带扩散的Logistic单种群模型及其最优收获

在一些合理的假设条件下,就空间分布非均匀的Ｌｏｇｉｓｔｉｃ型收获模型 得到了与空间分布均匀的Ｌｏｇｉｓｔｉｃ型收获模型［１,２,３］完全平行的结论,其中包括种群持续生存和灭绝时收获努力量 Ｅ（ｘ）须满足的充要条件、种群持续生存时趋于正平衡状态的速度估计、种群灭绝时其密度趋于０的速度估计以及在种群持续生存条件下的最优收获努力量 Ｅ、最优平衡解 ｐ（ｘ）和最大收获量 ｈ＊     

广义Logistic模型的捕获优化问题

以王寿松所提出的广义Ｌｏｇｉｓｔｉｃ模型为基础,讨论单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质。在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式,包括著名的Ｓｃｈａｅｆｅｒ模型作为特例,推广了相应的结果。     

具线性脉冲收获的单种群系统的优化控制策略

研究由logistic模型描述的脉冲收获系统的优化控制问题.在给定的时间周期内,选择适当的时刻对种群进行脉冲收获,收获函数既包含比例收获也含有常量收获,研究不同的收获时刻对种群系统的影响,并获得使种群在周期末存储量最大的最优收获策略.首先利用脉冲微分方程的极值原理得到了最优收获时刻应满足的必要条件,并研究当时间周期足够长时具有多次脉冲收获的最优收获策略,进一步考虑了对于任意给定的时间周期和初始种群情形下的最优收获策略问题.最后通过数值模拟验证了本文所得到的主要结果.     

具有阶段结构的自食单种群生长模型的稳定性及最有收获策略

本文讨论了一生中具有两个生长阶段－成年与未成年的种群模型,该模型收获成年种群并且成年种群食自身所产的卵,即模型为自食模型,得到了正平衡点全局渐近稳定的条件及收获成年种群的阈值和最优收获策略。     

复合种群管理的风险评估——以日本鲐为例

单一种群是目前渔业资源评估的基本假设,但渔业资源常由多个地方种群或产卵种群组成,并且种群间存在交流,构成复合种群。根据复合种群概念,以东、黄海日本鲐为例,对其12种种群动态情况进行了模拟。利用模拟所得的数据及剩余产量模型,分别分析了在复合种群、两独立种群及单一种群假设下所设置的10种评估管理方案,结果表明:(1)基于复合种群假设的评估管理方案与模拟的种群动态一致,在单位捕捞努力量渔获量(CPUE)观测误差较小情况下,该方案为最佳方案,可获得最大可持续产量,但随CPUE观测误差增大,该方案种群灭绝率增大,管理效果随之退化。(2)基于两独立种群假设的评估管理方案均使资源过度开发,不利于资源可持续利用。(3)在单一种群假设下,选择不同CPUE作为资源指数和采用不同捕捞量分配方法的评估管理方案存在过度捕捞和开发不足两种状况,其管理效果受种群本身参数及空间交换率等因素的影响而不同;若采用的CPUE反映部分种群动态信息,则其评估管理方案至少在一种模拟情况下出现种群100%灭绝;若CPUE能反映整个种群资源量的动态变化,且捕捞量能按种群的空间结构进行分配,则管理效果与(1)类似,但不能获得最大可持续产量,若忽略种群的空间结构影响而均匀分配捕捞量,则至少在一种模拟情况下出现种群100%灭绝。据此,对于复合种群的管理,建议:(A)如果种群数据收集及数据精度能得到保证,该资源的评估与管理应基于复合种群假设;(B)如果目前收集种群数据存在较大困难,且CPUE数据存在较大误差,则可采用单一种群假设,但必须设定更保守的捕捞量和采用基于种群空间结构的总许可渔获量(TAC)管理方案;(C)在制定渔业管理政策时,应结合种群生态、数据、模型假设及参数估计方法等方面的不确定性对管理控制规则进行系统的管理策略评价以避免风险。     

海北藏系绵羊种群结构及其出栏方案最优化的探讨

配置畜群结构是管理畜牧生产最重要的工作之一。目前我国普遍存在着畜群结构不合理的现象。藏羊是我国第二大绵羊品种,其生产管理落后,种群结构普遍不合理。为组织合理生产,本文用系统分析的方法对藏羊种群结构进行了研究。首先,根据实地调查研究,作者构成了一个矩阵模型,以描述藏羊种群的性别年龄结构状态: N_(t+1)=AN_t-BU_t 其中AN_t反映羊群的自然变动情况,U_t是人为控制量。 然后,以最大羊产品收获为目标,以牧草资源和种群平衡态为限制条件,本文构造了一个线性规划模型,用以计算最优藏羊种群结构及其出栏方案; 除了给出模型这个研究种群结构问题的方法之外,本文使用线性规划模型,利用作者在青海省门源县风闸口地区调查测定的数据,通过计算机,算出了该地最优藏羊种群结构及其出栏方案。在最大能量收获的目标下。最优结构应为,67.80％的繁殖母羊,28.36％的后备母羊,3.84％的种公羊和后备种公 羊。相应出栏方案是每年秋季出栏全部羯羊羔和老弱羊,并且出栏33.17％的成年母羊。在这种方案下,按现有羊只生产能力,出栏率可提高到52.79％,平均从每百公斤牧草中收获合11.72千千卡能量或3.65公斤活重的羊产品。     

一类具周期系数的单种群模型及其最优收获策略

文［１］用直接求解的方法,得到了具周期系数的广义Ｌｏｇｉｓｔｉｃ单种群收获模型的最优收获策略．本文在参照并推广文［２］中一类具周期系数的单种群收获模型周期解的全局渐近稳定性结果的基础上,用变分方法得到了其最优收获策略．所得结果包括了许多常见的自治单种群模型所对应的具周期系数的收获模型,如Ｌｏｇｉｓｔｉｃ型［１］,Ｇｉｌｐｉｎ和Ａｙａｌａ型, Ｇｏｍｐｅｒｔｚ型［３］,以及具类似于Ⅱ,Ⅲ类Ｈｏｌｌｉｎｇ型功能性反应的密度制约函数［４,５］的模型等．     

稳定有界的Logistic方程的最优捕获策略

考虑单种群非自治的Logistic方程的开采问题．在R^ 中都存在均值的意义下,作为周期和概周期函数的推广,首先给出稳定有界函数的概念．然后定义一个新的最终最优收获策略用于处理我们的问题．选择单位时间的最大持久收益的极限均值作为管理目标。同时得到了最佳的种群水平．作为应用,我们以概周期系数的Logistic方程为例,表明我们的结果不仅推广了经典的Clark关于自治的Logistic方程的收获问题,而且推广了范猛和王克的关于周期的Logistic方程的收获问题的结果．     

具脉冲收获切换单种群动力学模型控制阈值研究

建立具脉冲收获切换单种群动力学模型,利用离散动力系统频闪映射理论,得到系统种群灭绝与系统种群持续生存的控制阈值.结果表明一个周期内适当的二次收获种群对系统种群持久起着重要作用,从而为现实的生物资源管理与生物多样性保护提供了可靠的策略依据.     

羊草无性系植物种群觅养生长格局与资源分配的研究

本文按照理论种群生态学的研究方法,从生长参数的形态功能变化和发育参数的时间变化入手,系统地研究了羊草无性系植物种群觅养生长格局与资源分配的基本规律。研究结果表明,羊草无性系种群适合于用ψ＝0.5、μ=1.0、Tr=7和Ts＝2的分配函数模型描述其觅养生长格局与资源分配。文中建立了大小—制约分配模型,并用此模型预测了与觅养生长格局有关的资源分配。这一研究深刻地揭示了较为动物种群搜索途径复杂得多的无性系植物种群的觅养行为。     

The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model

The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided.     

一类生物种群投资的最优采收控制

在原有的Gauss白噪声刻画环境噪声项的基础上,考虑环境不可预知的跳跃性变化,运用Lévy白噪声建立了有界环境中的随机生物种群模型.并且,引入随机奇异控制来描述投资者的最优采收策略.进一步地,构造一族有着不同起点的控制问题,利用动态规划的思想,给出了最优采收控制问题解的充分条件,进而,将随机控制问题的求解转化为确定型偏微分方程的求解.     

Fishery policy when considering the future opportunity of harvesting

Free access to a common pool of resource in a country may lead to over-exploitation and sacrifice future opportunities of harvesting. As such, the protection of a common fishery resource is worth investigating. In this paper we develop a two-period model and a multi-period model to analyze the optimal inter-temporal utilization of a finite resource of stock and propose to impose a tax on the harvest rate as an efficient mechanism with an aim at economic sustainability by incorporating the future opportunity of harvesting into the models as a major component of social objectives. The sensitivity analysis of the two-period model shows that (1) labor inputs for harvesting in Period 1 should be reduced, the biomass of fishery stock will increase, but the harvesting in Period 2 should be amplified and the biomass of fishery stock in Period 2 will not be affected if the current generation owns a higher valuation on the future opportunity of harvesting; (2) a higher internal regeneration rate leads to higher harvesting in each period and a higher level of fishery stock in Period 1, but an uncertain level of fishery stock in Period 2; (3) with a higher discount rate the harvesting in Period 1 should increase, but the harvesting in Period 2 should fall and the level of fishery stock in each period will be reduced; (4) a higher fish price in Period 1 leads to higher harvesting in Period 1, but reduced harvesting in Period 2. As a consequence, the level of fishery stock in each period will be reduced; (5) the effect of a change in fish prices in Period 2 on the harvesting and the level of fishery stock in Period 1 is uncertain, but the change in fish prices in Period 2 gives a positive effect on harvesting in Period 2 and a negative effect on the level of fishery stock in Period 2; (6) higher labor wages in Period 1 lead to lower harvesting, but a higher level of fishery stock in Period 1. This encourages an increase in harvesting in Period 2 and leads to a higher level of fishery stock in Period 2; and (7) a change of the labor wage in Period 2 affects the harvesting and the level of fishery stock in Period 1 indecisively, but it gives negative effects on the harvesting in Period 2 and positive effects on the level of fishery stock in Period 2.     

Optimal harvesting of fish stocks under a time-varying discount rate

Optimal control theory has been extensively used to determine the optimal harvesting policy for renewable resources such as fish stocks. In such optimisations, it is common to maximise the discounted utility of harvesting over time, employing a constant time discount rate. However, evidence from human and animal behaviour suggests that we have evolved to employ discount rates which fall over time, often referred to as “hyperbolic discounting”. This increases the weight on benefits in the distant future, which may appear to provide greater protection of resources for future generations, but also creates challenges of time-inconsistent plans. This paper examines harvesting plans when the discount rate declines over time. With a declining discount rate, the planner reduces stock levels in the early stages (when the discount rate is high) and intends to compensate by allowing the stock level to recover later (when the discount rate will be lower). Such a plan may be feasible and optimal, provided that the planner remains committed throughout. However, in practice there is a danger that such plans will be re-optimized and adjusted in the future. It is shown that repeatedly restarting the optimization can drive the stock level down to the point where the optimal policy is to harvest the stock to extinction. In short, a key contribution of this paper is to identify the surprising severity of the consequences flowing from incorporating a rather trivial, and widely prevalent, “non-rational” aspect of human behaviour into renewable resource management models. These ideas are related to the collapse of the Peruvian anchovy fishery in the 1970's.     

Maximum sustainable yield of populations with continuous age-structure.

We address the problem of finding the harvesting policy that will maximize the yield and maintain a population in a steady state. The population is characterized by continuous age classes and therefore follows differential equations. Here, we assume that the equations are linear (no density dependence). Two possible constraints are considered: either recruitment or total population are fixed to a constant. Under these conditions, the optimal policy is to harvest the fraction theta of a younger age class ? and to harvest totally an older age class b. The optimal solution (theta, ?, b) can be calculated explicitly if the fecundity and mortality schedules are given. The solution is compared to the simpler strategy of harvesting all individuals beyond a single age class a. It is shown that the latter strategy can be much less profitable than harvesting two age classes because it cannot take account of the different values of individuals according to their age.     

Optimal harvesting strategies for a metapopulation

We consider optimal strategies for harvesting a population that is composed of two local populations. The local populations are connected by the dispersal of juveniles, e.g. larvae, and together form a metapopulation. We model the metapopulation dynamics using coupled difference equations. Dynamic programming is used to determine policies for exploitation that are economically optimal. The metapopulation harvesting theory is applied to a hypothetical fishery and optimal strategies are compared to harvesting strategies that assume the metapopulation is composed either of single unconnected populations or of one well-mixed population. Local populations that have high per capita larval production should be more conservatively harvested than would be predicted using conventional theory. Recognizing the metapopulation structure of a stock and using the appropriate theory can significantly improve economic gains.     

Optimization of harvesting age in an integral age-dependent model of population dynamics

The paper deals with optimal control in a linear integral age-dependent model of population dynamics. A problem for maximizing the harvesting return on a finite time horizon is formulated and analyzed. The optimal controls are the harvesting age and the rate of population removal by harvesting. The gradient and necessary condition for an extremum are derived. A qualitative analysis of the problem is provided. The model shows the presence of a zero-investment period. A preliminary asymptotic analysis indicates possible turnpike properties of the optimal harvesting age. Biological interpretation of all results is provided.     

Pontryagin's principle for control problems in age-dependent population dynamics

In this paper, Pontryagin's principle is proved for a fairly general problem of optimal control of populations with continuous time and age variable. As a consequence, maximum principles are developed for an optimal harvesting problem and a problem of optimal birth control.     

An ecological perspective on marine reserves in prey–predator dynamics

This paper describes a prey–predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.     

A theory for optimal monitoring of marine reserves

Monitoring of marine reserves has traditionally focused on the task of rejecting the null hypothesis that marine reserves have no impact on the population and community structure of harvested populations. We consider the role of monitoring of marine reserves to gain information needed for management decisions. In particular we use a decision theoretic framework to answer the question: how long should we monitor the recovery of an over‐fished stock to determine the fraction of that stock to reserve? This exposes a natural tension between the cost (in terms of time and money) of additional monitoring, and the benefit of more accurately parameterizing a population model for the stock, that in turn leads to a better decision about the optimal size for the reserve with respect to harvesting. We found that the optimal monitoring time frame is rarely more than 5 years. A higher economic discount rate decreased the optimal monitoring time frame, making the expected benefit of more certainty about parameters in the system negligible compared with the expected gain from earlier exploitation.