Thermodynamic extremization principles and their relevance to ecology

Theories based on simple principles have provided much insight into the common processes that underpin complex ecological systems. Although such theories (e.g. neutral theory, metabolic theories) often neglect specific ecological details, they compensate for this with their generality and broad applicability. We review several simple principles based on ‘thermodynamic extremization’ (the minimization or maximization of a thermodynamic quantity) and explore their application and relevance to ecology. Thermodynamic extremization principles predict that certain energetic quantities (e.g. entropy production) will tend towards maxima or minima within ecological systems, subject to local constraints (e.g. resource availability). These principles have a long history in ecology, but existing applications have had a theoretical focus and have made few quantitative predictions. We show that the majority of existing theories can be unified conceptually and mathematically, a result that should facilitate ecological applications of thermodynamic extremization principles. Recent developments in broader ecological research (e.g. metabolic theories) have allowed quantitative predictions of ecological patterns from thermodynamic extremization principles, and initial predictions have been supported by empirical data. We discuss how the application of extremization principles could be extended and demonstrate one possible extension, using an extremization principle to predict individual size distributions. A key focus in the application of thermodynamic extremization principles to mainstream ecological questions should be the generation of quantitative predictions and subsequent empirical validation.     

Predictive ecology: systems approaches

The world is experiencing significant, largely anthropogenically induced, environmental change. This will impact on the biological world and we need to be able to forecast its effects. In order to produce such forecasts, ecology needs to become more predictive--to develop the ability to understand how ecological systems will behave in future, changed, conditions. Further development of process-based models is required to allow such predictions to be made. Critical to the development of such models will be achieving a balance between the brute-force approach that naively attempts to include everything, and over simplification that throws out important heterogeneities at various levels. Central to this will be the recognition that individuals are the elementary particles of all ecological systems. As such it will be necessary to understand the effect of evolution on ecological systems, particularly when exposed to environmental change. However, insights from evolutionary biology will help the development of models even when data may be sparse. Process-based models are more common, and are used for forecasting, in other disciplines, e.g. climatology and molecular systems biology. Tools and techniques developed in these endeavours can be appropriated into ecological modelling, but it will also be necessary to develop the science of ecoinformatics along with approaches specific to ecological problems. The impetus for this effort should come from the demand coming from society to understand the effects of environmental change on the world and what might be performed to mitigate or adapt to them.     

Ecological hierarchies and self-organisation – Pattern analysis,modelling and process integration across scales

A continuing discussion in applied and theoretical ecology focuses on the relationship of different organisational levels and on how ecological systems interact across scales. We address principal approaches to cope with complex across-level issues in ecology by applying elements of hierarchy theory and the theory of complex adaptive systems. A top-down approach, often characterised by the use of statistical techniques, can be applied to analyse large-scale dynamics and identify constraints exerted on lower levels. Current developments are illustrated with examples from the analysis of within-community spatial patterns and large-scale vegetation patterns. A bottom-up approach allows one to elucidate how interactions of individuals shape dynamics at higher levels in a self-organisation process; e.g., population development and community composition. This may be facilitated by various modelling tools, which provide the distinction between focal levels and resulting properties. For instance, resilience in grassland communities has been analysed with a cellular automaton approach, and the driving forces in rodent population oscillations have been identified with an agent-based model. Both modelling tools illustrate the principles of analysing higher level processes by representing the interactions of basic components.The focus of most ecological investigations on either top-down or bottom-up approaches may not be appropriate, if strong cross-scale relationships predominate. Here, we propose an ‘across-scale-approach’, closely interweaving the inherent potentials of both approaches. This combination of analytical and synthesising approaches will enable ecologists to establish a more coherent access to cross-level interactions in ecological systems.     

The potential contribution of vegetation ecology to biodiversity research

The contribution of vegetation ecology to the study of biodiversity depends on better communication between the different research paradigms in ecology. Recent developments in vegetation theory and associated statistical modelling techniques are reviewed for their relevance to biodiversity. Species composition and collective properties such as species richness vary as a continuum in a multi-dimensional environmental space; a concept which needs to be incorporated into biodiversity studies. Different kinds of environmental gradients can be recognised and species responses to them vary. Species response curves of eucalypts to an environmental gradient of mean annual temperature have been shown to exhibit a particular pattern of skewed response curves. Generalised linear modelling (GLM) and generalised additive modelling (GAM) techniques are important tools for biodiversity studies. They have successfully distinguished the contribution of environmental (climatic) and spatial (history and species dispersal ability) variables in determining forest tree composition in New Zealand. Species richness studies are examined at global, regional and local scales. At all scales, direct and resource environmental gradients need to be incorporated into the analysis rather than indirect gradients e.g. latitude which have no direct physiological influence on biota. Evidence indicates that species richness at the regional scale is sensitive to environment, confounding current studies on local/regional species richness relationships. Plant community experiments require designs based on environmental gradients rather than dependent biological properties such as productivity or species richness to avoid confounding the biotic components. Neglect of climatic and other environmental gradients and the concentration on the collective properties of species assemblages has limited recent biodiversity studies. Conservation evaluation could benefit from greater use of the continuum concepts and statistical modelling techniques of vegetation ecology. The future development of ecology will depend on testing the different assumptions of competing research paradigms and a more inclusive synthesis of ecological theory.     

Interactions matter—complexity in landscapes and ecosystems

In this review we argue that theories and methodology arising from the field of complex systems form a new paradigm for ecology. Patterns and processes resulting from interactions between individuals, populations, species and communities in landscapes are the core topic of ecology. These interactions form complex networks, which are the subject of intense research in complexity theory, informatics and statistical mechanics. This research has shown that complex natural networks often share common structures such as loops, trees and clusters. The observed structures contribute to widespread processes including feedback, non-linear dynamics, criticality and self-organisation. Simulation modelling is a key tool in studying complex networks and has become popular in ecology, especially in adaptive management. Important techniques include cellular automata and individual-based models. The complex systems paradigm has led to advances in landscape ecology, including a deeper understanding of the dynamics of spatial pattern formation, habitat fragmentation, epidemic processes, and genetic variation. Network analysis reveals that underlying patterns of interactions, such as small worlds and clusters, in food webs and ecosystems have strong implications for their stability and dynamics. These investigations illustrate how complexity theory and associated methodologies are transforming ecological research, providing new perspectives on old questions as well as raising many new ones.     

When are alternative stable states more likely to occur?

T. Fukami and W. G. Lee argue that the logical expectation from ecological theory is that competitively-structured assemblages will be more likely to exhibit alternative stable states than abiotically-structured assemblages. We suggest that there are several important misinterpretations in their arguments, and that the substance of their hypothesis has both a weak basis in ecological theory and is not supported by empirical evidence which shows that alternative stable states occur more frequently in natural systems subject to moderate- to harsh abiotic extremes. While this debate is founded in ecological theory, it has important applied implications for restoration management. Sound theoretical predictions about when to expect alternative stable states can only aid more effective restoration if theoretical expectations can be shown to translate into predictable empirical outcomes. If strongly abiotically- or disturbance-structured systems are more likely to exhibit catastrophic phase shifts in community structure that can be resilient to management efforts, then restoration ecologists will need to treat these systems differently in terms of the types of management inputs that are required.     

Graph models of habitat mosaics

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights.     

Mathematical modelling of ecological succesion—a review

The present review gives an account of the applicability of mathematical modelling in ecological succession studies. The ability of particular model types to solve problems of both theory and management is discussed. The Markovian models are found to be useful for short term predictions, but of very limited value for theoretical considerations. Finally, the predictability of successional pathways is discussed. It is argued that the less we understand about processes in vegetation dynamics, the more we will see the course of succession as random and unpredictable.     

Integrating modelling of biodiversity composition and ecosystem function

There is increasing reliance on ecological models to improve our understanding of how ecological systems work, to project likely outcomes under alternative global change scenarios and to help develop robust management strategies. Two common types of spatiotemporally explicit ecological models are those focussed on biodiversity composition and those focussed on ecosystem function. These modelling disciplines are largely practiced separately, with separate literature, despite growing evidence that natural systems are shaped by the interaction of composition and function. Here we call for the development of new modelling approaches that integrate composition and function, accounting for the important interactions between these two dimensions, particularly under rapid global change. We examine existing modelling approaches that have begun to combine elements of composition and function, identifying their potential contribution to fully integrated modelling approaches. The development and application of integrated models of composition and function face a number of important challenges, including biological data limitations, system knowledge and computational constraints. We suggest a range of promising avenues that could help researchers overcome these challenges, including the use of virtual species, macroecological relationships and hybrid correlative‐mechanistic modelling. Explicitly accounting for the interactions between composition and function within integrated modelling approaches has the potential to improve our understanding of ecological systems, provide more accurate predictions of their future states and transform their management. Synthesis There is increasing attention from researchers and policy makers around the world on both assessing and projecting the state of the planet's biodiversity, its ecosystems and the essential services they provide to society. However, existing modelling approaches largely ignore the interactions between biodiversity composition and ecosystem function. We highlight the key challenges and potential solutions to developing integrated models of composition and function. Such models will require a new effort and focus from ecologists, yet the benefits are likely to be substantial, including better informing the management of natural systems at regional, national and international scales.     

Combining mechanism and drift in community ecology: a novel statistical mechanics approach

A key challenge for models of community ecology is to combine deterministic mechanism and stochastic drift in a systematic, transparent and tractable manner. Another challenge is to explain and unify different ecological patterns, hitherto modelled in isolation, within a single modelling framework. Here, we show that statistical mechanics provides an effective way to meet both challenges. We apply the statistical principle of maximum entropy (MaxEnt) to a simple resource-based, non-neutral model of a plant community. In contrast to previous ecological applications of MaxEnt, our use of MaxEnt emphasises its theoretical basis in the combinatorics of sampling frequencies, an approach that clarifies its ecological interpretation. In this approach, mechanism and drift are identified, respectively, with ecological resource constraints and entropy maximization. We obtain realistic predictions for species abundance distributions as well as contrasting stability-diversity relationships at community and population levels. The model also predicts critical behaviour that may provide a basis for understanding desertification and other ecological tipping points. Our results complement and extend previous ecological applications of MaxEnt to new areas of community ecology, and further illustrate MaxEnt as a powerful yet simple modelling tool for combining mechanism and drift in a way that unifies disparate ecological patterns.     

Behavioural ecology in traditional societies

Can models from behavioural ecology explain cultural diversity in human populations? Studies of variation in reproductive and productive behaviour, both within and between traditional societies, are beginning to show that specific predictions from sexual selection and optimal foraging theory can be developed and tested with human data. Greatest success has been in the study of foraging; whereas attempts to understand patterns of marriage and parental investment have been most convincing in those cases where behaviour is related to specific ecological and social conditions. The aim of human behavioural ecologists in the future will be to determine the constraints that the dual goals of reproduction and production place on individuals.     

The role of expert systems in vegetation science

An area of artificial intelligence known as experts systems (or knowledge-based systems) is being applied in many areas of science, technology and commerce. It is likely that the techniques will have an impact on vegetation science and ecology in general. This paper discusses some of those impacts and concludes that the main effects will be in areas of applied ecology especially where ecological expertise is needed either quickly (e.g. disaster management) or across a wide range of ecological disciplines (e.g. land management decisions). Expert systems will provide ecologists with valuable tools for managing data and interacting with other fields of expertise. The impact of expert systems on ecological theory will depend on the degree to which deep knowledge (i.e. knowledge based on first principles rather than on more empirical rules) is used in formulating knowledge bases.     

Simulation modelling of ecological hierarchies in constructive dynamical systems

Organized complexity is a characteristic feature of ecological systems with heterogeneous components interacting at several spatio-temporal scales. The hierarchy theory is a powerful epistemological framework to describe such systems by decomposing them vertically into levels and horizontally into holons. It was at first developed in a temporal and functional perspective and then, in the context of landscape ecology, extended to a spatial and structural approach. So far, most ecological applications of this theory were restricted to observational purposes, using multi-scale analysis to describe hierarchies. In spite of an increasing attention to dynamics of hierarchically structured ecological systems, current simulation models are still very limited in their representation of self-organization in complex adaptive systems. An ontological conceptualization of the hierarchy theory is outlined, focusing on key concepts, such as levels of organization and the compound and component faces of the holons. Various existing formalisms are currently used in simulation modelling, such as system dynamics, discrete event and agent based paradigms. Their ability to express the hierarchical organization of dynamical ecological systems is discussed. It turns out that a multi-modelling approach linking all these formalisms and oriented toward the specification of a constructive dynamical system would be able to express the dynamical structure of the hierarchy (creation, destruction and change of holons) and the functional and structural links between levels of organization.     

Individual-based modelling in ecology: what makes the difference?

Is individual-based modelling really a new approach in ecology? A large part of the uncertainty surrounding this question is a consequence of imprecisely delimited boundaries between classical and individual-based modelling. Genuine 'individual-based' models describe a population made up of individuals that may differ from one another; they also describe changes in numbers of individuals rather than in the population density, and take resource dynamics explicitly into account. Individual-based models that fulfil these criteria will not characterize ecological systems as 'stable' systems in their ideal form, with equilibrium states represented by points in the phase space.     

Statistical ecology comes of age

The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1–4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.     

Predicting distributions of Mexican birds using ecological niche modelling methods

We tested the utility of the modelling program Genetic Algorithm for Rule-set Prediction (GARP) for modelling ecological niches to make accurate predictions of geographical distributions for 25 bird species across Mexico. Specimen-based point-occurrence data were entered into the algorithm in the form of geographical coordinates, and related to digitized maps of environmental variables, including mean annual precipitation, elevation, mean annual temperature, and potential vegetation. Two Mexican states were used as test areas by withholding their points from model construction; these points were later overlaid on predictions to measure model performance. Statistically, most models (7890%) were significantly more powerful than random models in predicting occurrences in test states; model failures were most often due to low sample size for testing, rather than an inability to model distributions of particular species. The success of this test indicates that ecological niche modelling approaches such as GARP provide a promising tool for exploring a broad range of questions in ecology, biogeography and conservation.     

Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality?

A constant dilemma in theoretical ecology is knowing whether model predictions corrspond to real phenomena or whether they are artifacts of the modelling framework. The frequent absence of detailed ecological data against which models can be tested gives this issue particular importance. We address this question in the specific case of invasion in a predator-prey system with oscillatory population kinetics, in which both species exhibit local random movement. Given only these two basic qualitative features, we consider whether we can deduce any properties of the behaviour following invasion. To do this we study four different types of mathematical model, which have no formal relationship, but which all reflect our two qualitative ingredients. The models are: reaction-diffusion equations, coupled map lattices, deterministic cellular automata, and integrodifference equations. We present results of numerical simulations of the invasion of prey by predators for each model, and show that although there are certain differences, the main qualitative features of the behaviour behind invasion are the same for all the models. Specifically, there are either irregular spatiotemporal oscillations behind the invasion, or regular spatiotemporal oscillations with the form of a periodic travelling ''wake'', depending on parameter values. The observation of this behaviour in all types of model strongly suggests that it is a direct consequence of our basic qualitative assumptions, and as such is an ecological reality which will always occur behind invasion in actual oscillatory predator-prey systems.     

Integrating models with data in ecology and palaeoecology: advances towards a model-data fusion approach

It is increasingly being recognized that global ecological research requires novel methods and strategies in which to combine process-based ecological models and data in cohesive, systematic ways. Model-data fusion (MDF) is an emerging area of research in ecology and palaeoecology. It provides a new quantitative approach that offers a high level of empirical constraint over model predictions based on observations using inverse modelling and data assimilation (DA) techniques. Increasing demands to integrate model and data methods in the past decade has led to MDF utilization in palaeoecology, ecology and earth system sciences. This paper reviews key features and principles of MDF and highlights different approaches with regards to DA. After providing a critical evaluation of the numerous benefits of MDF and its current applications in palaeoecology (i.e., palaeoclimatic reconstruction, palaeovegetation and palaeocarbon storage) and ecology (i.e. parameter and uncertainty estimation, model error identification, remote sensing and ecological forecasting), the paper discusses method limitations, current challenges and future research direction. In the ongoing data-rich era of today's world, MDF could become an important diagnostic and prognostic tool in which to improve our understanding of ecological processes while testing ecological theory and hypotheses and forecasting changes in ecosystem structure, function and services.