Search

Individual-based models (IBMs) are increasingly used to explore ecological systems and, in particular, the emergent outcomes of individual-level processes. A major challenge in developing IBMs to investigate the movement ecology of animals is that such models must represent and parameterise unobserved behaviours occurring at multiple hierarchical levels. Approaches based on approximate Bayesian computation (ABC) methods have been used to support the parameterisation, calibration and evaluation of IBMs. However, a key component of the ABC approach is the use of multiple quantitative patterns derived from empirical data to exclude model structures and parameterisations that generate atypical or implausible patterns. We propose a modelling framework that integrates information derived from statistical inferential models, which are now widely used to describe the behaviour of moving animals, with ABC methodologies for the parameterisation and analysis of IBMs. To demonstrate its application, we apply this framework to high-resolution movement trajectories of the foraging trips of black petrels ( Procellaria parkinsoni ), an endangered seabird endemic to New Zealand. The outcomes of our study show that the use of inferential statistical models to summarise movement data can aid model selection and parameterisation procedures via ABC, and yield valuable insights into the modelling in movement ecology of animals.

Although biogeographic patterns are the product of complex ecological processes, the increasing complexity of correlative species distribution models (SDMs) is not always motivated by ecological theory, but by model fit. The validity of model projections, such as shifts in a species’ climatic niche, becomes questionable particularly during extrapolations, such as for future no-analog climate conditions. To examine the effects of model complexity on SDM predictive performance, we fit statistical models of varying complexity to simulated species occurrence data arising from data-generating processes that assume differing degrees of distributional symmetry in environmental space, interaction effects, and coverage in climate space. Mismatches between data-generating processes and statistical models (i.e., different functional forms) led to poor predictive performance when extrapolating to new climate-space and greater variation in extrapolated predictions for overly complex models. In contrast, performance issues were not apparent when using independent evaluation data from the training region. These results draw into question the use of highly flexible models for prediction without ecological justification.

The biodiversity paradox has been a long-standing enigma in theoretical ecology. It emerged as a contradiction between the competitive exclusion principle and the natural species richness. There are two competing ecological theories which try to explain this issue: niche theory and neutral theory. The problem is that both theories are based on nontransparent models which ignore local interactions between individuals and cannot provide an understanding of interspecific competition mechanisms. Mathematical models of complex systems may be of three general types: black-box, grey-box and white-box models. Classical ecological models – Malthusian, Verhulst and Lotka–Volterra models are of black-box type. Black-box models are nonmechanistic. They cannot help to create a mechanistic ecological theory as they do not provide a direct insight into individual-based mechanisms. Here we make some critical notes on the recent attempts to resolve the paradox by black-box and grey-box approaches. We critically discuss a contribution of the neutral theory and the attempts to solve the paradox by methods of the classical quantum mechanics. These attempts are rather ineffective due to the lack of mechanicalness and likely lead to more confusion than clarity in understanding of biodiversity mechanisms. We also discuss our solution to the biodiversity paradox through a verification of the competitive exclusion principle with using the white-box approach to mathematical modelling of competitive coexistence.

Species distribution modelling has gained importance since the introduction of the Water Framework Directive. Several efforts have been made for the development of decision support tools to aid river basin managers. However, there is a mismatch between the available ecological models and stakeholder needs. For example, models can be so complex that they can only be applied on a limited set of species, or models can be so qualitative that they fail to deliver insight in the underlying processes behind changing ecological quality. Yet, much is known already about ecology and ecography, in general and for specific species. To valorize this available knowledge, we have developed species distribution models for macroinvertebrates in Flanders grounded in ecological theories. We introduce a conceptual approach based on niche and landscape filter theories. To apply the concept on many different macroinvertebrate species, the model development uses both data from Flanders, expert knowledge and data from other similar river systems. Implementing these niche and migration models results in a moderate predictive accuracy (average Kappa of 0.19). For sensitive species that are essential for an ecological quality status the approach results in a higher accuracy. Despite the moderate predictive accuracy, the resulting models have a good applicability. The models concur well with ecological knowledge on species preferences. Furthermore, throughout the model development process stakeholders and end users have been involved to discuss model structure and its related assumptions. This ensures that the developed model is credible and acceptable. This model approach has shown to be a way forward for ecological decision support in river management in Flanders, but inclusion of additional knowledge on migration behaviour and species interactions could help to improve the predictive accuracy the models in the future.

The design of computational models is path-dependent: the choices made in each step during model development constrain the choices that are available in the subsequent steps. The actual path of model development can be extremely different, even for the same system, because the path depends on the question addressed, the availability of data, and the consideration of specific expert knowledge, in addition to the experience, background, and modelling preferences of the modellers. Thus, insights from different models are practically impossible to integrate, which hinders the development of general theory. We therefore suggest augmenting the current culture of communicating models as working just fine with a culture of presenting analyses in which we try to break models, i.e., model mechanisms explaining certain observations break down. We refer to the systematic attempts to break a model as “robustness analysis” (RA). RA is the systematic deconstruction of a model by forcefully changing the model's parameters, structure, and representation of processes. We discuss the nature and elements of RA and provide brief examples. RA cannot be completely formalized into specific techniques and instead corresponds to detective work that is driven by general questions and specific hypotheses, with strong attention focused on unusual behaviours. Both individual modellers and ecological modelling in general will benefit from RA because RA helps with understanding models and identifying “robust theories”, which are general principles that are independent of the idiosyncrasies of specific models. Integrating the results of RAs from different models to address certain systems or questions will then provide a comprehensive overview of when certain mechanisms control system behaviour and when and why this control ceases. This approach can provide insights into the mechanisms that lead to regime shifts in actual ecological systems.

The two main challenges of ecological modelling are to yield more general understanding and theory and to provide testable and robust predictions. To achieve this, emergence, structural realism, and prediction have to become key elements of designing models. In the special issue “Next-generation ecological modelling”, which is dedicated to Donald DeAngelis on the occasion of his 70th birthday, 16 contributions present and discuss main features of next-generation ecological modelling. One key feature is to base the description of individuals’ behaviour and interactions on first principles rooted in energetic or evolutionary theory. To cope with increasing model complexity, standardization, separate testing of alternative submodels against multiple output patterns, and documenting these tests will be required. Including micro-evolution is essential to capture organisms’ response to changing conditions. Functional types may be used instead of species for representing communities. Model analysis will be challenging, but robustness analysis, which tries to break models’ explanations, can help to tell signals from noise and identify general mechanisms underlying the internal organization of ecological systems. Ultimately, next-generation modelling should aim at developing general theory to better understand stability properties and mechanisms. This understanding then can provide the basis for restoring, maintaining, or strengthening the resilience of ecosystems and supporting sustainable management of natural resources.

Recent decades have seen great advances in ecological modelling and computing power, enabling ecologists to build increasingly detailed models to more accurately represent ecological systems. To better inform environmental decision-making, it is important that the predictions of these models are expressed in simple ways that are straightforward for stakeholders to comprehend and use. One way to achieve this is to predict threshold values for environmental perturbations (e.g. climate change, habitat modification, food loss, sea level rise) associated with negative impacts on individuals, populations, communities or ecosystems. These thresholds can be used by stakeholders to inform management and policy. In this paper we demonstrate how this approach can use individual-based models of birds, their prey and habitats, to provide the evidence-base for coastal bird conservation and shellfishery management. In particular, we show how such models can be used to identify threshold values for perturbations of food abundance that can impact negatively on bird populations. We highlight how environmental thresholds could be used more widely to inform management of species and habitats under environmental change.

The use of dynamic systems models by scientists, managers, and policy-makers is becoming more common due to the increasingly complex nature of ecological and socio-economic problems. Unfortunately, most scientific training in the life sciences only includes dynamic modeling as elective, supplementary courses at a beginners-level, which is not conducive to generating the expertise needed to properly develop, test, and learn from dynamic modeling approaches and risks utilization of poor quality models and adoption of unreliable recommendations. The objective of this paper is to fill part of that gap, particularly regarding model experimentation, by summarizing key concepts in experimental design for simulation experiments and illustrating hands-on examples of experiments needed for developing a deeper understanding of complex, dynamic systems. The experiments include extreme conditions testing, sensitivity analyses of model behaviors given variation in both parameter values and graphical (table) functions, and “what-if?” experiments (e.g., counterfactual trajectories, boundary-adequacy tests, and intervention threshold experiments). Each experimental example describes the theoretical foundation of the test, illustrates its application using an ecological systems model, and increases in degree of difficulty from novice to advanced skill levels. By doing so, we demonstrate consistent, scientific means to glean valuable insights about the model's structure-behavior link, uncover any unforeseen model flaws or incorrect formulations, and enhance the confidence (validity) of the model for its intended use.

Not all ecosystems are in a steady-state or approaching it. Some of them merely pass through the life-cycle stages. The best example is the forest ecosystems formed by even-aged forest stands, where ecosystem properties and functions are related to the stand age. The relationship is not strict, however, and so the stand age is not a general measure of ecosystem state. We propose and theoretically justify a thermodynamic measure for ecosystem state, which is named here as ecosystem biological age and defined as the period of time that some reference ecosystem needs to accumulate the same amount of exergy as the ecosystem under concern. The use of the concept is illustrated by analyzing the 30-year observations of larch stands growth.

Emergy is an important evaluative tool to understand the sustainability of ecological systems. This methodology normalizes natural and economic inputs to permit a more holistic evaluation of systems. Traditional ecological knowledge (TEK) is commonly not included in analyses of traditionally-designed ecosystems, or past evaluation has tended toward a qualitative valuation of TEK. Our research evaluated the emergy in the creation, maintenance, and transfer of TEK at the individual and community levels, as well as the biophysical and cultural resources that support this knowledge system. These evaluations took place within the Lacandon Maya village of Lacanja Chansayab, Mexico and with Zapotec farmers of Lalopa, Mexico. Respondents stressed the importance of inter-generational ties, the local forest, and community in their education. We found that TEK-based labor transformities (1.23E07 sej/J in Lacanja Chansayab, Mexico and 6.54E06 sej/J in Lalopa, Mexico) are similar to past qualitative estimates. TEK labor will result in minimal impact to the environment (i.e., environmental loading ratio) relative to Western education, which has comparable transformities, due to reliance on renewable local ecosystem inputs rather than fossil fuels and physical infrastructure. This research highlights the importance for sustainability of both preserving knowledge transfer systems resulting in TEK and in developing hands-on educational systems that rely upon the natural world as the primary classroom.

Resilience in dynamic ecological systems has been intuitively associated with the ability to withstand disturbances in system drivers represented as shocks. Typically shocks are characterized as instantaneous, and isolated non-interacting events with the system dynamics corresponding to a fixed potential well. However, ecological systems are subject to continuous variation in environmental drivers such as rainfall, temperature, etc. and these interact with the ecosystem dynamics to alter the potential well. These variations are typically represented as a stochastic process. Furthermore, with climate change, the stochastic characteristics of the environmental drivers also change, thereby impacting the well dynamics. To characterize the resilience behavior under continuous variation in system drivers, and contrast it with that subject to instantaneous shock in system drivers, we employ the canonical catastrophic shift system as an example, and demonstrate emergent and contrasting divergent resilience behavior of the measures as the properties of the system-driver couple change. These behaviors include variability induced stabilization or enhancement of dynamic regimes, regions of sensitivity to dynamic regime transitions and existence of trap or escape regions. Furthermore, we introduce the concept of iso-resilience curves which are employed to design travel paths in resilience landscapes. These results provide valuable insights for managing resilience attributes associated with dynamic regime transitions in catastrophic shift systems under instantaneous shock and continuous variability in system drivers.

Network ecologists investigate the structure, function, and evolution of ecological systems using network models and analyses. For example, network techniques have been used to study community interactions (i.e., food-webs, mutualisms), gene flow across landscapes, and the sociality of individuals in populations. The work presented here uses a bibliographic and network approach to (1) document the rise of Network Ecology, (2) identify the diversity of topics addressed in the field, and (3) map the structure of scientific collaboration among contributing scientists. Our aim is to provide a broad overview of this emergent field that highlights its diversity and to provide a foundation for future advances. To do this, we searched the ISI Web of Science database for ecology publications between 1900 and 2012 using the search terms for research areas of Environmental Sciences & Ecology and Evolutionary Biology and the topic tag ecology. From these records we identified the Network Ecology publications using the topic terms network, graph theory, and web while controlling for the usage of misleading phrases. The resulting corpus entailed 29,513 publications between 1936 and 2012. We document the rapid rise in Network Ecology publications per year reaching a magnitude of over 5% of the ecological publications in 2012. Drawing topical information from the publication record content (titles, abstracts, keywords) and collaboration information from author listing, our analysis highlights the diversity and clustering of topics addressed within Network Ecology and reveals the highly collaborative approach of scientists publishing in this field. We conclude that Network Ecology is a large and rapidly growing area of ecology, and we expect continued growth of this research field., 18 pages of text, 5 tables, 9 figures. Comments welcome

Specialization has often been suggested as one of the main factors influencing the stability of ecological systems at the population and community level. Generally, highly specialized systems are believed to be the most sensitive toward disturbances, as the dependence of specialized species on the availability of particular resources or partner species is greatest. The flip side of specialization is, however, that it reduces the intensity of interspecific competition and thus the risk of extinction through competitive exclusion. Moreover, since ecological stability is a highly ambiguous concept, general statements about the relationship between specialization and stability cannot be made based on a single stability criterion. In this study, we examine the relationship between specialization and stability in plant–animal mutualistic systems using a population dynamic model with two species in each group. We compare results for four different stability criteria, both for a general type of plant–animal mutualism and specifically for a plant–pollinator system. Contrary to previous studies which concluded that specialization increases system vulnerability to disturbances, we find that positive, negative and unimodal relationships are possible depending on the stability criterion applied and the characteristics of species interactions. Our results call for further investigations of the consequences of ecological specialization, and emphasize the special properties of pollination mutualisms.

This paper presents a new cognitive mapping approach for analysing systems of practices in social-ecological systems. These systems are mapped from people's views collected during open-ended interviews. Cognitive maps are made up of diverse variables (e.g., operations, drivers, constraints) linked to each other by a range of relationships: cause-effect, fluxes of matter, information flows and sequence of two operations. Individual cognitive maps heuristically model the practices and decision-making processes expressed by interviewees. The mathematical formulation of cognitive maps allows individual cognitive maps to be aggregated into a social cognitive map. The latter can be used to model the system of practices used by a particular group of people. Using this approach, we analysed the practices and decision-making processes linked to grassland management in a Belgian grassland-based livestock farming system. Our work confirmed that a social cognitive map could be drawn up for multiple locations. The results showed how this inductive cognitive mapping approach overcame two limitations frequently highlighted in previous studies: the diverse interpretations of variables and relationships; and the difficulty in revealing the rationale in cognitive maps. © 2012 Elsevier B.V.

The Phenomenological Universalities are a formal way to classify growth. We apply this concept to investigate interactive growth phenomena in biological and ecological systems. Using a vector formulation of these Universalities without any ad hoc assumptions on the nature of the interactions, we are able to characterize the joint growth of two or more interacting organisms and assess the direct mutual influences between them, as well as the indirect influences that operate through environment modifications. Various interactions, such as cooperation, parasitism, and mutual hindrance can be suitably described. We present several illustrative examples, including an examination of the growth dynamics in a mixed-species plantation and compare the predictions of our method with the conclusions obtained by biologists through direct observation. Fil: Barberis, Lucas Miguel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Física. Grupo de Teoria de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Condat, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina

Ecosystem services are usually interpreted as a free of charge “favour” provided to us and our society by nature. In other words, nature supplies us with a functionality that we would otherwise have to pay for. Our cost would be to provide resources either (1) to ensure the necessary inputs to drive our society, or (2) to assist in counteracting, absorbing or remediating unwanted effects that are results of our societal activities. Through ecosystem studies it has been found that a substantial part of the functionality of nature is laid out in all types of components—the compartments of the ecosystems together with the transactional interrelations (flows) and controls between them. Eventually, many so-called indicators have been proposed during the last decades. Such measures are dedicated to tell us about the quality side of ecosystem functionality, e.g. to tell us how well the system performs relatively to a theoretical maximum efficiency possible. As an additional hypothesis, such functions are thought to orient the systems and thus increase through time development, i.e. to be optimised under the given the constraints, through the evolution of the system. Recently is has been pointed out that natural and societal systems share the feature of being complex in their organisation. Meanwhile, it was remarked that societal systems in many ways evolved in opposite direction of how natural evolution would drive an ecosystem. Many philosophers of biology have stated that biological systems posses information and memory functions which improve their long-term capability to survive. This information is believed to be contained in the organisational structures of the system as much as in its gene pool. If we accept such arguments it means that studies of organisation and function of natural systems will provide us with another type of ecosystem services. This would namely give us information about in what direction to drive society in order to achieve a more sustainable system. This paper discusses what measures derived from modern ecosystem theory can possibly be used to study and compare the functionality of the two types of systems. The discussion takes an entrance point in two graphs—one that represents a natural system and one of a socio-economic system. The systems possess similar levels of complexity in terms of number of compartments whereas their connectivities do differ in quantity and quality. The differences between the systems are compared from both a network and a thermodynamic perspective. Indications of the best available options that we have at present, will help to increase our knowledge about and understanding of the systems given. As a main conclusion it is possible to view and treat our society as an ecosystem. This means that it is possible to apply the same measures (indicators) that we use in ecological theory. The idea to use these features is so clear, obvious and at the same time cheap that this option necessarily has to be tried out. It seems a bit surprising that we – from a “natural science point-of-view” – to a certain extent understand natural systems better than socio-economic ones. One major reason is that the latter type includes a large set of regulatory mechanisms that are exerted on a subjective basis as opposed to natural systems. As a consequence societal systems become much more difficult to evaluate, forecast and regulate than ecosystems.

Ecological systems are frequently modeled as dynamic systems. It is natural then to use the techniques of dynamic systems theory to analyze such models. However, the methods and results that are produced by dynamic systems theory do not always capture the aspects of ecological systems that are of greatest interest to managers and decision-makers. We identify some of the challenges of using dynamic systems theory to explore ecological systems and propose an alternative approach that emphasizes the understanding of transient effects in light of uncertainty and variability. We illustrate this method by an examination of a model for phosphorus levels in fresh water lakes.

A good theory is focused without being blurred by extraneous detail or overgenerality. Yet ecological theories frequently fail to achieve this desirable middle ground. Here, we review the reasons for the mismatch between what theorists seek to achieve and what they actually accomplish. In doing so, we argue on pragmatic grounds against mathematical literalism as an appropriate constraint to mathematical constructions: such literalism would allow mathematics to constrain biology when the biology ought to be constraining mathematics. We also suggest a method for differentiating theories with the potential to be “unreasonably effective” from those that are simply overgeneral. Simple axiomatic assumptions about an ecological system should lead to theoretical predictions that can then be compared with existing data. If the theory is so general that data cannot be used to test it, the theory must be made more specific.

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.

Current threats of invasive species have significant implications for ecological systems. Given their potential impacts, invasive species have been the subject of extensive empirical and theoretical studies. However, these studies have tended to focus on species that produce highly visible ecological and economic impacts. In our study, we take a step back from focusing on these high-impact invasive species, and examine the general colonization (invasion) process of exotic species that have various “competitive abilities” against the native species. Using a two-species cellular automaton model, we demonstrate that: (1) a threshold level of competitive ability is required for the exotic species to successfully establish in a new landscape and (2) an exotic species with superior competitive ability does not necessarily become dominant in a landscape (alternatively, a species that has inferior competitive ability may successfully colonize a new system). Our findings have significant implications for the study of species invasions and also provide clues to how species assemble in ecological communities.

Exergy function was basically developed in the fields of engineering and is the most useful function to solve problems related to cost-optimization procedures of energy conversion systems and energy policies. However, in the last decades, this function has also been proposed as a tool able to study complex systems, such as ecological systems. The exergy function proposed by Jorgensen, called eco-exergy, is investigated in this paper because of its formulation that differs from the classical one. The two main differences are in the changed reference state, which is more useful for ecological applications, and the contribution of informational exergy that is taken into account. This paper shows how moving from macroscopic to microscopic information storage the exergetic contribution due to information grows and it becomes even three orders of magnitude higher than physical one in the more complex living systems. The capacity of packaging information at the molecular level (DNA) that differs from one organism to another can be taken into account using eco-exergy function.

Individual-based models offer a structurally unique (and unifying) approach to ecological applications. Model results also provide an important input into ecological theory. The approach operates on the lowest organisational level considered in ecology (i.e. activities of individuals). Simulating the actions of single organisms allows to study how the properties of higher level ecological entities like swarms, populations, trophic networks and regional distribution patterns emerge. Unlike other approaches working on higher abstraction levels, individual-based models can represent structural–functional relationships similar to the pattern of available ecological knowledge. To demonstrate the range of applications of the approach we will address four issues using comprehensive data from two projects performed in Northern Germany. First, a generic model structure for individual-based models operating on the basis of object-oriented programming is explained. It allows to capture a large variety of different ecological interactions. In the second step, application examples from different fields of ecology are explicated. Plants and animals, active in terrestrial or aquatic environments, exhibit interaction types, which lead to self-organised structural–functional networks resulting from single organismic interactions. Spatial relations, dispersal, bio-energetics, plasticity of growth and form are topics which can be successfully dealt with in individual-based models. The wide range of qualitatively different interactions that can be represented is responsible for the importance the approach has gained in ecology. In the third step, we show how the approach is used in a current research project to anticipate implications of genetically modified plants in agriculture. An individual-based model is used to simulate small-scale dispersal and persistence. The results are used for geostatistic extrapolation to the regional scale. Oilseed rape (Brassica napus) serves as an example. The model represents cultivation practice, feral populations and environmental characteristics. The fourth and final step discusses epistemological implications of individual-based models. It is concluded that a successful application of the approach requires detailed biological information about the represented species. This makes a leading involvement of field ecologists essential for model development. On the other hand, it also opens a theoretical access how to connect quantitative and qualitative aspects of cause–effect chains in ecology across different hierarchical levels. These aspects are discussed in relation to possible limitations of the approach.

We focus on two paradoxes of ecological theory: the paradox of enrichment and the enrichment response. Both are counterintuitive theoretical predictions that have received little empirical support. We argue that both enrichment paradoxes could be theoretical artifacts and suggest that further experimental work is necessary to determine whether these paradoxes deserve their current status as ecological axioms.

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

We describe an approach in which a neural network (NN) can be trained on sets of driving variables (inputs) and output variables relating to spatial structure. The trained NN provides a predictive tool for defining spatial structure in a specified ecological system. We demonstrate the approach using a modified version of the Crawley and May [J. Theor. Biol. 125 (1987) 475] model that describes simplified annual/perennial plant interactions in a disturbed system. The model is implemented within a cellular automaton with randomised start conditions and is run for periods of up to 50 time steps (50 years). Neural networks are trained using a large set of modelled situations, and the ability of the network to predict plant spatial distributions is then measured. Different image analysis methods are applied to the plant array, and the ability of each method to provide an accurate description of the end-state of the modelled system is investigated. Reconstruction of the plant array from these image analysis measurements is carried out using a stochastic error minimisation method. The partial derivatives method is applied to the trained neural network in order to determine which variables input to the model most strongly influence the eventual plant population distribution. In the example presented, it is found that a relatively simple boundary:area ratio measurement provides a rapid and effective method of describing the spatial structure of the plant community, while the variables that are most influential on the system’s end-state are those describing annual fecundity and perennial mortality rates.

Understanding how “control” is exercised in ecological systems, even giving a more appropriate definition or meaning to the word “control” in this context, is an important theoretical issue and would increase our ability to manage ecosystems. Conventionally, in food web ecology, the distinction is drawn between bottom-up and top-down control. In that literature, the bottom-up hypothesis asserts that the primary producers are the source of system regulation and the top-down hypothesis states that keystone species at a higher trophic level can regulate the system. However, we know that in reality control of system behavior is much more complex and distributed than this dichotomy would suggest. Indeed, there is an urgent need for a succinct, yet more complete and comprehensive conceptual framework for thinking about control and for deriving insights into what governs ecosystem organization. In an ecosystem, each element contributes to the overall flow-storage pattern observed in the system through its interactions with the other elements; in this sense, control is distributed among the system elements. Those pair-wise system interactions can be identified and quantified using network analysis. Since the network analysis methodology accounts for both the input (recipient-oriented) and output (donor-oriented) influences from each element, it is possible to use this methodology to move beyond the simple top-down and bottom-up perspective of control. Here, I connect the network analysis methodology to traditional control theory, reintroduce a network-based control parameter using flow analysis and extend the methodology to network storage analysis. Model ecosystems are constructed and used to investigate these properties.

We re-analyze the assumptions underlying two recently proposed ontogenetic growth models [Nature 413 (2001) 628; Nature 417 (2002) 70] to find that the basic relations in which these models are grounded contradict the law of energy conservation. We demonstrate the failure of these models to predict and explain several important lines of empirical evidence, including (a) the organismal energy budget during embryonic development; (b) the human growth curve; (c) patterns of metabolic rate change during transition from embryonic to post-embryonic stages; and (d) differences between parameters of embryonic growth in different taxa. We show how a theoretical approach based on well-established ecological regularities explains the observations where the formal models fail. Within a broader context, we also discuss major principles of ontogenetic growth modeling studies in ecology, emphasizing the necessity of ecological theory to be based on assumptions that are testable and to be formulated in terms of variables and parameters that are measurable. © 2003 Published by Elsevier B.V.

Ecological systems are generally considered among the most complex because they are characterized by a large number of diverse components, nonlinear interactions, scale multiplicity, and spatial heterogeneity. Hierarchy theory, as well as empirical evidence, suggests that complexity often takes the form of modularity in structure and functionality. Therefore, a hierarchical perspective can be essential to understanding complex ecological systems. But, how can such hierarchical approach help us with modeling spatially heterogeneous, nonlinear dynamic systems like landscapes, be they natural or human-dominated? In this paper, we present a spatially explicit hierarchical modeling approach to studying the patterns and processes of heterogeneous landscapes. We first discuss the theoretical basis for the modeling approach—the hierarchical patch dynamics (HPD) paradigm and the scaling ladder strategy, and then describe the general structure of a hierarchical urban landscape model (HPDM-PHX) which is developed using this modeling approach. In addition, we introduce a hierarchical patch dynamics modeling platform (HPD-MP), a software package that is designed to facilitate the development of spatial hierarchical models. We then illustrate the utility of HPD-MP through two examples: a hierarchical cellular automata model of land use change and a spatial multi-species population dynamics model. © 2002 Elsevier Science B.V. All rights reserved.

The edge effect is one of the main phenomena studied by landscape ecology, since it plays a decisive role in determining the structure and dynamics of ecological patches. Most conservation issues involving spatial considerations (design of reserves, land use planning, etc.) require—implicitly or explicitly—an analysis of the edge effects under operation and of their consequences. These are classically analyzed through empirical measurements of linear gradients referenced to the patch border, which yield models of edge effects that: (i) wrongly assume a simple spatial relationship to a single point of the border (the nearest one), (ii) provide flawed predictions on the effect fields generated in ecological patches. Malcolm (1994) has recently addressed these problems by considering an alternative approach that formally integrates the edge effect of every point along a patch border (‘point edge effect’), to generate edge effect fields. In this paper, we deepen the analysis of this concept of addition of multiple point edge effects to generate total effect fields, revealing some important restrictions of Malcolm's method. These restrictions are: (i) linear point edge effects, and (ii) homogeneity of the point edge effect along the patch border. Here we carry out an extended application of this method to patch borders (homogeneous or heterogeneous in their point edge effects) of any geometry and to point edge effects of any kind, no matter how irregular or complex these might be. We provide a general numerical solution for the calculation of edge effect fields by means of a topological parameterization, which has been implemented in a program that can be easily run in MATHEMATICA software. We further show how patch shape and size can interfere with the point edge effect, giving rise to complex effect fields within the patches, which cannot be explained by edge effect penetration alone.

The debate on diversity–stability relationships has a long history of theoretical interest and plays a central role in development of modern ecology. But such debate has recently re-opened under critical scrutiny both in theoretical and empirical studies. In this paper we use allometric (or energetic) scaling and statistical physics approaches to this problem. On the basis of local Damuth symmetry, a Markov model of transfer of energy between different species, and the fluctuation–dissipation theorem, scaling rules of species number and population variability of biological communities near equilibrium are derived. These scaling rules indicate that the diversity–stability relationship may be an energetic and thermodynamic consequence of ecological systems near equilibrium, not a simple statistical consequence as derived by other recent theoretical work.

Understanding and managing environmental risk is one of the major challenges of our time. The variability of ecological systems, wherein disturbances occur with uncertain frequency and magnitude over time and space, is essential for maintaining ecosystem integrity and resilience. This paper uses sustainable development indicators to improve multiple-objective environmental decision making under conditions of unknown variability. Specifically, the robustness to uncertainty of competing policy alternatives is assessed using multi-attribute value theory and the recently developed information gap methodology. The management of spruce-budworm outbreaks in the forests of New Brunswick, Canada, is used as an illustrative example. Numerical and theoretical results show how the minimum required return and the available prior information determine which alternative can best cope with environmental uncertainty.

The traditional approach to modeling the state of complex ecological systems assumes realization of a series of numerical experiments with a dynamic model. The results obtained are difficult to evaluate for multicomponent systems. To give an integrated estimation of the state of an ecosystem as a whole is quite a complicated task. The synthesis of dynamic modeling for aggregated and averaged components of an ecosystem and ecoscreening approach for risk estimation is one way of overcoming this difficulty. The annual variations of the basic components of the ecological system (concentrations of phytoplankton, zooplankton, macroalgae, fish, nutrients, suspended and dissolved organic matter, and hydro-optical characteristics) are calculated from full dynamic modelling. The annual variations of ecological risk from effects on an ecological system are calculated based on the synthesis of the two approaches. This method was developed for prediction of variations of risk estimation for the north-western Black Sea shelf. The annual variations of risk are calculated when the ecological system is submitted to regular pollution and emergency situations. More accurate estimation of risk is reached by step wise application of each one of the approaches.

This paper formally introduces the rheomode orientation to network flow analysis and provides a quantitative test for the ecological property of network homogenization. Using network flow analysis, it is possible to identify and quantify the direct, indirect, and integral contributions of flow between any two components in a reticulated system. Inspection of the integral (direct plus indirect) flow matrix reveals many interesting properties not obvious from an empirical investigation of proximate transactions. Using network flow analysis, we observe that the composition of direct flows is comprised of a fairly uniform mixture of resources from all the system components. We call this evening out of flow network homogenization (Patten, B.C., Higashi, M., Burns, T.P., 1990. Ecol. Model. 51, 1–28). Here we introduce a standard statistical technique to provide a quantitative test for network homogenization. This property is the direct result of a flow oriented analysis of ecological systems. This has broader implications for the standard trophic dynamics paradigm currently dominating ecological research. The central results from this approach indicate that networks are holistic entities which must be analyzed as such.

A major problem in ecological modelling is finding the appropriate level of resolution when describing the processes and structures of ecological systems. When modelling basic ecological questions, as a rule the best approach is to ignore as much detail as possible in order to obtain general insights. However, for applied problems focusing in particular on ecological systems, there are no clear guidelines for identifying the most appropriate resolution in space, time and the detail of description. Spatially explicit modelling thus has to mainly rely on trial and error in scaling-up from modelling at the local scale to exploration of the model at the global scale. We demonstrate here a modelling strategy that takes the opposite approach: starting at the global scale, with a strategic model of minimum resolution, we proceed step by step to a model addressing applied questions. The strategic model is designed to reproduce a certain pattern observed in nature. As an example, we use the wave-like spreading pattern of rabies. The applied model addresses the question of whether rabies might persist in areas with a high proportion of foxes immunized by oral vaccination. As a consequence of our scaling-down strategy, the resolution of the applied model is not chosen a priori, but emerges from the step by step modelling strategy. During each step of model refinement, one module of the preceding model is described with a slightly increased resolution. This stepwise approach allows both a backward reference to the pattern reproduced by the strategic model and a cross-reference between the coarser and finer version of the module refined. The main potential of the scaling-down strategy is that it leads to efficient models in an efficient way, but since scaling-down is a complement to scaling-up approaches, it might also help to bridge the gap between theoretical and applied ecological modelling.

Twelve papers featured in a special issue on individual-based modelling in ecology are reviewed in an effort to identify common methodological and theoretical issues. The review focuses on issues related to the question of whether and how individual-based modelling is changing ecological theory. One major hindrance impeding the generation of theory from individual-based models (IBMs) is the fact that IBMs are more or less complex computer simulation models. They are thus hard to develop, hard to communicate, and hard to analyse. Solving this problem requires both software tools which help to implement and communicate IBMs and at least the same effort in analysing the models as is currently put into their development. A new field of application of IBMs is Virtual Ecology, i.e. the comparison of simulated data sets with those obtained by virtual (i.e. simulated) ecologists. This method allows field methods, empirical measures and sampling protocols to be optimised. As far as theoretical issues are concerned, individual variability was by far the most important issue discussed in the papers. Previously most studies concentrated on the mechanisms generating individual variability, but there is now also a growing number of models addressing the consequences of individual variability for population and community dynamics. In order to determine these consequences, a currency is required which allows the model populations to be evaluated. Persistence and other stability properties are proposed as such a unifying currency. The lesson contained in our review is that even with just twelve papers more or less explicitly oriented towards ecological theory, elements of a theory that might emerge from individual-based modelling in the future can already be identified.

Individual-based modelling is a reductionistic technique for describing ecological systems. In contrast to more traditional mathematical models, an individual-based model is not described ‘top-down’, like a black box, but ‘bottom-up’ by the structure and dynamics of the discrete entities of the system considered important for the issue under study. The majority of individual-based models are hand-coded software programs, designed and implemented by ecologists. In truth individual-based models are currently synonymous with their implementation on computer—for generally speaking no complete description of a model other than the executable program itself is available. This leads to a number of fundamental and technical problems, which may partly be overcome by the use of appropriate software tools. But although software tools are available for simulation studies in many other fields of application, the number of tools which assist individual-based modelling and simulation is limited. In this paper we examine different strategies for the software support of individual-based modelling. We identify three different layers of software support. Firstly, we discuss software frameworks being implemented on top of general purpose programming languages. Although software frameworks support the programming of any individual-based model, they can only be used by an ecologist able to develop computer programs. Secondly, we look at interactive modelling tools being used by ecologists who build models for specific fields of application. Thirdly, we investigate simulators which support users who do not want to build their own model but would rather use a predefined existing model. For each of these categories we briefly describe a tool that has been or is currently being developed at the OFFIS institute. Attention is mainly focused on the conception of a modelling tool ( wesp-tool ) designed to support the modelling and analysis of individual-based metapopulation models.