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.     

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.     

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.     

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.     

Multistate modeling of habitat dynamics: factors affecting Florida scrub transition probabilities

Many ecosystems are influenced by disturbances that create specific successional states and habitat structures that species need to persist. Estimating transition probabilities between habitat states and modeling the factors that influence such transitions have many applications for investigating and managing disturbance-prone ecosystems. We identify the correspondence between multistate capture-recapture models and Markov models of habitat dynamics. We exploit this correspondence by fitting and comparing competing models of different ecological covariates affecting habitat transition probabilities in Florida scrub and flatwoods, a habitat important to many unique plants and animals. We subdivided a large scrub and flatwoods ecosystem along central Florida's Atlantic coast into 10-ha grid cells, which approximated average territory size of the threatened Florida Scrub-Jay (Aphelocoma coerulescens), a management indicator species. We used 1.0-m resolution aerial imagery for 1994, 1999, and 2004 to classify grid cells into four habitat quality states that were directly related to Florida Scrub-Jay source-sink dynamics and management decision making. Results showed that static site features related to fire propagation (vegetation type, edges) and temporally varying disturbances (fires, mechanical cutting) best explained transition probabilities. Results indicated that much of the scrub and flatwoods ecosystem was resistant to moving from a degraded state to a desired state without mechanical cutting, an expensive restoration tool. We used habitat models parameterized with the estimated transition probabilities to investigate the consequences of alternative management scenarios on future habitat dynamics. We recommend this multistate modeling approach as being broadly applicable for studying ecosystem, land cover, or habitat dynamics. The approach provides maximum-likelihood estimates of transition parameters, including precision measures, and can be used to assess evidence among competing ecological models that describe system dynamics.     

Deriving state-and-transition models from an image series of grassland pattern dynamics

We present how state-and-transition models (STMs) may be derived from image data, providing a graphical means of understanding how ecological dynamics are driven by complex interactions among ecosystem events. A temporal sequence of imagery of fine scale vegetation patterning was acquired from close range photogrammetry (CRP) of 1 m quadrats, in a long term monitoring project of Themeda triandra (Forsskal) grasslands in north western Australia. A principal components scaling of image metrics calculated on the imagery defined the state space of the STM, and thereby characterised the different patterns found in the imagery. Using the state space, we were able to relate key events (i.e. fire and rainfall) to both the image data and aboveground biomass, and identified distinct ecological ‘phases’ and ‘transitions’ of the system. The methodology objectively constructs a STM from imagery and, in principle, may be applied to any temporal sequence of imagery captured in any event-driven system. Our approach, by integrating image data, addresses the labour constraint limiting the extensive use of STMs in managing vegetation change in arid and semiarid rangelands.     

Increased spatial variance accompanies reorganization of two continental shelf ecosystems

Phase transitions between alternate stable states in marine ecosystems lead to disruptive changes in ecosystem services, especially fisheries productivity. We used trawl survey data spanning phase transitions in the North Pacific (Gulf of Alaska) and the North Atlantic (Scotian Shelf) to test for increases in ecosystem variability that might provide early warning of such transitions. In both time series, elevated spatial variability in a measure of community composition (ratio of cod [Gadus sp.] abundance to prey abundance) accompanied transitions between ecosystem states, and variability was negatively correlated with distance from the ecosystem transition point. In the Gulf of Alaska, where the phase transition was apparently the result of a sudden perturbation (climate regime shift), variance increased one year before the transition in mean state occurred. On the Scotian Shelf, where ecosystem reorganization was the result of persistent overfishing, a significant increase in variance occurred three years before the transition in mean state was detected. However, we could not reject the alternate explanation that increased variance may also have simply been inherent to the final stable state in that ecosystem. Increased variance has been previously observed around transition points in models, but rarely in real ecosystems, and our results demonstrate the possible management value in tracking the variance of key parameters in exploited ecosystems.     

Exploring alternative states in ecological systems with a qualitative analysis of community feedback

Demonstrating and predicting the existence of alternative states in natural communities remains a challenge for ecologists and is essential for resource managers. Positive feedback is often presented as central in maintaining alternative ecosystem states, but no formal approach relates this part of theory to real world applications. Through qualitative modelling of community response to long-term perturbations, we define generic mechanistic links between positive feedback and the occurrence of alternative states. Positive feedback diminishes a system's overall resistance to change, and can create and maintain correlations in the relative abundance of variables that coincide with alternative states.Through specific models of the dynamics of Tasmanian rocky-reef communities, which are affected by climate and fishing and persist within alternative states, we demonstrate the ability of our theoretical framework to predict alternative states in ecosystems and inform management intervention. A qualitative knowledge of community structure permits a thorough analysis of system feedback and an assessment of the potential for an ecosystem to exhibit alternative states. We illustrate the usefulness of the approach to inform management priorities, and to focus monitoring and field research on the key drivers of ecosystem dynamics.     

Prioritizing Conservation Effort through the Use of Biological Soil Crusts as Ecosystem Function Indicators in an Arid Region

Abstract: Conservation prioritization usually focuses on conservation of rare species or biodiversity, rather than ecological processes. This is partially due to a lack of informative indicators of ecosystem function. Biological soil crusts (BSCs) trap and retain soil and water resources in arid ecosystems and function as major carbon and nitrogen fixers; thus, they may be informative indicators of ecosystem function. We created spatial models of multiple indicators of the diversity and function of BSCs (species richness, evenness, functional diversity, functional redundancy, number of rare species, number of habitat specialists, nitrogen and carbon fixation indices, soil stabilization, and surface roughening) for the 800,000‐ha Grand Staircase‐Escalante National Monument (Utah, U.S.A.). We then combined the indicators into a single BSC function map and a single BSC biodiversity map (2 alternative types of conservation value) with an unweighted averaging procedure and a weighted procedure derived from validations performance. We also modeled potential degradation with data from a rangeland assessment survey. To determine which areas on the landscape were the highest conservation priorities, we overlaid the function‐ and diversity‐based conservation‐value layers on the potential degradation layer. Different methods for ascribing conservation‐value and conservation‐priority layers all yielded strikingly similar results (r= 0.89–0.99), which suggests that in this case biodiversity and function can be conserved simultaneously. We believe BSCs can be used as indicators of ecosystem function in concert with other indicators (such as plant‐community properties) and that such information can be used to prioritize conservation effort in drylands.     

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.     

Modelling coral reef ecosystems with limited observational data

Ecosystem models represent potentially powerful tools for coral reef ecosystem managers. They can provide insight into ecosystem dynamics not achievable through alternative means allowing coral reef managers to assess the potential outcome of any given management decision. One of the main limitations in the applicability of ecosystem models is that they often require detailed empirical data and this can restrict their applicability to ecosystems that are either currently well studied or have the resources available to collect the required data. This study describes the development of a coral reef ecosystem model that can be calibrated to an ecosystem with limited empirical data. Based on the assumption that coral reef ecological structure is generic across all tropical coral reefs and that the magnitude of the interactions between ecological components is reef specific, the dynamics of the ecosystem can be replicated based on limited empirical data. The model successfully replicated the dynamics of three individual reef systems including an inshore and oceanic reef within the Great Barrier Reef and a Caribbean reef system. It highlighted the importance of understanding the specific dynamics of a given reef and that a positive management intervention in one system may result in a negative outcome for another. The model was also used to assess the importance of various interactions within coral reef ecosystems. It identified the interactions between hard corals and other non-algal benthic components as being an important (but currently understudied) facet of coral reef ecology. The development of this modelling approach provides access to ecosystem modelling tools for coral reef managers previously excluded due to a lack of resources or technical expertise.     

Representing mediating effects and species reintroductions in Ecopath with Ecosim

Ecosystem models play an important role in supporting ecosystem approaches to management. To improve the representation of how ecosystems work, ecosystem models should be able to represent mediating effects (e.g., habitat provision) that species provide to each other as well as species (re)introductions, both common situations that can strongly influence ecosystem dynamics. We examine how such processes can be incorporated into Ecopath with Ecosim (EwE), a widely used tool for represent aquatic ecosystems with the potential to support ecosystem-based management. We used the reintroduction of sea otters (Enhydralutris) to the west coast of Vancouver Island, British Columbia, Canada as a case study. The model demonstrates how to account for benefits provided by kelp forests by contributing to primary production, increased feeding areas and food availability through prey retention. It also demonstrates how the reintroduction and range expansion of sea otters can be represented in Ecospace, and the implications of these options.     

A simple plankton model for the Oregon upwelling ecosystem: Sensitivity and validation against time-series ocean data

Simple plankton models serve as useful platforms for testing our understanding of the mechanisms underlying ecosystem dynamics. A simple, one-dimensional plankton model was developed to describe the dynamics of nitrate, ammonium, two phytoplankton size-classes, meso-zooplankton, and detritus in the Oregon upwelling ecosystem. Computational simplicity was maintained by linking the biological model to a one-dimensional, cross-shelf physical model driven by the daily coastal upwelling index. The model sacrificed resolution of regional-scale and along-shore (north to south) processes and assumed that seasonal productivity is primarily driven by local cross-shelf Ekman transport of surface waters and upwelling of nutrient-rich water from depth.Our goals were to see how well a simple plankton model could capture the general temporal and spatial dynamics of the system, test system sensitivity to alternate parameter set values, and observe system response to the effective scale of potential retention mechanisms. Model performance across the central Oregon shelf was evaluated against two years (2000-2001) of chlorophyll and copepod time-series observations. While the modeled meso-zooplankton biomass was close in scale to the observed copepod biomass, phytoplankton was overestimated relative to that inferred from the observed surface chlorophyll concentration. Inshore, the system was most sensitive to the nutrient uptake kinetics of diatom-size phytoplankton and to the functional grazing response of meso-zooplankton. Meso-zooplankton was more sensitive to alternate parameter values than was phytoplankton. Reduction of meso-zooplankton cross-shelf advection rates (crudely representing behavioral retention mechanisms) reduced the scale of model error relative to the observed seasonal mean inshore copepod biomass but had little effect of the modeled meso-zooplankton biomass offshore nor upon phytoplankton biomass across the entire shelf.     

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.     

The Scotia Sea krill fishery and its possible impacts on dependent predators: modeling localized depletion of prey

The nature and impact of fishing on predators that share a fished resource is an important consideration in ecosystem-based fisheries management. Krill (Euphausia superba) is a keystone species in the Antarctic, serving as a fundamental forage source for predators and simultaneously being subject to fishing. We developed a spatial multispecies operating model (SMOM) of krill-predator fishery dynamics to help advise on allocation of the total krill catch among 15 small-scale management units (SSMUs) in the Scotia Sea, with a goal to reduce the potential impact of fishing on krill predators. The operating model describes the underlying population dynamics and is used in simulations to compare different management options for adjusting fishing activities (e.g., a different spatial distribution of catches). The numerous uncertainties regarding the choice of parameter values pose a major impediment to constructing reliable ecosystem models. The pragmatic solution proposed here involves the use of operating models that are composed of alternative combinations of parameters that essentially try to bound the uncertainty in, for example, the choice of survival rate estimates as well as the functional relationships between predators and prey. Despite the large uncertainties, it is possible to discriminate the ecosystem impacts of different spatial fishing allocations. The spatial structure of the model is fundamental to addressing concerns of localized depletion of prey in the vicinity of land-based predator breeding colonies. Results of the model have been considered in recent management deliberations for spatial allocations of krill catches in the Scotia Sea and their associated impacts on dependent predator species.     

Efficient and sustainable management of complex forest ecosystems

A large range of models has been developed for the analysis of optimal forest management strategies, with the well-known Faustmann models dating back to the mid-19th century. To date, however, there has been relatively little attention for the implications of complex ecosystem dynamics for optimal forest management. This paper examines the implications of irreversible ecosystem responses for efficient and sustainable forest management. The paper is built around two forest models that comprise two ecosystem components, forest cover and topsoil, the interactions between these components, and the supply of the ecosystem services ‘wood’ and ‘erosion control’. The first model represents a forest that responds in a reversible way to overharvesting. In the second model, an additional ecological process has been included and the ecosystem irreversibly collapses below certain thresholds in forest cover and topsoil depth. The paper presents a general model, and demonstrates the implications of pursuing efficient as well as sustainable forest management for the two forest ecosystems. Both fixed and variable harvesting cycles are examined. Efficient and sustainable harvesting cycles are compared, and it is shown that irreversible ecosystem behaviour reduces the possibilities to reconcile efficient and sustainable forest management through a variable harvesting cycle.     

Examining the relationship between ecosystem structure and function using structural equation modelling: A case study examining denitrification potential in restored wetland soils

An ongoing debate in ecology is the relationship between community or ecosystem structure and function. This relationship is particularly important in restored ecosystems because it is often assumed that restoring ecosystem structure will restore ecosystem functioning, but this assumption is frequently not tested. In this study, we used a novel application of structural equation modelling (SEM) to examine the relationship between ecosystem structure and function. To exemplify how to apply SEM to explore this relationship, we used a case study examining soil controls on denitrification potential (DNP) in two restored wetlands. Our objectives were to examine (1) whether both restored wetland soil ecosystems had similar relationships among soils variables (i.e. similar soil ecosystem structure) and (2) whether the soil variables driving denitrification potential (DNP) were similar at both sites (i.e. the soil ecosystems were functioning in a similar manner). Using the unique ability of SEM to test model structure, we proposed a SEM to represent the soil ecosystem and tested this structure with field data. We determined that the same model structure was supported by data from both systems suggesting that the two restored wetland systems had similar soil ecosystem structure. To test whether both ecosystems were functioning in a similar way, we examined the parameters of each model. We determined that the drivers of DNP function were not the same at both sites. Higher soil organic matter was the most important predictor of higher DNP at both sites. However, the other significant relationships among soils variables were different at each system indicating that the soils were not functioning in exactly the same way at each site. Overall, these results suggest that the restoration of ecosystem structure may not necessarily ensure the restoration of ecosystem functioning. In this study we capitalize on an inherent feature of SEM, the ability to test model structure, to test a fundamental ecological question. This novel approach is widely applicable to other systems and improves our understanding of the general relationship between ecosystem structure and function.     

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.