Ecological Orientors Research Articles

Effectiveness of entropy-based functions in the analysis of ecosystem state and development

Following the advances in the field of the thermodynamics of far-from-equilibrium systems, several ecological orientors (indicators able to describe the stage and orientation of ecosystem development) incorporating entropy terms have been proposed. Although most of the proposed functions have a good theoretical basis and have proved to perform adequately as ecological indicators, their suitability as ecological orientors has yet to receive a full confirmation in real case studies. The aim of the present contribution is to examine how several entropy-based indicators (exergy, structural information, entropy production, specific entropy production and the Eco-exergy index) perform as orientors when applied to a special case of ecological succession, i.e. eutrophication, in a homogeneous set of shallow lakes lying along a trophic gradient, from oligotrophy to hyper-eutrophy. The results show that a coherent pattern of response emerge, which is also consistent with the classical ecological theory. In particular, the maximisation of storage and the minimisation of specific entropy production are confirmed as the most reliable principles of ecosystem development, whereas the maximisation of dissipation (as entropy production) appears as a debatable criterion of development.

Exergy as an indicator: Observations of an aquatic ecosystem model

Exergy is considered as a goal function or ecological orientor. Normally at the edge of oscillation exergy reaches to its maximum value when the ecosystem had no adaptation on it. To study the variation of exergy in different states of ecosystem, a simple three species (phytoplankton, zooplankton and fish) food chain model has been considered. From the model it is shown that the system moves from steady state to chaotic state by decreasing zooplankton body volume in turn increasing its grazing rate. By the property of self-adaptability the system tries to overcome this situation. Two such possible processes are described here: (i) by the toxic effect of phytoplankton and (ii) by reducing half saturation constant of fishes. In both this cases exergy value reduces and the system reaches to stable state. Through the analysis of exergy variation in all these situations this paper shows that the system chose the process in which the reduction of exergy will be the minimum.

Testing the effectiveness of exergy-based tools on a seasonal succession in a coastal lagoon by using a size distribution approach

Although several exergy-based indicators of ecosystem state have been put forward during the last decades, their effectiveness still expect a full confirmation. Recently, Ludovisi has proposed a formulation of exergy based on classical thermodynamics, which includes three terms –size (C), concentration (X) and structural information (I) – accounting for the contribution to exergy due to the abiotic and biotic components of an ecosystem, with the latter being expressed as a function of (sub)community structure and diversity. In the present study, the response of the different exergy terms is analysed along the seasonal progression of environmental conditions and phytoplankton in the Lagoon of Lesina (Puglia, Italy). According to the proposed methodology, the equilibrium concentration of the main hydrochemical variables has been calculated on the basis of a suitable hydrochemical model. The estimate of the equilibrium concentration of the phytoplankton (the VECE values) has been performed for logarithmic body-size classes by applying the equilibrium condition to the complete oxidation of the biomass. The results show that: (i) hydrochemical and phytoplankton exergy, as well as exergy terms (size C, concentration X and structural information I) are positively correlated one another, thus suggesting that phytoplankton contributed to enhance the total exergy of the water column of the lagoon also affecting the hydrochemistry of the system, especially during massive blooms; (ii) exergy and structural information of phytoplankton increase with increasing phytoplankton biomass, thus indicating that the size spectrum of phytoplankton diverges from the equilibrium distribution as the biomass stored increases (or vice versa); (iii) the size-fractioned Shannon information of phytoplankton increases with increasing biomass density as well as structural information, before reaching a superior limit. On the whole, the observed trends are consistent with theoretical expectations based on thermodynamics and classical ecological theories of succession, thus confirming the effectiveness of exergy-based tools as indicators of ecosystem development, as well as ecological orientors.

Order and disorder in ecological time-series: Introducing normalized spectral entropy

Information theory and entropy measures have been extensively applied in ecology in different areas like biodiversity assessment, evolution, species interactions, spatial dynamics or landscape analysis. Ecological applications of entropy measures have been primarily focused on structural and functional complexity of systems and less attention has been paid to temporal evolution and dynamics. The aim of this paper is to present “normalized spectral entropy” (Hsn), an entropy related index able to measure part of the structural complexity of an ecological time series. Hsn quantifies the degree of order and predictability derived by the series’ power spectrum. The index sensitivity to data attributes is investigated by means of time-series surrogates of known properties (i.e., time-series length, power spectrum shape, and time-series values distribution). A procedure to calculate confidence intervals is outlined as a preliminary statistical tool to assess differences among values. Three examples of possible application are described using time series of meteorological variables, vegetation physiological responses and remote sensing images. Results show how Hsn is able to contribute to the ongoing debate on how to estimate spatio-temporal complexity of ecological systems, thus making a step forward in the proposed use of complexity as an ecological orientor.

Measuring ecological complexity

Complexity is an elusive term in ecology that is often used in different ways to describe the state of an ecosystem. Ecological complexity has been linked to concepts such as ecological integrity, diversity and resilience and has been put forth as a candidate ecological orientor. In this article, the concept of complexity as a system attribute is presented and candidate measures of ecological complexity are reviewed. The measures are distinguished by their ability to characterize the spatial, temporal, structural or spatiotemporal signatures of an ecosystem. Many of these measures have been adapted from disciplines such as physics and information theory that have a long history of quantifying complexity, however more work needs to be done to develop techniques adapted to ecological data. It is argued that if appropriate measures are developed and validated for ecosystems, ecological complexity could become a key ecological indicator.

Exergy vs information in ecological successions: Interpreting community changes by a classical thermodynamic approach

This work proposes a methodology based on classical thermodynamics, which allows the variation in ecosystem composition to be interpreted within the framework of the exergy concept. The basic equation of exergy [Mejer, H., Jorgensen, S.E., 1979. Exergy and ecological buffer capacity. State-of-the-art in Ecological Modelling 7, 829–846] was decomposed into three terms – size ( C), structural information ( I) and concentration ( X) – and their significance as indicators of ecosystem state was evaluated by simulating different scenarios of development in a simplified freshwater ecosystem. In order to calculate the exergy terms, the most critical issue in using exergy in an ecological context, i.e. the estimate of reference equilibrium values for organic matter and organisms, had to be faced. With this aim, the equations of classical thermodynamics in solution were applied, and “virtual” values of concentration at equilibrium were calculated for a number of organic compounds ( VEC) and freshwater organisms ( VECE). The results of the simulation showed that, whereas exergy and the exergy terms inherently connected with the a-biotic component varied consistently with the incorporation of biomass into the ecosystem, the structural information of the biotic component followed different, even opposite, pathways of variation, which were dependent only on the change in the size spectrum of the community. Due to the strict dependence of the VECE values on organism size, the increase of structural information with increasing abundance of large and complex species is also consistent with the general pattern of succession delineated by the classical r– K model. S tructural information is therefore proposed as an indicator of the development state, as well as an ecological orientor, whose maximisation is expected during ecosystem development. However, since an increase in structural information is not necessarily accompanied by an increase in exergy, a sort of “antagonism” between these two related orientors emerges, whose resolution may contribute to shed light on the fundamental forces which drive ecosystem development.

Implications of network particle tracking (NPT) for ecological model interpretation

Network particle tracking (NPT), building on the foundation of network environ analysis (NEA), is a new development in the definition of coherence relations within and between connected systems. This paper evaluates three ecosystem models in a comparison of throughflow- and storage-based NEA and NPT. Compartments in models with high indirect effects and Finn cycling showed low correlation of NEA storage and throughflow with particle repeat visits and numbers of particles in compartments at steady state. Conversely, the correlation between NEA and NPT results was high with two models having lower indirect effects and Finn cycling. Analysis of ecological orientors associated with NEA showed NPT to fully support conventional NEA results when the common conditions of donor control and steady state are satisfied. Particle trajectories are recorded in the new concept of a particle “passport”. Ability to track and record particle in-system histories enables views of multiple scales and opens the possibility of making pathway-dependent modeling decisions. NPT may also enable modeling of time, allowing integration of Newtonian, organismal and stochastic modeling perspectives in a single comprehensive analysis.

Measures of structural complexity in digital images for monitoring the ecological signature of an old-growth forest ecosystem

Conducting field samples for monitoring ecological dynamics across multiple spatiotemporal scales is a difficult task using standard protocols. One alternative is to measure a restricted set of variables which can serve as an ecological orientor (EO) for quantifying habitat change. The objective of this article is to derive from digital images a measure of structural complexity that may serve as a proximate EO for monitoring forest dynamics in space and time. The mean information gain (MIG) index was used as a measure of structural complexity in photographs taken directly in the field over the entire growing season. At a small scene extent, the complexity of light intensity variations in digital images was positively related to species richness. At larger scene extents, forest understorey and overstorey layers showed predictable ecological signatures in structural complexity. In general, intensity and chroma were the two color space components which yielded the greatest sensitivity to habitat change through time. Within the framework of a standardized photographic protocol, it seems therefore reasonable to consider MIG as a suitable EO for monitoring forest dynamics in both space and time. Our results support the idea that it is possible on one hand to adopt a more holistic view of ecological processes to gain, on the other hand, spatial and temporal degrees of freedom for testing multiple scale hypotheses in the field.

EXTREMAL PRINCIPLES WITH SPECIAL EMPHASIS ON EXERGY AND ASCENDENCY — THE MODERN APPROACH IN THEORETICAL ECOLOGY

Extremal principles or ecological orientors or goal functions are the most modern approach in theoretical ecology. There are many such principles proposed by different theoretical ecologists. In this paper, the most important extremal principles are discussed based on their theoretical backgrounds. Two widely accepted goal functions, i.e. exergy and ascendency are optimized and treated in a quantitative manner in an aquatic ecosystem model of planktonic and fish systems for their appropriateness. In the model varied body sizes of phytoplankton and zooplankton are considered. Parameter values varied according to the allometric principle with the body sizes. For self-organization of the model system two goal functions predict different results, however both are realistic.

Use of thermodynamic indices as ecological indicators of the development state of lake ecosystems: Specific dissipation

Abstract This paper proposes the ratio between the entropy produced and the exergy stored by the biological component of an ecosystem (which may be called the specific entropy production or the specific dissipation of a community) as a tool for understanding the evolution of ecological systems. Specific dissipation, which may be taken as representing a renewed version of Odum's Schrodinger ratio, is here proposed as an indicator of ecosystems maturity as well as an ecological orientor whose minimisation is expected throughout ecosystem development. After having presented an empirical method for estimating the specific dissipation in lake ecosystems, it has been applied to the characterization of the development state of the communities of a set of shallow lakes which lye from oligotrophic to hyper-eutrophic conditions. The adequacy of the proposed indicator has been tested and discussed along two different ecological series: the seasonal progression of phytoplankton and the trophic gradient. The results confirm that the ratio is an appropriate indicator of ecosystem maturity and support the hypothesis that its minimisation is one of the primary “goals” of ecosystem development.

Complementarity of Ecological Goal Functions

This paper summarizes, in the framework of network environ analysis, a set of analyses of energy–matter flow and storage in steady-state systems. The network perspective is used to codify and unify ten ecological orientors or extremal principles: maximum power (Lotka), maximum storage (Jørgensen–Mejer), maximum empower and emergy (Odum), maximum ascendency (Ulanowicz), maximum dissipation (Schneider–Kay), maximum cycling (Morowitz), maximum residence time (Cheslak–Lamarra), minimum specific dissipation (Onsager, Prigogine), and minimum empower to exergy ratio (Bastianoni–Marchettini). We show that, seen in this framework, these seemingly disparate extrema are all mutually consistent, suggesting a common pattern for ecosystem development. This pattern unfolds in the network organization of systems.

Indicating ecosystem integrity — theoretical concepts and environmental requirements

This paper discusses some conceptual fundamentals for the derivation of environmental indicator sets. On the one hand, it defines requirements from environmental politics, environmental management and legislation, reaching from political target hierarchies and sustainable management strategies to holistic protection concepts such as process protection, resource preservation, ecosystem health and ecological integrity. On the other hand, demands from ecosystem theory are described which include the consideration of features such as self-organization, emergence, thermodynamics, gradients and ecological orientors in environmental indicator sets. From that concept, collective and emergent properties are selected and eight holistic ecosystem features are presented that indicate the ecosystemic state as an ensemble. These general indicators of ecosystem integrity are supplemented by variables on structural changes and substance dynamics.