Investigations into a plankton population model: Mortality and its importance in climate change scenarios

The potential for marine plankton ecosystems to influence climate by the production of dimethylsulphide (DMS) has been an important topic of recent research into climate change. Several General Circulation Models, used to predict climate change, have or are being modified to include interactions of ecosystems with climate. Climate change necessitates that parameters within ecosystem models must change during long-term simulations, especially mortality parameters that increase as organisms are pushed toward the boundaries of their thermal tolerance. Changing mortality parameters can have profound influences on ecosystem model dynamics. There is therefore a pressing need to understand the influence of varying mortality parameters on the long-term behaviour of ecosystem models. This work examines the sensitivity of a model of DMS production by marine ecosystems to variations in three linear mortality coefficients. Significant differences in behaviour are observed, and we note the importance of these results in formulating ecosystem models for application in simulations of climate change.     

Response of balanced network models to large-scale perturbation: Implications for evaluating the role of small pelagics in the Gulf of Maine

Exploring the response of an ecosystem, and subsequent tradeoffs among its biological community, to human perturbations remains a key challenge for the implementation of an ecosystem approaches to fisheries (EAF). To address this and related issues, we developed two network (or energy budget) models, Ecopath and Econetwrk, for the Gulf of Maine ecosystem. These models included 31 network “nodes” or biomass state variables across a broad range of trophic levels, with the present emphasis to particularly elucidate the role of small pelagics. After initial network balancing, various perturbation scenarios were evaluated to explore how potential changes to different fish, fisheries and lower trophic levels can affect model outputs. Categorically across all scenarios and interpretations thereof, there was minimal change at the second trophic levels and most of the “rebalancing” after a perturbation occurred via alteration of the diet matrix. Yet the model results from perturbations to a balanced energy budget fall into one of three categories. First, some model results were intuitive and in obvious agreement with established ecological and fishing theory. Second, some model results were counter-intuitive upon initial observation, seemingly contradictory to known ecological and fishing theory; but upon further examination the results were explainable given the constraints of an equilibrium energy budget. Finally, some results were counter-intuitive and difficult to reconcile with theory or further examination of equilibrium constraints. A detailed accounting of biomass flows for example scenarios explores some of the non-intuitive results more rigorously. Collectively these results imply a need to carefully track biomass flows and results of any given perturbation and to critically evaluate the conditions under which a new equilibrium is obtained for these types of models, which has implications for dynamic simulations based off of them. Given these caveats, the role of small pelagics as a prominent component of this ecosystem remains a robust conclusion. We discuss how one might use this approach in the context of further developing an EAF, recognizing that a more holistic, integrated perspective will be required as we continue to evaluate tradeoffs among marine biological communities.     

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.     

Mortality and predation in ecosystem models: is it important how these are expressed?

The effects of the form of the grazing and mortality terms used in plankton models are well known. The same cannot be said for ecosystem models. As ecosystem models become more popular more needs to be known about the effects of model formulation on model behaviour and performance. The impact of the form of the grazing response function and mortality terms used in a biogeochemical ecosystem model are considered here. We show that in the large and inter-linked webs used in ecosystem models, model behaviour is far more sensitive to the form of the grazing term than to that of the mortality terms that close the modelled food web.When using biogeochemical ecosystem models in shallow marine ecosystems, the most dynamic and sophisticated functional responses describing grazing require more parameters and validation than the simpler Holling disk equation, but usually still lead to the same general conclusions about the system state and the effects of changes in forcing functions. Thus, the use of more complex functional responses is not necessarily warranted in many cases. Similarly, the extra effort and data required to explicitly represent the top predators (sharks, mammals and birds) is not necessary if they are not the focus of the study. A quadratic mortality term applied to intermediate predators (such as piscivores) is sufficient to achieve plausible model behaviour. It should be noted, however, that some degree of sophistication is required in the grazing and mortality terms. Use of simple linear functional responses and mortality terms is unsuitable for models used to consider a range of nutrient loading or harvesting scenarios.     

Adding rigor to ecological network models by evaluating a set of pre-balance diagnostics: A plea for PREBAL

The widespread use of ecological network models (e.g., Ecopath, Econetwrk, and related energy budget models) has been laudable for several reasons, chief of which is providing an easy-to-use set of modeling tools that can present an ecosystem context for improved understanding and management of living marine resources (LMR). Yet the ease-of-use of these models has led to two challenges. First, the veritable explosion of the use and application of these network models has resulted in recognition that the content and use of such models has spanned a range of quality. Second, as these models and their application have become more widespread, they are increasingly being used in a LMR management context. Thus review panels and other evaluators of these models would benefit from a set of rigorous and standard criteria from which the basis for all network models and related applications for any given system (i.e., the initial, static energy budget) can be evaluated. To this end, as one suggestion for improving network models in general, here I propose a series of pre-balance (PREBAL) diagnostics. These PREBAL diagnostics can be done, now, in simple spreadsheets before any balancing or tuning is executed. Examples of these PREBAL diagnostics include biomasses, biomass ratios, vital rates, vital rate ratios, total production, and total removals (and slopes thereof) across the taxa and trophic levels in any given energy budget. I assert that there are some general ecological and fishery principles that can be used in conjunction with PREBAL diagnostics to identify issues of model structure and data quality before balancing and dynamic applications are executed. I humbly present this PREBAL information as a simple yet general approach that could be easily implemented, could be considered for further incorporation into these model packages, and as such would ultimately result in a straightforward way to evaluate (and perhaps identify areas for improving) initial conditions in food web modeling efforts.     

Multiple sources of predictive uncertainty in modeled estimates of net ecosystem CO2 exchange

Net ecosystem CO₂ exchange (NEE) is typically measured directly by eddy covariance towers or is estimated by ecosystem process models, yet comparisons between the data obtained by these two methods can show poor correspondence. There are three potential explanations for this discrepancy. First, estimates of NEE as measured by the eddy-covariance technique are laden with uncertainty and can potentially provide a poor baseline for models to be tested against. Second, there could be fundamental problems in model structure that prevent an accurate simulation of NEE. Third, ecosystem process models are dependent on ecophysiological parameter sets derived from field measurements in which a single parameter for a given species can vary considerably. The latter problem suggests that with such broad variation among multiple inputs, any ecosystem modeling scheme must account for the possibility that many combinations of apparently feasible parameter values might not allow the model to emulate the observed NEE dynamics of a terrestrial ecosystem, as well as the possibility that there may be many parameter sets within a particular model structure that can successfully reproduce the observed data. We examined the extent to which these three issues influence estimates of NEE in a widely used ecosystem process model, Biome-BGC, by adapting the generalized likelihood uncertainty estimation (GLUE) methodology. This procedure involved 400,000 model runs, each with randomly generated parameter values from a uniform distribution based on published parameter ranges, resulting in estimates of NEE that were compared to daily NEE data from young and mature Ponderosa pine stands at Metolius, Oregon. Of the 400,000 simulations run with different parameter sets for each age class (800,000 total), over 99% of the simulations underestimated the magnitude of net ecosystem CO₂ exchange, with only 4.07% and 0.045% of all simulations providing satisfactory simulations of the field data for the young and mature stands, even when uncertainties in eddy-covariance measurements are accounted for. Results indicate fundamental shortcomings in the ability of this model to produce realistic carbon flux data over the course of forest development, and we suspect that much of the mismatch derives from an inability to realistically model ecosystem respiration. However, difficulties in estimating historic climate data are also a cause for model-data mismatch, particularly in a highly ecotonal region such as central Oregon. This latter difficulty may be less prevalent in other ecosystems, but it nonetheless highlights a challenge in trying to develop a dynamic representation of the terrestrial biosphere.     

Estimating landscape-scale species richness: reconciling frequency- and turnover-based approaches

One hypothesis for why estimators of species richness tend to underestimate total richness is that they do not explicitly account for increases in species richness due to spatial or environmental turnover in species composition (beta diversity). I analyze the similarity of a data set of native trees in Great Smoky Mountains National Park, USA, and assess the robustness of these estimators against recently developed ones that incorporate turnover explicitly: the total species accumulation method (T-S) and a method based on the distance decay of similarity. I show that the T-S estimator can give reliable estimates of species richness, given an appropriate grouping of sites. The estimator based on distance decay of similarity performed poorly. There are two main reasons for this: sample size effects and the assumption that distance decay of similarity exhibits a power law relationship. I show that estimators based on distance-decay relationships exhibit systematically lower rates of distance decay for samples with few individuals per site independent of environmental variation. Second, the data presented here and many other survey data sets exhibit exponential rather than power law distance-decay relationships. Richness estimators that explicitly incorporate beta diversity can be improved by beginning from an exponential distance-decay relationship and adjusting for the systematic errors introduced by small sample sizes.     

Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals

A surprisingly diverse variety of foragers have previously been concluded to exhibit movement patterns known as Lévy flights, a special type of random walk. These foragers range in size from microzooplankton in experiments to fishermen in the Pacific Ocean and the North Sea. The Lévy flight conclusion implies that all the foragers have similar scale-free movement patterns that can be described by a single dimensionless parameter, the exponent micro of a power-law (Pareto) distribution. However, the previous conclusions have been made using methods that have since been shown to be problematic: inaccurate techniques were used to estimate micro, and the power-law distribution was usually assumed to hold without testing any alternative hypotheses. Therefore, I address the open question of whether the previous data still support the Lévy flight hypothesis, and thus determine whether Lévy flights really are so ubiquitous in ecology. I present a comprehensive reanalysis of 17 data sets from seven previous studies for which Lévy flight behavior had been concluded, covering marine, terrestrial, and experimental systems from four continents. I use the modern likelihood and Akaike weights approach to test whether simple alternative models are more supported by the data than Lévy flights. The previously estimated values of the power-law exponent micro do not match those calculated here using the accurate likelihood approach, and almost all of them lie outside of the likelihood-based 95% confidence intervals. Furthermore, the original power-law Lévy flight model is overwhelmingly rejected for 16 out of the 17 data sets when tested against three other simple models. For one data set, the data are consistent with coming from a bounded power-law distribution (a truncated Lévy flight). For three other data sets, an exponential distribution corresponding to a simple Poisson process is suitable. Thus, Lévy flight movement patterns are not the common phenomena that was once thought, and are not suitable for use as ecosystem indicators for fisheries management, as has been proposed.     

State-of-the-art of ecological modelling with emphasis on development of structural dynamic models

The paper deals with two major problems in ecological modelling today, namely how to get reliable parameters? and how to build ecosystem properties into our models? The use of new mathematical tools to answer these questions is mentioned briefly, but the main focus of the paper is on development of structural dynamic models which are models using goal functions to reflect a current change of the properties of the biological components in the models. These changes of the properties are due to the enormous adaptability of the biological components to the prevailing conditions. All species in an ecosystem attempt to obtain most biomass, i.e. to move as far away as possible from thermodynamic equilibrium which can be measured by the thermodynamic concept exergy. Consequently, exergy has been proposed as a goal function in ecological models with dynamic structure, meaning currently changed properties of the biological components and in model language currently changed parameters. An equation to compute an exergy index of a model is presented. The theoretical considerations leading to this equation are not presented here but references to literature where the basis theory can be found are given. Two case studies of structural dynamic modelling are presented: a shallow lake where the structural dynamic changes have been determined before the model was developed, and the application of biomanipulation in lake management, where the structural dynamic changes are generally known. Moreover. it is also discussed how the same idea of using exergy as a goal function in ecological modelling may be applied to facilitate the estimation of parameters.     

Do microbial processes regulate the stability of a coral atoll's enclosed pelagic ecosystem?

Complex marine ecosystems contain multiple feedback cycles that can cause unexpected responses to perturbations. To better predict these responses, complicated models are increasingly being developed to enable the study of feedback cycles. However, the sparseness of ecological data often limits the direct empirical parameterization of all model parameters. Here we use a Bayesian inverse analysis approach to synthesize empirical data and ecological theory derived from published studies of a coral atoll's enclosed pelagic ecosystem (Takapoto Atoll, French Polynesia). We then use the estimates of flux magnitudes to parameterize probabilistic compartment models with two forms of heterotrophic consumption: (1) “bottom-up” donor-controlled heterotrophic consumption and (2) “top-down” mass-action heterotrophic consumption. We explore how the flux magnitudes affect the ecosystem's stability properties of resilience, reactivity, and resistance under both assumptions for heterotrophic consumption. The models suggest that the microbial uptake of dissolved organic carbon (DOC) regulates the long term rate of return to steady state following a temporary or pulse perturbation (resilience), and the cycling of carbon between abiotic pools and heterotrophic compartments regulates the short-term response (reactivity). In the bottom-up process model, the sensitivity of steady state masses following a sustained or press perturbation (resistance) is highest for the DOC pool following a sustained change to the microbial uptake rate of DOC. Further, a change in the microbial uptake of DOC propagates through the ecosystem and affects the steady state values of zooplankton. The analysis suggests that the food web is highly dependent on the recycling between the abiotic and biotic carbon pools, particularly as mediated by the microbial consumption of DOC, and this recycling determines how the ecosystem responds to perturbations.     

Region of influence method improves macroinvertebrate predictive models in Maryland

Stream biological assessment reflects not just conventional water quality, but an environmental quality that represents the integrity of the stream ecosystem. In Britain, Australia and the United States, macroinvertebrate predictive models were built and applied to stream assessment by employing multivariate analysis. There were variations in these models, where adaptations were made for different regions, but the philosophy underlying the models was similar: employ site classification to predict expected assemblage. Taxon assemblage is predicted from reference groups with similar stream features; these resulting models are RIVPACS-style models. Because every site has to belong to one group in the classification process, each reference group might include some dissimilar sites, and their dissimilarity in taxon assemblage impaired the results of taxon predictions from these models. To avoid this limitation, this study employed a Region-of-Influence-style (ROI-style) modeling method, selecting only similar reference sites and allowing each site to build its own reference group.Three different Region-of-Influence selection schemes were applied to improve the macroinvertebrate predictive model in Maryland: the Assessment by Nearest Neighbour Analysis (ANNA), the Burn's Region of Influence (BROI), and the New Datum Region of Influence (NROI) predictive schemes. The prediction results from ANNA, BROI, and NROI were compared, and the reference selections of each predictive scheme were examined. The comparison showed no preference for the total number of reference sites used by either predictive scheme. The number of reference sites did not correlate to the quality of reference sites used and thus does not control the predictability. The ROI-style model in Maryland had better prediction performance than the RIVPACS-style models, and could improve the bioassessment of streams.     

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.     

Fitting complex population models by combining particle filters with Markov chain Monte Carlo

We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm.     

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.     

Zooplankton community resilience after press-type anthropogenic stress in temporary ponds.

Temporary ponds are physically disturbed environments that fluctuate on seasonal and interannual scales. These ecosystems are also susceptible to anthropogenic perturbation such as contamination inputs. However, the interactive effects of natural disturbance and anthropogenic stress on ecosystem processes and community dynamics have hardly been assessed in these ecosystem types. We used a multiple before-after control-impact (MBACI) design to study zooplankton community recovery from low and high inputs of a fire retardant in artificially constructed ponds over three hydroperiods. The retardant caused a decline in species richness and an increase in rotifers during summer and winter months relative to controls and pretreatment dates, and the duration of these changes varied among retardant treatments. In nonmetric, multidimensional scaling analyses the increased rotifer densities were reflected in loops that showed recurring deviations from and (upon collapse) approaches to reference conditions, while the effects of the anthropogenic stressor persisted in the ponds. The amplitudes of fluctuation followed no regular patterns; it varied with retardant treatment level and was higher in the third hydroperiod compared to the second in one of the treatments. From a temporal perspective, this non-dampened pattern suggests a new cause-effect mechanism for disturbance ecology, which we refer to as a "protracted press disturbance, roller coaster response" relationship. This model emphasizes stochastic oscillations in community composition, punctuated by periods in which the community approaches reference conditions. From the applied viewpoint, this model suggests that the accurate detection of perturbation and the implementation of sound management and restoration strategies will require intensive sampling designs that span multiple hydroperiods in persistently degraded ponds.     

Assessment of herbaceous plant habitats in water-constrained environments: predicting indirect effects with fuzzy logic

Herbaceous plant production plays a key role in determining the function of rangeland ecosystems in the semi-arid and Mediterranean regions. Therefore, assessment of herbaceous plant habitats is important for understanding the ecosystem functioning in these regions and for applied purposes, such as range management and land evaluation. This paper presents a model to assess herbaceous plant habitats in a basaltic stony environment in a Mediterranean region. The model is based on geographic information systems (GIS), remote sensing and fuzzy logic, while four indirect variables, which represent major characteristics of herbaceous habitats, are modeled: rock cover fraction; wetness index (WI); soil depth; and slope orientation (aspect). A linear unmixing model was used to measure rock cover on a per pixel basis using a Landsat TM summer image. The wetness index and local aspect were determined from digital elevation data with 25 m × 25 m pixel resolution, while soil data were gathered in a field survey. The modeling approach adopted here is process-based and assumes that water availability plays a crucial role in determining herbaceous plant production in Mediterranean and semi-arid environments. The model rules are based on fuzzy logic and are written based on the hypothesized water requirements of the herbaceous vegetation. The results show that on a polygon basis there is positive agreement between the model proposed here and previous mapping of the herbaceous habitats carried out in the field using traditional methods. Intrapolygon tests show that the use of a continuous raster data model and fuzzy logic principles provide an added value to traditional mapping. Moreover, herbaceous biomass measurements at two time intervals—mid- and peak winter season—corresponded with the habitat assessment predictions achieved using a new scenario that is proposed in this research. This scenario suggests that rockiness increases herbaceous production on south-facing slopes, while in other slope aspects the rock cover has lower impact on herbaceous growth. Due to its simplicity, the model suggested here can be used by planners and managers, to adjust range activities over large areas. The process-based approach should allow adaptation of the model to other regions more effectively than models that were formulated on a purely empirical basis. The model could also be used to study the relationship between water availability and ecosystem productivity on a regional scale.     

Feasibility and stability in randomly assembled Lotka-Volterra models

For a Lotka-Volterra model to represent a viable ecosystem it's nontrivial equilibrium must be feasible. If m is the number of species, it is shown that in a set of randomly assembled Lotka-Volterra models, the fraction of models with a feasible equilibrium is some function of m which behaves like 2^?m. Moreover a subset of Lotka-Volterra models, each of which has a feasible equilibrium, has the same stability property as a set of linear models which is assembled randomly in the same manner. This contradicts a recent claim that a Lotka-Volterra model with a feasible equilibrium tends to be stable. Thus for two reasons the probability that a Lotka-Volterra model represents a viable and stable ecosystem decreases rapidly with the number of species. This supports the theme developed by May that stability in model ecosystems decreases with diversity.     

The probabilistic niche model reveals substantial variation in the niche structure of empirical food webs

The structure of food webs, complex networks of interspecies feeding interactions, plays a crucial role in ecosystem resilience and function, and understanding food web structure remains a central problem in ecology. Previous studies have shown that key features of empirical food webs can be reproduced by low-dimensional "niche" models. Here we examine the form and variability of food web niche structure by fitting a probabilistic niche model to 37 empirical food webs, a much larger number of food webs than used in previous studies. The model relaxes previous assumptions about parameter distributions and hierarchy and returns parameter estimates for each species in each web. The model significantly outperforms previous niche model variants and also performs well for several webs where a body-size-based niche model performs poorly, implying that traits other than body size are important in structuring these webs' niche space. Parameter estimates frequently violate previous models' assumptions: in 19 of 37 webs, parameter values are not significantly hierarchical, 32 of 37 webs have nonuniform niche value distributions, and 15 of 37 webs lack a correlation between niche width and niche position. Extending the model to a two-dimensional niche space yields networks with a mixture of one- and two-dimensional niches and provides a significantly better fit for webs with a large number of species and links. These results confirm that food webs are strongly niche-structured but reveal substantial variation in the form of the niche structuring, a result with fundamental implications for ecosystem resilience and function.