A note concerning time parameterization of Markovian models of ecosystem flow analysis

A continuous Markovian model of resource flow in a steady state ecosystem model is developed. This model calculates the mean and variance of the frequency of intercompartmental cyclings and duration of compartmental residence times. This model is compared with an analogous discrete Markovian flow model to demonstrate the sensitivity of discrete and continuous ecosystem flow analyses. Appropriate time parameterization of of discrete Markovian flow models is then discussed with special reference to Shannon's theorem of dynamic system sampling.     

A note on density dependence in population models

One of the most studied phenomena in ecology is density dependent regulation. The model most frequently used to study this behaviour is the theta-logistic model. However, disagreement has developed within the ecology community pertaining to the interpretation of this model’s parameters, and thus as to appropriate values for the parameters to assume. In particular, the parameter θ$\theta$ has been allowed to take negative values, resulting in the ‘growth rate parameter’ estimated to be negative for species which are extant and exhibit no signs of becoming extinct in the short-term. Here we explain this phenomenon by formulating the theta-logistic model in the manner in which the original logistic model was formulated by Verhulst (1838), in doing so providing a simple interpretation of model parameters and thus restrictions on values the parameters may assume. We conclude that θ$\theta$ should (almost always) be restricted to values greater than −1$-1$. This has implications for studies assessing the form of density dependence from data. Additionally, another model appearing in the literature is presented which provides a more flexible model of density dependence at the expense of only one additional parameter.     

A note on some mathematical models on the effects of Bt-maize exposure

Some mathematical models for the estimation of the effects of Cry1Ab and Cry1F Bt-maize exposure in the biodiversity are examined. Novel results about these models are obtained and described in this note. The exact formula for the proportion of population that suffers mortality exposed either to Cry1Ab or Cry1AF pollen is derived. Moreover, regarding Cry1F pollen effects, the species sensitivity of Lepidoptera is discussed.     

Adequacy of ecosystem models

A formal approach is developed to assess the adequacy of mathematical models to represent a given ecosystem. The procedure is based on the hypothesis that two or several models of an environment can be compared by using a vectorial approach: several model properties are analyzed and related to the model's capability to simulate the observed behaviour and to describe the ecosystem processes. The models are thus ordered from the standpoint of their adequacy. One preliminary model, a more recent one, and four lumped versions of the latter have been tested for adequacy. These models were developed by Wiegert and they describe the behaviour of an algal-fly community energetics in a thermal spring. Results obtained by our procedure agree with Wiegert's but some new points have been emphasized.     

村落生态系统分布特征和模式的探讨

村落生态系统的分布是地表突出和普遍的现象。本文概括总结了区域性村落生态系统分布的一般性原则，其分布特征表现为景观性、分散集聚性、动态迁移性、梯度性、趋适性、界限性以及人文性等各个方面；对诸如平原、山区、湖区、盆地、丘陵台地、岛屿以及过渡区等各种地貌类型区提出相应的理论分布模式。     

Relative stability of ecosystem linear models

A method to test the relative stability of ecosystem linear models is developed. This method uses the eigenvalue sensitivity to parameter perturbations to compute the relative stability of the model. The procedure is applied to the analysis of two models describing the ca;cium cycle in a forested watershed ecosystem and the magnesium cycle in a tropical rain forest respectively.     

Eigengroup analyses of linear ecosystem models

Eigenvalue analysis has been widely used for characterization of model ecosystems, and utilization of the total eigensystem information has been demonstrated for ecosystem models. Solution of the unique eigenvectors, termed eigengroups, associated with specified perturbation initial conditions allows proper assignment of the ecosystem model content to each exponential decay function. Such eigengroup solutions of Monte Carlo assigned perturbations are reported here for a nine-compartment tropical moist forest phosphorus model and for a set of seven six-compartment general nutrient cycling models. Confirmed by CSMP III STIFF numerical integration, results indicate that the dynamics of these multi-compartment models, each having many internal closed cycles, are adequately described by only one or two exponential decay functions, even at massive perturbation levels. For these models, conjugate complex noncritical eigenvalues were found to be common, but the decay rates of the envelopes of oscillation are consistently so rapid that system-intrinsic oscillations are undetectable. The techniques used here are presented as efficient means of identifying the transient response space of linear ecosystem models.     

A trait-based approach for downscaling complexity in plankton ecosystem models

Although predator–prey cycles can be easily predicted with mathematical models it is only since recently that oscillations observed in a chemostat predator–prey (rotifer–algal) experiment offer an interesting workbench for testing model soundness. These new observations have highlighted the limitations of the conventional modelling approach in correctly reproducing some unexpected characteristics of the cycles. Simulations are improved when changes in algal community structure, resulting from natural selection operating on an assemblage of algal clones differing in competitive ability and defence against rotifer predation, is considered in multi-prey models. This approach, however, leads to extra complexity in terms of state variables and parameters. We show here that multi-prey models with one predator can be effectively approximated with a simpler (only a few differential equations) model derived in the context of adaptive dynamics and obtained with a moment-based approximation. The moment-based approximation has been already discussed in the literature but mostly in a theoretical context, therefore we focus on the strength of this approach in downscaling model complexity by relating it to the chemostat predator–prey experiment. Being based on mechanistic concepts, our modelling framework can be applied to any community of competing species for which a trade-off between competitive ability and resistance to predators can be appropriately defined. We suggest that this approach can be of great benefit for reducing complexity in biogeochemical modelling studies at the basin or global ocean scale.     

基于生态系统管理的湿地概念生态模型研究

湿地是地球上的一种重要生态系统,基于生态系统管理理念,进行湿地保护与管理,既是湿地科学发展的必然结果.也是当前湿地保护与管理的客观需求.湿地生态模型是以湿地生态系统作为研究对象的模型,是对湿地生态系统组成、结构、过程和功能进行简化、类比或抽象,是用来反映湿地生态系统各种过程和关系的定性或定量化工具.湿地概念生态模型是各类湿地生态模型中最基本的类型,是对湿地生态系统组成及其相互关系的一种简约的定性表达,特别是指人类活动影响下湿地生态系统因子变化及其相互关系的概念性表达.湿地概念生态模型构建的主要目的是旨在识别人类活动对湿地生态系统的驱动与胁迫,这些驱动与胁迫产生的一系列生态效应,以及湿地生态系统对此所表现出来的特征.湿地生态系统是一个多层次、多因子组成的,结构复杂、功能多样、具有多向反馈和调节机制的复杂大系统或巨系统.影响系统状态或驱动系统变化的因子众多,既有来自系统内部的、也有来自系统外部的,它们对系统造成的影响往往具有联动关系和因果效应.湿地概念生态模型就是在生态系统管理理论指导下,将这些系统因子及其关系抽象并提取出来,以"驱动-胁迫-效应-表征"为主线,判断系统变化与演化背后存在的因果关系,构建能够反映系统变化与演化特征和规律的结构性关系网络模型.湿地概念生态模型研究的意义在于在科学与决策之间架起一座桥梁,为实施湿地生态保护与管理提供指导,同时为建立湿地数量化模型奠定基础.     

A new scheme for initializing process-based ecosystem models by scaling soil carbon pools

Process-based ecosystem models are useful tools, not only for understanding the forest carbon cycle, but also for predicting future change. In order to apply a model to simulate a specific time period, model initialization is required. In this study, we propose a new scheme of initialization for forest ecosystem models, which we term a “slow-relaxation scheme”, that entails scaling of the soil carbon and nitrogen pools slowly during the spin-up period. The proposed slow-relation scheme was tested with the CENTURY version 4 ecosystem model. Three different combinations of scaled soil pools were also tested, and compared to the results from a fast-relaxation regime. The fast-relaxation of soil pools produced unstable, transient model behaviour whereas slow-relaxation overcame this instability. This approach holds promise for initializing ecosystem models, and for starting simulations with more realistic initial conditions.     

A note on the allocation of investment

It is shown by example that the results obtained by Gruver [11 concerning specialization of investment in either directly productive or pollution control capital arise because of an implicit linearity assumption on the underlying technology. Utilizing a strictly concave “eighth sphere” technology, results are obtained which imply joint investment in the two types of capital except in “rare” instances. The results indicate the need for incorporating more general technologies into the analysis of such problems.     

Some stochastic differential equation models of an aquatic ecosystem

A set of stochastic differential equations has been used to model an aquatic ecosystem. The randomness in the system has been introduced through initial conditions of the state variables, parameters, and input variables (light and temperature). These models were analysed using Monte Carlo simulation procedures and the results were similar to those observed in the experimental and field data. They were different, however, from the results of a deterministic simulation. This approach allows us to incorporate the maximum degree of information in the model and to study the behavior of the system without arbitrarily manipulating the values of the parameters. Some possible refinements and generalizations of this approach are also discussed.     

Evaluating the ecological benefits of wildfire by integrating fire and ecosystem simulation models

Fire managers are now realizing that wildfires can be beneficial because they can reduce hazardous fuels and restore fire-dominated ecosystems. A software tool that assesses potential beneficial and detrimental ecological effects from wildfire would be helpful to fire management. This paper presents a simulation platform called FLEAT (Fire and Landscape Ecology Assessment Tool) that integrates several existing landscape- and stand-level simulation models to compute an ecologically based measure that describes if a wildfire is moving the burning landscape towards or away from the historical range and variation of vegetation composition. FLEAT uses a fire effects model to simulate fire severity, which is then used to predict vegetation development for 1, 10, and 100 years into the future using a landscape simulation model. The landscape is then simulated for 5000 years using parameters derived from historical data to create an historical time series that is compared to the predicted landscape composition at year 1, 10, and 100 to compute a metric that describes their similarity to the simulated historical conditions. This tool is designed to be used in operational wildfire management using the LANDFIRE spatial database so that fire managers can decide how aggressively to suppress wildfires. Validation of fire severity predictions using field data from six wildfires revealed that while accuracy is moderate (30-60%), it is mostly dictated by the quality of GIS layers input to FLEAT. Predicted 1-year landscape compositions were only 8% accurate but this was because the LANDFIRE mapped pre-fire composition accuracy was low (21%). This platform can be integrated into current readily available software products to produce an operational tool for balancing benefits of wildfire with potential dangers.     

A note on the feeding of Calanus helgolandicus on detritus

Experiments on the feeding of Calanus helgolandicus females on detrital material were carried out. Natural detritus from the ocean was never ingested, whereas dead diatoms were readily eaten. Furthermore, it was shown that C. helgolandicus females ingested large amounts of fecal material produced by the same species in other vessels. These results indicate that the copepod C. helgolandicus feeds not only on living organisms, but also on dead particles.     

The representation of cyanobacteria life cycle processes in aquatic ecosystem models

Two simplified versions of a numerical life cycle model for diazotrophic cyanobacteria (of the order Nostocales) are developed and evaluated. Both consider two-life cycle stages, one growing, nitrogen-fixing stage and one stage that combines the resting, germinating and vegetative stages. The versions differ in the vertical resolution of the non-diazotrophic stage: version 1 collects the biomass in one layer at the bottom, version 2 considers sinking and rising of biomass explicitly. The results of the two versions are compared with a complex cyanobacteria life cycle model which describes four different life cycle stages each with two internal quotas for energy and nitrogen. The two simplified approaches show a good agreement with respect to the main characteristics of cyanobacteria dynamics (timing and duration of blooms, magnitude of nitrogen fixation, interannual variability). Our model study shows that both simplified approaches are suitable to be implemented into three-dimensional coastal or lake models.     

A note on natural production functions

Two techniques are presented for estimation of natural animal populations, both of which may incorporate the effect of pollutants on populations. Both techniques assume specific underlying population dynamics which may not be applicable to certain species or ecosystems. However, both techniques allow for testing the hypothesis that the population dynamics specified is applicable. The techniques are used to criticize two recent empirical investigations of fisheries.     

Analysis and prediction of ecological and ecosystem dynamics with response structure models

A method of directly using data concerning species' responses to various combinations of levels of environmental factors is outlined. Examples of its utilization to analyze (and predict) the dynamics of the ecological processes of population growth, interspecific competition, and predation are given for simple systems; a simulation is presented wherein all of these processes interact within a simple ecosystem. A technique of summarizing the pattern and detail of variation of levels of combination of important environmental factors is also introduced. Together these methods permit application of real world information about the components of the biological community and the environment toward the modeling of ecosystems and the making of predictions concerning them to whatever degree of accuracy which may be useful.There are several major advantages of this approach: (1) It makes maximum use of real world data; the limits of its precision are determined only by the adequacy of the data available (hypothetical values also may be used where real data are unavailable and/or where such hypothetical values may be useful in model and theory development). (2) It is powerful (and applicable to the dynamics of diverse kinds of systems), mathematically very simple, and has important advantages in that non-linearities, thresholds, etc. are automatically and accurately taken into account. (3) It can be expressed numerically or graphically, and therefore is especially helpful in permitting visualization of ecological processes and the results of their action.     

A note on the welfare-economic consequences of extended fishing limits

A standard two countries-two commodities model is developed to consider the gains in efficiency resulting from transferring common property fish stocks to the jurisdiction of coastal states attempting to reach allocative efficiency. As a result of this transfer, the long-term catch from seriously overexploited fish stocks will be greater than otherwise, causing the price of fish to fall. This will transfer some, and possibly all, of the gains from more efficient fishing to fish consumers in the rest of the world. The note concludes with some remarks on the plausibility of the assumption that governments will pursue allocative efficiency.     

A note on the development of the thermocline in temperate lakes

An exact solution has been obtained for a non-linear partial differential equation governing the vertical transport of heat in a lake. The equation, derived and analyzed numerically by Sundaram and Rehm (1971, 1973) is based on a balance between thermal buoyany forces and wind induced turbulence. The exact solution displays the qualitative features of the numerical solution and its representation of the seasonal descent of the thermocline is accurate.     

A note on the effect of tax brackets on non-renewable resource extraction

Tax brackets are a common feature of non-renewable resource taxes. Although the introduction of brackets would seem to be an innocuous way of approximating a non-linear tax system, the dynamic effects are surprising. This paper shows that the presence of tax brackets in both a severance tax system and a profits tax system can induce the extractive firm to depart from the well-known monotonically declining extraction profile and to choose instead a profile which has constant extraction rates over some interval of time.