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Approaches to highly parameterized inversion-A guide to using PEST for groundwater-model calibration

Highly parameterized groundwater models can create calibration difficulties. Regularized inversion-the combined use of large numbers of parameters with mathematical approaches for stable parameter estimation-is becoming a common approach to address these difficulties and enhance the transfer of information contained in field measurements to parameters used to model that system. Though commonly used in other industries, regularized inversion is somewhat imperfectly understood in the groundwater field. There is concern that this unfamiliarity can lead to underuse, and misuse, of the methodology. This document is constructed to facilitate the appropriate use of regularized inversion for calibrating highly parameterized groundwater models. The presentation is directed at an intermediate- to advanced-level modeler, and it focuses on the PEST software suite-a frequently used tool for highly parameterized model calibration and one that is widely supported by commercial graphical user interfaces. A brief overview of the regularized inversion approach is provided, and techniques for mathematical regularization offered by PEST are outlined, including Tikhonov, subspace, and hybrid schemes. Guidelines for applying regularized inversion techniques are presented after a logical progression of steps for building suitable PEST input. The discussion starts with use of pilot points as a parameterization device and processing/grouping observations to form multicomponent objective functions. A description of potential parameter solution methodologies and resources available through the PEST software and its supporting utility programs follows. Directing the parameter-estimation process through PEST control variables is then discussed, including guidance for monitoring and optimizing the performance of PEST. Comprehensive listings of PEST control variables, and of the roles performed by PEST utility support programs, are presented in the appendixes.

Scientific Investigations Report↗

Seed dispersal and tree legacies influence spatial patterns of plant invasion dynamics

Invasive plant species alter community dynamics and ecosystem properties, potentially leading to regime shifts. Here, the invasion of a non-native tree species into a stand of native tree species is simulated using an agent-based model. The model describes an invasive tree with fast growth and high seed production that produces litter with a suppressive effect on native seedlings, based loosely on Melaleuca quinquenervia , invasive to southern Florida. The effect of a biocontrol agent, which reduces the invasive tree's growth and reproductive rates, is included to study how effective biocontrol is in facilitating the recovery of native trees. Even under biocontrol, the invader has some advantages over native tree species, such as the ability to tolerate higher stem densities than the invaded species and its litter's seedling suppression effect. We also include a standing dead component of both species, where light interception from dead canopy trees influences neighboring tree demographics. The model is applied to two questions. The first is how the mean seedling dispersal rate affects the spread of the invading species into a pure stand of natives, assuming the same mean dispersal distance for both species. For assumed litter seedling suppression that roughly balances the fitness levels of the two species, which species dominates depends on the mean dispersal distance. The invader dominates at both very high and very low mean seedling dispersal distances, while the native tree dominates for dispersal distances in the intermediate range. The second question is how standing dead trees affect either the rate of spread of the invader or the rate of recovery of the native species. The legacy of standing dead invasive trees may delay the recovery of native vegetation. The results here are novel and show that agent-based modeling is essential in illustrating how the fine-scale modeling of local interactions of trees leads to effects at the population level.

Frontiers in Applied Mathematics and Statistics↗

Managing the threat of infectious disease in fisheries and aquaculture using structured decision making

Fisheries and aquaculture provide food and economic security, especially in the developing world, but both face challenges from infectious disease. Here, we consider management of disease issues from a structured decision-making perspective to examine how infectious disease can threaten seafood production and influence management decisions. For both wild fisheries and aquaculture, disease-management objectives generally aim to mitigate the severity and economic burden of outbreaks. General management strategies include manipulating host densities, reducing system connectivity, conserving or improving habitat, and implementing direct treatments or some other biological interventions. To inform decisions, mathematical models can be used to explore disease dynamics and to forecast the potential effectiveness of alternative management actions. Developing and implementing disease-management strategies also involve considering uncertainties and balancing competing stakeholder interests and risk tolerances. We conclude by outlining several steps for applying structured decision making that are broadly useful to decision makers facing issues related to disease.

Frontiers in Ecology and the Environment↗

Guides to understanding the aeromagnetic expression of faults in sedimentary basins: Lessons learned from the central Rio Grande rift, New Mexico

High-resolution aeromagnetic data acquired over several basins in the central Rio Grande rift, north-central New Mexico, prominently display low-amplitude (5–15 nT) linear anomalies associated with faults that offset basin-fill sediments. The linear anomalies give an unparalleled view of concealed faults within the basins that has significant implications for future basin studies. These implications provide the impetus for understanding the aeromagnetic expression of faults in greater detail. Lessons learned from the central Rio Grande rift help to understand the utility of aeromagnetic data for examining concealed faults in sedimentary basins in general. For example, linear anomalies in the rift can be explained entirely by the tectonic juxtaposition of magnetically differing strata rather than the product of chemical processes acting at the fault zone. Differences in layer thickness, depth to the layer(s), and magnetic susceptibility govern the variability of the anomaly shape. Further investigations of these variables using simple models provide graphical, mathematical, and conceptual guides for understanding the aeromagnetic expression of faults, including the criteria for aeromagnetic expression of faults, how to locate fault traces from aeromagnetic anomalies, the effect of fault dip, and how to assess the role of topography. The horizontal gradient method applied to reduced-to-pole aeromagnetic data is particularly effective in mapping fault locations, especially at regional scales. With our new understanding of the aeromagnetic expression of faults, we updated interpretations of faults from the aeromagnetic data for the central Rio Grande rift. These interpretations, along with the guides, should provide direction and fuel for future work in a wide variety of multidisciplinary basin-related topics.

New Mexico↗

The principle of superposition and its application in ground-water hydraulics

The principle of superposition, a powerful mathematical technique for analyzing certain types of complex problems in many areas of science and technology, has important applications in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that problem solutions can be added together to obtain composite solutions. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to ground-water hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader.

Techniques of Water-Resources Investigations↗

Analysis and Management of Animal Populations: Modeling, Estimation and Decision Making

This book deals with the processes involved in making informed decisions about the management of animal populations. It covers the modeling of population responses to management actions, the estimation of quantities needed in the modeling effort, and the application of these estimates and models to the development of sound management decisions. The book synthesizes and integrates in a single volume the methods associated with these themes, as they apply to ecological assessment and conservation of animal populations. KEY FEATURES * Integrates population modeling, parameter estimation and * decision-theoretic approaches to management in a single, cohesive framework * Provides authoritative, state-of-the-art descriptions of quantitative * approaches to modeling, estimation and decision-making * Emphasizes the role of mathematical modeling in the conduct of science * and management * Utilizes a unifying biological context, consistent mathematical notation, * and numerous biological examples

Book↗

A new mathematical solution for predicting char activation reactions

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

Carbon↗

Three-dimensional trend mapping from wire-line logs

Mapping of lithofacies and porosities of stratigraphic units is complicated because these properties vary in three dimensions. The method of moments was proposed by Krumbein and Libby (1957) as a technique to aid in resolving this problem. Moments are easily computed from wireline logs and are simple statistics which summarize vertical variation in a log trace. Combinations of moment maps have proved useful in understanding vertical and lateral changes in lithology of sedimentary rock units. Although moments have meaning both as statistical descriptors and as mechanical properties, they also define polynomial curves which approximate lithologic changes as a function of depth. These polynomials can be fitted by least-squares methods, partitioning major trends in rock properties from finescale fluctuations. Analysis of variance yields the degree of fit of any polynomial and measures the proportion of vertical variability expressed by any moment or combination of moments. In addition, polynomial curves can be differentiated to determine depths at which pronounced expressions of facies occur and to determine the locations of boundaries between major lithologic subdivisions. Moments can be estimated at any location in an area by interpolating from log moments at control wells. A matrix algebra operation then converts moment estimates to coefficients of a polynomial function which describes a continuous curve of lithologic variation with depth. If this procedure is applied to a grid of geographic locations, the result is a model of variability in three dimensions. Resolution of the model is determined largely by number of moments used in its generation. The method is illustrated with an analysis of lithofacies in the Simpson Group of south-central Kansas; the three-dimensional model is shown as cross sections and slice maps. In this study, the gamma-ray log is used as a measure of shaliness of the unit. However, the method is general and can be applied, for example, to suites of neutron, density, or sonic logs to produce three-dimensional models of porosity in reservoir rocks. ?? 1985 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗

Flood characteristics of Oklahoma streams techniques for calculating magnitude and frequency of floods in Oklahoma, with compilations of flood data through 1971

The 2-, 5-, 10-, 25-, 50-, and 100-year recurrence interval floods are related to basin and climatic parameters for natural streams in Oklahoma by multiple regression techniques through the mathematical model, Q x =aA b S c P d , where Q x is peak discharge for recurrence interval x, A is contributing drainage area, S is main channel slope, P is mean annual precipitation, and a, b, c, and d are regression constants and coefficients. One equation for each recurrence interval applies statewide for all natural streams of less than 2,500 mil (6,500 km 2 ), except where manmade works, such as dams, flood-detention structures, levees, channelization, and urban development, appreciably affect flood runoff. The equations can be used to estimate flood frequency of a stream at an ungaged site if drainage area size, main channel slope, and mean annual precipitation are known. At or near gaged sites, a weighted average of the regression results and the gaging station data is recommended. Individual relations of flood magnitude to contributing drainage area are given for all or parts of the main stems of the Arkansas, Salt Fork Arkansas, Cimarron, North Canadian, Canadian, Washita, North Fork Red, and Red Rivers. Parts of some of these streams, and all of the Neosho and Verdigris Rivers are not included because the effects of. major regulation from large reservoirs cannot be evaluated within the scope of the report. Graphical relations of maximum floods of record for eastern and western Oklahoma provide a guide to maximum probable floods. A random sampling of the seasonal occurrence of floods indicated about two-thirds of all annual floods in Oklahoma occur during. April through July. Less than one-half of one percent of annual floods occur in December. A compilation of flood records at all gaging sites in Oklahoma and some selected sites in adjacent States is given in an appendix. Basin and climatic parameters and log-Pearson Type III frequency data and statistics are given for most station records. A second appendix gives a reprint of the U.S. Water Resources Council Bulletin 15 which describes procedures for fitting a log-Pearson Type III distribution to gaging station data.

Oklahoma↗

Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.

Mathematical Biosciences↗

Detection limits of quantitative and digital PCR assays and their influence in presence-absence surveys of environmental DNA

A set of universal guidelines is needed to determine the limit of detection (LOD) in PCR-based analyses of low concentration DNA. In particular, environmental DNA (eDNA) studies require sensitive and reliable methods to detect rare and cryptic species through shed genetic material in environmental samples. Current strategies for assessing detection limits of eDNA are either too stringent or subjective, possibly resulting in biased estimates of species’ presence. Here, a conservative LOD analysis grounded in analytical chemistry is proposed to correct for overestimated DNA concentrations predominantly caused by the concentration plateau, a nonlinear relationship between expected and measured DNA concentrations. We have used statistical criteria to establish formal mathematical models for both quantitative and droplet digital PCR. To assess the method, a new Grass Carp ( Ctenopharyngodon idella ) TaqMan assay was developed and tested on both PCR platforms using eDNA in water samples. The LOD adjustment reduced Grass Carp occupancy and detection estimates while increasing uncertainty – indicating that caution needs to be applied to eDNA data without LOD correction. Compared to quantitative PCR, digital PCR had higher occurrence estimates due to increased sensitivity and dilution of inhibitors at low concentrations. Without accurate LOD correction, species occurrence and detection probabilities based on eDNA estimates are prone to a source of bias that cannot be reduced by an increase in sample size or PCR replicates. Other applications also could benefit from a standardized LOD such as GMO food analysis, and forensic and clinical diagnostics.

Molecular Ecology Resources↗

Resource-driven pattern formation in consumer-resource systems with asymmetric dispersal on a plane

This paper considers resource-driven pattern formation in consumer-resource systems. Here, a planar pattern consists of many big patches, and a big patch can be regarded as combination of many patches on the plane. The consumer moves between patches asymmetrically, while the asymmetry is driven by the resource abundance. Based on experimental models with linearly-linked patches, we propose a planarly-linked-patch model with asymmetric dispersal. Using dynamical systems theory, we show global stability of equilibria in the model, and demonstrate how the resource-driven dispersal forms patterns. It is shown that appropriate asymmetry in dispersal would make the consumer persist in the system, even in sink patches. The asymmetry could also make the consumer’s total population abundance larger than that without dispersal. However, inappropriate asymmetry would make the consumer go into extinction, even in source patches. Dispersal rates are also shown to play a role in the persistence and abundance increase. Our results are consistent with experimental observations and provide new insights. Numerical simulations by the model reproduce various vegetation patterns in the real world. This work has potential applications in spatial pattern formation in biological research.

SIAM Journal on Applied Mathematics↗

United States geological survey's reserve-growth models and their implementation

The USGS has developed several mathematical models to forecast reserve growth of fields both in the United States (U.S.) and the world. The models are based on historical reserve growth patterns of fields in the U.S. The patterns of past reserve growth are extrapolated to forecast future reserve growth. Changes of individual field sizes through time are extremely variable, therefore, the reserve growth models take on a statistical approach whereby volumetric changes for populations of fields are used in the models. Field age serves as a measure of the field-development effort that is applied to promote reserve growth. At the time of the USGS World Petroleum Assessment 2000, a reserve growth model for discovered fields of the world was not available. Reserve growth forecasts, therefore, were made based on a model of historical reserve growth of fields of the U.S. To test the feasibility of such an application, reserve growth forecasts were made of 186 giant oil fields of the world (excluding the U.S. and Canada). In addition, forecasts were made for these giant oil fields subdivided into those located in and outside of Organization of Petroleum Exporting Countries (OPEC). The model provided a reserve-growth forecast that closely matched the actual reserve growth that occurred from 1981 through 1996 for the 186 fields as a whole, as well as for both OPEC and non-OPEC subdivisions, despite the differences in reserves definition among the fields of the U.S. and the rest of the world. ?? 2005 International Association for Mathematical Geology.

Conference Paper↗

Use of a reactive gas transport model to determine rates of hydrocarbon biodegradation in unsaturated porous media

A mathematical model is presented that simulates the transport and reaction of any number of gaseous phase constituents (e.g. CO 2 , O 2 , N 2 , and hydrocarbons) in unsaturated porous media. The model was developed as part of a method to determine rates of hydrocarbon biodegradation associated with natural cleansing at petroleum product spill sites. The one-dimensional model can be applied to analyze data from column experiments or from field sites where gas transport in the unsaturated zone is approximately vertical. A coupled, non-Fickian constitutive relation between fluxes and concentration gradients, together with the capability of incorporating heterogeneity with respect to model parameters, results in model applicability over a wide range of experimental and field conditions. When applied in a calibration mode, the model allows for the determination of constituent production/consumption rates as a function of the spatial coordinate. Alternatively, the model can be applied in a predictive mode to obtain the distribution of constituent concentrations and fluxes on the basis of assumed values of model parameters and a biodegradation hypothesis. Data requirements for the model are illustrated by analyzing data from a column experiment designed to determine the aerobic degradation rate of toluene in sediments collected from a gasoline spill site in Galloway Township, New Jersey.

Water Resources Research↗

Internal inconsistencies in dispersion-dominated models that incorporate chemical and microbial kinetics

Current understanding of transport processes in aquifers is limited by lack of precise point chemical concentration measurements. Recently, however, some careful measurements of vertical chemical concentration profiles have been made at several locations around the world that appear to support a consistent picture concerning the persistence of large vertical concentration gradients in aquifers and, by implication, the existence of very small vertical transverse dispersivities. These data were obtained in aquifers supporting microbial activity. Data analysis using a mathematical model which considers microbial degradation coupled to nutrient and oxygen transport indicates that a vertical transverse dispersivity on the order of 0.1 cm or less is consistent with the concentration gradients that were measured. The existence of such large gradients and low dispersivities is not consistent with the use of two-dimensional vertically averaged (areal) models as currently applied, especially if one is interested in the development of transport models with predictive capability beyond that associated with standard calibration and extrapolation. Even three-dimensional models with large vertical transverse dispersivities compared to those measured will produce results inconsistent with measurements. Microbial-chemical activity is very sensitive to concentration distributions. Smearing of the oxygen profile can result in the prediction of aerobic activity where, in fact, none exists.

Water Resources Research↗

Groundwater salinity mapping using geophysical log analysis within the Fruitvale and Rosedale Ranch oil fields, Kern County, California, USA

A method is presented for deriving a volume model of groundwater total dissolved solids (TDS) from borehole geophysical and aqueous geochemical measurements. While previous TDS mapping techniques have proved useful in the hydrogeologic setting in which they were developed, they may yield poor results in settings with lithological heterogeneity, complex water chemistry, or limited data. Problems arise because of assumed values for empirical constants in Archie’s Equation, unrealistic porosity and temperature gradients, or bicarbonate-rich groundwater. These issues become critical in complex geologic settings such as the San Joaquin Valley of California, USA. To address this, a method to map TDS in three dimensions is applied to the Fruitvale and Rosedale Ranch oil fields near Bakersfield, California. Borehole resistivity, porosity, and temperature data are used to derive TDS using Archie’s Equation, and are then kriged to interpolate TDS. Archie’s a and m (tortuosity factor and cementation exponent, respectively) are found by comparing model predictions, after kriging, to TDS measurements, and minimizing the differences via mathematical optimization. Contributions of abundant bicarbonate ions to TDS were corrected using an empirical model. This work was motivated by federal and state law requirements to monitor and protect underground sources of drinking water. Modeling shows the legally significant boundary of 10,000 ppm TDS is at ~1,067 m below sea level in Rosedale Ranch, and deepens into Fruitvale to ~1,341 m. Mapping groundwater TDS at this resolution reveals that TDS is primarily controlled by depth, recharge, stratigraphy, and in some places, by faulting and facies changes.

California↗

Native Prairie Adaptive Management: a multi region adaptive approach to invasive plant management on Fish and Wildlife Service owned native prairies

Much of the native prairie managed by the U.S. Fish and Wildlife Service (FWS) in the Prairie Pothole Region (PPR) of the northern Great Plains is extensively invaded by the introduced cool-season grasses, smooth brome ( Bromus inermis ) and Kentucky bluegrass ( Poa pratensis ). Management to suppress these invasive plants has had poor to inconsistent success. The central challenge to managers is selecting appropriate management actions in the face of biological and environmental uncertainties. In partnership with the FWS, the U.S. Geological Survey (USGS) developed an adaptive decision support framework to assist managers in selecting management actions under uncertainty and maximizing learning from management outcomes. This joint partnership is known as the Native Prairie Adaptive Management (NPAM) initiative. The NPAM decision framework is built around practical constraints faced by FWS refuge managers and includes identification of the management objective and strategies, analysis of uncertainty and construction of competing decision models, monitoring, and mechanisms for model feedback and decision selection. Nineteen FWS field stations, spanning four states of the PPR, have participated in the initiative. These FWS cooperators share a common management objective, available management strategies, and biological uncertainties. Though the scope is broad, the initiative interfaces with individual land managers who provide site-specific information and receive updated decision guidance that incorporates understanding gained from the collective experience of all cooperators. We describe the technical components of this approach, how the components integrate and inform each other, how data feedback from individual cooperators serves to reduce uncertainty across the whole region, and how a successful adaptive management project is coordinated and maintained on a large scale. During an initial scoping workshop, FWS cooperators developed a consensus management objective: increase the composition of native grasses and forbs on native sod while minimizing cost. Cooperators agreed that decision guidance should be provided annually and should account for local, real-time vegetation conditions observed on the ground. Over the course of development, two prototypes of the decision framework were considered. The final framework recognized four alternative actions that managers could take in any given year: (1) Graze—targeted use of grazing ungulates to achieve defoliation, (2) Burn—application of prescribed fire as the single form of defoliation, (3) Burn/Graze—a combination treatment, and (4) Rest—no action. The study area included northern mixed-grass and tallgrass prairie. Native vegetation in mixed–grass prairie has a strong cool-season component and thus the dominant native species have a phenology similar to that of smooth brome and Kentucky bluegrass, making management of those species challenging. In contrast, tallgrass prairie has a strong warm-season native component, leading to an existence of cool-season windows, periods of time in the fall and spring when cool‐season invasive grass species are actively growing and vulnerable to damage via select management actions, but warm‐season grass species are not active and are thus less susceptible to damage via the same actions. This dichotomy between prairie types necessitated the development of separate but parallel decision support systems for mixed-grass and tallgrass biomes. Management units are parcels of native prairie that receive a single management treatment at any one time over their entire extent. At any particular time, the vegetation state of each management unit is characterized by the amount of cover of native grasses and forbs and the type of invasive grass that is dominant. In addition, each unit has a defoliation state which reflects the number of years since the last defoliation event and an index to how intensively the unit was managed during the previous 7 years. State-transition models are used to predict the state of a management unit in year t+1 from its state in year t and a prescribed management action that was applied between the two monitoring events. Alternative models are built around key uncertainties that make choice of a management action difficult. Three uncertainties revolve around whether the effect of management actions depends on (1) type of dominant invader, (2) past defoliation history, and (3) level of invasion. Two additional uncertainties are considered when choosing a management action for tallgrass units: (4) the effectiveness of grazing within the cool-season window as a surrogate for burning when smooth brome is the dominant invader, and (5) the differential effect of active management outside the window as compared to rest. Because data on the probability of transitioning from one state to another under the various models were lacking, expert opinion and elicitation were used to parameterize the models. In addition, cooperators participated in elicitation exercises to extract their beliefs regarding the value of having native prairie compared to the cost of achieving it. Quantifying the subjective expression of utility in this way allowed for mathematical representation of the management objective into an objective function. By maximizing the objective function, cumulative utility is maximized, leading to the identification of a sequence of decisions that will achieve the management objective. The NPAM system adopted a vegetation monitoring protocol that was rapid, inexpensive, and familiar to many of the cooperators. The monitoring protocol served three purposes: (1) determining current vegetation and defoliation states of each unit, (2) evaluating progress toward the management objective, and (3) assessing predictive performance of the alternative models. The management year runs from September 1 to August 31. Management can be applied anytime during that period and monitoring takes places from late June to mid-August. Cooperators enter vegetation data and management information into a centralized database by August 25 of each year. Given the current state of the system (vegetation and defoliation states) and the current understanding of the system (or the belief state), identifying the current best management decision is a matter of looking up the combination (that is, system state and belief state) in the appropriate (mixed-grass or tallgrass) optimal decision table. Given complete uncertainty at the outset of decision-making, initial assignment of equal belief weights to each model was believed reasonable. The decisions in the optimal decision table that correspond to the current belief state constitute the current optimal decision policy. By August 31 of each year, individual cooperators are provided with a recommended management action for each of their management units for the upcoming management year. Upon receiving the management recommendations for their units, managers consider the recommendation, along with other relevant information, and at some point during the year one of the management alternatives is carried out. This iterative cycle of making and implementing a management decision, predicting the response, monitoring the outcome, comparing predicted and observed outcomes, updating model weights, and recommending a management action for the next cycle is expected to result in an accumulation of weight on a representative model of system dynamics, thereby increasing understanding needed to effectively manage native prairies. The NPAM system is now entering its second full year of complete operation, and represents one of only a few fully implemented applications of adaptive management within the U.S. Fish and Wildlife Service. NPAM is truly unique in that it originated from the ground up as a result of the leadership and steadfastness of several refuge biologists and managers confronted with a common problem. These biologists recognized that working together across a large landscape presented perhaps the best opportunity for halting and reversing the invasion of native grasslands by non-native cool-season grasses. Importantly, the NPAM system encapsulates the collective thinking and experience of tens if not hundreds of individuals who have battled this vexing problem for much of their careers. The NPAM initiative is rooted in principles of adaptive management, thereby affording the opportunity for grassland managers to pursue management objectives while acquiring information to reduce uncertainty and improve future management. The project introduced a number of technical innovations that will serve as templates for conservation efforts throughout and beyond the U.S. Fish and Wildlife Service. First, NPAM is an on-the-ground implementation of active adaptive management—possibly the first of its kind in conservation management—in which recommended management actions result from a prospective analysis of future learning (Williams, 1996). Second, by the use of dynamic optimization, NPAM demonstrates how decisions can be made that take into account possible future transitions of the system. Third, NPAM demonstrates how models of partial controllability are an effective means of accommodating unpredictable circumstances that cause a manager to follow a different course than was intended. Finally, the database developed for NPAM is an unparalleled system that enables the rapid integration of data from the field for the generation of ‘just-in-time’ management recommendations. In all, NPAM provides an example of how a science-management partnership can be forged to achieve large-scale conservation objectives.

Minnesota;Montana;North Dakota;South Dakota↗

Modeling protected species distributions and habitats to inform siting and management of pioneering ocean industries: A case study for Gulf of Mexico aquaculture

Marine Spatial Planning (MSP) provides a process that uses spatial data and models to evaluate environmental, social, economic, cultural, and management trade-offs when siting (i.e., strategically locating) ocean industries. Aquaculture is the fastest-growing food sector in the world. The United States (U.S.) has substantial opportunity for offshore aquaculture development given the size of its exclusive economic zone, habitat diversity, and variety of candidate species for cultivation. However, promising aquaculture areas overlap many protected species habitats. Aquaculture siting surveys, construction, operations, and decommissioning can alter protected species habitat and behavior. Additionally, aquaculture-associated vessel activity, underwater noise, and physical interactions between protected species and farms can increase the risk of injury and mortality. In 2020, the U.S. Gulf of Mexico was identified as one of the first regions to be evaluated for offshore aquaculture opportunities as directed by a Presidential Executive Order. We developed a transparent and repeatable method to identify aquaculture opportunity areas (AOAs) with the least conflict with protected species. First, we developed a generalized scoring approach for protected species that captures their vulnerability to adverse effects from anthropogenic activities using conservation status and demographic information. Next, we applied this approach to data layers for eight species listed under the Endangered Species Act, including five species of sea turtles, Rice’s whale, smalltooth sawfish, and giant manta ray. Next, we evaluated four methods for mathematically combining scores (i.e., Arithmetic mean, Geometric mean, Product, Lowest Scoring layer) to generate a combined protected species data layer. The Product approach provided the most logical ordering of, and the greatest contrast in, site suitability scores. Finally, we integrated the combined protected species data layer into a multi-criteria decision-making modeling framework for MSP. This process identified AOAs with reduced potential for protected species conflict. These modeling methods are transferable to other regions, to other sensitive or protected species, and for spatial planning for other ocean-uses.

PLoS ONE↗