What did Lotka really say? A critical reassessment of the “maximum power principle”

This paper presents a critical discussion of the so-called “maximum power principle”, often quoted in studies about the energy balance of living systems and also known in the emergy literature as “maximum em-power principle”. Several authors consider this principle highly relevant and some even proposed it as a “fourth law of thermodynamics”. A critical analysis of the original source, namely Alfred Lotka's 1921-22 papers, conducted both in an historical perspective (the connection between Lotka's writings and the ongoing debate at his time) and in a more modern context, leads to a more detailed and less biased assessment. It turns out that in spite of Lotka's very anticipatory and incredibly sharp vision of the possible interconnections between the second law of thermodynamics and evolutionism, doubts arise about the general applicability of his “maximum power principle”. From an accurate analysis of his writings, it can be concluded that: (a) Lotka explicitly and consistently addressed the “optimal use” of the flow of exergy (available energy), and therefore the quantity defined as “em-power” is an incorrect interpretation of Lotka's constrained maximum power principle; (b) “Lotka's principle” can be reformulated within Ziegler's “maximum entropy production” or Prigogine “minimum entropy generation” paradigm only under two different respective sets of rather stringent additional conditions which Lotka was probably already aware of but never explicitly stated.     

Practical evaluation for water utilities in China by using analytic hierarchy process

The risk of water utilities would include the water quality failure and the water quantity failure, from the source to the tap, including the catchment, treatment, distribution and the customer plumbing system. In this paper, we proposed a practical evaluation method based on the analytic hierarchy process (AHP). The hierarchical structure of the water utilities was established in terms of the fault event analysis from the past failure accidents. The severity of criteria was preset by the experts and the probability of criteria was determined by a modified CUWA-TSM sheet with the consideration of the actual situations of the supply system. The evaluation model was successfully performed by a case study. Although, the method in this paper may not be as good as the framework of WSPs, it has a great advantage compared to WSPs and TSM. The risk management can be applied through specific software packages with a user-friendly interface, which means it is easier to implement. In addition, it can point out the critical control points (CCPs) for the decision-makers. So we believe this method will improve and play a more and more active role in the development of the risk management in China water works.     

Prevalence-adjusted optimisation of fuzzy models for species distribution

Most performance criteria which have been applied to train ecological models focus on the accuracy of the model predictions. However, these criteria depend on the prevalence of the training set and often do not take into account ecological issues such as the distinction between omission and commission errors. Moreover, a previous study indicated that model training based on different performance criteria results in different optimised models. Therefore, model developers should train models based on different performance criteria and select the most appropriate model depending on the modelling objective. This paper presents a new approach to train fuzzy models based on an adjustable performance criterion, called the adjusted average deviation (aAD). This criterion was applied to develop a species distribution model for spawning grayling in the Aare River near Thun, Switzerland. To analyse the strengths and weaknesses of this approach, it was compared to model training based on other performance criteria. The results suggest that model training based on accuracy-based performance criteria may produce unrealistic models at extreme prevalences of the training set, whereas the aAD allows for the identification of more accurate and more reliable models. Moreover, the adjustable parameter in this criterion enables modellers to situate the optimised models in the search space and thus provides an indication of the ecological model relevance. Consequently, it may support modellers and river managers in the decision making process by improving model reliability and insight into the modelling process. Due to the universality and the flexibility of the approach, it could be applied to any other ecosystem or species, and may therefore be valuable to ecological modelling and ecosystem management in general.     

How might we model an ecosystem?

Predicting ecosystem effects is of crucial importance in a world at threat from natural and human-mediated change. Here we propose an ecologically defensible representation of an ecosystem that facilitates predictive modelling. The representation has its roots in the early trophic and energetic theory of ecosystem dynamics and more recent functional ecology and network theory. Using the arable ecosystem of the UK as an example, we show that the representation allows simplification from the many interacting plant and invertebrate species, typically present in arable fields, to a more tractable number of trophic-functional types. Our compound hypothesis is that “trophic-functional types of plants and invertebrates can be used to explain the structure, diversity and dynamics of arable ecosystems”. The trophic-functional types act as containers for individuals, within an individual-based model, sharing similar trophic behaviour and traits of biomass transformation. Biomass, or energy, flows between the types and this allows the key ecological properties of individual abundance and body mass, at each trophic height, to be followed through simulations. Our preliminary simulation results suggest that the model shows great promise. The simulation output for simple ecosystems, populated with realistic parameter values, is consistent with current laboratory observations and provides exciting indications that it could reproduce field scale phenomena. The model also produces output that links the individual, population and community scales, and may be analysed and tested using community, network (food web) and population dynamic theory. We show that we can include management effects, as perturbations to parameter values, for modelling the effects of change and indicating management responses to change. This model will require robust analysis, testing and validation, and we discuss how we will achieve this in the future.     

种间关系预测(ICE)模型在水质基准研究中的应用

水质基准研究主要是基于物种的实验室测试的毒性数据开展的。对于一些毒性数据相对缺乏的化学品,水质基准研究就会受到一定的影响。本文从水质基准研究方法的角度,阐述了种间关系预测(ICE)的基本原理和基本方法,系统介绍了ICE模型的毒性预测方法在水质基准研究中的应用,并通过锌的ICE案例研究证明了模型在中国的可利用性。同时,对ICE模型的不确定性和适用性进行了分析。最后,对ICE模型存在的问题和未来的发展方向进行了探索和展望。     

2,4,6-三氯酚在模型水生生态系统中的归宿

测定了模型水生生态系统水、底泥中2.4,6-三氯酚(TCP)浓度随时间的变化值,以及TCP从水中挥发、光解、底泥吸附、解吸、微生物降解的速率常数.假设水中TCP的迁移和转化遵循—级速率过程,水中物质平衡能通过数学等式来描述,显示出室系统教学模型能粗略预测模型水生生态系统中TCP浓度随时间的变化.最后,应用该模型预测了排放到天津室外兼性塘中TCP的迁移、归宿,发现15d后出口水中TCP浓度已降低到入口水中浓度的10%     

A hierarchical analysis of terrestrial ecosystem model Biome-BGC: Equilibrium analysis and model calibration

The increasing complexity of ecosystem models represents a major difficulty in tuning model parameters and analyzing simulated results. To address this problem, this study develops a hierarchical scheme that simplifies the Biome-BGC model into three functionally cascaded tiers and analyzes them sequentially. The first-tier model focuses on leaf-level ecophysiological processes; it simulates evapotranspiration and photosynthesis with prescribed leaf area index (LAI). The restriction on LAI is then lifted in the following two model tiers, which analyze how carbon and nitrogen is cycled at the whole-plant level (the second tier) and in all litter/soil pools (the third tier) to dynamically support the prescribed canopy. In particular, this study analyzes the steady state of these two model tiers by a set of equilibrium equations that are derived from Biome-BGC algorithms and are based on the principle of mass balance. Instead of spinning-up the model for thousands of climate years, these equations are able to estimate carbon/nitrogen stocks and fluxes of the target (steady-state) ecosystem directly from the results obtained by the first-tier model. The model hierarchy is examined with model experiments at four AmeriFlux sites. The results indicate that the proposed scheme can effectively calibrate Biome-BGC to simulate observed fluxes of evapotranspiration and photosynthesis; and the carbon/nitrogen stocks estimated by the equilibrium analysis approach are highly consistent with the results of model simulations. Therefore, the scheme developed in this study may serve as a practical guide to calibrate/analyze Biome-BGC; it also provides an efficient way to solve the problem of model spin-up, especially for applications over large regions. The same methodology may help analyze other similar ecosystem models as well.     

Dynamic model of Lake Chozas (León, NW Spain)—Decrease in eco-exergy from clear to turbid phase due to introduction of exotic crayfish

We developed a dynamic model of the phosphorus cycle in Lake Chozas, a small shallow water body in León (NW Spain). The calibrated model simulated seasonal dynamics of phosphorus concentrations in major components of the lake's ecological network before and after 1997, the year when an invasive allochthonous crustacean, the Louisiana red swamp crayfish (Procambarus clarkii), was introduced into the lake. The shift from clean to turbid phase, due to grazing by crayfish on submerged vegetation, caused a gradual decrease in eco-exergy, reflecting an increase in entropy, related to breakdown of ecosystem internal equilibria. This case study verifies the hypothesis of Marchi et al. (2010) that, after an initial relatively stable state, the allochthonous species may cause an increase in entropy indicating perturbation of the ecosystem.     

Water and carbon fluxes above European coniferous forests modelled with artificial neural networks

Artificial neural networks are used to select a minimal set of input variables to model water vapour and carbon exchange of coniferous forest ecosystems, independently of tree species and without detailed physiological information. Neural networks are used because of their power to fit highly non-linear relations between input and output-variables. Radiation, temperature, vapour pressure deficit and time of the day showed to be the dynamic input variables that determine ecosystem water fluxes. The same variables, together with projected leaf area index are needed for modelling CO₂-fluxes. The results for the individual sites show that the neural networks found mean water and carbon flux responses to the driving variables valid for all sites. The sensitivity analysis of the derived neural networks shows that the LAI-effect of the CO₂-flux model is overfitted because of the low variability of LAI. However, the predictions of CO₂-fluxes of sites not included in the calibration set indicate that the LAI-response of the network is reliable and that results can be used as a first estimate of the net ecosystem carbon exchange of the forest sites. Independent predictions of forest ecosystem vapour fluxes were equally satisfying as empirical models specifically calibrated for the individual sites. The results indicate that both short term water and carbon fluxes of European coniferous forests can be modelled without using detailed physiological and site specific information.     

Implementation of ecological modeling as an effective management and investigation tool: Lake Kinneret as a case study

The need for scientifically based management of lakes, as key water resources, requires the establishment of quantitative relationships between in-lake processes responsible for water quality (WQ) and the intensity of major management measures (MM, e.g. nutrient loading). In this paper, we estimate the impact of potential changes in nutrient loading on the Lake Kinneret ecosystem. Following validation of the model against a comprehensive dataset, we applied an approach that goes beyond scenario testing by linking the lake ecosystem model DYRESM–CAEDYM with a set of ecosystem variables included in a pre-assessed system of water quality indices. The emergent properties of the ecosystem predicted from the model simulations were also compared with lake data as a form of indirect validation of the model. Model output, in good agreement with lake data, indicated differential effects of nitrogen and phosphorus nutrient loading on concentrations, and major in-lake fluxes, of TN and TP, and dynamics and algal community structure. Both model output and lake data indicated a strong relationship between nitrogen loading and in-lake TN values. This relationship is not apparent for phosphorus and only a weak relationship exists between phosphorus loading and in-lake TP. The modeling results, expressed in terms of water quality, allowed establishment of critical/threshold values for the nutrient loads. Implementation of the ecological modeling supplemented with the quantified set of WQ indices allowed us to take a step towards establishment of the association between permissible ranges for water quality and major management measures, i.e. towards sustainable management.     

Modelling coral reef ecosystems with limited observational data

Ecosystem models represent potentially powerful tools for coral reef ecosystem managers. They can provide insight into ecosystem dynamics not achievable through alternative means allowing coral reef managers to assess the potential outcome of any given management decision. One of the main limitations in the applicability of ecosystem models is that they often require detailed empirical data and this can restrict their applicability to ecosystems that are either currently well studied or have the resources available to collect the required data. This study describes the development of a coral reef ecosystem model that can be calibrated to an ecosystem with limited empirical data. Based on the assumption that coral reef ecological structure is generic across all tropical coral reefs and that the magnitude of the interactions between ecological components is reef specific, the dynamics of the ecosystem can be replicated based on limited empirical data. The model successfully replicated the dynamics of three individual reef systems including an inshore and oceanic reef within the Great Barrier Reef and a Caribbean reef system. It highlighted the importance of understanding the specific dynamics of a given reef and that a positive management intervention in one system may result in a negative outcome for another. The model was also used to assess the importance of various interactions within coral reef ecosystems. It identified the interactions between hard corals and other non-algal benthic components as being an important (but currently understudied) facet of coral reef ecology. The development of this modelling approach provides access to ecosystem modelling tools for coral reef managers previously excluded due to a lack of resources or technical expertise.     

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.     

State-of-the-art of ecological modelling with emphasis on development of structural dynamic models

The paper deals with two major problems in ecological modelling today, namely how to get reliable parameters? and how to build ecosystem properties into our models? The use of new mathematical tools to answer these questions is mentioned briefly, but the main focus of the paper is on development of structural dynamic models which are models using goal functions to reflect a current change of the properties of the biological components in the models. These changes of the properties are due to the enormous adaptability of the biological components to the prevailing conditions. All species in an ecosystem attempt to obtain most biomass, i.e. to move as far away as possible from thermodynamic equilibrium which can be measured by the thermodynamic concept exergy. Consequently, exergy has been proposed as a goal function in ecological models with dynamic structure, meaning currently changed properties of the biological components and in model language currently changed parameters. An equation to compute an exergy index of a model is presented. The theoretical considerations leading to this equation are not presented here but references to literature where the basis theory can be found are given. Two case studies of structural dynamic modelling are presented: a shallow lake where the structural dynamic changes have been determined before the model was developed, and the application of biomanipulation in lake management, where the structural dynamic changes are generally known. Moreover. it is also discussed how the same idea of using exergy as a goal function in ecological modelling may be applied to facilitate the estimation of parameters.     

Simulation experiments comparing alternative process formulations using a factorial design

This paper reviews methods for exploring the differences between alternative equations in complex ecosystem models. A factorial design is proposed as a method for exposing possible interactions between equation forms in their effect on model output as well as to clarify differences between the main candidate equations. A number of display methods arising from statistical analysis are used including normal Q-Q plots, linear rank plots and interaction diagrams. The methods were illustrated using a complex ecosystem model of Lake Ontario. We found the methods effective at illustrating major differences between equations although several difficulties arose due to the complexity of the models and the diffuse nature of the data supporting model validation. Questions of the method for standardization of equation forms so that the compared equations are in some way analogous, are important. These methods are probably most useful in cases where the data are of sufficient quality to indicate not only how different equation forms affect model output but also which are to be preferred.     

Landscape consequences of aggregation rules for functional equivalence in compensatory mitigation programs

Mitigation and offset programs designed to compensate for ecosystem function losses due to development must balance losses from affected ecosystems with gains in restored ecosystems. Aggregation rules applied to ecosystem functions to assess site equivalence are based on implicit assumptions about the substitutability of functions among sites and can profoundly influence the distribution of restored ecosystem functions on the landscape. We investigated the consequences of rules applied to the aggregation of ecosystem functions for wetland offsets in the Beaverhill watershed in Alberta, Canada. We considered the fate of 3 ecosystem functions: hydrology, water purification, and biodiversity. We set up an affect‐and‐offset algorithm to simulate the effect of aggregation rules on ecosystem function for wetland offsets. Cobenefits and trade‐offs among functions and the constraints posed by the quantity and quality of restorable sites resulted in a redistribution of functions between affected and offset wetlands. Hydrology and water purification functions were positively correlated with one another and negatively correlated with biodiversity function. Weighted‐average rules did not replace functions in proportion to their weights. Rules prioritizing biodiversity function led to more monofunctional wetlands and landscapes. The minimum rule, for which the wetland score was equal to the worst performing function, promoted multifunctional wetlands and landscapes. The maximum rule, for which the wetland score was equal to the best performing function, promoted monofunctional wetlands and multifunctional landscapes. Because of implicit trade‐offs among ecosystem functions, no‐net‐loss objectives for multiple functions should be constructed within a landscape context. Based on our results, we suggest criteria for the design of aggregation rules for no net loss of ecosystem functions within a landscape context include the concepts of substitutability, cobenefits and trade‐offs, landscape constraints, heterogeneity, and the precautionary principle.     

The development of a multi-species algal ecodynamic model for urban surface water systems and its application

An ecodynamic model that can simulate four phytoplankton species has been developed to deal with the unique characteristics of urban river systems which has manmade river profile, flow controlled by gates, severe eutrophication status, and fragile aquatic ecosystem. The ecodynamic model was developed referencing two typical models: the water quality simulation model WASP and ecological model CAEDYM. The model can simulate 11 state variables: dissolved oxygen, carbonaceous biochemical oxygen demand, ammonia nitrogen, nitrate nitrogen, organic nitrogen, inorganic phosphorus, organic phosphorus and four phytoplankton species with zooplankton as a boundary condition. The ecodynamic model was applied to Sihai section of the Beijing urban river system, where serious algal blooms broke out in recent years. The dominant phytoplankton species are Cyanophyta, Chlorophyta, Bacillariophyta, and Cryptophyta. Site-specific data on geometry, meteorology, pollution sources, and existing ecosystem parameters were collected and used for model calibration and verification The model results mimic observed trends of water quality and phytoplankton species succession and can be used for forecasting algal blooms as well as assessment of river management measures.     

On modelling temporal patterns in stressed ecosystems — Recreation in a coniferous forest

A system of ordinary differential equations is presented as being appropriate for modelling the impact of stress on the temporal behaviour of certain components within an ecosystem. The modelling problem is fist discussed in general terms and then in terms specifically relating to the impact of recreational activities (hunting, fishing, sightseeing, etc.) on a coniferous forest ecosystem.Using crude data, the model is used to simulate over a 3-year period the biomass levels of four compartments of the ecosystem (viz, timber, deer, fish and forage) in the absence of recreational activities. These results are then contrasted with simulation results obtained by introducing a “moderate” and then “high” degree of recreational activity, as well as the response of the system under moderate recreation to management strategies involving the construction of dams and the harvesting of timber.     

Modelling nature-like fishway flow around unsubmerged obstacles using a 2D shallow water model

In the scope to create efficient nature like fish ramps using large-scale roughness elements, the present study is an audit of modelling such complex 3D free surface flows using an industrial 2D code solving shallow water equations. Validation procedure is based upon the comparison between numerous experimental measurements and numerical runs around large-scale roughness patterns disposed on the flume bottom in order to determine what 2D reliable numerical results can be expected. In this paper, we focused on cases of unsubmerged obstacles. The results demonstrate that 2D shallow water modelling using an industrial code such as TELEMAC-2D can be a convenient way for the hydraulic engineer to help design a nature-like fishway. This article emphasizes the limitations due to 2D depth integration of velocities and turbulence modelling and gives the domain of validity of the method.