Craig A. Stow

Skill assessment for coupled biological/physical models of marine systems

Coupled biological/physical models of marine systems serve many purposes including the synthesis of information, hypothesis generation, and as a tool for numerical experimentation. However, marine system models are increasingly used for prediction to support high-stakes decision-making. In such applications it is imperative that a rigorous model skill assessment is conducted so that the models capabilities are tested and understood. Herein, we review several metrics and approaches useful to evaluate model skill. The definition of skill and the determination of the skill level necessary for a given application is context specific and no single metric is likely to reveal all aspects of model skill. Thus, we recommend the use of several metrics, in concert, to provide a more thorough appraisal. The routine application and presentation of rigorous skill assessment metrics will also serve the broader interests of the modeling community, ultimately resulting in improved forecasting abilities as well as helping us recognize our limitations.

On Monte Carlo methods for Bayesian inference

Bayesian methods are experiencing increased use for probabilistic ecological modelling. Most Bayesian inference requires the numerical approximation of analytically intractable integrals. Two methods based on Monte Carlo simulation have appeared in the ecological/environmental modelling literature. Though they sound similar, the Bayesian Monte Carlo (BMC) and Markov Chain Monte Carlo (MCMC) methods are very different in their efficiency and effectiveness in providing useful approximations for accurate inference in Bayesian applications. We compare these two methods using a low-dimensional biochemical oxygen demand decay model as an example. We demonstrate that the BMC is extremely inefficient because the prior parameter distribution, from which the Monte Carlo sample is drawn, is often a poor surrogate for the posterior parameter distribution, particularly if the parameters are highly correlated. In contrast, MCMC generates a chain that converges, in distribution, on the posterior parameter distribution, that can be regarded as a sample from the posterior distribution. The inefficiency of the BMC can lead to marginal posterior parameter distributions that appear irregular and may be highly misleading because the important region of the posterior distribution may never be sampled. We also point out that a priori specification of the model error variance can strongly influence the estimation of the principal model parameters. Although the BMC does not require that the model error variance be specified, most published applications have treated this variance as a known constant. Finally, we note that most published BMC applications have chosen a uniform prior distribution, making the BMC more similar to a likelihood-based inference rather than a Bayesian method because the posterior is unaffected by the prior. Though other prior distributions could be applied, the treatment of Monte Carlo samples with any other choice of prior distribution has not been discussed in the BMC literature.

Macrosystems ecology: understanding ecological patterns and processes at continental scales

Macrosystems ecology is the study of diverse ecological phenomena at the scale of regions to continents and their interactions with phenomena at other scales. This emerging subdiscipline addresses ecological questions and environmental problems at these broad scales. Here, we describe this new field, show how it relates to modern ecological study, and highlight opportunities that stem from taking a macrosystems perspective. We present a hierarchical framework for investigating macrosystems at any level of ecological organization and in relation to broader and finer scales. Building on well-established theory and concepts from other subdisci- plines of ecology, we identify feedbacks, linkages among distant regions, and interactions that cross scales of space and time as the most likely sources of unexpected and novel behaviors in macrosystems. We present three examples that highlight the importance of this multiscaled systems perspective for understanding the ecology of regions to continents.

Long-term changes in watershed nutrient inputs and riverine exports in the Neuse River, North Carolina.

We compared patterns of historical watershed nutrient inputs with in-river nutrient loads for the Neuse River, NC. Basin-wide sources of both nitrogen and phosphorus have increased substantially during the past century, marked by a sharp increase in the last 10 years resulting from an intensification of animal production. However, this recent increase is not reflected in changes in river loading over the last 20 years. Temporal patterns in river loads more closely parallel short-term changes in point sources and cropland nutrient application despite their overall lower magnitude. Total phosphorus loads have declined at all stations considered, corresponding to a 1988 phosphate detergent ban. Nitrogen load temporal patterns vary by location and the nitrogen fraction considered. The furthest upstream station exhibited nitrogen decreases after the completion of a dam in 1983. At a station just downstream of a rapidly growing urban area, the total nitrogen load has increased since the mid-1980s, primarily as a nitrate concentration increase. This is consistent with concurrent increases in chemical fertilizer use and point source discharges, as well as increased nitrification at treatment plants. This increase in nitrate loading is not reflected at the most downstream station, where no clear nitrogen trends are discernable. The lack of clear downstream nutrient increases suggests that current water quality impairment in the lower river and estuary may result from chronic nutrient overload rather than recent changes in the watershed. If this is true, then the impact of a planned 30% nitrogen loading reduction may not be immediately apparent. We calculate that, given annual variability, detecting a load reduction of this magnitude will take at least four years, and, should nutrients accumulated in the watershed become a significant source, detecting the resulting ecological improvements is likely to take substantially longer.

A bayesian hierarchical model to predict benthic oxygen demand from organic matter loading in estuaries and coastal zones

Ecological models that have a theoretical basis and yet are mathematically simple enough to be parameterized using available data are likely to be the most useful for environmental management and decision-making. Mechanistic foundations improve confidence in model predictions, while statistical methods provide empirical support for parameter selection and allow for estimates of predictive uncertainty. However, even models that are mechanistically simple can be overparameterized when system-specific data are limited. To overcome this problem, models are often fit to data sets composed of observations from multiple systems. The resulting parameter estimates are then used to predict changes within a single system, given changes in management variables. However, the assumption of common parameter values across all systems may not always be valid. This assumption can be relaxed by adopting a hierarchical approach. Under the hierarchical structure, each system has its own set of parameter values, but some commonality in values is assumed across systems. An underlying population distribution is employed to structure this commonality among parameters, thereby avoiding the problems of overfitting. The hierarchical approach is, therefore, a practical compromise between entirely site-specific and globally-common parameter estimates. We applied the hierarchical method to annual data on organic matter loading and benthic oxygen demand from 34 estuarine and coastal systems. Both global and system-specific parameters were estimated using Bayes Theorem. Compared to the global model, the hierarchical model results in predictions of oxygen demand that more accurately represent site-specific observation but are less precise than the global model. Lower precision occurs because, by allowing each system to have its own parameter values, we effectively reduce the amount of information we have to estimate those parameters. However, if, by permitting model parameters to differ by location, the hierarchical model is believed to be more realistic than the global model, then the lower precision represents a more proper translation of our knowledge into predictions. Appropriate representation of prediction precision can have important implications for management intended to reduce oxygen depletion. Depending on the predictive precision resulting from the availability and nature of site-specific data, the hierarchical model may suggest more or less stringent organic matter loading rates than a model assuming global parameter commonality. The generality of the hierarchical approach makes it suitable for a number of ecological modeling applications in which cross-system data are required for empirical parameter estimation, yet only partial commonality can be assumed across sampling units.

Cross‐scale interactions: quantifying multi‐scaled cause–effect relationships in macrosystems

Ecologists are increasingly discovering that ecological processes are made up of components that are multi-scaled in space and time. Some of the most complex of these processes are cross-scale interactions (CSIs), which occur when components interact across scales. When undetected, such interactions may cause errors in extrapolation from one region to another. CSIs, particularly those that include a regional scaled component, have not been systematically investigated or even reported because of the challenges of acquiring data at sufficiently broad spatial extents. We present an approach for quantifying CSIs and apply it to a case study investigating one such interaction, between local and regional scaled land-use drivers of lake phosphorus. Ultimately, our approach for investigating CSIs can serve as a basis for efforts to understand a wide variety of multi-scaled problems such as climate change, land-use/land-cover change, and invasive species.

Discontinuities, cross-scale patterns, and the organization of ecosystems

Ecological structures and processes occur at specific spatiotemporal scales, and interactions that occur across multiple scales mediate scale-specific (e.g., individual, community, local, or regional) responses to disturbance. Despite the importance of scale, explicitly incorporating a multi-scale perspective into research and management actions remains a challenge. The discontinuity hypothesis provides a fertile avenue for addressing this problem by linking measureable proxies to inherent scales of structure within ecosystems. Here we outline the conceptual framework underlying discontinuities and review the evidence supporting the discontinuity hypothesis in ecological systems. Next we explore the utility of this approach for understanding cross-scale patterns and the organization of ecosystems by describing recent advances for examining nonlinear responses to disturbance and phenomena such as extinctions, invasions, and resilience. To stimulate new research, we present methods for performing discontinuity analysis, detail outstanding knowledge gaps, and discuss potential approaches for addressing these gaps.

Using Landscape Limnology to Classify Freshwater Ecosystems for Multi-ecosystem Management and Conservation

Governmental entities are responsible for managing and conserving large numbers of lake, river, and wetland ecosystems that can be addressed only rarely on a case-by-case basis. We present a system for predictive classification modeling, grounded in the theoretical foundation of landscape limnology, that creates a tractable number of ecosystem classes to which management actions may be tailored. We demonstrate our system by applying two types of predictive classification modeling approaches to develop nutrient criteria for eutrophication management in 1998 north temperate lakes. Our predictive classification system promotes the effective management of multiple ecosystems across broad geographic scales by explicitly connecting management and conservation goals to the classification modeling approach, considering multiple spatial scales as drivers of ecosystem dynamics, and acknowledging the hierarchical structure of freshwater ecosystems. Such a system is critical for adaptive management of complex mosaics of freshwater ecosystems and for balancing competing needs for ecosystem services in a changing world.

The dual role of nitrogen supply in controlling the growth and toxicity of cyanobacterial blooms

Historically, phosphorus (P) has been considered the primary limiting nutrient for phytoplankton assemblages in freshwater ecosystems. This review, supported by new findings from Lake Erie, highlights recent molecular, laboratory, and field evidence that the growth and toxicity of some non-diazotrophic blooms of cyanobacteria can be controlled by nitrogen (N). Cyanobacteria such as Microcystis possess physiological adaptations that allow them to dominate low-P surface waters, and in temperate lakes, cyanobacterial densities can be controlled by N availability. Beyond total cyanobacterial biomass, N loading has been shown to selectively promote the abundance of Microcystis and Planktothrix strains capable of synthesizing microcystins over strains that do not possess this ability. Among strains of cyanobacteria capable of synthesizing the N-rich microcystins, cellular toxin quotas have been found to depend upon exogenous N supplies. Herein, multi-year observations from western Lake Erie are presented demonstrating that microcystin concentrations peak in parallel with inorganic N, but not orthophosphate, concentrations and are significantly lower (p<0.01) during years of reduced inorganic nitrogen loading and concentrations. Collectively, this information underscores the importance of N as well as P in controlling toxic cyanobacteria blooms. Furthermore, it supports the premise that management actions to reduce P in the absence of concurrent restrictions on N loading may not effectively control the growth and/or toxicity of non-diazotrophic toxic cyanobacteria such as the cosmopolitan, toxin-producing genus, Microcystis.

Using a Bayesian hierarchical model to improve Lake Erie cyanobacteria bloom forecasts

The last decade has seen a dramatic increase in the size of western Lake Erie cyanobacteria blooms, renewing concerns over phosphorus loading, a common driver of freshwater productivity. However, there is considerable uncertainty in the phosphorus load-bloom relationship, because of other biophysical factors that influence bloom size, and because the observed bloom size is not necessarily the true bloom size, owing to measurement error. In this study, we address these uncertainties by relating late-summer bloom observations to spring phosphorus load within a Bayesian modeling framework. This flexible framework allows us to evaluate three different forms of the load-bloom relationship, each with a particular combination of statistical error distribution and response transformation. We find that a novel implementation of a gamma error distribution, along with an untransformed response, results in a model with relatively high predictive skill and realistic uncertainty characterization, when compared to models based on more common statistical formulations. Our results also underscore the benefits of a hierarchical approach that enables assimilation of multiple sets of bloom observations within the calibration processes, allowing for more thorough uncertainty quantification and explicit differentiation between measurement and model error. Finally, in addition to phosphorus loading, the model includes a temporal trend component indicating that Lake Erie has become increasingly susceptible to large cyanobacteria blooms over the study period (2002–2013). Results suggest that current phosphorus loading targets will be insufficient for reducing the intensity of cyanobacteria blooms to desired levels, so long as the lake remains in a heightened state of bloom susceptibility.