MODELING THE EFFECT OF RARITY VALUE ON THE EXPLOITATION OF A WILDLIFE SPECIES SUBJECTED TO THE ALLEE EFFECT

The overexploitation of wildlife species is a serious problem in the field of biodiversity conservation. The species subjected to natural Allee effects are even more threatened by exploitation. Moreover, for many wildlife species, their rarity can fuel their exploitation by making them disproportionately desirable and consequently increasing their market price. In this paper, a mathematical model is proposed and analyzed to study how the value that consumers place on rarity can threaten the survival of a species subjected to natural Allee effects. It is assumed that the value of a species increases as its density declines. The analysis of model shows that the increase in the consumers' response to rarity can drive the system to admit Hopf‐bifurcation and heteroclinic bifurcation. The occurrence of the heteroclinic cycle indicates that the increase in consumers' response to rarity can cause the extinction of the species. It is found that an increase in the Allee threshold causes a decrease in the threshold value of consumers' response below which extinction is inevitable.     

CABRI AS A COGNITIVE TOOL FOR THE EVOLUTION OF A SENSE OF PROVING

Cognitive technologies have been described in the literature as reorganisers of thinking processes, especially where problem solving is concerned. This paper aims to analyse the possible use of Cabri-Géomètre as a cognitive tool in the elaboration of mathematical justifications in the context of problem-based mathematics. Some empirical examples are given to illustrate the significance of the specific learning situation. The complexity of learning environments incorporating computer-based activities is stressed as a condition for them to be effective in the introduction of the idea of mathematical justification and its evolution towards a sense of proving.     

污染环境中三维竞争系统的生存阈值

本文用积分均值法，首次讨论了带有毒素影响的三维竞争系统的Lotka－Volterra模型，得到了各种群平均持续生存与绝灭的阈值．文中所得结论对环境污染以及生物种群影响的理论研究和实际应用有重要意义．文[5,6]的主要结论包含在本文的结果中．     

CONSERVATION OF WILDLIFE. A BIO‐ECONOMIC MODEL OF A WILDLIFE RESERVE UNDER THE PRESSURE OF HABITAT DESTRUCTION AND HARVESTING OUTSIDE THE RESERVE

ABSTRACT. Biodiversity is today threatened by many factors of which destruction and reduction of habitats are considered most important for terrestrial species. One way to counteract these threats is to establish reserves with restrictions on land use and exploitation. However, very few reserves can be considered islands, wildlife species roam over large expanses, often via some density dependent dispersal process. As a consequence, habitat destruction, and exploitation, taking place outside will influence the species abundance inside the conservation area. The paper presents a theoretical model for analyzing this type of management problem. The model presented allows for both the common symmetric dispersal as well as what is called asymmetric dispersal between reserve and outside area. The main finding is that habitat destruction outside may not necessarily have negative impact upon the species abundance in the reserve. As a consequence, economic forces working in the direction of reducing the surrounding habitat have unclear effects on the species abundance within the protected area. We also find that harvesting outside the reserve may have quite modest effect on the species abundance in the reserve. This underlines the attractiveness of reserves from a conservation viewpoint.     

ON THE MANAGEMENT OF INTERCONNECTED WILDLIFE POPULATIONS

Abstract Economic interdependency of wildlife or fish stocks is usually attributed to ecological interdependency, such as predator–prey and competitive relationships, or to density‐dependent migration of species between different areas. This paper provides another channel for economic interdependency of wildlife where density‐independent migration and market price interaction affect the management strategies among different landowners. Management is studied under three market conditions for selling hunting licenses: price taking behavior, monopoly market, and duopoly market. Harvesting of the Scandinavian moose is used as an example. The paper provides several results on how economic interdependency works through the migration pattern. When a duopoly market is introduced, hunting license price interaction among the landowners plays an additional role in determining the optimal harvesting strategy.     

A NOTE ON GLOBAL ATTRACTIVITY OF THE MODEL FOR THE SURVIVAL OF THE RED BLOOD CEELS WITH SEVERAL DELAYS

1 IntroductionConsider the red blood ceels growth model with several delayswhere r(t) E C([0, oo), (0, oo)), Pil ri) n e (0, oo), and r1 2 r2 2'' 2 rm.Eq.(l) was used first by Wazewska-Czyzewska and Lasota [l] as a model forthe survival of the red blood ceels in an animal, see also Arino and Kimmel[2]. There are a lot of activities concerning the asymptotic behavior of (1),see for examp1e [3] and the references cited therein. The following results wasobtained in [l, 3, 4].N'(t) = --pN(t)…     

MODELING THE DYNAMICS OF FISHERY STOCK RECOVERY: IMPLICATIONS FOR THE ASSESSMENT OF NATURAL RESOURCE DAMAGES

ABSTRACT. During the restoration planning phase of the natural resource damage assessment (NRDA) process, potential injuries to natural resources and services are evaluated in terms of the nature, degree and extent of injury so that the need for and scale of restoration actions can be ascertained. Injuries are quantified by comparing the condition of the injured natural resource relative to baseline (pre‐injury) conditions. The “Type A” procedures are used to quantify damages from smaller spills and rely on a standardized methodology and computer model to calculate injury and value of damages. In this model, fishery stock changes from injuries and resulting changes in user participation are not treated as dynamic. If true stock growth and re‐growth are indeed dynamic, then the Type A model is likely underestimating fishery losses. The purpose of this paper is to illustrate the potential for such underestimation by comparing simulated stock and harvest losses under dynamic treatment and a static treatment that more closely represents the way stock and service losses are estimated under the current NRDA process.     

INVESTIGATING THE VIABILITY OF SQUIRREL POPULATIONS; A MODELING APPROACH FOR THE ISLAND OF LESVOS,GREECE

ABSTRACT. Habitat loss and fragmentation are considered to be the most important factors responsible for population decreases in small mammal populations. Particularly important is also the effect of insularity that can act syn‐ergistically with the previous factors. Population Viability Analysis (PVA) combines the spatial component of the problem with the species population structure offering an integrated platform for testing and assessing the effects of critical parameters upon the population viability. Various management options can also be quantified and tested. In the case of Sciurus anomalous, a vulnerable squirrel species endemic in Lesvos, a series of threats and management problems were identified and assessed. A stochastic simulation model was developed and parameterized with field data for the species using the program Ramas/GIS. The results suggested that special attention has to be paid to the planning of road system networks and to stopping illegal hunting, especially when extinction risks for vulnerable populations are higher with the above threats.     

THE SURVIVAL ANALYSIS FOR SINGLE-SPECIES SYSTEM IN A POLLUTED ENVIRONMENT

This article concentrates on the study of a mathematical model for the effect of toxicant levels on a single-species ecosystem in the case where there is a constant emission of a toxicant. Some sufficient conditions for weak persistence and extinction are found. The threshold between persistence and extinction can be established in some cases.     

THE TRACE INDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS （III）

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MODELING OF A BLOCK TARIFF SYSTEM FOR GROUNDWATER REGULATION

The block tariff system is widely used by public utility companies and governments. Because the unit rate is determined at the same time as are choice variables, the resulting endogeneity has been the subject of studies on residential water demand and in labor economics. Without discussing any mechanism that helps people come to their final decisions, these studies rely on observed data and econometric tools to estimate parameters in demand or supply functions. Because their main concern is the amount of resources devoted to a prespecified activity, their methodologies cannot analyze problems in which resources could flow to more than one outlet. This study constructs a computable framework that can deal with the endogeneity issue and help allocate scarce resources to mutually exclusive activities. Using a block tariff system for regulating groundwater extraction by aquaculture farmers in Taiwan as an example, we will show how the government and farmers can rely on the proposed framework to meet their interests.     

综合国力的数学建模

本文考虑社会文明与社会导恶现象的制约机制，建立一个综合国力的非线性数学模型，从数学上讨论了相应的二次微分系统的Ｈｏｐｆ分叉，中心与细焦点的判定，极限环的存在唯一性等问题，并对数学结论予以合理解释，把社会相平面划成社发展区域，社会动荡区域和社会崩溃区域，研讨社会走向，确定纳入社会发展区域的途径。     

SUSTAINABLE FOREST MANAGEMENT FOR OPTIMIZING MULTISPECIES WILDLIFE HABITAT: A COASTAL DOUGLAS-FIR EXAMPLE

Wildlife species viability optimization models are developed to convert a given set of initial forest conditions, through a combination of natural growth and management treatments, to a forest system which addresses the joint habitat needs of multispecies populations over time. A linear model of forest cover and wildlife populations is used to form a system of forest management control variables for wildlife habitat modification. The paper examines two objective functions coupled to this system for optimizing sustainable joint species viability. The first maximizes the product of periodic joint viabilities over all time periods, focusing management resources on long-term equilibria, with less emphasis on conversion strategy. The second iteratively maximizes the minimum periodic joint viability over all time periods. This focuses management resources on the most limiting time periods, typically the conversion phase periods. Both objective functions resulted in either point or cyclic equilibria, with cycle lengths equal to minimum forest treatment ages. A third objective, based on maximizing the minimum individual species periodic viability is used to examine single species emphasis. Examples are developed through a case study of 92 vertebrate species found in coastal Douglas-fir stands of northwestern California.     

MODELING REGENERATION AND PEST CONTROL ALTERNATIVES FOR A FOREST SYSTEM IN THE PRESENCE OF FIRE RISK

This paper addresses a fire and pest protection forest management modeling problem by developing a flexible model which integrates the concepts of: 1) species diversity 2) infestation of susceptible species; 3) natural regeneration and planting; 4) conversion of susceptible to non-susceptible species by planting; 5) pest protection by spraying; 6) age-specific harvesting; 7) intertemporal harvest flow policies; and 8) catastrophic loss due to fire. A linear programming (LP) model economically evaluates alternative regimes for protection spraying of susceptible forest species against insect infestations and alternative harvesting strategies which include conversion of susceptible species to non-susceptible, by planting. These strategies are evaluated subject to catastrophic loss due to fire. An iterative simulation-LP approach tests how well the deterministic model holds in a simulated stochastic environment. This validation procedure involves solving the optimization problem deterministically using average values for the fire and infestation proportions and also at each time period updating the system state by simulating the state transition for the next time period using randomly generated updates and re-solving using the updated state as the new initial condition. An optimal wood supply trajectory in a simulated stochastic environment is therefore constructed. The results from the iterative stochastic solution provide a confidence measure for the deterministic solution.     

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

1991MRSubjectClassification62G05,62E201IntroductionandtheMainResultsInthisarticlewestudysllrvivaldatawhicharesubjecttobothlefttrull(:ationandrightcensoring(LTRC).Morespecifically,let(X,T,Y)denoterandomvariableswhereXisthevariableofinterest,calledthelifetimevariable,withunknowndistributionfullctioll(d.f.)F;Tistherandomlefttruncatiolltiliiewitharbitraryd.f.G,andYistherandorl.1rightcensoringtirliewitharbitraryd.f.H.ItisassumedthatX,T,Yarerxlutuallyindependent.Intheran相似文献   

奖惩系统的数学建模与稳态分析

奖惩系统(Bonus- Malus Systems)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文在最一般的框架下,以有限齐次马尔科夫链对奖惩系统建模,证明了任一奖惩系统皆存在唯一的平稳分布,此外,给出了求解这一平稳分布的一般算法,并揭示了此平稳分布的结构.特别地,针对两种具有特定转移法则的奖惩系统,还给出了它们平稳分布的简明显式表示.     

THE SINGULAR CONVERGENCE OF A CHEMOTAXIS-FLUID SYSTEM MODELING CORAL FERTILIZATION

The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system modeling coral fertilization■ converges to that of the parabolic-elliptic type chemotaxis-fluid system modeling coral fertiliz ation■ in a certain Fourier-Herz space as ε^-1→0.     

相依竞争风险场合下生存函数的广义自相合估计

近些年来,生存函数的非参数估计问题受到了很大的关注.首先,Kaplan 和 Meier(1958)提出了乘积限(product limit)估计,并且证明这种估计实际上也是极大似然估计.而后 Breslow 和 Crowley(1974)、F(?)ldes 和 Rejt(?)(1981)在特定的删失机制和某些连续性假定下探讨了 PL 估计(即乘积限估计)的一些基本性质.Langberg,Proschan 及Quinzi(1981)在相依竞争风险场合下进一步推广了 PL 估计,并证明了 PL 估计是强相合的.Tsai(1986)推广了 Efron 定义的自相合性,在一个风险及—个删失变量的场     

ECONOMIC MODELING OF THE PERSISTENCE OF ANTIMICROBIAL RESISTANCE

Abstract According to the dynamic relationship between antibiotic use and the incidence of multidrug‐resistant bacteria, the effectiveness of antibiotics is characterized as a natural resource exploited by antibiotic use. A major question is whether antibiotic effectiveness should be considered a renewable or an exhaustible resource. This paper presents a model combining epidemiological aspects of the decrease of resistance over time with an economic approach, modeling antimicrobial resistance as a negative externality of antibiotic use. The article concludes that the relative fitness of resistant bacteria is one driving factor for an estimation of the externality. If we, for instance, assume a low degree of relative fitness of resistant bacteria it is shown that resistance decreases fastest directly after antibiotic treatment. Accordingly, cycling of nonidentical drugs improves antibiotic effectiveness because cycling lowers the frequency of use of the individual antibiotic. In this case, antibiotic effectiveness must be characterized as a renewable resource in much the same way as a stock of fish in a lake. In contrast, if we assume a high degree of relative fitness of resistant bacteria, antibiotic effectiveness must be treated as an exhaustible resource because it is declined by every use of antibiotics.     

A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES

In this work, we propose an efficient numerical method for computing the electrostaticinteraction between two like-charged spherical particles which is governed by the nonlinearPoisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterativemethod which leads to a sequence of linearized equations. A modified central finite differ-ence scheme is developed to solve the linearized equations on an exterior irregular domainusing a uniform Cartesian grid. With uniform grids, the method is simple, and as aconsequence, multigrid solvers can be employed to speed up the convergence. Numericalexperiments on cases with two isolated spheres and two spheres confined in a chargedcylindrical pore are carried out using the proposed method. Our numerical schemes arefound efficient and the numerical results are found in good agreement with the previouspublished results.