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1.
The Leslie population projection matrix may be used to project forward in time the age distribution or age-sex distribution of a population. As it is a singular matrix, it does not have an inverse, and so it is not clear that there is a corresponding procedure for backward projection. In terms of the eigenvalues and eigenvectors of the Leslie matrix, certain generalized inverses are constructed that can sometimes be used advantageously for backward projection. 相似文献
2.
A discrete time model is developed for periodic survivorship and maternal frequency rates. The Leslie matrix is subdivided by an additional variable representing time of birth (season of birth in the example presented) to accommodate both age-specific and time-specific variations in vital rates. Thus, in contrast to the standard time-invariant model, significant periodic alterations in age-specific birth and death rates are explicitly accounted for and may realistically include observed recurrent changes, such as zero or reduced birth rates during unfavorable seasons, etc. Conditions for stability of the extended projection matrix are developed and are shown to be analogous to those of the Leslie model. The periodic model is applicable to populations with overlapping generations in seasonal environments. 相似文献
3.
David H. Anderson 《Mathematical biosciences》1985,76(2):247-248
For the Leslie-matrix population projection model, a simple auxiliary quantity, termed the single-year reduced growth factor, is introduced and used to deduce bounds for the growth factor of the model, i.e. the dominant eigenvalue of the Leslie matrix involved. Extension to the case of internal survival in the age groups and reformulation of parameter sensitivity are briefly discussed. 相似文献
4.
L J Allen 《Mathematical biosciences》1989,95(2):179-187
A density-dependent Leslie matrix model introduced in 1948 by Leslie is mathematically analyzed. It is shown that the behavior is similar to that of the constant Leslie matrix. In the primitive case, the density-dependent Leslie matrix model has an asymptotic distribution corresponding to the logistic equation. However, in the imprimitive case, the asymptotic distribution is periodic, with period depending on the imprimitivity index. 相似文献
5.
A scale of ontogenetic states has been developed for woodreed Calamagrostis canescens, a perennial species dominating the grass layer of fell forest areas. The population structure is considered as a set of age-stage groups of individuals differing both in the ontogenetic stage and the chronological age measured in years. to describe the dynamics through years a special kind of matrix formalism has been proposed which is reducible neither to the classic Leslie matrix for an age-structured population, nor to the well-known Lefkovitch matrix for a stage-structured one, and which does not suffer from excessiveness of the "two-dimensional" representation for the structure implying the projection matrix of a block pattern. It has been shown however that the protection matrix corresponding to C. canescens life-history graph embodies the canonical features of matrix formalism for structured population dynamics, such as the exponential population growth or decline, the convergence to a stable equilibrium structure, the calculable indicator of growth/decline/equilibrium (i.e., a measure of the population reproductive potential) as well as possibility to determine the relative reproductive value of each group. On the other hand, "left-sidedness of the age spectrum", a property that is often observed in real populations and is inherent in Leslie models of growing populations, may fail in the age-stage-structured model. The aggregation of age-stage groups into the age classes is possible only under special strict relationship among the age-stage-specific vital rates of the population. The both circumstances serve a methodical indication that an additional dimension such as the stages, for example, ought to be introduced into the age structure of the model population. 相似文献
6.
Richard A. Hinrichsen 《Population Ecology》2023,65(3):146-166
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. 相似文献
7.
The population projection model based on generalized age-dependent branching processes developed by Mode and Busby (1981) involves the solution of a large number of renewal type equations. It is shown that these equations may be solved recursively. Such a solution has two implications. One is that the projection model may be very efficiently computerized. Second, the recursive algorithm developed has striking similarities to two traditional methods of population projection used by demographers: the Leslie matrix and cohort component methods. The results presented here associate traditional projection techniques with the theory of age-dependent branching processes. 相似文献
8.
A. L. Jensen 《Bulletin of mathematical biology》1997,59(2):255-262
A logistic density-dependent matrix model is developed in which the matrices contain only parameters and recruitment is a
function of adult population density. The model was applied to simulate introductions of white-tailed deer into an area; the
fitted model predicted a carrying capacity of 215 deer, which was close to the observed carrying capacity of 220 deer. The
rate of population increase depends on the dominant eigenvalue of the Leslie matrix, and the age structure of the simulated
population approaches a stable age distribution at the carrying capacity, which was similar to that generated by the Leslie
matrix. The logistic equation has been applied to study many phenomena, and the matrix model can be applied to these same
processes. For example, random variation can be added to life history parameters, and population abundances generated with
random effects on fecundity show both the affect of annual variation in fecundity and a longer-term pattern resulting from
the age structure. 相似文献
9.
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. 相似文献
10.
A generalized subspace approach is proposed for single channel brain evoked potential (EP) extraction from background electroencephalogram (EEG) signal. The method realizes the optimum estimate of EP signal from the observable noisy signal. The underlying principle is to project the signal and noise into signal and noise coefficient subspace respectively by applying projection matrix at first. Secondly, coefficient weighting matrix is achieved based on the autocorrelation matrices of the noise and the noisy signal. With the coefficient weighting matrix, we can remove the noise projection coefficients and estimate the signal ones. EP signal is then obtained by averaging the signals estimated with the reconstruction matrix. Given different signal-to-noise ratio (SNR) conditions, the algorithm can estimate the EP signal with only two sweeps observable noisy signals. Our approach is shown to have excellent capability of estimating EP signal even in poor SNR conditions. The interference of spontaneous EEG has been eliminated with significantly improved SNR. The simulation results have demonstrated the effectiveness and superior performance of the proposed method. 相似文献
11.
Poul. E. Hansen 《Journal of mathematical biology》1983,18(2):149-161
An illustrative method, labelled Strip and Mask, to raise a Leslie matrix to powers is introduced. Starting from a recent article in this journal, the Strip and Mask method is utilized to determine the primitivity pattern of a Leslie matrix, and to discuss some properties of the corresponding population model. 相似文献
12.
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 总被引:1,自引:0,他引:1
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。 相似文献
13.
利用Leslie矩阵,给出了特定雌性动物群周期性地获得稳定收获量的数学模型,并对模型适用于集约化饲养家畜的特殊情况进行了讨论。 相似文献
14.
用Leslie矩阵法预测人口——四川省彭县清平公社1978年人口资料分析 总被引:1,自引:0,他引:1
人口分析是种群生态学研究的主要对象之一。Leslie矩阵则是Leslie(1945)提出的分析动物种群数量变动的一种数学模型。现在它的应用已经推广到资源管理、生态系统的分析等许多方面(Jeffers,1978;Pallard,(1973),Leslie曾利用1960年澳大利亚女性人口资料,从理论上讨论了他自己提出的随机模型的性质。 本文的打算是:借Leslie矩阵法,用四川省彭县清平公社1978年(指从1978年7月1日到1979年6月30日的人口统计年)的人口调查资料作典型,来预测川西平原农村人口的发展趋势和稳定人口分析,从而对四川省在控制人口中采取的人工流产、引产等计划生育补救措施作初步评价。 相似文献
15.
Matrix population models have become popular tools in research areas as diverse as population dynamics, life history theory, wildlife management, and conservation biology. Two classes of matrix models are commonly used for demographic analysis of age‐structured populations: age‐structured (Leslie) matrix models, which require age‐specific demographic data, and partial life cycle models, which can be parameterized with partial demographic data. Partial life cycle models are easier to parameterize because data needed to estimate parameters for these models are collected much more easily than those needed to estimate age‐specific demographic parameters. Partial life cycle models also allow evaluation of the sensitivity of population growth rate to changes in ages at first and last reproduction, which cannot be done with age‐structured models. Timing of censuses relative to the birth‐pulse is an important consideration in discrete‐time population models but most existing partial life cycle models do not address this issue, nor do they allow fractional values of variables such as ages at first and last reproduction. Here, we fully develop a partial life cycle model appropriate for situations in which demographic data are collected immediately before the birth‐pulse (pre‐breeding census). Our pre‐breeding census partial life cycle model can be fully parameterized with five variables (age at maturity, age at last reproduction, juvenile survival rate, adult survival rate, and fertility), and it has some important applications even when age‐specific demographic data are available (e.g., perturbation analysis involving ages at first and last reproduction). We have extended the model to allow non‐integer values of ages at first and last reproduction, derived formulae for sensitivity analyses, and presented methods for estimating parameters for our pre‐breeding census partial life cycle model. We applied the age‐structured Leslie matrix model and our pre‐breeding census partial life cycle model to demographic data for several species of mammals. Our results suggest that dynamical properties of the age‐structured model are generally retained in our partial life cycle model, and that our pre‐breeding census partial life cycle model is an excellent proxy for the age‐structured Leslie matrix model. 相似文献
16.
Daniel Goodman 《Theoretical population biology》1984,25(1):1-20
It has long been conjectured, though without satisfactory proof, that life tables with a long reproductive span are advantageous in an environment where fecundity or immature survival rates fluctuate randomly. In the present analysis we recast the nonlinear Leslie matrix problem as an autoregressive time series model for the birth rate, with random addition and removal of newborn. This transformation renders the model linear with respect to the environmental variation, allowing ready solution for the ultimate population size and for the conditions resulting in stationarity of the population distribution. We show that for life tables where the fecundities of all adult age classes are the same (no restrictions are put on the survivorship schedule, or on the age at first reproduction), and where density dependence operates via total adult density, the realized growth rate is less than the growth rate calculated from the mean Leslie matrix associated with the population's growth history. The degree of the discrepancy increases with the environmental variability, and decreases with iteroparity, thus completing a proof which confirms the correctness of the initial conjecture for a class of biologically reasonable lifetable models. 相似文献
17.
Shandelle M. Henson 《Journal of mathematical biology》1998,37(4):309-328
High dimensional Leslie matrix models have long been viewed as discretizations of McKendrick PDE models. However, these two
fundamental classes of models can be linked in a completely different way. For populations with periodic birth pulses, Leslie
models of any dimension can be viewed as “stroboscopic snapshots” (in time) of an associated impulsive McKendrick model; that
is, the solution of the discrete model matches the solution of the corresponding continuous model at every discrete time step.
In application, McKendrick models of populations with birth pulses can be used to identify the state of the population between
the discrete census times of the associated Leslie model. Furthermore, McKendrick models describing populations with near-synchronous
birth pulses can be viewed as realistic perturbations of the associated Leslie model.
Received: 7 August 1997 / Revised version: 15 January 1998 相似文献
18.
Paine RR 《American journal of physical anthropology》2000,112(2):181-190
Catastrophic episodes (e.g., epidemics, natural disasters) strike with only limited regard for age. A large percentage of catastrophic mortality in a population can lead to a death distribution that resembles the living distribution, which includes greater numbers of older children, adolescents, and young adults than typical mortality profiles. This paper examines both the population implications of a large catastrophic mortality event, based on the Black Death as it ravaged medieval Europe, and its long-term effects on age-at-death distributions. An increased prevalence of epidemic disease is a common feature of reconstructions of the shift to agriculture and the rise of urban centers. The model begins with a hypothetical Medieval living population. This population is stable and characterized by slow growth. It has fertility and mortality rates consistent with a natural-fertility, agrarian population. The effects of catastrophic episodes are simulated by projecting the model population and subjecting it to one large (30% mortality) catastrophic episode as part of a 100-year population projection. A pair of Leslie matrices forms the basis of the projection. The catastrophic episode has important, long-term effects on both the living population and the cumulative distribution of death. The living population fails to recover from plague losses; at the end of the projection, population is still less than 75% its pre-plague level. The age-at-death distribution takes on the juvenile-young adult-heavy profile characteristic of many archaeological samples. The cumulative death profile based on the projection differs from that produced by the stable model significantly (P < 0.05) for 25-50 years after the plague episode, depending on sample size. 相似文献
19.
D. R. Grey 《Journal of mathematical biology》1988,26(2):193-197
The problem of optimal harvesting in equilibrium is considered in a Leslie matrix model in which both mortality and fecundity in all age-classes may be density-dependent. The conclusion is that the optimal strategy is of the two-age-class type, in common with results obtained previously for simpler models. 相似文献
20.
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。 相似文献