Combining state and transition models with dynamic Bayesian networks

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

Predicting modes of spatial change from state-and-transition models

State-and-transition models (STMs) can represent many different types of landscape change, from simple gradient-driven transitions to complex, (pseudo-) random patterns. While previous applications of STMs have focused on individual states and transitions, this study addresses broader-scale modes of spatial change based on the entire network of states and transitions. STMs are treated as mathematical graphs, and several metrics from algebraic graph theory are applied—spectral radius, algebraic connectivity, and the S-metric. These indicate, respectively, the amplification of environmental change by state transitions, the relative rate of propagation of state changes through the landscape, and the degree of system structural constraints on the spatial propagation of state transitions. The analysis is illustrated by application to the Gualalupe/San Antonio River delta, Texas, with soil types as representations of system states. Concepts of change in deltaic environments are typically based on successional patterns in response to forcings such as sea level change or river inflows. However, results indicate more complex modes of change associated with amplification of changes in system states, relatively rapid spatial propagation of state transitions, and some structural constraints within the system. The implications are that complex, spatially variable state transitions are likely, constrained by local (within-delta) environmental gradients and initial conditions. As in most applications, the STM used in this study is a representation of observed state transitions. While the usual predictive application of STMs is identification of local state changes associated with, e.g., management strategies, the methods presented here show how STMs can be used at a broader scale to identify landscape scale modes of spatial change.     

Estimating the critical phosphorus loading of shallow lakes with the ecosystem model PCLake: Sensitivity, calibration and uncertainty

There is a vast body of knowledge that eutrophication of lakes may cause algal blooms. Among lakes, shallow lakes are peculiar systems in that they typically can be in one of two contrasting (equilibrium) states that are self-stabilizing: a ‘clear’ state with submerged macrophytes or a ‘turbid’ state dominated by phytoplankton. Eutrophication may cause a switch from the clear to the turbid state, if the P loading exceeds a critical value. The ecological processes governing this switch are covered by the ecosystem model PCLake, a dynamic model of nutrient cycling and the biota in shallow lakes. Here we present an extensive analysis of the model, using a three-step procedure. (1) A sensitivity analysis revealed the key parameters for the model output. (2) These parameters were calibrated on the combined data on total phosphorus, chlorophyll-a, macrophytes cover and Secchi depth in over 40 lakes. This was done by a Bayesian procedure, giving a weight to each parameter setting based on its likelihood. (3) These weights were used for an uncertainty analysis, applied to the switchpoints (critical phosphorus loading levels) calculated by the model. The model was most sensitive to changes in water depth, P and N loading, retention time and lake size as external input factors, and to zooplankton growth rate, settling rates and maximum growth rates of phytoplankton and macrophytes as process parameters. The results for the ‘best run’ showed an acceptable agreement between model and data and classified nearly all lakes to which the model was applied correctly as either ‘clear’ (macrophyte-dominated) or ‘turbid’ (phytoplankton-dominated). The critical loading levels for a standard lake showed about a factor two uncertainty due to the variation in the posterior parameter distribution. This study calculates in one coherent analysis uncertainties in critical phosphorus loading, a parameter that is of great importance to water quality managers.     

Ecosystem states: Creating a data-derived, ecosystem-scale ecological response model that is explicit in space and time

Increasing difficulties associated with balancing consumptive demands for water and achieving ecological benefits in aquatic ecosystems provide opportunities for new ecosystem-scale ecological response models to assist managers. Using an Australian estuary as a case study, we developed a novel approach to create a data-derived state-and-transition model. The model identifies suites of co-occurring birds, fish, benthic invertebrates and aquatic macrophytes (as ‘states’) and the changing physico-chemical conditions that are associated with each (‘transitions’). The approach first used cluster analysis to identify sets of co-occurring biota. Differences in the physico-chemical data associated with each state were identified using classification trees, with the biotic distinctness of the resultant statistical model tested using analysis of similarities. The predictive capacity of the model was tested using new cases. Two models were created using different time-steps (annual and quarterly) and then combined to capture both longer-term trends and more-recent declines in ecological condition. We identified eight ecosystem states that were differentiated by a mix of water-quantity and water-quality variables. Each ecosystem state represented a distinct biotic assemblage under well-defined physico-chemical conditions. Two ‘basins of attraction’ were identified, with four tidally-influenced states, and another four independent of tidal influence. Within each basin, states described a continuum of relative health, manifest through declining taxonomic diversity and abundances. The main threshold determining relative health was whether freshwater flows had occurred in the region during the previous 339 days. Canonical analyses of principal coordinates tested the predictive capacity of the model and demonstrated that the variance in the environmental data set was well captured (87%) with 52% of the variance in the biological data set also captured. The latter increased to >80% when long- and short-term biological data were analysed separately, indicating that the model described the available data for the Coorong well. This approach thus created a data-derived, multivariate model, where neither states nor transitions were determined a priori. The approach did not over-fit the data, was robust to patchy or missing data, the choice of initial clustering technique and random errors in the biological data set, and was well-received by local natural resource managers. However, the model did not capture causal relationships and requires additional testing, particularly during future episodes of ecological recovery. The approach shows significant promise for simplifying management definitions of ecological condition and, via scenario analyses, can be used to assist in manager decision-making of large, complex aquatic ecosystems in the future.     

Using single- and multi-target regression trees and ensembles to model a compound index of vegetation condition

An important consideration in conservation and biodiversity planning is an appreciation of the condition or integrity of ecosystems. In this study, we have applied various machine learning methods to the problem of predicting the condition or quality of the remnant indigenous vegetation across an extensive area of south-eastern Australia—the state of Victoria. The field data were obtained using the ‘habitat hectares’ approach. This rapid assessment technique produces multiple scores that describe the condition of various attributes of the vegetation at a given site. Multiple sites were assessed and subsequently circumscribed with GIS and remote-sensed data.     

Indicators of ecosystem function identify alternate states in the sagebrush steppe

Models of ecosystem change that incorporate nonlinear dynamics and thresholds, such as state-and-transition models (STMs), are increasingly popular tools for land management decision-making. However, few models are based on systematic collection and documentation of ecological data, and of these, most rely solely on structural indicators (species composition) to identify states and transitions. As STMs are adopted as an assessment framework throughout the United States, finding effective and efficient ways to create data-driven models that integrate ecosystem function and structure is vital. This study aims to (1) evaluate the utility of functional indicators (indicators of rangeland health, IRH) as proxies for more difficult ecosystem function measurements and (2) create a data-driven STM for the sagebrush steppe of Colorado, USA, that incorporates both ecosystem structure and function. We sampled soils, plant communities, and IRH at 41 plots with similar clayey soils but different site histories to identify potential states and infer the effects of management practices and disturbances on transitions. We found that many IRH were correlated with quantitative measures of functional indicators, suggesting that the IRH can be used to approximate ecosystem function. In addition to a reference state that functions as expected for this soil type, we identified four biotically and functionally distinct potential states, consistent with the theoretical concept of alternate states. Three potential states were related to management practices (chemical and mechanical shrub treatments and seeding history) while one was related only to ecosystem processes (erosion). IRH and potential states were also related to environmental variation (slope, soil texture), suggesting that there are environmental factors within areas with similar soils that affect ecosystem dynamics and should be noted within STMs. Our approach generated an objective, data-driven model of ecosystem dynamics for rangeland management. Our findings suggest that the IRH approximate ecosystem processes and can distinguish between alternate states and communities and identify transitions when building data-driven STMs. Functional indicators are a simple, efficient way to create data-driven models that are consistent with alternate state theory. Managers can use them to improve current model-building methods and thus apply state-and-transition models more broadly for land management decision-making.     

Modelling the responses of wildlife to human disturbance: An evaluation of alternative management scenarios for black-crowned night-herons

The impact of anthropogenic disturbance on wildlife is increasing becoming a source of concern as the popularity of outdoor recreation rises. There is now more pressure on site managers to simultaneously ensure the continued persistence of wildlife and provide recreational opportunities. Using ‘Simulation of Disturbance Activities’, a model designed to investigate the impact of recreational disturbance on wildlife, we demonstrate how a simulation modelling approach can effectively inform such management decisions. As an example, we explored the implications of various design and management options for a proposed recreational area containing a historic breeding bird colony. By manipulating the proximity, orientation and intensity of recreation, we were able to evaluate the impact of recreational activities on the behaviour of black-crowned night-heron nestlings (Nycticorax nycticorax). Using a classification and regression tree (CART) procedure to analyse simulation output, we explored the dynamics of multiple strategies in concert. Our analysis revealed that there are inherent advantages in implementing multiple strategies as opposed to any single strategy. Nestlings were not disturbed by recreation when bird-watching facility placement (proximity and orientation) and type were considered in combination. In comparison, proximity alone only led to a <10% reduction in disturbance. Thus we demonstrate how simulation models based on customised empirical data can bridge the gap between field studies and active management, enabling users to test novel management scenarios that are otherwise logistically difficult. Furthermore, such models potentially have broad application in understanding human-wildlife interactions (e.g. exploring the implications of roads on wildlife, probability of bird strikes around airports, etc.). They therefore represent a valuable decision-making tool in the ecological design of urban infrastructures.     

Imposed and inherent scales in cellular automata models of habitat

Both observational and modelling studies of the natural environment are characterised by their ‘grain’ and ‘extent’, the smallest and largest scales represented in time and space. These are imposed scales that should be chosen to ensure that the natural scales of the system are captured in the study. A simple cellular automata model of habitat represents only the presence or absence of vegetation, with global and local interactions described by four empirical parameters. Such a model can be formulated as a nonlinear Markov equation for the habitat probability. The equation produces inherent space and time scales that may be considered as transition scales or the scales for recovery from disturbance. However, if the resolution of the model is changed, the empirical parameters must be changed to preserve the properties of the system. Further, changes in the spatial resolution lead to different interpretations of the spatial structure. In particular, as the resolution is reduced, the apparent dominance of one habitat type over the other increases. The model provides an ability to compare both field and model investigations conducted at different resolutions in time and space.     

Empirical assessment of state-and-transition models with a long-term vegetation record from the Sonoran Desert

Resilience-based frameworks, including state-and-transition models (STM), are being increasingly called upon to inform policy and guide ecosystem management, particularly in rangelands. Yet, multiple challenges impede their effective implementation: (1) paucity of empirical tests of resilience concepts, such as alternative states and thresholds, and (2) heavy reliance on expert models, which are seldom tested against empirical data. We developed an analytical protocol to identify unique plant communities and their transitions, and applied it to a long-term vegetation record from the Sonoran Desert (1953-2009). We assessed whether empirical trends were consistent with resilience concepts, and evaluated how they may inform the construction and interpretation of expert STMs. Seven statistically distinct plant communities were identified based on the cover of 22 plant species in 68 permanent transects. We recorded 253 instances of community transitions, associated with changes in species composition between successive samplings. Expectedly, transitions were more frequent among proximate communities with similar species pools than among distant communities. But unexpectedly, communities and transitions were not strongly constrained by soil type and topography. Only 18 transitions featured disproportionately large compositional turnover (species dissimilarity ranged between 0.54 and 0.68), and these were closely associated with communities that were dominated by the common shrub (burroweed, Haplopappus tenuisecta); indicating that only some, and not all, communities may be prone to large compositional change. Temporal dynamics in individual transects illustrated four general trajectories: stability, nondirectional drift, reversibility, and directional shifts that were not reversed even after 2-3 decades. The frequency of transitions and the accompanying species dissimilarity were both positively correlated with fluctuation in precipitation, indicating that climatic drivers require more attention in STMs. Many features of the expert models, including the number of communities and participant species, were consistent with empirical trends, but expert models underrepresented recent increases in cacti while overemphasizing the introduced Lehmann's lovegrass (Eragrostis lehmanniana). Quantification of communities and transitions within long-term vegetation records presents several quantitative metrics such as transition frequency, magnitude of accompanying compositional change, presence of unidirectional trajectories, and lack of reversibility within various timescales, which can clarify resilience concepts and inform the construction and interpretation of STMs.     

Regulatory attitudes and environmental innovation in a model combining internal and external R&D

The extent to which environmental regulatory institutions are either ‘green’ or ‘brown’ impacts not just the intensity of regulation at any moment, but also the incentives for the development of new pollution-control technologies. We set up a strategic model of R&D in which a polluter can deploy technologies developed in-house, or license technologies developed by specialist outsiders (an ‘eco-industry’). Polluters exert R&D effort and may even develop redundant technologies to improve the terms on which they procure technology from outside. We find that, while regulatory bias has an ambiguous impact on the best-available technology, strategic delegation to systematically biased regulators can improve social welfare.     

Information processing in models for density-dependent emigration: A comparison

Density-dependent emigration has been recognized as a fitness enhancing strategy. Yet, especially in the modelling literature there is no consensus about how density-dependent emigration should quantitatively be incorporated into metapopulation models. In this paper we compare the performance of five different dispersal strategies (defined by the functional link between density and emigration probability). Four of these strategies are based on published functional relationships between local population density and emigration probability, one assumes density-independent dispersal. We use individual-based simulations of time-discrete metapopulation dynamics and conduct evolution experiments for a broad range of values for dispersal mortality and environmental stochasticity. For each set of these conditions we analyze the evolution of emigration rates in ‘monoculture experiments’ (with only one type of dispersal strategy used by all individuals in the metapopulation) as well as in selection experiments that allow a pair-wise comparison of the performance of each functional type. We find that a single-parameter ‘asymptotic threshold’ strategy - derived from the marginal value theorem - with a decelerating increase of emigration rate with increasing population density, out-competes any other strategy, i.e. density-independent emigration, a ‘linear threshold’ strategy and a flexible three-parameter strategy. Only when environmental conditions select for extremely high emigration probabilities (close to one), strategies may perform approximately equally. A simple threshold strategy derived for the case of continuous population growth performs even worse than the density-independent strategy. As the functional type of the dispersal function implemented in metapopulation models may severely affect predictions concerning the survival of populations, range expansion, or community changes we clearly recommend to carefully select adequate functions to model density-dependent dispersal.     

Knowing fire incidence through fuel phenology: A remotely sensed approach

Fire is a basic ecological factor that contributes to determine vegetation diversity and dynamics in time and space. Fuel characteristics play an essential role in fire ignition and propagation; at the landscape scale fuel availability and flammability are closely related to the vegetation phenology that directly affects wildfire pattern in time and space. In this view, the annual normalized difference vegetation index (NDVI) profiles derived from high temporal resolution satellites, like SPOT Vegetation, represent an effective tool for monitoring the coarse-scale vegetation seasonal timing. The objective of this study thus consists in quantifying the explanatory power of multitemporal NDVI profiles on the fire regime characteristics of the potential natural vegetation (PNV) types of Sardinia (Italy) over a 5-year period (2000-2004). The results obtained show a good association between the NDVI temporal dynamics of the PNV of Sardinia and the corresponding fire regime characteristics, emphasizing the role of the bioclimatic timing of the vegetation in controlling the coarse-scale wildfire spatio-temporal distribution of Sardinia. By providing a sound phytogeographical framework for describing different wildfire regimes, PNV maps can thus be considered helpful cartographic documents for fire management strategies at the landscape scale.     

Environmental variability and allocation trade-offs maintain species diversity in a process-based model of succulent plant communities

Ecological theory suggests that environmental variability can promote coexistence, provided that species occupy differential niches. In this study, we focus on two questions: (1) Do allocation trade-offs provide a sufficient basis for niche differentiation in succulent plant communities? (2) What is the relative importance of different forms of environmental variability on species diversity and community composition? We approach these questions with a generic, individual-based simulation model. In our model, plants compete for water in a spatially explicit environment. Species differ in their size at maturity and in the allocation of carbon to roots, leaves and storage tissue. The model was fully specified with independent literature data. Model output was compared to characteristics of a species-rich community in the semi-arid Richtersveld (South Africa). The model reproduced the coexistence of plants with different sizes at maturity, the dominance of succulent shrubs, and the level of vegetation cover. We analyzed the effects of three forms of environmental variability: (a) temporal fluctuations in precipitation (rain and fog), (b) spatial heterogeneity of water supply due to run-on and run-off processes and (c) ‘rock pockets’ that limit root competition in space. The three types of variability had differential effects on diversity: diversity exhibited a strong hump-shaped response to temporal variation. Spatial variability increased diversity, with the strongest increase occurring at intermediate levels of temporal variability. Finally, rock pockets had the weakest effect, but contributed to diversity by providing refuges for small species, particularly at low temporal variability. The model thus shows that spatio-temporal variation of resource supply can maintain diversity over long time scales even in small systems, as is the case in the Richtersveld succulent communities. Trade-offs in allocation provide the basis for necessary niche differentiation. By describing resource competition between individual plants, our model provides a mechanistic basis for the link from species traits to community composition at given environmental conditions. It thereby contributes to an understanding of the forces shaping plant communities. Such an understanding is critical to reduce the threats environmental change poses to biodiversity and ecosystem services.     

Landsat Thematic Mapper: Detection of Shifts in Community Composition of Coral Reefs

Abstract: We assembled a time series of 20 Landsat thematic mapper images from 1982 to 1996 for Key Largo, Florida, to ascertain whether satellite imagery can detect temporal changes in coral reef communities. Selected reef and control areas were examined for changes in brightness, spectral reflectance, band ratios, spatial texture, and temporal texture (  pixel-to-pixel change over time). We compared the data to known changes in the reef ecosystem of Carysfort Reef and terrestrial sample sites. Changes in image brightness and spectral-band ratios were suggestive of shifts from coral- to algal-dominated community structure, but the trends were not statistically significant. The spatial heterogeneity of the reef community decreased in the early 1980s at scales consistent with known ecological changes to the coral community on Carysfort Reef. An analysis of pixel-scale variation through time, termed temporal texture, revealed that the shallow reef areas are the most variable in regions of the reef that have experienced significant ecological decline. Thus, the process of reef degradation, which alters both the spatial patterning and variability of pixel brightness, can be identified in unclassified thematic mapper images.     

Fish population dynamics in a seasonally varying wetland

Small fishes in seasonally flooded environments such as the Everglades are capable of spreading into newly flooded areas and building up substantial biomass. Passive drift cannot account for the rapidity of observed population expansions. To test the ‘reaction-diffusion’ mechanism for spread of the fish, we estimated their diffusion coefficient and applied a reaction-diffusion model. This mechanism was also too weak to account for the spatial dynamics. Two other hypotheses were tested through modeling. The first—the ‘refuge mechanism’—hypothesizes that small remnant populations of small fishes survive the dry season in small permanent bodies of water (refugia), sites where the water level is otherwise below the surface. The second mechanism, which we call the ‘dynamic ideal free distribution mechanism’ is that consumption by the fish creates a prey density gradient and that fish taxis along this gradient can lead to rapid population expansion in space. We examined the two alternatives and concluded that although refugia may play an important role in recolonization by the fish population during reflooding, only the second, taxis in the direction of the flooding front, seems capable of matching empirical observations. This study has important implications for management of wetlands, as fish biomass is an essential support of higher trophic levels.     

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

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

Capacity building in tropical coastal resource monitoring in developing countries: A re-appreciation of the oldest remote sensing method

Long-term decadal retrospection in spatio-temporal imagery analyses can only be carried out using aerial photographs, which are still the most detailed remotely sensed data available. Visual interpretation of such imagery is most efficient and inexpensive in the light of ecosystem monitoring research in developing countries, which are often unable to cope with the development or the cost of acquisition of commercial space-borne imaging (e.g. IKONOS, Quickbird). In this light, the present paper explicitly analyses the methodological use of image attributes of air-borne imagery from mangrove forests, and investigates the consistency and constraints of mangrove image attributes in visually interpreted air-borne imagery. Six image attributes are analysed, and their application is illustrated using various mangrove sites in Kenya and Sri Lanka. Comparison of identification keys reveals that minor attributes such as 'ecological position' are informative, and that image attributes for a particular species or genus are apparently less plastic and more widely applicable than formerly assumed. Emphasis on compulsory fieldwork is made and constraints related to reflection and interference, amongst others, are discussed.     

Integrated models to support multiobjective ecological restoration decisions

Many objectives motivate ecological restoration, including improving vegetation condition, increasing the range and abundance of threatened species, and improving species richness and diversity. Although models have been used to examine the outcomes of ecological restoration, few researchers have attempted to develop models to account for multiple, potentially competing objectives. We developed a combined state‐and‐transition, species‐distribution model to predict the effects of restoration actions on vegetation condition and extent, bird diversity, and the distribution of several bird species in southeastern Australian woodlands. The actions reflected several management objectives. We then validated the models against an independent data set and investigated how the best management decision might change when objectives were valued differently. We also used model results to identify effective restoration options for vegetation and bird species under a constrained budget. In the examples we evaluated, no one action (improving vegetation condition and extent, increasing bird diversity, or increasing the probability of occurrence for threatened species) provided the best outcome across all objectives. In agricultural lands, the optimal management actions for promoting the occurrence of the Brown Treecreeper (Climacteris picumnus), an iconic threatened species, resulted in little improvement in the extent of the vegetation and a high probability of decreased vegetation condition. This result highlights that the best management action in any situation depends on how much the different objectives are valued. In our example scenario, no management or weed control were most likely to be the best management options to satisfy multiple restoration objectives. Our approach to exploring trade‐offs in management outcomes through integrated modeling and structured decision‐support approaches has wide application for situations in which trade‐offs exist between competing conservation objectives.