根茎型木本克隆植物准噶尔无叶豆的种群数量动态

 根据根茎型木本克隆植物的特征, 不以种群的分株数量代表种群大小, 而尝试以不同茎级的根茎长度代表种群大小, 运用种群静态生命表、存活曲线、生殖力表和Leslie矩阵模型, 研究了准噶尔无叶豆(Eremosparton songoricum)的两个种群——A种群(46°31.09′ N, 88°33.06′ E, 紧邻乌伦古湖)和B种群(46°28.07′ N, 88°33.07′ E, 位于沙漠腹地)的种群数量动态。结果表明: 种群存活表现为Deevey-I型。A种群在中龄阶段受到的人为干扰较大, 死亡率出现高峰, 种群的净增长率(R₀)、内禀增长率(r_m)和周限增长率(λ)较低, 表现为衰退型种群, Leslie矩阵模型的模拟结果表明, 15 a内种群呈现下降趋势; B种群所受到的压力主要是干旱贫瘠的荒漠环境所导致的系统压力, 种群的R₀、r_m和λ值适中, 表现为缓慢增长型种群, Leslie矩阵模型的模拟结果表明, 15 a内种群呈现先下降、再上升的趋势。此外, 研究结果验证了Leslie矩阵模型可以扩展应用到根茎型木本克隆植物这类特殊生活型植物的种群数量动态研究上。     

Matrix models and sensitivity analysis of populations classified by age and stage: a vec-permutation matrix approach

Matrix population models in which individuals are classified by both age and stage can be constructed using the vec-permutation matrix. The resulting age-stage models can be used to derive the age-specific consequences of a stage-specific life history or to describe populations in which the vital rates respond to both age and stage. I derive a general formula for the sensitivity of any output (scalar, vector, or matrix-valued) of the model, to any vector of parameters, using matrix calculus. The matrices describing age-stage dynamics are almost always reducible; I present results giving conditions under which population growth is ergodic from any initial condition. As an example, I analyze a published stage-specific model of Scotch broom (Cytisus scoparius), an invasive perennial shrub. Sensitivity analysis of the population growth rate finds that the selection gradients on adult survival do not always decrease with age but may increase over a range of ages. This may have implications for the evolution of senescence in stage-classified populations. I also derive and analyze the joint distribution of age and stage at death and present a sensitivity analysis of this distribution and of the marginal distribution of age at death.     

濒危植物长柄双花木自然种群数量动态

 运用种群生命表、生殖力表、Leslie矩阵模型和时间序列预测分析方法,研究了濒危植物长柄双花木(Disanthus cercidifolius var. longipes)种群的动态变化过程,揭示了长柄双花木各龄级植株的数量动态规律。结果表明：长柄双花木为缓慢负增长型种群;种群的净增殖率、内禀增长率以及周限增长率都较低,世代平均周期较长;Leslie矩阵模型和时间序列预测分析均表明在未来50年内长柄双花木各年龄级种群数量会出现波动性的消长,但其种群总数将逐步下降。导致种群下降的主要原因可能是人为砍伐及由此造成的生境破碎化等。     

Models for age structured populations with distributed maturation rates

In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called distributed delay method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.     

濒危植物南川升麻种群数量动态的分析

运用种群静态生命表、生殖力表和Leslie矩阵模型,研究了中国特有的濒危植物南川升麻种群数量动态过程。结果表明,南川升麻种群为衰退型种群,种群的净增殖率、内禀增长率和周限增长率较低,种群世代周期偏长,在25a内种群幼苗数量和总数量呈现出持续下降的趋势。南川升麻种群经历了两次死亡高峰期,受到了环境筛的强烈过滤作用。     

陕西不同地区栓皮栎种群年龄结构动态模型的研究

栓皮栎种群动态模型能阐明其自然种群动态的规律,揭示种群的内在机制和对种群行为进行预测。矩阵模型是一种i状态分布方法,依靠矩阵形式来处理种群的特征分布,可以模拟和预测种群中各个年龄组的数量动态和年龄结构的变化,它能够从目前已知的年龄结构及种群的生存率和生育率,来推测种群的未来年龄结构。在研究栓皮栎种群动态时,也借用该模型对栓皮栎种群各年龄组的结构和数量动态作出预测。Leslie矩阵模型就是该模型中的一种,利用该模型的理论和方法,对栓皮栎种群的自然变化过程进行了模拟和预测。结果发现,从分布中心到分布边缘,随着生境的差异,栓皮栎种群产生幼苗的年龄级、内禀增长率、生育力和幼苗的数量都发生变化,预测结果与实际反映的情况基本一致,表明Leslie矩阵模型是一种较为理想的反映种群动态的模型。模型表达形式简单,参数生态学意义确切,应用精度高,从而达到准确预测栓皮栎种群动态的目的。     

Aggregation of Leslie matrix models with application to ten diverse animal species

Some grouping is necessary when constructing a Leslie matrix model because it involves discretizing a continuous process of births and deaths. The level of grouping is determined by the number of age classes and frequency of sampling. It is largely unknown what is lost or gained by using fewer age classes, and I address this question using aggregation theory. I derive an aggregator for a Leslie matrix model using weighted least squares, determine what properties an aggregated matrix inherits from the original matrix, evaluate aggregation error, and measure the influence of aggregation on asymptotic and transient behaviors. To gauge transient dynamics, I employ reactivity of the standardized Leslie matrix. I apply the aggregator to 10 Leslie models developed for animal populations drawn from a diverse set of species. Several properties are inherited by the aggregated matrix: (a) it is a Leslie matrix; (b) it is irreducible whenever the original matrix is irreducible; (c) it is primitive whenever the original matrix is primitive; and (d) its stable population growth rate and stable age distribution are consistent with those of the original matrix if the least squares weights are equal to the original stable age distribution. In the application, depending on the population modeled, when the least squares weights do not follow the stable age distribution, the stable population growth rate of the aggregated matrix may or may not be approximately consistent with that of the original matrix. Transient behavior is lost with high aggregation.     

Random Leslie matrices in population dynamics

We generalize the concept of the population growth rate when a Leslie matrix has random elements (correlated or not), i.e., characterizing the disorder in the vital parameters. In general, we present a perturbative formalism to deal with linear non-negative random matrix difference equations, then the non-trivial effective eigenvalue of which defines the long-time asymptotic dynamics of the mean-value population vector state is presented as the effective growth rate. This effective eigenvalue is calculated from the smallest positive root of a secular polynomial. Analytical (exact and perturbative calculations) results are presented for several models of disorder. In particular, a 3 × 3 numerical example is applied to study the effective growth rate characterizing the long-time dynamics of a biological population model. The present analysis is a perturbative method for finding the effective growth rate in cases when the vital parameters may have negative covariances across populations.     

Effects of delay,truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models

Understanding effects of hypotheses about reproductive influences, reproductive schedules and the model mechanisms that lead to a loss of stability in a structured model population might provide information about the dynamics of natural population. To demonstrate characteristics of a discrete time, nonlinear, age structured population model, the transition from stability to instability is investigated. Questions about the stability, oscillations and delay processes within the model framework are posed. The relevant processes include delay of reproduction and truncation of lifetime, reproductive classes, and density dependent effects. We find that the effects of delaying reproduction is not stabilizing, but that the reproductive delay is a mechanism that acts to simplify the system dynamics. Density dependence in the reproduction schedule tends to lead to oscillations of large period and towards more unstable dynamics. The methods allow us to establish a conjecture of Levin and Goodyear about the form of the stability in discrete Leslie matrix models.This research was supported in part by the US Environmental Protection Agency under cooperation agreement CR-816081     

濒危植物大花黄牡丹(Paeonia ludlowii)种群数量动态

运用种群静态生命表、存活曲线、生殖力表和Leslie矩阵模型,研究了西藏特有的濒危植物大花黄牡丹种群数量动态过程。静态生命表和种群存活曲线反映出大花黄牡丹在树龄10a之前和20~25a之间分别经历了强烈的环境筛和竞争自疏,20a左右为其生理寿命,35a左右为极限寿命;大花黄牡丹种群的净增长率、内禀增长率和周限增长率较低,表现为衰退型种群;Leslie矩阵模型的模拟结果表明,在20a内种群幼苗数量和总数量呈现出下降趋势,下降了大约30%;大花黄牡丹种群存活表现为Deevey-Ⅰ型,早期个体死亡极高,幼龄苗木严重不足;现行种群数量主要是靠自身的萌蘖繁殖来维持。导致大花黄牡丹濒危的可能原因是大花黄牡丹的生物学特性以及人为干扰。     

Population Dynamics of Didelphis marsupialis in Northern Colombia

A population of the common opossum, Didelphis marsupialis, inhabiting a highly degraded agricultural area in northern Colombia was studied by live-trapping for over two years. Three transects were established in strips of riparian vegetation within a matrix of agricultural crops. Sampling was performed once in October 1993 and then monthly from August 1994 through December 1995. Four population-level characteristics were estimated: abundance, sex ratio, age structure, and breeding activity. Abundance was very high at the beginning of the study but declined dramatically and then fluctuated at low numbers. The sex ratio did not vary among high-abundance, decline, and low-abundance population phases, but there was a deficiency of females with young at high abundance and of adults during the decline. The impact of these characteristics on the population dynamics of D. marsupialis is discussed with special emphasis on reproductive traits. These characteristics may also contribute to the potential of D. marsupialis as a reservoir for a wide variety of infectious agents.     

Iteroparous reproduction strategies and population dynamics

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are derived for iteroparous populations. First, the governing equations are presented for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile period, and at specific equidistant ages, which are determined by the iteroparous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortality function. Mortality in the period between two reproductive events is assumed to be a continuous process where the death rate for the adults is a function of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the steady-state solution of the continuous-time formulation. Conclusions include that there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the ratio between the maximal age and the reproductive period) is fundamental to determining this convergence. When the vital ratio is rational, an equivalent discrete-time model for the population can be derived whose asymptotic dynamics are periodic and when there are a finite number of founder cohorts, the number of cohorts remains finite. When the ratio is an irrational number, effectively there is convergence to the steady-state age distribution. With a finite number of founder cohorts, the number of cohorts becomes countably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age distribution. The applicability in ecotoxicology of the population matrix model formulation for iteroparous populations is discussed.     

濒危植物大花黄牡丹（Paeonia ludlowii）种群数量动态

运用种群静态生命表、存活曲线、生殖力表和Leslie矩阵模型,研究了西藏特有的濒危植物大花黄牡丹种群数量动态过程。静态生命表和种群存活曲线反映出大花黄牡丹在树龄10a之前和20～25a之间分别经历了强烈的环境筛和竞争自疏,20a左右为其生理寿命,35a左右为极限寿命;大花黄牡丹种群的净增长率、内禀增长率和周限增长率较低,表现为衰退型种群;Leslie矩阵模型的模拟结果表明,在20a内种群幼苗数量和总数量呈现出下降趋势,下降了大约30%;大花黄牡丹种群存活表现为Deevey-Ⅰ型,早期个体死亡极高,幼龄苗木严重不足;现行种群数量主要是靠自身的萌蘖繁殖来维持。导致大花黄牡丹濒危的可能原因是大花黄牡丹的生物学特性以及人为干扰。     

Correlation between numerical dynamics and reproductive behavior in Cypripedium lentiginosum

Isolation, molecular identification and phylogenetic analysis were carried out to investigate the biodiversity of manganese bacteria in sediments which were collected from the Arctic Ocean during the 2^nd Chinese Arctic Scientific Expedition. 21 and 19 species of cultivable strains were isolated from sediments at Stations P11 and S11, respectively, according to their distinct morphological character on the screening plate of manganese medium. Molecular identification and phylogenetic analysis showed that the cultivable manganese bacteria from Station P11 were basically composed of γ-Proteobacteria (γ subgroup of the Proteobacteria branch of the domain Bacteria) and Actinobacteria, which accounted for 86% and 14%, respectively. The isolates of γ-Proteobacteria mainly included Psychrobacter, Shewanella, Acinetobacter and Marinobacter, of which Psychrobacter was the major genus, which accounted for 67% of the γ-Proteobacteria. The cultivable manganese bacteria from Station S11 included α-Proteobacteria, γ-Proteobacteria and Flavobacteria of Bacteroides. The γ-Proteobacteria mainly included Shewanella, Marinomonas and Alteromonas. The majority of α-Proteobacteria was Sphingomonas. The phylogenetic analysis indicated that bacteria from sediments at Stations P11 and S11 had different cultivable manganese microbial communities. All tested strains had higher resistance to Mn²⁺, of which Marinomonas sp. S11-S-4 had the highest resistant ability.     

Asymptotic properties of infinite Leslie matrices

The stable population theory is classically applicable to populations in which there is a maximum age after which individuals die. Demetrius [1972. On an infinite population matrix. Math. Biosci. 13, 133-137] extended this theory to infinite Leslie matrices, in which the longevity of individuals is potentially infinite. However, Demetrius had to assume that the survival probability per time step tends to 0 with age. We generalise here the conditions of application of the stable population theory to infinite Leslie matrix models and apply these results to two examples, including or not senescence.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve, Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rate r₀. The equilibrium recruitment rate r_s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates of r_s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger than r_s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.     

长白山林区核桃楸种群数量动态变化的研究

运用种群年龄结构、存活曲线统计和Leslie模型对长白山核桃楸种群在水胡林、针阔混交林、核桃楸占优杂木林和杂木林4种不同群落类型中种群数量动态变化进行了研究和预测。结果表明,核桃楸种群表现出衰退型的年龄结构特点,幼苗和幼树比例较小,种群在幼年期死亡率较高,反映出核桃楸种群15~20龄在个体经历了比较强烈的环境筛作用;Leslie模型预测显示,核桃楸幼苗数量和种群总数量在今后35年基本呈下降趋势,除在核桃楸占优的林分中种群维持增长外,在其它3中森林类型都表现出衰退趋势。因此,促进核桃楸的天然更新、加强幼苗幼树的抚育工作对长白山地区核桃楸种群的发展至关重要。     

Integrating Temperature-Dependent Life Table Data into a Matrix Projection Model for Drosophila suzukii Population Estimation

Temperature-dependent fecundity and survival data was integrated into a matrix population model to describe relative Drosophila suzukii Matsumura (Diptera: Drosophilidae) population increase and age structure based on environmental conditions. This novel modification of the classic Leslie matrix population model is presented as a way to examine how insect populations interact with the environment, and has application as a predictor of population density. For D. suzukii, we examined model implications for pest pressure on crops. As case studies, we examined model predictions in three small fruit production regions in the United States (US) and one in Italy. These production regions have distinctly different climates. In general, patterns of adult D. suzukii trap activity broadly mimicked seasonal population levels predicted by the model using only temperature data. Age structure of estimated populations suggest that trap and fruit infestation data are of limited value and are insufficient for model validation. Thus, we suggest alternative experiments for validation. The model is advantageous in that it provides stage-specific population estimation, which can potentially guide management strategies and provide unique opportunities to simulate stage-specific management effects such as insecticide applications or the effect of biological control on a specific life-stage. The two factors that drive initiation of the model are suitable temperatures (biofix) and availability of a suitable host medium (fruit). Although there are many factors affecting population dynamics of D. suzukii in the field, temperature-dependent survival and reproduction are believed to be the main drivers for D. suzukii populations.     

高原鼠兔种群生产量生态学的研究Ⅲ.高原鼠兔生命率非密度制约与密度制约的种群动态趋势

本文以高原鼠兔(Ochotona curzoniae)自然种群生命表的统计参数为基础,根据非密度制约Leslie模型及具有密度制约反馈的标准Leslie修正模型,分别预测了该种群在1982-2001年间的发展趋势。在菲密度制约条件下,该种群呈指数增长。在密度制约存在肘,种群增长趋于平衡状态,且存滔率密度制约较繁殖率密度制约对种群的作用更大。存活率密度制约与非密度制约的年龄结构均为Leslie分布,繁殖率密度制约作用的种群稳定年龄分布更平均,其平衡状态的种群大小则由模型的参数决定。     

Is the impact of environmental noise visible in the dynamics of age-structured populations?

Climate change has ignited lively research into its impact on various population-level processes. The research agenda in ecology says that some of the fluctuations in population size are accountable for by the external noise (e.g. weather) modulating the dynamics of populations. We obeyed the agenda by assuming population growth after a resource-limited Leslie matrix model in an age-structured population. The renewal process was disturbed by superimposing noise on the development of numbers in one or several age groups. We constructed models for iteroparous and semelparous breeders so that, for both categories, the population growth rate was matching. We analysed how the modulated population dynamics correlates with the noise signal with different time-lags. No significant correlations were observed for semelparous breeders, whereas for iteroparous breeders high correlations were frequently observed with time-lags of 71 year or longer. However, the latter occurs under red-coloured noise and for low growth rates when the disturbance is on the youngest age group only. It is laborious to find any clear signs of the (red) noise- and age group-specific fluctuations if the disturbance influences older age groups only. These results cast doubts on the possibility of detecting the signature of external disturbance after it has modulated temporal fluctuations in age-structured populations.