What does ecological modelling model? A proposed classification of ecological niche models based on their underlying methods

Species distribution model is the term most frequently used in ecological modelling, but other authors used instead predictive habitat distribution model or species-habitat models. A consensual ecological modelling terminology that avoids misunderstandings and takes into account the ecological niche theory does not exist at present. Moreover, different studies differ in the type of niche that is represented by similar distribution models. I propose to use as standard ecological modelling terminology the terms “ecological niche”, “potential niche”, “realized niche” models (for modelling their respective niches), and “habitat suitability map” (for the output of the niche models). Therefore, the user can understand more easily that models always forecast species’ niche and relate more closely the different types of niche models.     

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.     

An interregional ecological approach for modelling sustainability in a globalizing world—Reviewing existing approaches and emerging directions

In recent decades international trade has become a major source of supplying the need and wants of billions of people around the world. Virtually everyone now consumes resource commodities and manufactured products imported from ‘elsewhere’. In effect, globalization and trade enable consuming populations to support themselves on the output of distant ecosystems half a world away. However, while economic integration implies greater ‘connectivity’ within the global village, the spatial separation of material production (including resource extraction) from consumption eliminates some of the signals i.e., the negative feedbacks coming from supporting eco-systems from reaching those who depend on these ecosystems for their sustainability. At present, despite increasing global connectedness, most environmental studies and models apply to a single spatial scale: local, national or global; analysing diverse pressures on human well-being and ecosystems integrity. This paper argues that both economic globalization and global ecological change should force us to add an interregional scale for quantifying and modelling sustainability. Such an approach recognizes that, in a globalizing world, the sustainability of any given region increasingly depends, directly and indirectly, on the sustainability of many other regions. The following pages describe the interregional approach and illustrate some existing and emerging methods for quantifying, analysing and modelling interregional linkages. It then identifies some of what is still missing, and discusses some of the implications in a changing world.     

Greenhouse gas emissions and natural resources use by the world economy: Ecological input-output modeling

For the world economy as a biophysical network associated with financial links, an ecological endowment inventory and corresponding ecological input-output modeling are presented to investigate the greenhouse gas emissions and natural resources use in 2000. A forty-sector global economic input-output table is constructed through an integration and extension of existing statistics which covers thirty-four countries accounting for about 80% of the world economy. Global inventories for ecological endowments of six categories, i.e., greenhouse gas emissions, energy sources, water resources, exergy resources, solar emergy resources, and cosmic emergy resources, are accounted in detail. As a result of the modeling, embodied intensities of different ecological endowments are obtained for all forty sectors, based on which the sectoral embodiments for consumptive and productive uses are presented separately. Results of this study provide a sound scientific database for policy making on global climate change mitigation as well as on global resources management.     

Ecological Modelling by ‘Ecological Modelling'

On the basis of a statistical analysis of the papers published in Ecological Modelling from 1975 to 1996, it has been attempted to examine the development of the field of ecological modelling and systems ecology. It was found that while models of aquatic ecosystems and management issues were more in focus in the 1970s, terresterial ecosystems and ecological theory have gained attention during the 1990s. Interest in ecotoxicological models seems to have increased only slightly during the entire period. It is interesting that financial support for the area of ecological modelling and systems ecology is closely related to the number of publications, which can be seen from the number of papers published by various countries in the journal. Hopefully, this clear message can be used to show to politicians that these relationships are real.     

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.     

A comparison of four process-based models and a statistical regression model to predict growth of Eucalyptus globulus plantations

In forest management and ecological research, consideration of the impacts and risks of climate change or management optimisation is complex. Computer models have long been applied as tools for these tasks. Process-based forest growth models claim to overcome the limitations of empirical statistical models, but the capacity of different process-based models and modelling approaches have rarely been compared directly. This study evaluates stepwise multiple regression models in comparison to four process-based modelling approaches (3-PG, 3-PG+, CABALA and Forest-DNDC) for greenfield predictions of Eucalyptus globulus plantation growth from 2 to 8 years after planting throughout southern Australia.     

Species distribution models and ecological theory: A critical assessment and some possible new approaches

Given the importance of knowledge of species distribution for conservation and climate change management, continuous and progressive evaluation of the statistical models predicting species distributions is necessary. Current models are evaluated in terms of ecological theory used, the data model accepted and the statistical methods applied. Focus is restricted to Generalised Linear Models (GLM) and Generalised Additive Models (GAM). Certain currently unused regression methods are reviewed for their possible application to species modelling.A review of recent papers suggests that ecological theory is rarely explicitly considered. Current theory and results support species responses to environmental variables to be unimodal and often skewed though process-based theory is often lacking. Many studies fail to test for unimodal or skewed responses and straight-line relationships are often fitted without justification.Data resolution (size of sampling unit) determines the nature of the environmental niche models that can be fitted. A synthesis of differing ecophysiological ideas and the use of biophysical processes models could improve the selection of predictor variables. A better conceptual framework is needed for selecting variables.Comparison of statistical methods is difficult. Predictive success is insufficient and a test of ecological realism is also needed. Evaluation of methods needs artificial data, as there is no knowledge about the true relationships between variables for field data. However, use of artificial data is limited by lack of comprehensive theory.Three potentially new methods are reviewed. Quantile regression (QR) has potential and a strong theoretical justification in Liebig's law of the minimum. Structural equation modelling (SEM) has an appealing conceptual framework for testing causality but has problems with curvilinear relationships. Geographically weighted regression (GWR) intended to examine spatial non-stationarity of ecological processes requires further evaluation before being used.Synthesis and applications: explicit theory needs to be incorporated into species response models used in conservation. For example, testing for unimodal skewed responses should be a routine procedure. Clear statements of the ecological theory used, the nature of the data model and sufficient details of the statistical method are needed for current models to be evaluated. New statistical methods need to be evaluated for compatibility with ecological theory before use in applied ecology. Some recent work with artificial data suggests the combination of ecological knowledge and statistical skill is more important than the precise statistical method used. The potential exists for a synthesis of current species modelling approaches based on their differing ecological insights not their methodology.     

Potentialities,problems, policies and progress in modelling sustainable development: A dynamic,hierarchical approach

This paper discusses some of the potentials, problems, policies and progress in modelling sustainable development. After briefly describing ten approaches to modelling sustainable development, some of the methodological problems still to be resolved are addressed. It is then suggested that policies to promote sustainable development should operate at six different spatial levels connecting global, multinational, national, regional, local and individual. Attempting to model sustainable development in such a hierarchical manner is exceedingly difficult. One way of modelling sustainable development is to develop the concept of a sustainable corridor, combining ecological, economic and equity considerations in a hierarchical fashion and through space-time. A preliminary dynamic, hierarchical model is described connecting global and national patterns of development. Using global and national data for Scotland, the calibrated model, running under the business-as-usual scenario, shows that current development paths are unsustainable. It is shown that, by implementing a judicious choice of policies, a sustainable corridor for a global and a national system can be achieved. The ways in which this preliminary model can be developed to connect all six hierarchical levels are discussed.     

Modelling plant species richness using functional groups

Conservation biologists increasingly rely on spatial predictive models of biodiversity to support decision-making. Therefore, highly accurate and ecologically meaningful models are required at relatively broad spatial scales. While statistical techniques have been optimized to improve model accuracy, less focus has been given to the question: How does the autecology of a single species affect model quality? We compare a direct modelling approach versus a cumulative modelling approach for predicting plant species richness, where the latter gives more weight to the ecology of functional species groups. In the direct modelling approach, species richness is predicted by a single model calibrated for all species. In the cumulative modelling approach, the species were partitioned into functional groups, with each group calibrated separately and species richness of each group was cumulated to predict total species richness. We hypothesized that model accuracy depends on the ecology of individual species and that the cumulative modelling approach would predict species richness more accurately. The predictors explained plant species richness by ca. 25%. However, depending on the functional group the deviance explained varied from 3 to 67%. While both modelling approaches performed equally well, the models of the different functional groups highly varied in their quality and their spatial richness pattern. This variability helps to improve our understanding on how plant functional groups respond to ecological gradients.     

The concepts of emergent and collective properties in individual-based models—Summary and outlook of the Bornhöved case studies

Ecology requires the conceptual and technical ability to analyse complex and dynamic systems consisting of a high and variable number of components and relations. These components are part of a variable interaction structure in a spatially heterogeneous context. The components of ecological interaction networks can give rise to self-organised, and scale-dependent interaction patterns and processes, which are the underlying causes of the overall ecological systems states.The individual-based modelling approach provides a widely applicable simulation framework based on a ‘hierarchy theory’ view of ecological systems.Here, we summarise and generalise the theoretical implications of the modelling studies presented in this volume in the field of terrestrial and aquatic, animal and plant ecology. The case studies cover a representative profile of processes related to ecological applications, such as food web interactions, population dynamics, dispersal, energy physiology, nutrient allocation and mutual impact of morphological and physiological development. The generic approach applied in this context allows a hierarchical representation of ecological systems and their components. Model results are obtained as self-organised structural relation networks and as aggregated quantitative states. In order to address different model characteristics we distinguish collective and emergent properties. Collective properties are those that are attributed equally to different organisation levels of the system. Emergent properties result from the activities of lower level entities on a higher organisation level, while not being present on the lower level. They can be subdivided into aggregational and connective properties. Emergent properties that are aggregational are those which emerge as a result of an aggregation procedure by an observer on the higher level which does not make sense or is not applicable on lower levels. Emergent properties that are connective, however, are based on an interaction network of lower level entities, which brings about the specific system characteristic.This classification of model results will allow to generalise the achievements and potential of the individual-based modelling approach in ecology.     

Investigation of some nonlinear singular model ecosystems and new concerned mathematical problems

The work is devoted to the investigation of nonlinear singular ecological models with initial functional conditions and determination of solutions of problems, which are connected with these models. It is also considered some of its applications in field of ecological modelling under formulation and investigation of the so-called keeping and protection problems. We shall investigate nonlinear models that are described with the help of partial differential equation of first and second orders. Solutions of linear and some singular nonlinear problems with functional initial conditions are obtained in the form depending from initial parameters.     

Single-species versus multiple-species models: the economic implications

Ecologists frequently note the importance of modelling entire ecosystems rather than individual species, but most bioeconomic models in the current literature focus on a single species. While the mathematical difficulty of modelling multiple species may be substantial, it is important to recognise the implications of the single-species assumption to a model’s results. In this paper, the authors address the economic significance of this assumption through the development of an analytical multiple-species model and demonstrate the importance of ecological interrelationships and economic values to the survival of endangered species.     

Ecological relevance of performance criteria for species distribution models

Species distribution models have often been developed based on ecological data. To develop reliable data-driven models, however, a sound model training and evaluation procedures are needed. A crucial step in these procedures is the assessment of the model performance, with as key component the applied performance criterion. Therefore, we reviewed seven performance criteria commonly applied in presence-absence modelling (the correctly classified instances, Kappa, sensitivity, specificity, the normalised mutual information statistic, the true skill statistic and the odds ratio) and analysed their application in both the model training and evaluation process. Although estimates of predictive performance have been used widely to assess final model quality, a systematic overview was missing because most analyses of performance criteria have been empirical and only focused on specific aspects of the performance criteria. This paper provides such an overview showing that different performance criteria evaluate a model differently and that this difference may be explained by the dependency of these criteria on the prevalence of the validation set. We showed theoretically that these prevalence effects only occur if the data are inseparable by an n-dimensional hyperplane, n being the number of input variables. Given this inseparability, different performance criteria focus on different aspects of model performance during model training, such as sensitivity, specificity or predictive accuracy. These findings have important consequences for ecological modelling because ecological data are mostly inseparable due to data noise and the complexity of the studied system. Consequently, it should be very clear which aspect of the model performance is evaluated, and models should be evaluated consistently, that is, independent of, or taking into account, species prevalence. The practical implications of these findings are clear. They provide further insight into the evaluation of ecological presence/absence models and attempt to assist modellers in their choice of suitable performance criteria.     

A new synergetic paradigm in environmental numerical modeling: Hybrid models combining deterministic and machine learning components

A new type of environmental numerical models, hybrid environmental numerical models (HEMs) based on combining deterministic modeling and machine learning components, is introduced and formulated. Conceptual and practical possibilities of developing HEM, as an optimal synergetic combination of the traditional deterministic/first principles modeling (like that used for solving PDEs on the sphere representing model dynamics of global climate models) and machine learning components (like accurate and fast neural network emulations of model physics or chemistry processes), are discussed. Examples of developed HEMs (hybrid climate models and a hybrid wind–wave ocean model) illustrate the feasibility and efficiency of the new approach for modeling extremely complex multidimensional systems.     

Adaptive speciation theory: a conceptual review

Speciation—the origin of new species—is the source of the diversity of life. A theory of speciation is essential to link poorly understood macro-evolutionary processes, such as the origin of biodiversity and adaptive radiation, to well understood micro-evolutionary processes, such as allele frequency change due to natural or sexual selection. An important question is whether, and to what extent, the process of speciation is ‘adaptive’, i.e., driven by natural and/or sexual selection. Here, we discuss two main modelling approaches in adaptive speciation theory. Ecological models of speciation focus on the evolution of ecological differentiation through divergent natural selection. These models can explain the stable coexistence of the resulting daughter species in the face of interspecific competition, but they are often vague about the evolution of reproductive isolation. Most sexual selection models of speciation focus on the diversification of mating strategies through divergent sexual selection. These models can explain the evolution of prezygotic reproductive isolation, but they are typically vague on questions like ecological coexistence. By means of an integrated model, incorporating both ecological interactions and sexual selection, we demonstrate that disruptive selection on both ecological and mating strategies is necessary, but not sufficient, for speciation to occur. To achieve speciation, mating must at least partly reflect ecological characteristics. The interaction of natural and sexual selection is also pivotal in a model where sexual selection facilitates ecological speciation even in the absence of diverging female preferences. In view of these results, it is counterproductive to consider ecological and sexual selection models as contrasting and incompatible views on speciation, one being dominant over the other. Instead, an integrative perspective is needed to achieve a thorough and coherent understanding of adaptive speciation.     

Integrating selected ecological effects of mixed European beech–Norway spruce stands in bioeconomic modelling

The simplicity of many bioeconomic models has been criticised several times, due to their lack of realism resulting from a deterministic nature and a single-species focus. In this context it was interesting to test the financial sensitivity of bioeconomic modelling against fairly well documented ecological effects in mixed forests. For this purpose our study linked existing results of ecological research with bioeconomic modelling. The presented methodological approach could not only show the importance of considering ecological effects in bioeconomic models; it in fact enabled prioritising ecological research from a financial point of view.In a first step, the possible influence of the tree species mixture on forest stand resistance, productivity and timber quality was derived from existing studies. In a second step, the available Monte Carlo simulations for Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica L.), simulated under site conditions and risks typical of southern Germany, were extended by the mentioned ecological effects and then evaluated from a financial perspective.The results showed a clear influence of all tested ecological effects on the financial indicators, financial risk and return. While testing each ecological effect separately, an increased resistance against wind, snow and insect attacks had the greatest influence on financial risk and return. It over-proportionally enhanced the financial return while simultaneously the financial risk was reduced. In contrast, a degraded timber quality could eliminate the positive effect of risk compensation in mixed forests almost completely. The least influence on the financial indicators finally showed a changed volume growth in mixed forests.A combination of the separately tested ecological effects (increased resistance, changed volume growth and decreased timber quality), between both tree species, underlined the dominating importance of the stand resistance. The integration of ecological effects, induced by interdependent tree species, in our bioeconomic model resulted in significantly lower financial risk than ignoring these effects. Moreover, the financial return of mixed stand variants with a proportion of Norway spruce greater than 60% even exceeded that of the most profitable pure stand.In conclusion this paper clearly confirmed that ignoring ecological effects in bioeconomic models could lead to seriously biased financial results. While a changed volume growth proved rather to be of minor importance for European beech/Norway spruce stands, tree resistance and timber quality may change the financial results significantly.     

A review of recent developments in lake modelling

This paper reviews the lake models published the last five years, mainly in Ecological Modelling. The review shows that structurally dynamic modelling and coupling between hydrodynamic and ecological models are applied increasingly. A number of processes that have not been included in lake models before have been proposed. It has been shown that these additional processes in specific case studies are significant, for instance the competition between phytoplankton and macrophytes or cyanobacteria growth and growth of mussels. It is recommended to study these models for the development of models for case studies where these processes are relevant.     

Combining state and transition models with dynamic Bayesian networks

Bashari et al. (2009) propose combining state and transition models (STMs) with Bayesian networks for decision support tools where the focus is on modelling the system dynamics. There is already an extension of Bayesian networks - so-called dynamic Bayesian networks (DBNs) - for explicitly modelling systems that change over time, that has also been applied in ecological modelling. In this paper we propose a combination of STMs and DBNs that overcome some of the limitations of Bashari et al.’s approach including providing an explicit representation of the next state, while retaining its advantages, such an the explicit representation of transitions. We then show that the new model can be applied iteratively to predict into the future consistently with different time frames. We use Bashari et al.’s rangeland management problem as an illustrative case study. We present a comparative complexity analysis of the different approaches, based on the structure inherent in the problem being modelled. This analysis showed that any models that explicitly represent all the transitions only remain tractable when there are natural constraints in the domain. Thus we recommend modellers should analyse these aspects of their problem before deciding whether to use the framework.