开发生物资源的最优策略

以dx/dt=rx(1-x/k)-E(t)x为模型,讨论在[0,T]时间内,在初始条件x0和终端条件xT限制下,对生物资源进行开发的最优策略。     

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.     

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.     

Mathematical analysis of a model describing evolution of an asexual population in a changing environment

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection.This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum.From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.     

Micro-arthropod seasonally in streams of varying pH

SUMMARY. 1. Micro-arthropods were sampled seasonally (January, May, August and October) during 1986 from ten, stony riffle sites on streams in the Ashdown Forest of southern England, using both standard benthic and interstitial samplers.
2. Total densities peaked at most sites in summer. Species richness reached a maximum at acid sites in summer but at cireumneutral sites in autumn, when Hydrachnellae and Cladocera were particularly species rich.
3. Individual species showed no obvious differences in seasonally between sites; the majority peaking in summer or autumn, regardless of pH. However, cyclopoid copepods were particularly numerous at acid sites in summer, a pattern not observed at circumneutral sites.
4. Multivariate ordination and classification of data sets from the separate seasons, and all four seasons combined, showed that mean site pH, conductivity, and aluminium and calcium concentrations were the most important variables explaining between-site variation in species composition. This clear distinction between the community structure at acidic and circumneutral sites was evident in all seasons except winter. Species composition was also more predictable throughout the year at low-pH sites.
5. A number of species were taken consistently in interstitial samples and the cyclopoids Diacydops languidus and D. languidoides were restricted to the hyporheos at circumneutral sites. The similar faunal composition of the hyporheos and the epibenthos indicated that the separation of these communities was not well defined in Ashdown Forest streams.     

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．     

Seasonal selection and resource dynamics in a seasonally polyphenic butterfly

Seasonal polyphenisms are widespread in nature, yet the selective pressures responsible for their evolution remain poorly understood. Previous work has largely focussed either on the developmental regulation of seasonal polyphenisms or putative ‘top‐down’ selective pressures such as predation that may have acted to drive phenotypic divergence. Much less is known about the influence of seasonal variation in resource availability or seasonal selection on optimal resource allocation. We studied seasonal variation in resource availability, uptake and allocation in Araschnia levana L., a butterfly species that exhibits a striking seasonal colour polyphenism consisting of predominantly orange ‘spring form’ adults and black‐and‐white ‘summer form’ adults. ‘Spring form’ individuals develop as larvae in the late summer, enter a pupal diapause in the fall and emerge in the spring, whereas ‘summer form’ individuals develop directly during the summer months. We find evidence for seasonal declines in host plant quality, and we identify similar reductions in resource uptake in late summer, ‘spring form’ larvae. Further, we report shifts in the body composition of diapausing ‘spring form’ pupae consistent with a physiological cost to overwintering. However, these differences do not translate into detectable differences in adult body composition. Instead, we find minor seasonal differences in adult body composition consistent with augmented flight capacity in ‘summer form’ adults. In comparison, we find much stronger signatures of sex‐specific selection on patterns of resource uptake and allocation. Our results indicate that resource dynamics in A. levana are shaped by seasonal fluctuations in host plant nutrition, climatic conditions and intraspecific interactions.     

Adaptation to a seasonally varying environment: a strong latitudinal cline in reproductive diapause combined with high gene flow in Drosophila montana

Adaptation to seasonal changes in the northern hemisphere includes an ability to predict the forthcoming cold season from gradual changes in environmental cues early enough to prepare for the harsh winter conditions. The magnitude and speed of changes in these cues vary between the latitudes, which induces strong selection pressures for local adaptation.We studied adaptation to seasonal changes in Drosophila montana, a northern maltfly, by defining the photoperiodic conditions leading to adult reproductive diapause along a latitudinal cline in Finland and by measuring genetic differentiation and the amount of gene flow between the sampling sites with microsatellites. Our data revealed a clear correlation between the latitude and the critical day length (CDL), in which half of the females of different cline populations enter photoperiodic reproductive diapause. There was no sign of limited gene flow between the cline populations, even though these populations showed isolation by distance. Our results show that local adaptation may occur even in the presence of high gene flow, when selection for locally adaptive life-history traits is strong. A wide range of variation in the CDLs of the fly strains within and between the cline populations may be partly due to gene flow and partly due to the opposing selection pressures for fly reproduction and overwinter survival. This variation in the timing of diapause will enhance populations' survival over the years that differ in the severity of the winter and in the length of the warm period and may also help them respond to long-term changes in environmental conditions.     

具有周期传染率的SIR传染病模型的周期解

考虑了具有周期传染率的SIR流行病模型,定义了基本再生数^-R0=β／（μ＋γ）,分析了该模型的动力学性态,证明了当^-R0〈1时无病平衡点是全局稳定的;^-R0〉1时,无病平衡点是不稳定的,模型至少存在一个周期解。对小振幅的周期传染率模型,给出了模型周期解的近似表达式,证明了该周期解的稳定性,最后做了数值模拟,结果显示周期解可能是全局稳定的。     

一类带时滞竞争模型的周期解

研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统．用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件．     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

Two species competition in a periodic environment

The classical Lotka-Volterra equations for two competing species have constant coefficients. In this paper these equations are studied under the assumption that the coefficients are periodic functions of a common period. As a generalization of the existence theory for equilibria in the constant coefficient case, it is shown that there exists a branch of positive periodic solutions which connects (i.e. bifurcates from) the two nontrivial periodic solutions lying on the coordinate axes. This branch exists for a finite interval or spectrum of bifurcation parameter values (the bifurcation parameter being the average of the net inherent growth rate of one species). The stability of these periodic solutions is studied and is related to the theory of competitive exclusion. A specific example of independent ecological interest is examined by means of which it is shown under what circumstances two species, which could not coexist in a constant environment, can coexist in a limit cycle fashion when subjected to suitable periodic harvesting or removal rates.Research supported by National Science Foundation Grant No. MCS-7901307     

Commons and anticommons in a simple renewable resource harvest model

We consider a model where agents harvesting from a renewable resource can impose limitations on the harvesting efforts of other agents. Obstructing the harvesting of others comes at a cost, and is viewed as regulation of resource access. Thus, the agent population comprises agents that do not obstruct (“cooperators”) and agents that obstruct (“obstructors”). As the economically better performing strategy spreads in the population, the system self-organizes at a level of obstruction which depends on the costs of obstruction, the obstruction efficiency and the history of the system. We show that commons and anticommons can be considered as the end points of a continuum of varying degrees of obstruction and we identify three regimes for the stationary state of the evolution dynamics: (i) a state where the system ends up in a tragedy of the commons, (ii) a tragedy of the anticommons state and (iii) a moderately regulated state in between both extremes. The more a policy environment in the moderately regulated state is tuned for optimality, the higher the danger that a fluctuation destabilizes the system into severe overexploitation.     

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature. Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.     

Monthly survival of African Sylvia warblers in a seasonally arid tropical environment

Latitudinal gradients of life-history traits in animals are thought to be shaped by environmental variables. For example, it has been suggested that the increase in avian clutch size from the tropics towards the northern temperate regions is caused by a reduced survival of adult birds in the north due to increasing environmental seasonality. However, the tropical savannahs of East Africa show pronounced seasonality in resources caused by distinct rainy and dry seasons. This raises the question of whether survival and other life-history traits of birds living in these tropical savannahs are influenced by this seasonality, making them more similar to northern temperate species. We used 2-year monthly resighting data, a multistate modelling approach and the program MARK to test whether survival, transition probabilities between breeding states and other life-history traits of two resident Kenyan Sylvia species (Aves: Passeriformes: Sylviidae) are shaped by seasonality of rainfall in their environment. Contradicting our hypotheses, the two species showed only very slight influence of seasonality of rainfall on their survival. Survival in the dry months was hardly lower than in the rainy months. The species in the more seasonal environment ( S. boehmi , annual survival 71%) survived as well as the one in the more constant environment ( S. lugens , 56%). The observed survival rates correspond well to other life-history traits of the two species and are of similar magnitude to survival rates of other tropical passerines. This implies that either seasonality is not the driving force behind the life-history traits of the two species or the birds do not experience their environment as seasonal, as might be suggested by fluctuations in rainfall.     

Deterministic genetic models in varying environments

Summary J. B. S. Haldane and S. D. Jayakar [J. Genet. 58, 237–242 (1963)] argue that, when genotype fitnesses fluctuate from generation to generation, if the geometric and arithmetic means of the fitnesses satisfy certain inequalities, there will be a protected polymorphism. Their assertions are biologically interesting, but their mathematical analysis is not sufficient to support their conclusions. We present a firm mathematical analysis and several examples that demonstrate the need for stronger hypotheses and, in some cases, weaker conclusions.Journal Paper No. J-10136 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project 1669. Partial support by National Institutes of Health, Grant GM 13827