Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization

This paper is concerned with the question of ranking a finite collection of objects when a suite of indicator values is available for each member of the collection. The objects can be represented as a cloud of points in indicator space, but the different indicators (coordinate axes) typically convey different comparative messages and there is no unique way to rank the objects while taking all indicators into account. A conventional solution is to assign a composite numerical score to each object by combining the indicator information in some fashion. Consciously or otherwise, every such composite involves judgments (often arbitrary or controversial) about tradeoffs or substitutability among indicators. Rather than trying to combine indicators, we take the view that the relative positions in indicator space determine only a partial ordering and that a given pair of objects may not be inherently comparable. Working with Hasse diagrams of the partial order, we study the collection of all rankings that are compatible with the partial order (linear extensions). In this way, an interval of possible ranks is assigned to each object. The intervals can be very wide, however. Noting that ranks near the ends of each interval are usually infrequent under linear extensions, a probability distribution is obtained over the interval of possible ranks. This distribution, called the rank-frequency distribution, turns out to be unimodal (in fact, log-concave) and represents the degree of ambiguity involved in attempting to assign a rank to the corresponding object. Stochastic ordering of probability distributions imposes a partial order on the collection of rank-frequency distributions. This collection of distributions is in one-to-one correspondence with the original collection of objects and the induced ordering on these objects is called the cumulative rank-frequency (CRF) ordering; it extends the original partial order. Although the CRF ordering need not be linear, it can be iterated to yield a fixed point of the CRF operator. We hypothesize that the fixed points of the CRF operator are exactly the linear orderings. The CRF operator treats each linear extension as an equal voter in determining the CRF ranking. It is possible to generalize to a weighted CRF operator by giving linear extensions differential weights either on mathematical grounds (e.g., number of jumps) or empirical grounds (e.g., indicator concordance). Explicit enumeration of all possible linear extensions is computationally impractical unless the number of objects is quite small. In such cases, the rank-frequencies can be estimated using discrete Markov chain Monte Carlo (MCMC) methods.     

Assessing biological variation from the perspective of diversity

Particularly in ecological and evolutionary genetics, methods of discerning complex traits are improving at a considerable rate. As a consequence, the resolution of intrinsically qualitative traits such as species affiliation or genetic type is increasing to degrees that blur their distinction from continuously varying characteristics. The common notion of diversity, however, relies on distinct features such as the states of qualitative traits, and it aims to assess variation as a counting of these features or types. This situation brings up the question of whether and how the diversity perspective of variation can be broadened to cover higher levels of complexity without sacrificing its concept. The present paper suggests two approaches that refer to established criteria for measures of diversity and that complement each other. The partitions approach treats complexity through general measures of difference between trait states, and the relations approach rests on general binary relations that capture structural aspects of diversity. Both approaches are shown to consistently imply effective numbers of types even in cases where distinct types are not explicitly specified. Practically all of the common methods of measuring diversity can be classified into either of the two approaches, and new opportunities for analyses of the diversity of complex traits are provided. The latter analyses include those of diversity in subdivided collections. Other perspectives of variation (such as dispersion, variances, etc.) are discussed and analyzed for their distinction from the diversity perspective. In many cases, the distinction can be made apparent with the help of diversity portraits.     

Planktic community assembly in flowing water and the ecosystem health of rivers

Some of the modern criteria for assessing ecosystem health are compared with current understanding of ecosystem function in rivers. Owing to the predominance of catchment imports over autochthonous primary production, most rivers are naturally heterotrophic. This does not make them unhealthy but the pristine condition is that much harder to determine. The case is put for an index of ecosystem health and sustainability that takes into account the system's capacity for processing its resources, the species richness and its interdependence and its resilience to external forcing. Although these are not easily quantified, the qualitative indicators of healthy ecosystem function are easily checked. The sensitivity of organisms in suspension to fluvial flow may seem to counter the suitability of plankton as a reliable state indicator of river health. On the other hand, the rules governing the assembly of planktic communities in rivers are often strict and quantifiable: this makes them attractive candidates to act as indicators of the ecological condition of rivers.     

Ecosystem network analysis indicators are generally robust to parameter uncertainty in a phosphorus model of Lake Sidney Lanier, USA

Understanding how data uncertainty influences ecosystem analysis is critical as we move toward ecosystem-based management. Here, we investigate how 18 Ecological Network Analysis (ENA) indicators that characterize ecosystem growth, development, and condition are affected by uncertainty in an ecosystem model of Lake Sidney Lanier (USA). We applied ENA to 122 plausible parameterizations of the ecosystem developed by Borrett and Osidele (2007, Ecological Modelling 200, 371-387), and then used the coefficient of variation (CV) to compare system indicator variability. We considered Total System Throughput (TST) as a measure of the underlying model uncertainty and tested three hypotheses. First, we hypothesized that non-ratio indicators whose calculation includes the TST would be at least as variable as TST if not more variable. Second, we postulated that indicators calculated as ratios, with TST in the numerator and denominator would tend to be less variable than TST because its influence will cancel. Last, we expected the Average Mutual Information (AMI) to be less variable than TST because it is a bounded function. Our work shows that the 18 indicators grouped into four categories. The first group has significantly larger CVs than the CV for TST. In this group, model uncertainty is amplified rendering these three indicators less useful. The second group of four indicators shows no significant difference in variability with respect to TST. Finally, there are two groups whose CV values are significantly lower than that for TST. The least variable group includes the ratio-based indicators and Average Mutual Information. Due to their low variability, we conclude that these indicators are the most robust to the parameter uncertainty and most useful for ecosystem assessment and comparative ecosystem analysis. In summary, this work suggests that we can be as certain, or more certain, in most of the selected ENA indicators as we are in the parameters of the model analyzed.     

Indicators of sustainability as a tool in agricultural development: partitioning scientific and participatory processes

SUMMARY

Sustainable indicators have become popular tools by which policymakers can assess progress towards a more sustainable agriculture. Varying approaches to defining sustainability lead to disagreement about the value of indicators and yet some form of measurement is required so that society can judge the effects of policy. Environmental and social problems and their causes span national boundaries. An international framework for assessing agricultural activities, their effects and the pressures that drive those activities is therefore required. However, a guiding principle of the UN Agenda for Sustainable Development is that global problems require local action. Thus, indicators must provide information for policymakers as well as guidance for farmers and other practitioners. Many indicator programmes currently proposed do not provide this level of guidance as no evaluation as to what level of activity is sustainable has been agreed. A model is presented, to show how scientific and political or participatory approaches may be combined to meet the multiple objectives of involving people, maintaining scientific integrity and providing guidance for policymakers and practitioners alike.     

An Ecosystem Management Program and Assessment Process for Ontario National Parks

Abstract: An ecosystem management program and assessment process was developed to standardize an ecosystem-based approach to protecting the ecological integrity of Ontario's national parks. The elements of the ecosystem management program collectively represent the dominant planning and technical aspects of ecosystem management. Within the program, 11 specific products—ecosystem conservation plan, greater park ecosystem inventory and analysis, greater park ecosystem scope, area of cooperation, stakeholder analysis, partnership group management guidelines, scientific research program, ecological indicators, ecological integrity monitoring program, information network, and communication strategy—are considered requisite tools to improve the scientific understanding required for park management within the context of greater park ecosystems and to increase communication and coordination among governments and citizens to improve decision making. The formal process uses evaluation criteria associated with the 11 products to assess progress in developing an ecosystem management program and the content of the related products. The assessment process, which provides comprehensive identification of a park's specific ecosystem management needs, has been applied to all national parks in Ontario in the past year, which has had the immediate effect of refining their ecosystem management programs.     

Ecosystem development in roadside grasslands: biotic control, plant-soil interactions, and dispersal limitations

Roadside grasslands undergoing secondary succession are abundant, and represent ecologically meaningful examples of novel, human-created ecosystems. Interactions between plant and soil communities (hereafter plant-soil interactions) are of major importance in understanding the role of biotic control in ecosystem functioning, but little is known about these links in the context of ecosystem restoration and succession. The assessment of the key biotic communities and interactions driving ecosystem development will help practitioners to better allocate the limited resources devoted to roadside grassland restoration. We surveyed roadside grasslands from three successional stages (0-2, 7-9, and >20 years) in two Mediterranean regions of Spain. Structural equation modeling was used to evaluate how interactions between plants, biological soil crusts (BSCs), and soil microbial functional diversity (soil microorganisms) affect indicators of ecosystem development and restoration: plant similarity to the reference ecosystem, erosion control, and soil C storage and N accumulation. Changes in plant community composition along the successional gradient exerted the strongest influence on these indicators. High BSC cover was associated with high soil stability, and high soil microbial functional diversity from late-successional stages was associated with high soil fertility. Contrary to our expectations, the indirect effects of plants, mediated by either BSCs or soil microorganisms, were very weak in both regions, suggesting a minor role for plant-soil interactions upon ecosystem development indicators over long periods. Our results suggest that natural vegetation dynamics effectively improved ecosystem development within a time frame of 20 years in the grasslands evaluated. They also indicate that this time could be shortened if management actions focus on: (1) maintaining well-conserved natural areas close to roadsides to enhance plant compositional changes towards late-successional stages, (2) increasing BSC cover in areas under strong erosion risk, to avoid soil loss, and (3) enhancing soil microbial functional diversity in resource-limited areas, to enhance soil C and N accumulation.     

Urban ecosystem health assessment based on emergy and set pair analysis—A comparative study of typical Chinese cities

Regarding various energy and materials flowing in the urban ecosystem and the merit of emergy as an embodied energetic equivalent for integrated ecological economic evaluation, an evaluation framework of emergy-based urban ecosystem health indicators (UEHI_em) was established in view of five aspects including vigor, structure, resilience, ecosystem service function maintenance and environmental impact to depict the urban ecosystem health states. Further, set pair analysis (SPA) was employed to assess the urban ecosystem health level based on the UEHI_em, by which the approximate degree of real index set to the optimal one was defined and evaluated to describe the relative health state of the concerned urban ecosystems. Choosing twenty typical Chinese cities in 2005 as cases, we evaluated and compared their urban ecosystem health levels based on UEHI_em and SPA. The results showed that health levels of Xiamen, Qingdao, Shenzhen and Shanghai are pretty well, while those of Wuhan, Harbin, Yinchuan, Beijing and Urumchi are relatively weak. Moreover, the relative health levels were analyzed by SPA to discern the influences of the mentioned five aspects on the UEHI_em. It is concluded that emergy synthesis combined with SPA can serve as an effective relative-measure to compare different ecosystem health levels of urban ecosystems.     

War and sustainability

SUMMARY

In order to use the planet's ecological life-support systems sustainably, damage to them must be both prevented and repaired. However, repair requires awareness of damage which, in this case, mandates a high level of ecological literacy. Prevention of ecological damage will only be successful on a planetary scale if human society endorses precautionary practices that reduce the probability of ecosystem damage. Society is beginning to endorse precautionary practices to protect human health, which is no longer regarded as merely absence of symptoms of disease and malfunction. Health is regarded as a robust function — an approach toward optimal conditions. Similar views are beginning to emerge regarding ecosystem health, and a close link between human and ecosystem health is gaining increased recognition. However, to achieve health, ecological ‘wounds’ must be repaired, which is impossible until society ‘sees’ the wounds. After this recognition, society must become more literate on the attributes of ecosystem health. The methods and procedures are in place, but they will not be used effectively until a major paradigm shift occurs.     

Applicability of Montreal Process Criterion 5 — maintenance of rangeland contribution to global carbon cycles

SUMMARY

Within the Montreal Process, Criterion 5 — Maintenance of Forest Contribution to the Global Carbon Cycle — encompasses: Indicator 26, biomass and carbon pools; Indicator 27, carbon fluxes from these pools; and Indicator 28, contribution of forest products. I have reviewed the applicability of each indicator to rangelands, the potential limitations of these indicators for rangelands ecosystems, the data available to quantify these indicators and have identified research needs. Indicator 26, and 27 are applicable to rangeland ecosystems. Estimation of the total ecosystem biomass and carbon pools from rangelands is currently feasible, albeit precision is limited by data availability. Simulation models quantify fluxes from rangeland ecosystems, however, belowground dynamics, particularly under changing management, are not well known. For Indicator 28, rangeland products do not constitute a large potential for carbon sequestration.     

Using MCA tools for evaluating community-managed forests from a green economy perspective: lessons from Nepal

ABSTRACT

Nepal is in the process of formulating its forest policies at the provincial level . Various community-managed forests have been designed in the past by the Nepal government to decentralize the forest for its sustainable management practice. This study facilitates the process of identifying appropriate forest management options in two of the provinces, namely Provinces Three and Gandaki. Four forest management options – passive, active, scientific and multiple – were identified following the existing management practices. For the evaluation of the overall performance of the options, a framework with three criteria, 10 indicators and 28 verifiers were designed. The framework followed the green economy perspective considering the improvement of the forest conditions, economic and social well-being, and low carbon emission. The Analytical Hierarchy Process was used to prioritize the best management option and analyse trade-offs to guide future decision-making and reduce the risk of unwanted consequences. Our results show that the elicitation of preferences for the evaluation criteria varied by stakeholder groups. Their preference was largely guided by improving the forest resource condition and economic well-being. Foresters prefer scientific and active forest management, policymakers prefer multiple-use forest management and scientific management, whereas community forest user groups prefer active forest management. We argue that a scientific management approach may contribute better to economic aspects, although it may often compromise the other aspects. The multiple forest management option seems to be the best for green economy considering ecological, economic and social consequences.     

Identifying potential indicators of conservation value using natural heritage occurrence data.

Conservation planning based on the occurrence of rare species has been criticized as being too limited in scope to conserve biodiversity as a whole. Conversely, planning based on indicator taxa may lack sufficient focus to conserve those species in greatest need of conservation. An alternative approach is to identify a variety of species at risk that are associated with areas of conservation value, which is defined based on species-independent characteristics. We identified potential indicators of conservation value using occurrence data on species at risk and independent information on conservation value that incorporated indices of ecosystem integrity. We propose a taxonomically diverse group of indicator species that are strongly associated with areas of exceptional ecosystem integrity, to serve as a focus for further research and in planning for biodiversity conservation. We identify potential indicator species by defining a null model in which species at risk are equally associated with areas of high ecosystem integrity, then by conducting randomization tests to identify noncompliant species in the state of Michigan, USA. Areas of high ecosystem integrity are selected using criteria to flag (1) secure biotic communities with structural integrity and few exotic species, (2) natural areas subjected to expert review, (3) contiguous relict areas of forest interior, (4) contiguous areas of unmodified wetland, and (5) all these areas combined. We determine the spatial occurrence of species at risk using data from Michigan's statewide Natural Heritage database. The potential indicators include plants, insects, and birds. Their species identity and distribution of occurrences varies with the five scenarios, and together the species broadly cover the entire state. These species at risk, many of which occur throughout the Great Lakes region, may be used to identify additional areas potentially high in conservation value and to monitor their conservation. The ecological criteria and numerical methods we employ may be broadly applicable as Heritage Program databases in North America and parts of Latin America grow to become representative of species distributions.     

Impact of rubble mound groyne structural interventions in restoration of Koggala lagoon,Sri Lanka; numerical modelling approach

Physical processes of the lagoon are influenced by structural interventions. Understanding the complex reality of physical processes sometimes difficult with field observations thus a model provides a simplified abstract view. Two dimensional hydrodynamic model is used to describe, restoration efforts to Koggala lagoon, a combined freshwater and estuarine complex of rich ecosystem on the southern coast of Sri Lanka. The lagoon mouth was naturally closed by a sand bar which controlled the seawater intrusion. Due to large-scale sand removal at lagoon mouth, formation of the sandbar shifted towards the lagoon. After the removal of natural sand barrier, rubble mound groyne structures were built to avoid sand deposition in the lagoon and to protect the highway bridge from the sea wave attack. Construction of the groyne resulted in the lagoon mouth being permanently open which in turn led to many environmental problems with saline intrusion. The aim of this study is to evaluate the current situation of the lagoon and propose alternative structural interventions for minimization of seawater intrusion and subsequently improve lagoon ecosystem. Hydrological parameters were investigated and mathematical models for hydrodynamic behavior of the lagoon were applied in order to describe the lagoon physical processes and flow characteristics. Existing rubble mound structures were redesigned in order to minimize the seawater intrusion. Numerical simulations were carried out for two different mouth widths (40 m and 20 m) with appropriate structural interventions. Existing salting factor for the lagoon is 0.68 and numerical simulation results showed salting factor for 40 m and 20 m openings are 0.61 and 0.54 respectively. This shows the mouth width can be reduced up to 20 m in order to obtain a slating factor close to 0.5, which indicates the predominant influence of fresh water which in turn leads lagoon to a fresh water ecosystem.     

The phenology of phytoplankton blooms: Ecosystem indicators from remote sensing

Remote sensing offers many advantages in the development of ecosystem indicators for the pelagic zone of the ocean. Particularly suitable in this context are the indicators arising from time series that can be constructed from remotely sensed data. For example, using ocean-colour radiometry, the phenology of phytoplankton blooms can be assessed. Metrics defined in this way show promise as informative indicators for the entire pelagic ecosystem. A simple phytoplankton–substrate model, with forcing dependent on latitude and day number is used to explore the qualitative features of bloom phenology for comparison with the results observed in a suite of 10-year time series of chlorophyll concentration, as assessed by remote sensing, from the Northwest Atlantic Ocean. The model reveals features of the dynamics that might otherwise have been overlooked in evaluation of the observational data.     

Understanding the functional principles of nature—Proposing another type of ecosystem services

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.     

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. Structural 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.     

Environ indicator sensitivity to flux uncertainty in a phosphorus model of Lake Sidney Lanier, USA

Effective environmental impact assessment and management requires improved understanding of the organization and transformation of ecosystems in which independent agents are linked through an intricate network of energy, matter, and informational interactions. While advances have been made, we still lack a complete understanding of the processes that create, constrain, and sustain ecosystems. Network environ analysis (NEA) provides one approach for building novel ecosystem insights, but it is model dependent. As ecological modeling is an imprecise art, often complicated by inadequate empirical data, the utility of NEA may be limited by model uncertainty. Here, we investigate the sensitivity of NEA indicators of ecosystem growth and development to flow and storage uncertainty in a phosphorus model of Lake Sidney Lanier, USA. The indicators are total system throughflow (TST), total system storage (TSS), total boundary input (Boundary), Finn cycling index (FCI), ratio of indirect-to-direct flows (Indirect/Direct), indirect flow index (IFI), network aggradation (AGG), network homogenization (HMG), and network amplification (AMP). Our results make two primary contributions. First, they demonstrate that five of the indicators – FCI, Indirect/Direct, IFI, AGG and HMG – are relatively robust to the flow and storage uncertainty in the Lake Lanier model. This stability lets us draw robust conclusions about the Lake Lanier ecosystem organization (e.g., phosphorus flux in the lake is dominated by internal processes) in spite of uncertainties in the model. Second, we show that the majority of the indicators co-vary and that most of their common variation could be mapped onto two latent factors, which we interpret as (1) system integration and (2) boundary influences.