Using the maximum principle of impulse control for ecology-economical models

In this work we present mathematical models for population of single cohort and homogeneous animals. Investigating these mathematical models, we determine structure of optimal impulsive control which used maximum principle for optimal processes with impulse control.     

惠州市土地资源及其利用保护

从惠州市土地资源及其利用现状入手，分析其在土地资源利用上存在的耕地面积锐减、土地资源承载力下降、耕地土壤肥力下降、水土流失严重以及土壤和农作物被污染等问题，提出相应的土地资源利用和保护措施。     

Sustainability of urban drainage management: a perspective on infrastructure resilience and thresholds

Urban wastewater infrastructures have been threatened by natural and socioeconomic disturbances. This study investigates infrastructure resilience against the risks of long-term changes rather than natural disasters. Urban expansion that leads to an increased urban runoff and massive population movements that cause fluctuations in domestic emissions are considered in this study. Pollution permits for water bodies are adopted as constraints on wastewater infrastructures. A land use-based accounting method, combined with a grid-based database, is developed to map domestic discharge and urban runoff to service areas of wastewater treatment plants. The results of a case study on downtown Sanya, the most famous seashore tourist attraction in China, show that the average resilient values of three sub-catchment areas in 2010 were -0.57, 0.10 and 0.27, respectively, a significant spatial variation. The infrastructure in the Sanya River sub-region is the least flexible, and is more likely to fail due to unstable inflows. The resiliencies will increase to 0.59, 1.01 and 0.54, respectively, in 2020, a considerable improvement in robustness. The study suggests that infrastructure resilience needs to be taken into further consideration for urban planning and the related realm of urban governance to foster more robust wastewater management under various risks.     

环境约束下牧区人口和种群持续增长模型研究

利用多元统计分析方法,对青海湖地区历年人口和种群的统计数据进行分析,并建立在环境约束下人口和种群持续增长模型,对区域人口适度规模、畜群最大环境容纳量和最大持续产量进行了估算和分析。通过估算得出:青海湖地区牦牛环境容纳量为51.9327万头,最大可持续产量为12.9831万头;藏羊环境容纳量为231.203万只,最大可持续产量为57.8007万只。在此分析的基础上,利用建立的相关模型以5a为时间段对青海湖地区未来25a的人口和牲畜数量进行了预测。最后,针对性地提出了大力改善草地生态环境、提高草地利用率和增加草地面积、采取人为措施调节牲畜出栏率、改变草畜生态环境等高原牧区人口、资源与环境可持续发展的对策。     

Influence of host migration between woodland and pasture on the population dynamics of the tick Ixodes ricinus: A modelling approach

Ticks act as vectors of pathogens that can be harmful to animals and/or humans. Epidemiological models can be useful tools to investigate the potential effects of control strategies on diseases such as tick-borne diseases. The modelling of tick population dynamics is a prerequisite to simulating tick-borne diseases and the corresponding spread of the pathogen. We have developed a dynamic model to simulate changes in tick density at different stages (egg, larva, nymph and adult) under the influence of temperature. We have focused on the tick Ixodes ricinus, which is widespread in Europe. The main processes governing the biological cycles of ticks were taken into account: egg laying, hatching, development, host (small, mainly rodents, or large, like deer and cattle, mammals) questing, feeding and mortality. This model was first applied to a homogeneous habitat, where simulations showed the ability of the model to reproduce the general patterns of tick population dynamics. We considered thereafter a multi-habitat model, where three different habitats (woodland, ecotone and meadow) were connected through host migration. Based on this second application, it appears that migration from woodland, via the ecotone, is necessary to sustain the presence of ticks in the meadow. Woodland can therefore be considered as a source of ticks for the meadow, which in turn can be regarded as a sink. The influence of woodland on surrounding tick densities increases in line with the area of this habitat before reaching a plateau. A sensitivity analysis to parameter values was carried out and demonstrated that demographic parameters (sex ratio, development, mortality during feeding and questing, host finding) played a crucial role in the determination of questing nymph densities. This type of modelling approach provides insight into the influence of spatial heterogeneity on tick population dynamics.     

Selecting parameters for calibration via sensitivity analysis: An individual-based model of mosquitofish population dynamics

A stochastic individual-based model (IBM) of mosquitofish population dynamics in experimental ponds was constructed in order to increase, virtually, the number of replicates of control populations in an ecotoxicology trial, and thus to increase the statistical power of the experiments. In this context, great importance had to be paid to model calibration as this conditions the use of the model as a reference for statistical comparisons. Accordingly, model calibration required that both mean behaviour and variability behaviour of the model were in accordance with real data. Currently, identifying parameter values from observed data is still an open issue for IBMs, especially when the parameter space is large. Our model included 41 parameters: 30 driving the model expectancy and 11 driving the model variability. Under these conditions, the use of “Latin hypercube” sampling would most probably have “missed” some important combinations of parameter values. Therefore, complete factorial design was preferred. Unfortunately, due to the constraints of the computational capacity, cost-acceptable “complete designs” were limited to no more than nine parameters, the calibration question becoming a parameter selection question. In this study, successive “complete designs” were conducted with different sets of parameters and different parameter values, in order to progressively narrow the parameter space. For each “complete design”, the selection of a maximum of nine parameters and their respective n values was carefully guided by sensitivity analysis. Sensitivity analysis was decisive in selecting parameters that were both influential and likely to have strong interactions. According to this strategy, the model of mosquitofish population dynamics was calibrated on real data from two different years of experiments, and validated on real data from another independent year. This model includes two categories of agents; fish and their living environment. Fish agents have four main processes: growth, survival, puberty and reproduction. The outputs of the model are the length frequency distribution of the population and the 16 scalar variables describing the fish populations. In this study, the length frequency distribution was parameterized by 10 scalars in order to be able to perform calibration. The recently suggested notion of “probabilistic distribution of the distributions” was also applied to our case study, and was shown to be very promising for comparing length frequency distributions (as such).     

区域农田畜禽承载量预测模型构建与应用:以赤峰市为例

为对区域现有生猪养殖数量的合理性进行评价及对生猪养殖承载量进行预测,从畜禽养殖-耕地-作物系统出发,基于农田养分平衡理论及有机和无机肥合理配施方法,构建区域农田畜禽承载量预测模型。以赤峰市为例,设定有机和无机肥配施比例为5∶5,并保持现有农田N或P2O5养分盈余量不变,分别基于N和P2O5养分盈余量不变实地应用该模型。结果表明,基于N时可新增生猪养殖数量43.6万头,承载量为630.8万头;基于P2O5时可新增生猪养殖数量369.3万头,承载量为1 041.3万头。位于西拉木伦河南岸的松山区、翁牛特旗、喀喇沁旗、宁城县和敖汉旗是可新增生猪养殖的主要区域。从环境压力角度考虑,推荐基于N的预测值作为计算赤峰市可新增生猪养殖量和承载量的依据。     

Measuring and modeling the seasonal changes of an urban Green Treefrog (Hyla cinerea) population

Green Treefrogs (Hyla cinerea) were captured, marked, measured and released at an urban study site in Lafayette, LA, during the 2004 and 2005 breeding seasons. A statistical method based on a generalization of the hypergeometric distribution was used to derive weekly time-series estimates of the population sizes. To describe the population dynamics, a stage structured mathematical model was developed and compared to time-series obtained from the weekly population estimates study using a least-squares approach. Two fitting experiments were done: (1) Using uniform distribution for the birth rate during the breeding season; (2) Using a birth rate distributed according to weekly data on frog calling intensity. Although both model-to-data fits look very promising during the years 2004 and 2005 and result in similar inherent survivorship rates for the tadpoles, juvenile and adult frogs, the fit that uses the calling data predicts a lower number of tadpoles and frogs in the long term than the one that uses uniform birth distribution. The parameter estimates resulting from these fitting experiments are used in the context of stochastic simulations to derive extinction and persistence probabilities for this population. Due to the oscillatory dynamics (with high amplitude) evidenced by the capture-recapture data and corroborated by the model, it is suggested that anuran monitoring efforts should take into account the natural intra-annual variation in population size.     

小流域可持续发展能力的生态足迹法分析--以重庆市万州区五桥河流域为例

以三峡库区五桥河流域为例,将生态足迹理论与方法运用于小流域尺度的可持续发展研究中,采用问卷调查的数据获取方式,保守地估算了该区居民的生态足迹需求和生态足迹供给,并与其他国家(地区)作比较,分析了该区的资源利用效益.结果表明,五桥河流域人均生态足迹需求为1.020 7 hm2·人-1,而生态承载力仅为0.465 2 hm2·人-1,生态赤字达到-0.555 5 hm2·人-1;生态足迹需求及亏缺主要源于林地和草地类产品的消费;五桥河流域生态足迹赤字已经高于全球水平(-0.4 hm2·人-1),资源利用效率仅为世界平均水平的12%,该区发展呈相对不可持续状态.     

Using a fisheries ecosystem model with a water quality model to explore trophic and habitat impacts on a fisheries stock: A case study of the blue crab population in the Chesapeake Bay

Recent calls for the development of ecosystem-based fisheries management compel the development of resource management tools and linkages between existing fisheries management tools and other resource tools to enable assessment and management of multiple impacts on fisheries resources. In this paper, we describe the use of the Chesapeake Bay Fisheries Ecosystem Model (CBFEM), developed using the Ecopath with Ecosim (EwE) software, and the Chesapeake Bay Water Quality Model (WQM) to demonstrate how linkages between available modeling tools can be used to inform ecosystem-based natural resource management. The CBFEM was developed to provide strategic ecosystem information in support of fisheries management. The WQM was developed to assess impacts on water quality. The CBFEM was indirectly coupled with the WQM to assess the effects of water quality and submerged aquatic vegetation (SAV) on blue crabs. The output from two WQM scenarios (1985-1994), a baseline scenario representing actual nutrient inputs and another with reduced inputs based on a tributary management strategy, was incorporated into the CBFEM. The results suggested that blue crab biomass could be enhanced under management strategies (reduced nutrient input) when the effective search rate of blue crab young-of-the-year's (YOY's) predators or the vulnerability of blue crab YOY to its predators was adjusted by SAV. Such model linkages are important for incorporating physical and biological components of ecosystems in order to explore ecosystem-based fisheries management options.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

Solitary behavior in a high-altitude population of the social sweat bee Halictus rubicundus (Hymenoptera: Halictidae)

In the subalpine region of the Rocky Mountains of Colorado, United States, Halictus rubicundus has a solitary life cycle, but it is social in other parts of its known range. The brood is protandrous, with a nearly equal investment in the sexes. Productivity averages 6.5 offspring per foundress female, similar to the second brood of social nests in New York, but less than the combined productivity of both New York broods. Leucophora sp. (Diptera: Anthomyiidae) is the principal cause of brood mortality in Colorado. Foundress females in about half the nests survive until brood emerge as adults. Retention of these foundresses decreases offspring mortality by 68%. Comparable abilities to express solitary behavior with a single brood may characterize other eusocial halictine lineages that have successfully invaded high altitudes in the Rocky Mountains. The apparent inability to do this may help explain the absence of other eusocial halictine bees and polistine wasps at high altitudes, despite their success at lower elevations in the same mountains. Presence or absence of this ability may help explain latitudinal distributions of these lineages in North America. Holarctic distributions of lineages with eusocial behavior can be explained by migration as solitary populations from Eurasia to North America across Pleistocene Bering land bridges, with re-expression of double-brooded, eusocial behavior when the species then extended their ranges southward in North America. Received: 4 November 1994/Accepted after revision: 23 October 1995     

Modeling the brown bear population in Slovenia: A tool in the conservation management of a threatened species

In this paper, we address three aspects of the brown bear population in Slovenia: its size (and its evolution over time), its spatial expansion out of the core area, and its potential habitat based on natural habitat suitability. Data collected through measurement/observation of the bear population and from the literature are used. A model is developed for each aspect. The results are estimates of population size, a picture of the spatial expansion of the population and maps of its optimal and maximal potential habitat (based on natural suitability). Overall, the brown bear population has been increasing since the establishment of a core protective area and has been expanding outside this area. The habitat suitability maps show that there is room for further expansion. Based on habitat suitability and bear population density, as well as human activity and current damage reports, we recommend that the Alps should be temporarily kept free of the bears, until the necessary mitigation measures regarding human–bear conflicts are carried out. On the other hand it is of crucial importance to adapt human activities and improve bear management in the optimal habitat, with which the goals of successful conservation of the species might be achieved.     

Modelling the spatial population dynamics of the green oak leaf roller (Tortrix viridana) using density dependent competitive interactions: Effects of herbivore mortality and varying host-plant quality

Cyclic population dynamics of forest insects with periods of more than two generations have been discussed in relation to a variety of extrinsic and intrinsic forces. In the present study, we employed the selection pressure of density dependent competitive interactions according to Witting's equations (Witting, 2000) as driver for a discrete spatiotemporal model of the green oak leaf roller (Tortrix viridana). The model was successfully parameterised to rebuild the cyclic population dynamics of an empirical data set of a 30-year leaf roller monitoring in Russia. Our analysis focussed on the role of herbivore mortality and host plant food quality, which have a significant effect on T. viridana population dynamics. An additional egg or larvae mortality lowers population density and can lead to selection pressures that favour individuals with higher growth rate. This increased population growth rate can not only compensate the additional mortality, but also can lead to higher average moth abundances in subsequent generations. Furthermore, we analysed the effect of inter- and intraspecific variation in host plant quality on herbivore population dynamics and the spatial distribution of abundance and defoliation patterns. We found significant effects of the qualitative composition of a trees neighbourhood on the herbivore population of the respective tree. Also, the patchy damage patterns observable in reality have been reproduced by the present model. The applicability of the model approach and the putative genetic processes underlying Witting's model are discussed.     

Mark-recapture estimators for dual frame population size of prominent nesting structures: the effect of uncertain detection probability

The combined mark-recapture and line transect sampling methodology proposed by Alpizar-Jara and Pollock [Journal of Environmental and Ecological Statistics, 3(4), 311–327, 1996; In Marine Mammal Survey and Assessment Methods Symposium. G.W. Garner, S.C. Amstrup, J.L. Laake, B.F.J. Manly, L.L. McDonald, and D.C. Robertson (Eds.), A.A. Balkema, Rotterdam, Netherlands, pp. 99–114, 1999] is used to illustrate the estimation of population size for populations with prominent nesting structures (i.e., bald eagle nests). In the context of a bald eagle population, the number of nests in a list frame corresponds to a pre-marked sample of nests, and an area frame corresponds to a set of transect strips that could be regularly monitored. Unlike previous methods based on dual frame methodology using the screening estimator [Haines and Pollock (Journal of Environmental and Ecological Statistics, 5, 245–256, 1998a; Survey Methodology, 24(1), 79–88, 1998b)], we no longer need to assume that the area frame is complete (i.e., all the nests in the sampled sites do not need to be seen). One may use line transect sampling to estimate the probability of detection in a sampled area. Combining information from list and area frames provides more efficient estimators than those obtained by using data from only one frame. We derive an estimator for detection probability and generalize the screening estimator. A simulation study is carried out to compare the performance of the Chapman modification of the Lincoln–Petersen estimator to the screening estimator. Simulation results show that although the Chapman estimator is generally less precise than the screening estimator, the latter can be severely biased in presence of uncertain detection. The screening estimator outperforms the Chapman estimator in terms of mean squared error when detection probability is near 1 wheareas the Chapman estimator outperforms the screening estimator when detection probability is lower than a certain threshold value depending on particular scenarios.     

世纪之交土壤学研究的挑战和契机──从第16届世界土壤学大会看土壤学的未来

第１６届国际土壤学大会包括全会和４５个分会,内容涵盖土壤学所有分支并反映了本世纪土壤学的进展。本文综述了土壤学在全球资源与环境问题中的重要地位,分析了世纪之交土壤学面临的挑战和契机,提出土壤学只有拓展与其它学科以及社会的联系,服务于社会的可持续发展,保持自己的特色并在基础研究和应用研究中不断创新,才能在未来更好地生存和发展。     

Habitat Change and Plant Demography: Assessing the Extinction Risk of a Formerly Common Grassland Perennial

Abstract:  An important aim of conservation biology is to understand how habitat change affects the dynamics and extinction risk of populations. We used matrix models to analyze the effect of habitat degradation on the demography of the declining perennial plant Trifolium montanum in 9 calcareous grasslands in Germany over 4 years and experimentally tested the effect of grassland management. Finite population growth rates (λ) decreased with light competition, measured as leaf-area index above T. montanum plants. At unmanaged sites λ was <1 due to lower recruitment and lower survival and flowering probability of large plants. Nevertheless, in stochastic simulations, extinction of unmanaged populations of 100 flowering plants was delayed for several decades. Clipping as a management technique rapidly increased population growth because of higher survival and flowering probability of large plants in managed than in unmanaged plots. Transition-matrix simulations from these plots indicated grazing or mowing every second year would be sufficient to ensure a growth rate ≥1 if conditions stayed the same. At frequently grazed sites, the finite growth rate was approximately 1 in most populations of T. montanum . In stochastic simulations, the extinction risk of even relatively small grazed populations was low, but about half the extant populations of T. montanum in central Germany are smaller than would be sufficient for a probability of survival of >95% over 100 years. We conclude that habitat change after cessation of management strongly reduces recruitment and survival of established individuals of this perennial plant. Nevertheless, our results suggest extinction processes may take a long time in perennial plants, resulting in an extinction debt. Even if management is frequent, many remnant populations of T. montanum may be at risk because of their small size, but even a slight increase in size could considerably reduce their extinction risk.     

Effects of climate change on moose populations: Exploring the response horizon through biometric and systems models

Interest in the response of moose to climate change has increased because of the potential role they play in the conservation of woodland caribou, and threatened loss to recreational and economic opportunities. The objective of this study is to develop a plausible, parsimonious, systems-level model of moose population dynamics that will be useful in exploring the response of moose populations to climate projections. The study begins with a statistical model of moose carrying capacity, which is then integrated into a systems-level model that predicts moose density based on explicit causal factors. Scenario analysis was conducted using a variety of assumptions concerning biotic and abiotic interactions, and under the A2 climate scenario all model scenarios predict a decline of moose density at the southern limits of the Ontario distribution and an increase at the northern extents. Predicted declines are a result of lower carrying capacity and higher heat stress, parasite loads and wolf predation. Given the sensitivity of the model to density-dependent factors, the indirect effect of parasites on decreased recruitment may have greater impact on moose than the direct effect of increased death rate. Results indicate that conservation planning for woodland caribou populations should account for possible increases in moose and wolf populations.