集合种群的理论框架与应用研究进展

集合种群的研究是当今国际生态学的重要前沿与热点。随着全球范围的生境破坏和破碎化,集合种群的研究方法已成为数学生态学、理论生态学和保护生物学的重要手段。由于其迅速的发展,集合种群的概念与理论得到迅速扩展与丰富。为了能总观集合种群进展的全局并开展进一步的工作．首先对集合种群的已有概念、理论和模型做了全面的分析和总结;其次对集合种群的发展和概念进行了探讨,以集合种群模型的中心框架：Levins的斑块占据模型为基础,展开对其它原理、效应和机制的探讨;主要包括了Levins原理．即当生境遭到破坏时,空斑块比例在集合种群灭绝前保持不变,然后还分析了Allee效应(集合种群的Allee效应主要是由于建群困难和扩散损失造成的);第三,分析了援救效应：迁入个体可以降低斑块中现有局域种群的灭绝风险。援救效应会增强集合种群的生存力,使空斑块比例下降。第四,探讨了两竞争集合种群的共存机制,即竞争,侵占妥协,其共存机制为空间生境中物种共存提供了有力的理论解释。最后,对集合种群群落中的灭绝债务进行了讨论。并给出了2种最为主要的集合种群空间模拟方法。     

集合种群的Allee效应研究进展

随着全球环境破坏的加剧,物种丧失的速度加快,人们日益关注生物多样性的保护。种群生物学和自然保护生物学的一些研究表明,如果一个局域种群受到Allee效应的影响,最终可能走向灭绝。从物种保护的角度考虑,分别介绍了集合种群水平上的Allee效应的和似Allee效应,比较了集合种群的Allee效应和似Allee效应产生的原因,以及集合种群的Allee效应和局域种群的Allee效应之间的关系、集合种群的似Allee效应和局域种群的Allee效应之间的关系,并提出集合种群的Allee效应还需要进一步的研究。     

Allee效应对具有生境恢复的集合种群的影响

Allee效应与种群的灭绝密切相关,其研究对生态保护和管理至关重要。Allee效应对物种续存是潜在的干扰因素,濒危物种更容易受其影响,可能会增加生存于生境破碎化斑块的濒危物种的死亡风险,因此研究Allee效应对种群的动态和续存的影响是必要的。从包含由生物有机体对环境的修复产生的Allee效应的集合种群模型出发,引入由其他机制形成的Allee效应,建立了常微分动力系统模型和基于网格模型的元胞自动机模型。通过理论分析和计算机模拟表明:(1)强Allee效应不利于具有生境恢复的集合种群的续存;(2)生境恢复有利于种群续存;(3)局部扩散影响了集合种群的空间结构、动态行为和稳定性,生境斑块之间的局部作用将会减缓或消除集合种群的Allee效应,有利于集合种群的续存。     

似Allee效应对2-物种集合种群竞争动态的影响

集合种群具有与局域种群Allee效应相似的现象被称为似Allee效应.将似Allee效应引入2-竞争物种集合种群系统,建立了具有似Allee效应的2-物种集合种群演化动态模型.大量的数值模拟表明:(1)似Allee效应导致集合种群水平上两竞争物种构成的系统具有多个平衡态;(2)似Allee效应使竞争共存物种无法续存甚至全部灭绝,即使种群具有很高的初始斑块占有率,并且最终平衡态随初始斑块占有率变化而改变;(3)似Allee效应可能使竞争排斥物种共同灭绝,且效应越强,物种存活时间越短;但似Allee效应不会增强强物种对弱物种的排斥强度,反而可能使强物种变为弱物种,弱物种变为强物种,其具有与栖息地毁坏类似的影响种群竞争等级排序的作用;(4)似Allee效应对竞争集合种群续存是一个不稳定的干扰因素,微小的变化都将引起系统平衡态的剧变.但对于已经达到平衡态的集合种群系统,似Allee效应对强弱种群多度起到调节与制约的作用,有助于平衡态集合种群的稳定与共存,这一结论更完整的揭示了似Allee效应在竞争集合种群系统发展的不同阶段所起的不同作用.以上这些结论对物种保护及集合群落的管理具有重要的指导意义.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

荒漠破碎化生境中长爪沙鼠集合种群野外验证研究

近年来,人类活动和自然干扰,导致内蒙古阿拉善荒漠区生境的破碎化,出现了长爪沙鼠在不同斑块间的不连续分布,每一斑块内可能存在一个局域种群,而集合种群建立的前提条件,是局域种群斑块状分布在离散的栖息地环境中。2002~2012年每年的4~10月,在阿拉善荒漠区禁牧、轮牧、过牧和开垦4种人为不同利用方式形成的生境斑块中,采用标志重捕法对长爪沙鼠（Meriones unguiculatus）种群进行定点监测。通过分析长爪沙鼠种群动态,计算各局域种群的灭绝风险,利用Spearman秩相关系数检验种群动态的空间同步性,同时以种群周转率对长爪沙鼠扩散能力进行评估,以检验阿拉善荒漠区长爪沙鼠种群空间结构是否具有经典集合种群的功能。结果表明：（1） 不同生境斑块可被长爪沙鼠局域种群占据,11年间捕获长爪沙鼠2~7次不等;（2） 长爪沙鼠所有局域种群均具有灭绝风险,在轮牧区和禁牧区灭绝率高达1.000 0,开垦区灭绝率最低,也达到0.333 4,而本研究期间最大局域种群（2008年过牧区,26只/hm²）,在2010年发生了局域灭绝;（3） 不同生境斑块间没有明显的空间隔离而阻碍局域种群的重新建立,长爪沙鼠扩散能力较强,绝大部分月份的种群周转率在50.0%以上,特别是周转率达到100.0%的月份较多;（4） 不同生境斑块间仅轮牧区和禁牧区中长爪沙鼠种群密度显著正相关（P<0.05）,而其他生境斑块间相关性均不显著（P >0.05）,长爪沙鼠局域种群整体显示出明显的非同步空间动态。阿拉善荒漠区长爪沙鼠种群满足作为经典集合种群物种区域续存的4个条件,具有作为研究小哺乳动物集合种群的潜在价值。     

集合种群空间混沌的模拟研究以及Allee效应、拥挤效应与捕食效应对空间模式的影响

集合种群的空间模式研究是当今生态学的核心问题之一。本研究利用常微分动力系统以及基于网格模型的元胞自动机模型对Allee效应、拥挤效应以及捕食作用集合种群的空间分布模式做了全面的模拟研究。Allee效应描述当种群水平低于某一阈值时会发生由生殖成功几率下降造成的种群负增长率,而拥挤效应是指当种群密度过高时引起的个体性为异常从而达到调节种群增长率的作用。文章组建了3个空间确定性模型：局部作用模型(CIM)、距离敏感模型(DSM)和集合种群捕食模型(MMP)。局部作用模型显示在一维生境中空斑块形成金字塔状,二维模型显示出明显的动态拟周期性以及由空间混沌所形成的异质性。距离敏感模型可导致由迁移个体中密度制约强度决定的集合种群大小复杂动态与种群密度的双峰分布。这些结果说明动态行为的复杂性,不仅可用于表征研究物种的特性,而且可以表明该物种的续存能力与灭绝风险。集合种群捕食模型是概率转换空间模型,利用该模型得出了依赖于模型参数和生境尺度的白组织种群概率空间分布模式。模拟的结果表明,系统的内在机制和这种白组织模式导致捕食者形成集团型不明显的“捕食小组”或“杀手小组”,并具有较高扩散力．但却包括侵占率低、灭绝率高的特点。而使猎物种群形成高集团性、高侵占率、低灭绝率、低扩散力的种群集团。这种特点又使捕食者种群在生境中处于中心地带,而使猎物种群形成在捕食者和生境边缘间的环状分布。这些结果还说明了尺度对于生态学的研究是至关重要的,不同的尺度将产生不同的系统模式。     

生境破坏的模式对集合种群动态和续存的影响

构建了空间关联的集合种群模型,该模型不但包含了种群的空间结构信息,而且引入了破坏生境的全局密度和局部密度两个指标,它们描述了破坏生境的模式.模型揭示了破坏生境的空间分布格局复杂地影响了集合种群的动态和续存,破坏和未破坏生境斑块的均匀混合不利于集合种群的增长和续存,而生境类型聚集分布可以促进集合种群的快速增长和长期续存;对于两种斑块类型相对均匀混合的生境来说,均匀场假设可能会高估集合种群的续存,对于相对斑块类型高度聚集的生境,均匀场假设可能会低估集合种群的续存;物种的迁移范围也会影响集合种群的续存,迁移范围越大的物种越容易抵御生境的破坏而免遭灭绝.这意味着在生物保护中不能仅仅考虑生境的恢复和斑块质量的改善,生境结构的构建也是很重要的,加强生境斑块之间的连通性也有利于物种的长期续存.     

生境丧失对具有似Allee效应集合种群的影响及对策——以江苏盐城为例

似Allee效应对物种续存是潜在的扰动因素,稀有物种更易受其影响,可能增加生存于破碎化栖息地中的珍稀物种的死亡风险;但似Allee效应对多物种集合种群续存的影响及其在珍稀物种保护中的应用未能引起足够重视。将似Allee效应引入集合种群动力模式,建立了生境丧失下具有似Allee效应的n-珍稀物种的集合种群模式,并以江苏盐城滩涂湿地中的29种珍稀物种为研究实例。研究结果表明:(1)似Allee效应导致n-物种集合种群多度作长期变周期振荡,原本竞争共存物种可能无法继续共存,甚至灭绝。(2)似Allee效应增强对次强种及劣势种的生存极为不利,导致次强物种由强至弱灭绝,劣势物种由弱至强依次灭绝。(3)盐城天然湿地丧失29%后,11种劣势物种的集合种群由弱到强将最终依次灭绝,灭绝迟豫时间为304～890a,这些物种即Hanski所指的"活死者"。(4)适度增加栖息地面积是保护珍稀物种多样性的有效方法之一,在盐城现存3200km2的天然湿地基础上适度增加1801～2064km2左右栖息地面积,可以有效保护29种濒危物种的多样性,同时应注意结合针对具体物种的保护措施来提高濒危物种多度。研究结果对物种多样性保护及自然保护区建设具有重要的理论指导意义。     

生境破坏的空间结构对集合种群续存的影响

生境破坏及其影响是生态学亟待解决的问题之一,目前的研究主要集中在破坏数量,即遭破坏生境的比例,对物种续存的影响方面;其中最主要的结论是Levins原理和适合生境斑块最小数量(MASH),而关于生境破坏的空间结构的研究却比较稀少,在本文中,我们首先将偶对近似引入到集合种群的研究当中,并替代原有的均匀场假设.然后我们对生境破坏导致的集合种群大小、空间结构以及分布等做了全面讨论.结果显示:随破坏比例的增加,集合种群大小将下降并且其分布将远离破坏生境.进一步聚集式分布结构将瓦解.随着破坏规则化的下降,集合种群将萎缩并使其聚集结构崩溃,在破坏生境周围集合种群起初将增加然后迅速消失.根据这些结果,我们可以对边界效应进行分析:不能用破坏比例描述生境破坏的程度和影响,而只能用破坏区域边界的长短来描述.根据边界效应,我们可以得出在一连通生境上物种保护的条件是生境破坏后剩余的适合生境比例应该大于破坏前原始生境的一半.居住在斑块环境中的物种比连续生境中生存的物种可以更好地抵抗生境破坏带来的影响.     

Evolutionary dynamics and strong Allee effects

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.     

A general model for stochastic SIR epidemics with two levels of mixing

This paper is concerned with a general stochastic model for susceptible→infective→removed epidemics, among a closed finite population, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribution ‘centred’ on that infective, and each global contact is with an individual chosen independently and uniformly from the whole population. The asymptotic situation in which the local contact distribution remains fixed as the population becomes large is considered. The concepts of local infectious clump and local susceptibility set are used to develop a unified approach to the threshold behaviour of this class of epidemic models. In particular, a threshold parameter R_* governing whether or not global epidemics can occur, the probability that a global epidemic occurs and the mean proportion of initial susceptibles ultimately infected by a global epidemic are all determined. The theory is specialised to (i) the households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective’s household; (ii) the overlapping groups model, in which the population is partitioned in several ways, with local uniform mixing within the elements of the partitions; and (iii) the great circle model, in which individuals are equally spaced on a circle and local contacts are nearest-neighbour.     

Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

Evolution of Complex Density-Dependent Dispersal Strategies

The question of how dispersal behavior is adaptive and how it responds to changes in selection pressure is more relevant than ever, as anthropogenic habitat alteration and climate change accelerate around the world. In metapopulation models where local populations are large, and thus local population size is measured in densities, density-dependent dispersal is expected to evolve to a single-threshold strategy, in which individuals stay in patches with local population density smaller than a threshold value and move immediately away from patches with local population density larger than the threshold. Fragmentation tends to convert continuous populations into metapopulations and also to decrease local population sizes. Therefore we analyze a metapopulation model, where each patch can support only a relatively small local population and thus experience demographic stochasticity. We investigated the evolution of density-dependent dispersal, emigration and immigration, in two scenarios: adult and natal dispersal. We show that density-dependent emigration can also evolve to a nonmonotone, “triple-threshold” strategy. This interesting phenomenon results from an interplay between the direct and indirect benefits of dispersal and the costs of dispersal. We also found that, compared to juveniles, dispersing adults may benefit more from density-dependent vs. density-independent dispersal strategies.     

On fitness in structured metapopulations

In this paper we derive a general expression measuring fitness in general structured metapopulation models. We apply the theory to a model structured by local population size and in which local dynamics is explicitly modelled. In particular, we calculate the evolutionarily stable dispersal strategy for individuals that can assess the local population density in the case where only dispersal is subject to evolutionary control but all other model ingredients are assumed fixed. We show that there exists a threshold size such that at ESS everyone should stay as long as the population size is below the threshold and everyone should disperse immediately as the population size reaches the threshold. Received: 13 August 1999 / Revised version: 2 May 2001 / Published online: 12 October 2001     

Allee-like effects in metapopulation dynamics

The existences of the Allee effect at the local population level and of the Allee-like effect at the metapopulation level are important for both ecology and conservation. Although there have been a great many papers on the Allee effect, they have mainly referred to only local populations and have not dealt with the relationship between the two. In this paper, we begin with local population dynamics and then construct a model including both local population and metapopulation dynamics. Then we simulate with computer at these two levels. The results indicate that the Allee-like effect in a metapopulation may emerge from the imposed Allee effect at the local population level. This threshold fraction of occupied patches below which the metapopulation goes extinct is seriously affected by the per capita migration rate, the survival rate during migration and the initial population size on the occupied patches. We also find that severe demographic stochasticity may compound the metapopulation extinction risk posed by the Allee effect. These conclusions are helpful for nature conservation, especially for the preservation of rare species.     

Critical Mutation Rate Has an Exponential Dependence on Population Size in Haploid and Diploid Populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events.     

Geographic variation in performance of a widespread generalist insect herbivore

1. Generalist herbivores are often widespread and occur in a variety of environments. Due to their broad distribution, it is likely that some populations of generalists will encounter host plants with geographic variation in traits that could affect the herbivore's growth and survival (i.e. performance). However, the geographic pattern of performance has rarely been studied for generalists, especially across large geographic ranges. 2. This study used one of the most generalist herbivore species known, the fall webworm (Hyphantria cunea Drury 1773, Erebidae, Lepidoptera), to experimentally test how the performance of a local population of fall webworms varies with increasing geographic distance of the host plant population from the local herbivore population. Specifically, a transplant experiment was used to compare the performance of one fall webworm population feeding on its local host plants with its performance on host populations from two other locations, 1300 and 2600 km away. 3. It was found that fall webworms performed better on their local host plant populations than on populations from other regions, with performance at its lowest when reared on hosts of the same species from the farthest region. It was also found that local fall webworms do not perform well on hosts commonly used by fall webworms at the other two, more distant sites. 4. This study helps to elucidate how the performance of generalist herbivores varies along their geographic range and suggests possible local adaptation to different sets of hosts across sites.     

Compact model of the quantum short-channel threshold voltage in symmetric Double-Gate MOSFET

A compact model for the threshold voltage in Double-Gate (DG) MOSFET is developed. The model takes into account short-channel effects, carrier quantization and temperature dependence of the threshold voltage. We assume a parabolic variation of the potential with the vertical position in the silicon film at threshold. An analytical expression for the surface potential dependence as a function of bias and position in the silicon film is also developed and used for the inversion charge calculation. The model has been fully validated by 2D quantum numerical simulation and is used to predict the threshold voltage roll-off in DG MOSFET with very short channel lengths and thin films. The comparison with measured threshold voltages shows that the model reproduces with an excellent accuracy the experimental data.     

Dynamics of an age-structured population with Allee effects and harvesting

We propose a discrete-time, age-structured population model to study the impact of Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one. The model can have multiple attractors and the asymptotic dynamics of the population depend on its initial distribution if the maximal growth rate is larger than one. An Allee threshold depending on the components of the unstable interior equilibrium is derived when only the last age class can reproduce. The population becomes extinct if its initial population distribution is below the threshold. Harvesting on any particular age class can decrease the magnitude of the possible stable interior equilibrium and increase the magnitude of the unstable interior equilibrium simultaneously.