我国人口发展总量的中长期预测模型

通过对1994―2005年男、女出生人口性别比的变化和2001―2005年城镇化趋势的分析,建立了我国人口发展总量的中长期预测模型,并针对在总和生育率四种不同情况下2006-2100年的人口发展状况进行了长期预测和详细分析.在目前人口结构状况下,将总和生育率控制在更替水平左右,既可保证总人口不超过15亿,又能降低人口老龄化程度,可为人口控制、决策提供较为科学的依据.     

工业互联网环境下预防性维修管理多目标协同优化

工期、成本、质量通常作为传统项目管理过程中三大目标,而工业互联网环境下预防性维修管理除了以上三大目标之外还更多的考虑了安全因素.根据设备机群内不同设备分析了其四大目标不同构成和内涵,四大目标决策权重采用经改进的带置信度的专家确定方法,根据工期约束等因素导出资源使用均衡条件.在此基础上构建了非线性条件下四方关系多属性效用函数模型.采用线性递减收敛因子改进下的多点交叉遗传算法进行优化求解,促使种群快速寻找最优解,算法表现出较好的收敛性和多样性使得寻优过程更加合理.     

The chaos and control of a food chain model supplying additional food to top-predator

The control and management of chaotic population is one of the main objectives for constructing mathematical model in ecology today. In this paper, we apply a technique of controlling chaotic predator–prey population dynamics by supplying additional food to top-predator. We formulate a three species predator–prey model supplying additional food to top-predator. Existence conditions and local stability criteria of equilibrium points are determined analytically. Persistence conditions for the system are derived. Global stability conditions of interior equilibrium point is calculated. Theoretical results are verified through numerical simulations. Phase diagram is presented for various quality and quantity of additional food. One parameter bifurcation analysis is done with respect to quality and quantity of additional food separately keeping one of them fixed. Using MATCONT package, we derive the bifurcation scenarios when both the parameters quality and quantity of additional food vary together. We predict the existence of Hopf point (H), limit point (LP) and branch point (BP) in the model for suitable supply of additional food. We have computed the regions of different dynamical behaviour in the quantity–quality parametric plane. From our study we conclude that chaotic population dynamics of predator prey system can be controlled to obtain regular population dynamics only by supplying additional food to top predator. This study is aimed to introduce a new non-chemical chaos control mechanism in a predator–prey system with the applications in fishery management and biological conservation of prey predator species.     

A common age effect model for the mortality of multiple populations

We introduce a model for the mortality rates of multiple populations. To build the proposed model we investigate to what extent a common age effect can be found among the mortality experiences of several countries and use a common principal component analysis to estimate a common age effect in an age–period model for multiple populations. The fit of the proposed model is then compared to age–period models fitted to each country individually, and to the fit of the model proposed by Li and Lee (2005).Although we do not consider stochastic mortality projections in this paper, we argue that the proposed common age effect model can be extended to a stochastic mortality model for multiple populations, which allows to generate mortality scenarios simultaneously for all considered populations. This is particularly relevant when mortality derivatives are used to hedge the longevity risk in an annuity portfolio as this often means that the underlying population for the derivatives is not the same as the population in the annuity portfolio.     

Coherent modeling of male and female mortality using Lee–Carter in a complex number framework

Forecasts of female and male mortality that are conducted independently run the risk of projecting implausible sex differentials and fail to exploit correlations that are known to exist between the sexes. We present a new model for the simultaneous modeling of female and male mortality. The model casts mortality as a complex-valued process where the real and imaginary parts correspond to female and male mortalities, respectively. Calculations proceed similarly to the usual Lee–Carter model, via the singular value decomposition, albeit in complex form. Initial applications suggest that the complex Lee–Carter gives fits that are broadly comparable to independent real fits, while offering the advantage of explicit modeling of the relationship between the sexes. Furthermore, model parameters are informative and easily-interpretable.     

Resonance in Beverton–Holt population models with periodic and random coefficients

An increase in the mean population density in a fluctuating environment is known as resonance. Resonance has been observed in laboratory experiments and has been studied in discrete-time population models. We investigate this phenomenon in the Beverton–Holt model with either periodic or random variables for two biologically relevant coefficients: the intrinsic growth rate and the carrying capacity. Three types of resonance are defined: arithmetic, geometric and harmonic. Conditions are derived for each type of resonance in the case of period-2 coefficients and some results for period p>2. For period 2, regions in parameter space where each type of resonance occurs are shown to be subsets of each other. For the case of random coefficients with constant intrinsic growth rate, it is shown that the three types of resonance do not occur. Numerical examples illustrate resonance and attenuance (decrease in the mean population density) in the Beverton–Holt model when the coefficients are discrete random variables.     

Enhanced interactive satisficing method via alternative tolerance for fuzzy goal programming with progressive preference

This paper proposes an enhanced interactive satisficing method via alternative tolerance for fuzzy goal programming with progressive preference. The alternative tolerances of the fuzzy objectives with three types of fuzzy relations are used to model progressive preference of decision maker. In order to improve the dissatisficing objectives, the relaxed satisficing objectives are sacrificed by modifying their tolerant limits. By means of attainable reference point, the auxiliary programming is designed to generate the tolerances of the dissatisficing objectives for ensuring feasibility. Correspondingly, the membership functions are updated or the objective constraints are added. The Max–Min goal programming model (or the revised one) and the test model of the M-Pareto optimality are solved lexicographically. By our method, the dissatisficing objectives are improved iteratively till the preferred result is acquired. Illustrative examples show its power.     

A New Proof for the Convergence of an Individual Based Model to the Trait Substitution Sequence

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and the process is viewed in the timescale of mutations. Using averaging techniques due to Kurtz (in Lecture Notes in Control and Inform. Sci., vol. 177, pp. 186–209, 1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (in Trends in Ecology and Evolution 7(6), 198–202, 1992), first worked out by Dieckman and Law (in Journal of Mathematical Biology 34(5–6), 579–612, 1996) and rigorously proved by Champagnat (in Theoretical Population Biology 69, 297–321, 2006): rigging the model such that “invasion implies substitution”, we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population.     

A Side-by-Side Single Sex Age-Structured Human Population Dynamic Model: Exact Solution and Model Validation

A side-by-side single sex age-structured population dynamic model is presented in this paper. The model consists of two coupled von Foerster-McKendrick-type quasi-linear partial differential equations, two initial conditions, and two boundary conditions. The state variables of the model are male and female population densities. The solutions of these partial differential equations provide explicit time and age dependence of the variables. The initial conditions define the male and female population densities at the initial time, while the boundary conditions compute the male and female births at zero-age by using fertility rates. The assumptions of the nontime-dependence of the death and fertility rates and a specific factorization of the migratory balances allow us to obtain exact solutions for male and female population densities. In addition, the hypotheses about the mathematical structure of the input variables are formulated, and the exact solution of the model is obtained. Next, the model is applied to the case study of Spain for the time period 1996–2004. Model validation demonstrates that this approach is a powerful prediction tool. Code and data are available upon request.     

A continuous-time stochastic model for the mortality surface of multiple populations

We formulate, study and calibrate a continuous-time model for the joint evolution of the mortality surface of multiple populations. We model the mortality intensity by age and population as a mixture of stochastic latent factors, that can be either population-specific or common to all populations. These factors are described by affine time-(in)homogeneous stochastic processes. Traditional, deterministic mortality laws can be extended to multi-population stochastic counterparts within our framework. We detail the calibration procedure when factors are Gaussian, using centralized data-fusion Kalman filter. We provide an application based on the joint mortality of UK and Dutch males and females. Although parsimonious, the specification we calibrate provides a good fit of the observed mortality surface (ages 0–89) of both sexes and populations between 1960 and 2013.     

A multi-objective heuristic approach for the casualty collection points location problem

In this paper, we formulate the casualty collection points (CCPs) location problem as a multi-objective model. We propose a minimax regret multi-objective (MRMO) formulation that follows the idea of the minimax regret concept in decision analysis. The proposed multi-objective model is to minimize the maximum per cent deviation of individual objectives from their best possible objective function value. This new multi-objective formulation can be used in other multi-objective models as well. Our specific CCP model consists of five objectives. A descent heuristic and a tabu search procedure are proposed for its solution. The procedure is illustrated on Orange County, California.     

Periodic solutions of a Lotka–Volterra type multi‐species population model with time delays

A delayed periodic Lotka–Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Delta-hedging longevity risk under the M7–M5 model: The impact of cohort effect uncertainty and population basis risk

In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7–M5 model is developed and recommended as an industry standard for the assessment of population basis risk. In this paper, we contribute a delta hedging strategy for use with the M7–M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (2) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness.     

STANDARDIZATION OF CATCH-PER-UNIT-EFFORT FOR SHORT-TERM TRENDS IN CATCHABILITY

Examination of daily catch–per–unit–effort (CPUE) information on Pacific halibut revealed sharp declines that could not be explained by natural and fishing mortality. Catchability may have decreased during a fishing period because of local depletions of fish, changes in fish behavior, and other causes. Mathematical models of CPUE with a short–term catchability function of time or effort were based on a generalization of the DeLury method. A method of standardization was developed to account for the length of a fishing period and to correct for catchability. The effort model was best for Pacific halibut data and the application showed that standardization of CPUE is necessary to have a valid index of abundance when short–term changes in catchability occur.     

Modelling to optimise consumptive use of game

There has been a rapid increase in the number of private game ranches established in South Africa in recent years. These ranches are good for conservation but many are driven by the profit motive. A number of models have been used to help managers formulate strategies for achieving their economic objectives. These models are discussed and their use illustrated.A detailed sex and age structured model is presented first with an illustration of its use in attaining two different management objectives. For a given management objective this model generates the returns per unit of food consumed for each species. These returns are then fed into a model to determine the relative abundance of each species in a multispecies herbivory that is required to maximise income.Finally, some problems with the use of these models are discussed. Suggestions and current modelling activities towards improving the tools available to African game ranch managers are presented.     

AN INDIVIDUAL‐BASED MODEL FOR FERAL HOGS IN GREAT SMOKY MOUNTAINS NATIONAL PARK

The expansion of feral hog (Sus scrofa) populations in the United States has resulted in increased efforts to develop and implement control strategies designed to minimize the impacts done by this invasive species. We describe an individual‐based model for feral hogs in Great Smoky Mountains National Park (GSMNP). The objectives of the model are to provide an understanding of the population dynamics of this feral hog population and to determine the efficacy of the annual harvest as a population control method. Results suggest that the dynamics of the population are driven by fall hard mast production and the GSMNP harvests currently limit growth of the population, but these control efforts have not reduced the population.     

Bifurcations in a predator–prey model with general logistic growth and exponential fading memory

A multiparameter predator–prey system generalizing the model introduced in [6] is considered. The system studied in this paper corresponds to the type of models with exponential fading memory where the logistic per capita rate growth of the prey is given by an arbitrary function of class C^k, k ≥ 3. We prove that the model has a Hopf bifurcation and that there exist open sets in the parameter space such that the system exhibits singular attractors and asymptotically stable limit cycles. A numerical simulation is conducted in order to show the existence of critical attractor elements.As pointed out by Ayala et al. in [14], the Lotka–Volterra model of interspecific competition, which is based on the logistic theory of population growth and assumes that the intra and interspecific competitive interactions between species are linear, does not explain satisfactorily the population dynamics of some species. This is due to fact that the model does not take into account some important features of the population, which affect its dynamics. The model introduced in this paper provides independent conditions of these facts, for the existence of a Hopf bifurcation and the asymptotically stable limit cycles.     

POSSIBILITIES AND LIMITATIONS OF USING HISTORIC PROVENANCE TESTS TO INFER FOREST SPECIES GROWTH RESPONSES TO CLIMATE CHANGE

Abstract. Under projected changes in global climate, the growth and survival of existing forests will depend on their ability to adjust physiologically in response to environmental change. Quantifying their capacity to adjust and whether the response is species‐ or population‐specific is important to guide forest management strategies. New analyses of historic provenance tests data are yielding relevant insights about these responses. Yet, differences between the objectives used to design the experiments and current objectives impose limitations to what can be learned from them. Our objectives are (i) to discuss the possibilities and limitations of using such data to quantify growth responses to changes in climate and (ii) to present a modeling approach that creates a species‐ and population‐specific model. We illustrate the modeling approach for Larix occidentalis Nutt. We conclude that the reanalysis of historic provenance tests data can lead to the identification of species that have population‐specific growth responses to changes in climate, provide estimates of optimum transfer distance for populations and species, and provide estimates of growth changes under different climate change scenarios. Using mixed‐effects modeling techniques is a sound statistical approach to overcome some of the limitations of the data.     

Hierarchical Bayesian autoregressive models for large space–time data with applications to ozone concentration modelling

Increasingly large volumes of space–time data are collected everywhere by mobile computing applications, and in many of these cases, temporal data are obtained by registering events, for example, telecommunication or Web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space–time autoregressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method is extended to include autoregressive terms of latent space–time processes. Specifically, a space–time autoregressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space–time process. The resulting model is specified within a hierarchical Bayesian framework, and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8‐h average ground level ozone concentration data from 1997 to 2006 from a large study region in the Eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of noncompliance with respect to the standard, are obtained and illustrated. Copyright © 2012 John Wiley & Sons, Ltd.     

An Age-Structured Population Dynamics Model with Females' Pregnancy and Child Care

We present a deterministic model for an age-structured population dynamics taking into account females' pregnancy, maternal care of offsprings, and environmental pressure with or without spatial migration. The model is based on the age-density notion for a group formed by a mother and her offsprings under maternal care. A harmonic-mean-type mating function of sexes without formation of permanent pairs is used. It is assumed that each sex has the pre-reproductive, reproductive, and post-reproductive age intervals. All adult individuals are divided into males, single females, fertilized females, and females taking child care. Individuals of post-reproductive age belong to the group of singles. All individuals of pre-reproductive age are divided into the young and juvenile groups. Only young offsprings are assumed to be under maternal care. Juvenile individuals can live without maternal care. The model consists of integro-PDEs subject to the conditions of integral type. The existence and uniqueness theorem is proved in the case of unlimited population. Separable solutions and their long-time behavior are studied for the limited nondispersing population. In the case of random migration two types of separable solutions and their long-time behavior for the homogeneous Dirichlet and Neumann boundary conditions are studied. In the case of directed migration in one-dimensional domain with special initial and Dirichlet boundary conditions, the unlimited invasive population dynamics is studied. In particular, an explicit formula for the migration front is given.