一类具有退偿增长曲线的生物种群的捕获优化问题

本文研究一类具有延偿增长曲线的生物种群,讨论了该种群的动力学性质及捕获问题,确定了最优捕获努力量、相应的种群密度和最大可持续捕获量、讨论了开放条件下的生物资源的管理。     

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＊     

环境污染下基于最优捕获策略的近海-远海捕鱼模型的动力学性质(英文)

近年来,由于人类的过度开发,使得海洋资源(尤其是近海海洋资源)急剧下降,加上日益严重的海洋污染,给海洋资源管理带来很大的困难.为了更好的管理和利用海洋资源,本文考虑到环境污染中脉冲扩散对种群的影响,建立了一个近海-远海渔业模型,给出了正周期解存在性及平凡周期解和正周期解全局渐近稳定性的充分条件.进一步,在环境污染的情况下,给出了最优捕获策略,得到了最大持续产量和相应的捕获努力量.最后,通过数值模拟证实了我们所得的结论的正确性.     

害虫种群突变模型的bang-bang控制

本文基于害虫种群的尖点突变模型,结合经济学原理,建立相应的最优捕获模型.根据bang-bang控制理论,设计控制器使害虫种群密度保持在不危害作物种群正常生长的水平,且捕获成本最小.最后利用Matlab软件进行数值仿真,以验证结论的正确性.     

污染环境中可再生资源的最优收获问题

探讨了污染环境下双种群的最优收获问题．利用Pontryagin极大值原理得到一种最优分配方案——处理资源种群体内毒素的努力度与收获资源种群的努力度的分配方案,使经营者的经济收入达到最大,同时也得到次最优均衡解。     

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。     

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。     

具空间扩散的时变种群系统的最优捕获控制

讨论了一类时变种群扩散系统的最优捕获控制的非线性问题,证明了最优捕获控制的存在性,并给出了控制u（t,x）∈Uad为最优的必要条件和最优性组．     

三化螟种群系统的最优管理决策

以三化螟Tryporyza invertulas(Walker)种群动态模型和水稻产量损失预测模型为基础,根据水稻插植期、品种抗性,保护利用自然天敌和杀虫剂多次使用等控制措施以及它们的各种不同组合对该虫种群动态、水稻产量损失串和净收益的影响,以净收益最大为目标函数,研究三化螟种群的最优管理决策。其中,对昆虫种群动态模拟方法作了一点改进,它综合了前人所提出的种群动态模型的优点。建立的系统模型能够提供包括农业防治、生物防治和化学防治措施在内的、对三化螟种群实施有效管理的最优决策方案。     

离散的互惠生态系统的最优捕获策略

本文利用离散的两种群互惠模型给出了在捕获能力不同状况下的不同最优捕获策略,指出了理论上和实践上可获得的最大经济效益。     

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．     

Maximum sustainable yield of a density dependent sex-age-structured population model

The maximum sustainable yield of an age-structured, density dependent, sex-differentiated population is investigated. The model is based on the nonlinear version of the McKendrick [11] model introduced by Gurtin and MacCamy [8], modified to include sex-differentiated dynamics. It is determined that the maximum sustainable yield is attainable by an age specific harvesting policy in which the number of harvesting ages for males and the harvesting ages for females total at most five.     

The Beverton-Holt model with periodic and conditional harvesting

In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton-Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic and conditional harvesting strategies. We find that for large initial populations, constant harvest is more beneficial to both the population and the maximum sustainable yield. However, periodic harvest has a short-term advantage when the initial population is low, and conditional harvest has the advantage of lowering the risk of depletion or extinction. Also, we investigate the periodic character under each strategy and show that periodic harvesting drives population cycles to be multiples (period-wise) of the harvesting period.     

The Beverton–Holt model with periodic and conditional harvesting

In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton–Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic and conditional harvesting strategies. We find that for large initial populations, constant harvest is more beneficial to both the population and the maximum sustainable yield. However, periodic harvest has a short-term advantage when the initial population is low, and conditional harvest has the advantage of lowering the risk of depletion or extinction. Also, we investigate the periodic character under each strategy and show that periodic harvesting drives population cycles to be multiples (period-wise) of the harvesting period.     

Dynamics and Management of Stage-Structured Fish Stocks

With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (in Theor. Popul. Biol. 73, 47–62, 2008) have derived as an approximation of a physiologically-structured counterpart. First, we rigorously prove the existence of steady states in both models, that the models share the same steady states, and that there exists at most one positive steady state. Furthermore, we carry out numerical investigations which suggest that a steady state is globally stable if it is locally stable. Second, we consider multiobjective harvesting strategies which account for yield, profit, and the recovery potential of the fish stock. The recovery potential is a measure of how quickly a fish stock can recover from a major disturbance and serves as an indication of the extinction risk associated with a harvesting strategy. Our analysis reveals that a small reduction in yield or profit allows for a disproportional increase in recovery potential. We also show that there exists a harvesting strategy with yield close to the maximum sustainable yield (MSY) and profit close to that associated with the maximum economic yield (MEY). In offering a good compromise between MSY and MEY, we believe that this harvesting strategy is preferable in most instances. Third, we consider the impact of harvesting on population size structure and analytically determine the most and least harmful harvesting strategies. We conclude that the most harmful harvesting strategy consists of harvesting both adults and juveniles, while harvesting only adults is the least harmful strategy. Finally, we find that a high percentage of juvenile biomass indicates elevated extinction risk and might therefore serve as an early-warning signal of impending stock collapse.     

An assessment of the maximum sustainable yield of ivory from African elephant populations.

A general, logistic population model is used to explore the dynamics of harvested elephant populations. The model includes two features peculiar to elephant populations and the harvesting of ivory. First, because of the shape of the growth curve of tusks with age, the conversion factor that relates the number of elephants killed to the ivory yield in weight is not constant, but a function of the population size. Second, tusks from animals that die from natural causes can be retrieved and included in the total yield of ivory. The implications of the relationship between tusk size and age of an animal on the maximum sustainable yield in terms of ivory tonnage and in terms of the number of tusks are explored. The nonequilibrium implications of the tusk growth curve on the population dynamics under different harvesting strategies are also investigated. Results indicate that the maximum sustainable yield is achieved at very low harvest rates with population levels close to the pristine equilibrium. When tusks from animals that die of natural causes are included in the harvest, the maximum yield may, depending on the mortality and recruitment parameters, occur when there is no direct harvest.     

Analysis of optimal harvesting of a predator-prey model with Holling type IV functional response

This paper investigates a series of harvesting problems of a harvested predator-prey system with Holling type IV functional response. The bionomic equilibrium, the maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system are studied. It is proved that the MSTY does not exist under the independent harvesting mode, while it may be found with the same predator and prey harvesting efforts mode. By applying the Bang-Bang control and the singular control to the harvesting strategy, the optimal equilibrium state of the discussed system converges faster than that of the system utilizing a single harvesting strategy with the fixed harvesting effort. The MISER 3 software package is adopted to obtain the optimization schemes of two control problems by using the control parameterization method. The findings of our study provide a theoretical basis for biological resource management.     

Maximum sustainable yield and species extinction in a prey–predator system: some new results

Though the maximum sustainable yield (MSY) approach has been legally adopted for the management of world fisheries, it does not provide any guarantee against from species extinction in multispecies communities. In the present article, we describe the appropriateness of the MSY policy in a Holling–Tanner prey–predator system with different types of functional responses. It is observed that for both type I and type II functional responses, harvesting of either prey or predator species at the MSY level is a sustainable fishing policy. In the case of combined harvesting, both the species coexist at the maximum sustainable total yield (MSTY) level if the biotic potential of the prey species is greater than a threshold value. Further, increase of the biotic potential beyond the threshold value affects the persistence of the system.     

Optimal harvesting of an age-structured population

Here we investigate the optimal harvesting of an age-structured population. We use the McKendrick model of population dynamics, and optimize a discounted yield on an infinite time horizon. The harvesting function is allowed to depend arbitrarily on age and time and its magnitude is unconstrained. We obtain, in addition to existence, the qualitative result that an optimal harvesting policy consists of harvesting at no more than three distinct ages.     

Harvesting in seasonal environments

Most harvest theory is based on an assumption of a constant or stochastic environment, yet most populations experience some form of environmental seasonality. Assuming that a population follows logistic growth we investigate harvesting in seasonal environments, focusing on maximum annual yield (M.A.Y.) and population persistence under five commonly used harvest strategies. We show that the optimal strategy depends dramatically on the intrinsic growth rate of population and the magnitude of seasonality. The ordered effectiveness of these alternative harvest strategies is given for different combinations of intrinsic growth rate and seasonality. Also, for piecewise continuous-time harvest strategies (i.e., open / closed harvest, and pulse harvest) harvest timing is of crucial importance to annual yield. Optimal timing for harvests coincides with maximal rate of decline in the seasonally fluctuating carrying capacity. For large intrinsic growth rate and small environmental variability several strategies (i.e., constant exploitation rate, linear exploitation rate, and time-dependent harvest) are so effective that M.A.Y. is very close to maximum sustainable yield (M.S.Y.). M.A.Y. of pulse harvest can be even larger than M.S.Y. because in seasonal environments population size varies substantially during the course of the year and how it varies relative to the carrying capacity is what determines the value relative to optimal harvest rate. However, for populations with small intrinsic growth rate but subject to large seasonality none of these strategies is particularly effective with M.A.Y. much lower than M.S.Y. Finding an optimal harvest strategy for this case and to explore harvesting in populations that follow other growth models (e.g., involving predation or age structure) will be an interesting but challenging problem.