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．     

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.     

一类具年龄结构的线性周期种群动力系统的最优控制

研究一类具有年龄结构的线性周期种群线性动力系统的最优控制问题,即讨论了具有周期的生死率和周期变化的控制项的模型．利用Mazur's定理,证明了最优控制问题最优解的存在性,同时由法锥概念的特征刻画,我们还得到了最优控制问题最优解存在的必要条件．     

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。     

一类周期种群系统的稳定性分析及最优控制问题

本文讨论了一类线性时变周期种群系统的稳定性和最优控制问题.利用Lyapunov函数.对系统的稳定性进行了分析.给出了系统稳定的充分条件.并且利用Banach空间理论,证明了最优收获控制的存在性和唯一性.并且给出了最优控制所满足的必要性条件.     

昆虫种群的遗传调控

昆虫种群的遗传调控是利用昆虫自身生长发育的关键基因,采用性别控制开关,通过遗传转化使雄虫成为携带导致后代雌虫发育异常或雌性不育的遗传控制复合体（性别开关元件和靶标基因的复合体）．昆虫种群遗传调控是一种基于不育技术的昆虫种群控制系统,具有种类特异、环境友好和便捷高效等特点．目前为止,已经由早期的通过辐射不育方法发展到释放携带显性致死基因昆虫的方法,并在多种昆虫中获得成功．本文综述了昆虫种群遗传调控的发展历程,介绍了昆虫种群遗传调控相关的理论与方法,包括特异的调控元件、致死或缺陷基因和遗传转化体系的应用,并列举了几种昆虫种群遗传调控的实例,最后对于昆虫种群遗传调控系统中存在的问题以及可能的发展方向进行了展望．     

一类食饵种群中具有传染病的捕食-被捕食系统

对疾病仅在食饵种群传播的有比例依赖的捕食-被捕食系统的动力学进行了分析,给出了每个平衡点附近系统的性态,定义了决定疾病灭绝和成为地方病的阁值R_0．得出的结论是:在比例依赖的捕食-被捕食系统中,染病食饵种群可以充当一个生物控制量,以抑制种群的绝灭．     

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.     

斜纹夜蛾天敌作用的评价

通过组建斜纹夜蛾第４代和第８代自然种群生命表,运用排除作用控制指数分析了生物因子对斜纹夜蛾种群的自然控制作用．结果表明,低龄（１～３龄）幼虫的捕食性天敌是影响斜纹夜蛾种群数量动态的重要因子．对第４代和第８代种群的排除作用控制指数分别为１３．９０４和１２．９４６．如果没有捕食性天敌的作用,下代种群数量将分别增长到当代的１５．１２０６和７４．６７８倍．病原微生物是影响第４代斜纹夜蛾种群数量的另一重要因子,其排除作用控制指数为２．４７２６．     

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．     

An evolutionary model of stature, age at first birth and reproductive success in Gambian women

We have built a model to predict optimal age at first birth for women in a natural fertility population. The only existing fully evolutionary model, based on Ache hunter-gatherers, argues that as women gain weight, their fertility (rate of giving birth) increases-thus age at first birth represents a trade-off between time allocated to weight gain and greater fertility when mature. We identify the life-history implications of female age at first birth in a Gambian population, using uniquely detailed longitudinal data collected from 1950 to date. We use height rather than weight as an indicator of growth as it is more strongly correlated with age at first birth. Stature does not greatly influence fertility in this population but has a significant effect on offspring mortality. We model age at first reproduction as a trade-off between the time spent growing and reduced infant mortality after maturation. Parameters derived from this population are fitted to show that the predicted optimal mean age of first birth, which maximizes reproductive success, is 18 years, very close to that observed. The reaction norm associated with variation in growth rate during childhood also satisfactorily predicts the variation in age at first birth.     

Estimation of the fertility rates of Japanese wild boars (Sus scrofa leucomystax) using fetuses and corpora albicans

Effective population control of Japanese wild boar (Sus scrofa leucomystax) requires reliable information about population dynamics. Fertility rate is the fundamental component of reproduction to evaluate population dynamics. However, little is known regarding the fertility rate of Japanese wild boar. The traditional hunting practices make it difficult to obtain pregnant females and calculate the fertility rate by checking fetuses as is performed in other countries. Therefore, we focused on the corpora albicans (CA) as the CA remains in the ovaries of postpartum females after pregnancy. This study aimed to evaluate the utility of CA and estimate the fertility rate of Japanese wild boars using CA. Histological analysis of ovaries enabled us to discriminate type 1 CA, which remains for 1 year after breeding. Type 1 CA is a superior indicator compared with lactation in the non-pregnancy season because it allows verification of postpartum females over a long period. The fertility rate was calculated by the combination of pregnant and postpartum females using fetuses and type 1 CA from April to November. The fertility rate of the females captured after the second pregnancy season was 90.3 % during the pregnancy period and 100 % during the non-pregnancy period. The high fertility rate of adult females suggests that intensive adult female harvesting is needed. Our new method to determine fertility rates contributes to developing a monitoring system to adequately control Japanese wild boar population.     

Population growth with stochastic fluctuations in the life table

Monte Carlo simulations with the Leslie matrix and similar population models show that as the variance in survivorship or fecundity increases, the expected population growth rate decreases. This is attributed to Jensen's inequality with the observation that the rate of increase is a concave function of age-specific survivorship and fertility rates. Applications of this observation are advised for demographic studies, population simulation, optimal harvest strategies, and natural selection for variance in fertility and survivorship rates.     

Age-structured optimal control in population economics

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (both age-dependent). By using a new maximum principle for age-structured control systems we derive meaningful results for the optimal migration and saving rate in an aging population. The model used in the numerical calculations is calibrated for Austria.     

Stable controls in age-dependent population dynamics

The classical age-dependent population model is considered, in which mortality depends on total population and fertility is age-dependent. It is shown that in general such systems are not completely controllable with respect to a control variable in the mortality function, but that in certain circumstances a suitable control can be found to hold the population at a specified level.     

短效不育剂控制下季节性繁殖害鼠种群的动态模型

害鼠给人类带来很大的危害,人们可以利用杀鼠剂和不育剂对其进行控制.害鼠在摄食不育剂后导致不育,但有时不育鼠会恢复生育能力,生育后代,使种群规模增大.本文建立了灭杀控制和短效不育控制下害鼠种群的动态模型,在模型中每隔固定时间施行两种控制,在害鼠的繁殖具有季节性的前提下,分析了模型的形态以及害鼠不育率、灭杀率、控制间隔、不育剂有效期等参数对种群动态的影响.结果表明： 较高的不育率和灭杀率,以及较短的控制间隔会达到更好的控制效果,可以使种群较小,甚至灭绝.短效不育剂限制了不育剂在控制害鼠上的作用,也降低了控制的效果.在使用短效不育剂控制害鼠的情况下,在繁殖季节后期,害鼠种群会有小的恢复.     

Reproductive pattern in agrarian and immigrant receptor populations: a survey of El Ejido (SE Spain)

This paper deals with the fertility pattern of the El Ejido population, an agricultural Spanish community characterised by the rapid development of its modern agrarian economy. Consequently, the arrival of immigrants has sharply increased throughout the second half of the twentieth century, with important demographic consequences as well as reproductive changes. The analyses of the age-specific fertility rate (fx) and the total fertility rate (TFR) were used in order to describe the reproductive pattern of this population in 2000. The main characteristics were the following: a) Regarding the temporal change, an important decrease of fx has been observed in all age groups for the last twenty years, as a consequence of progressive birth control. However, the reproductive pattern has kept almost invariable and has been characterised by a maximum fertility at age group of 25-29 years old. b) Regarding the general Spanish fertility, the comparison of fx in both populations suggests a younger maternity in the agricultural population than in the national, the maximum fertility delayed to the 30-34 age group. c) Moreover, the El Ejido population showed a clear higher offspring per woman (TFR = 1.42) than the national (TFR = 1.24), according to the agrarian character of the El Ejido population. d) Finally, this greater reproductive level of El Ejido is also due to the arrival of women at fertile age, who come mainly from Africa, and above all from Morocco.     

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。     

Some extensions of the use of matrices in population theory

This paper extends Leslie's vector and matrix treatment of populations. A simple matrix is given for species in which adult mortality and fertility are independent of age, but in which the juvenile mortality rate differs from the adult. The population vector can be changed into a population matrix. This should allow equations using functions of the size of the population to be developed. Genetic variables such as sex or other polymorphisms can be introduced, and the notation allows different systems of selection or non-random mating to be specified.     

A comparison of management options for leatherjacket populations in organic crop rotations using mathematical models

1 Pest management in organic systems is challenged by the paucity of options for direct interventions to control damaging populations compared with conventional agriculture. Consequently, a greater emphasis has to be placed on managing pest numbers through a rotation. In the present study, simulation modelling is used to evaluate the effects of different management options on populations of Tipula paludosa (leatherjackets) in organic rotations.
2 The growth of leatherjacket populations in grass was simulated over 5 years for different starting numbers. A significant risk of leatherjacket attack to subsequent crops can be avoided by limiting the fertility building phase of a rotation to a maximum of 2 years.
3 The effect of cultural control through additional cultivation interventions was compared in rotations comprising a grass/clover fertility building phase with host and/or nonhost crops. It is concluded that the effects are marginal and that prophylactic use cannot be recommended.
4 The prophylactic use of biological control agents in permanent grass and grass/arable rotations was investigated. Maximum population reductions in grass were achieved through annual autumn applications but the optimal economic strategy was less frequent than this. Application in the autumn preceding a spring-sown arable crop provided the best risk reduction.
5 A model decision support system for the control of pests in organic systems using data for leatherjacket damage to spring barley is presented. Economic threshold concepts are used to define when cultural control (as additional cultivation) and biocontrol applications should be used.
6 The present study shows the potential benefits of simulation modelling for the rapid evaluation of a wide range of pest management options. Any conclusions drawn from such simulations, however, are provisional until they can be tested experimentally.