系统越稳定。在捕食者与食饵同时扩散的时候．只有适中或较小的参数f才可以实现系统的长期稳定。其次研究了系统中种群空间平均平衡密度随扩散速率增加的变化趋势。模拟结果表明：系统中食饵种群的空间平均平衡密度随扩散速率增加而减小;捕食者种群平衡密度的变化趋势则取决于系统斑块之间的扩散形式：只有食饵发生扩散时．捕食者种群的空间平衡密度先保持不变．然后缓慢下降;捕食者与食饵同时扩散的时候．捕食者种群平衡密度呈上升趋势。上述结论是由空间异质的捕食风险所决定的．也就是一种下行控制力所限制的结果。综合以上两个结论．认为斑块之间的扩散形式决定了扩散对系统动态的作用和种群空间平均平衡密度对扩散速率增加的反应。     

草间小黑蛛对棉铃虫幼虫的捕食作用及其模拟模型的研究——Ⅱ.捕食者——多种猎物系统的研究

草间小黑蛛Erigonidium graminicolum(Sundevall)与单种猎物的作用关系已在上文述及(李超等,1982),然而草间小黑蛛在自然情形下是一种多食性的捕食性天敌,它的捕食对象不止棉铃虫Heliothis armigera H(?)bner一种。我们在对草间小黑蛛捕食行为的观察中也发现,捕食对象除棉铃虫外还有棉蚜等,并且在棉花上主要是徘徊式地捕获猎物。这样,在草间小黑蛛-棉铃虫作用系统的动态中就必须考虑替代食物的影响。替代食物的存在使捕食者对不同种类的猎物由于有不同的相对喜好程度而产生了对食物的选择,而该相对喜好程度的     

真水狼蛛对褐飞虱捕食作用的初步研究

应用二次正交旋转组合的设计方法,研究了在不同的天敌密度、害虫密度、温度和光照时间的动态系统中,真水狼蛛对稻田主要害虫褐飞虱的捕食作用。得出其控制作用的数学模型为:y=27.4087 3.1667 x_1 6.8333 x_2-1.1667 x_3 0.5000 x_4-0.4258 x_1~2-0.9258 x_2~2-3.1758 x_3~2 .2500 x_1x_2 0.5000 x_1x3-1.5000 x_3x_4通过模型的主效应分析.得出了各环境因子对天敌捕食作用的影响。真水狼蛛对褐飞虱的日捕食量为19.372头。     

The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs

This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.     

棉铃虫卵及幼虫阶段动态的一个计算机模型

本文提出一个棉铃虫卵及幼虫阶段的计算机模拟模型。该模型本质上是按发育和存活的逻辑关系的一个生命表模型。模型的输入信息是逐日白卵量,而它的输出包括每个虫态及年龄的种群大小。模拟方法如下: 其中n_(i,j)~((t))为处于第i虫态第j天年龄的昆虫数量;f_(i,j)为处于第i虫态的昆虫于第j天年龄完成本阶段发育而在下一天进入下一虫态的比例;S_(i,j)为处于第i虫态第j天年龄的昆虫在下一天未完成本阶段的发育但存活的比例。 模拟的结果能较为令人满意地接近自然情形。     

Incorporating prey refuge in a prey–predator model with a Holling type I functional response: random dynamics and population outbreaks

A prey–predator discrete-time model with a Holling type I functional response is investigated by incorporating a prey refuge. It is shown that a refuge does not always stabilize prey–predator interactions. A prey refuge in some cases produces even more chaotic, random-like dynamics than without a refuge and prey population outbreaks appear. Stability analysis was performed in order to investigate the local stability of fixed points as well as the several local bifurcations they undergo. Numerical simulations such as parametric basins of attraction, bifurcation diagrams, phase plots and largest Lyapunov exponent diagrams are executed in order to illustrate the complex dynamical behavior of the system.     

Modeling and analysis of a predator-prey model with disease in the prey

A system of retarded functional differential equations is proposed as a predator-prey model with disease in the prey. Mathematical analyses of the model equations with regard to invariance of non-negativity, boundedness of solutions, nature of equilibria, permanence and global stability are analyzed. If the coefficient in conversing prey into predator k=k(0) is constant (independent of delay tau;, gestation period), we show that positive equilibrium is locally asymptotically stable when time delay tau; is suitable small, while a loss of stability by a Hopf bifurcation can occur as the delay increases. If k=k(0)e(-dtau;) (d is the death rate of predator), numerical simulation suggests that time delay has both destabilizing and stabilizing effects, that is, positive equilibrium, if it exists, will become stable again for large time delay. A concluding discussion is then presented.     

Effect of resource subsidies on predator–prey population dynamics: a mathematical model

The influence of a resource subsidy on predator–prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator–prey-subsidy interactions also increases.     

Effect of resource subsidies on predator-prey population dynamics: a mathematical model

The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.     

Stabilizing effects of spatial heterogeneity in predator-prey systems

A general predator is assumed to divide its hunting time between two sub-habitats with different prey species, spending a larger fraction (φ) of search time in an area as the relative prey abundance there increases. This always causes switching in the model, and changes a functional response from one that imposes a risk on the average prey that decreases with prey density in the direction of one that imposes an increasing risk. I discuss the conditions for a response that is density dependent, and those predatory attributes that make such a response more likely. Transit time between subhabitats always increases the density dependent effect, and is necessary for “system stability” in a Lotka-Volterra model with two prey species. Experiments have confirmed the model's basic assumption. General predators do not fit easily into classical predator-prey models of simple “closed” communities, and then the degree of density dependence of the functional response becomes a useful measure of a predator's short-term stabilizing effect on a prey species. The model demonstrates how spatial heterogeneity can be stabilizing.     

Alternative prey can change model–mimic dynamics between parasitism and mutualism

Classical (conventional) Müllerian mimicry theory predicts that two (or more) defended prey sharing the same signal always benefit each other despite the fact that one species can be more toxic than the other. The quasi‐Batesian (unconventional) mimicry theory, instead, predicts that the less defended partner of the mimetic relationship may act as a parasite of the signal, causing a fitness loss to the model. Here we clarify the conditions for parasitic or mutualistic relationships between aposematic prey, and build a model to examine the hypothesis that the availability of alternative prey is crucial to Müllerian and quasi‐Batesian mimicry. Our model is based on optimal behaviour of the predator. We ask if and when it is in the interest of the predator to learn to avoid certain species as prey when there is alternative (cryptic) prey available. Our model clearly shows that the role of alternative prey must be taken into consideration when studying model–mimic dynamics. When food is scarce it pays for the predator to test the models and mimics, whereas if food is abundant predators should leave the mimics and models untouched even if the mimics are quite edible. Dynamics of the mimicry tend to be classically Müllerian if mimics are well defended, while quasi‐Batesian dynamics are more likely when they are relatively edible. However, there is significant overlap: in extreme cases mimics can be harmful to models (a quasi‐Batesian case) even if the species are equally toxic. A crucial parameter explaining this overlap is the search efficiency with which indiscriminating vs. discriminating predators find cryptic prey. Quasi‐Batesian mimicry becomes much more likely if discrimination increases the efficiency with which the specialized predator finds cryptic prey, while the opposite case tends to predict Müllerian mimicry. Our model shows that both mutualistic and parasitic relationship between model and mimic are possible and the availability of alternative prey can easily alter this relationship.