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At least 73 records · Page 4Linked to original sources

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

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

Landslide disparities, flume discoveries, and Oso despair

Landslide dynamics is the branch of science that seeks to understand the motion of landslides by applying Newton's laws. This memoir focusses on a 40‐year effort to understand motion of highly mobile—and highly lethal—landslides such as debris avalanches and debris flows. A major component of this work entailed development and operation of the U.S. Geological Survey debris flow flume, a unique, large‐scale experimental facility in Oregon. Experiments there yielded new insights that informed development of mathematical models that were aimed not only at explaining landslide dynamics but also at evaluating landslide and debris flow hazards. The most sophisticated of these models, called D‐Claw, found its first practical application during investigations of the 2014 Oso, Washington, landslide disaster. That event provided indelible lessons about the utility and sociology of science in the real world.

Washington

Uncertainty estimation for resource assessment-an application to coal

The U.S. Geological Survey is conducting a national assessment of coal resources. As part of that assessment, a geostatistical procedure has been developed to estimate the uncertainty of coal resources for the historical categories of geological assurance: measured, indicated, inferred, and hypothetical coal. Data consist of spatially clustered coal thickness measurements from coal beds and/or zones that cover, in some cases, several thousand square kilometers. Our procedure involved trend removal, an examination of spatial correlation, computation of a sample semivariogram, and fitting a semivariogram model. This model provided standard deviations for the uncertainty estimates. The number of sample points (drill holes) in each historical category also was estimated. Measurement error in the thickness of the coal bed/zone was obtained from the fitted model or supplied exogenously. From this information approximate estimates of uncertainty on the historical categories were computed. We illustrate the methodology using drill hole data from the Harmon coal bed located in southwestern North Dakota. The methodology will be applied to approximately 50 coal data sets.

Mathematical Geology

Performance assessments of nuclear waste repositories: A dialogue on their value and limitations

Performance Assessment (PA) is the use of mathematical models to simulate the long-term behavior of engineered and geologic barriers in a nuclear waste repository; methods of uncertainty analysis are used to assess effects of parametric and conceptual uncertainties associated with the model system upon the uncertainty in outcomes of the simulation. PA is required by the U.S. Environmental Protection Agency as part of its certification process for geologic repositories for nuclear waste. This paper is a dialogue to explore the value and limitations of PA. Two “skeptics” acknowledge the utility of PA in organizing the scientific investigations that are necessary for confident siting and licensing of a repository; however, they maintain that the PA process, at least as it is currently implemented, is an essentially unscientific process with shortcomings that may provide results of limited use in evaluating actual effects on public health and safety. Conceptual uncertainties in a PA analysis can be so great that results can be confidently applied only over short time ranges, the antithesis of the purpose behind long-term, geologic disposal. Two “proponents” of PA agree that performance assessment is unscientific, but only in the sense that PA is an engineering analysis that uses existing scientific knowledge to support public policy decisions, rather than an investigation intended to increase fundamental knowledge of nature; PA has different goals and constraints than a typical scientific study. The “proponents” describe an ideal, sixstep process for conducting generalized PA, here called probabilistic systems analysis (PSA); they note that virtually all scientific content of a PA is introduced during the model-building steps of a PSA, they contend that a PA based on simple but scientifically acceptable mathematical models can provide useful and objective input to regulatory decision makers. The value of the results of any PA must lie between these two views and will depend on the level of knowledge of the site, the degree to which models capture actual physical and chemical processes, the time over which extrapolations are made, and the proper evaluation of health risks attending implementation of the repository. The challenge is in evaluating whether the quality of the PA matches the needs of decision makers charged with protecting the health and safety of the public.

Risk Analysis

Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback

This paper studies a parsimonious model of landslide motion, which consists of the one-dimensional diffusion equation (for pore pressure) coupled through a boundary condition to a first-order ODE (Newton's second law). Velocity weakening of sliding friction gives rise to nonlinearity in the model. Analysis shows that solutions of the model equations exhibit a subcritical Hopf bifurcation in which stable, steady sliding can transition to cyclical, stick-slip motion. Numerical computations confirm the analytical predictions of the parameter values at which bifurcation occurs. The existence of stick-slip behavior in part of the parameter space is particularly noteworthy because, unlike stick-slip behavior in classical models , here it arises in the absence of a reversible (elastic) driving force. Instead, the driving force is static (gravitational), mediated by the effects of pore-pressure diffusion on frictional resistance.

SIAM Journal on Applied Mathematics

Bayesian multimodel inference for dose-response studies

Statistical inference in dose-response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose-response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Environmental Toxicology and Chemistry

Multi-state succession in wetlands: a novel use of state and transition models

The complexity of ecosystems and mechanisms of succession are often simplified by linear and mathematical models used to understand and predict system behavior. Such models often do not incorporate multivariate, nonlinear feedbacks in pattern and process that include multiple scales of organization inherent within real-world systems. Wetlands are ecosystems with unique, nonlinear patterns of succession due to the regular, but often inconstant, presence of water on the landscape. We develop a general, nonspatial state and transition (S and T) succession conceptual model for wetlands and apply the general framework by creating annotated succession/management models and hypotheses for use in impact analysis on a portion of an imperiled wetland. The S and T models for our study area, Water Conservation Area 3A South (WCA3), Florida, USA, included hydrologic and peat depth values from multivariate analyses and classification and regression trees. We used the freeware Vegetation Dynamics Development Tool as an exploratory application to evaluate our S and T models with different management actions (equal chance [a control condition], deeper conditions, dry conditions, and increased hydrologic range) for three communities: slough, sawgrass ( Cladium jamaicense ), and wet prairie. Deeper conditions and increased hydrologic range behaved similarly, with the transition of community states to deeper states, particularly for sawgrass and slough. Hydrology is the primary mechanism for multi-state transitions within our study period, and we show both an immediate and lagged effect on vegetation, depending on community state. We consider these S and T succession models as a fraction of the framework for the Everglades. They are hypotheses for use in adaptive management, represent the community response to hydrology, and illustrate which aspects of hydrologic variability are important to community structure. We intend for these models to act as a foundation for further restoration management and experimentation which will refine transition and threshold concepts.

Florida

Effects of dispersal on total biomass in a patchy, heterogeneous system: Analysis and experiment

An intriguing recent result from mathematics is that a population diffusing at an intermediate rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. We extended the current mathematical theory to apply to logistic growth and also showed that the result applies to patchy systems with dispersal among patches, both for continuous and discrete time. This allowed us to make specific predictions, through simulations, concerning the biomass dynamics, which were verified by a laboratory experiment. The experiment was a study of biomass growth of duckweed ( Lemna minor Linn.), where the resources (nutrients added to water) were distributed homogeneously among a discrete series of water-filled containers in one treatment, and distributed heterogeneously in another treatment. The experimental results showed that total biomass peaked at an intermediate, relatively low, diffusion rate, higher than the total carrying capacity of the system and agreeing with the simulation model. The implications of the experiment to dynamics of source, sink, and pseudo-sink dynamics are discussed.

Mathematical Biosciences

Approaches to highly parameterized inversion: A guide to using PEST for model-parameter and predictive-uncertainty analysis

Analysis of the uncertainty associated with parameters used by a numerical model, and with predictions that depend on those parameters, is fundamental to the use of modeling in support of decisionmaking. Unfortunately, predictive uncertainty analysis with regard to models can be very computationally demanding, due in part to complex constraints on parameters that arise from expert knowledge of system properties on the one hand (knowledge constraints) and from the necessity for the model parameters to assume values that allow the model to reproduce historical system behavior on the other hand (calibration constraints). Enforcement of knowledge and calibration constraints on parameters used by a model does not eliminate the uncertainty in those parameters. In fact, in many cases, enforcement of calibration constraints simply reduces the uncertainties associated with a number of broad-scale combinations of model parameters that collectively describe spatially averaged system properties. The uncertainties associated with other combinations of parameters, especially those that pertain to small-scale parameter heterogeneity, may not be reduced through the calibration process. To the extent that a prediction depends on system-property detail, its postcalibration variability may be reduced very little, if at all, by applying calibration constraints; knowledge constraints remain the only limits on the variability of predictions that depend on such detail. Regrettably, in many common modeling applications, these constraints are weak. Though the PEST software suite was initially developed as a tool for model calibration, recent developments have focused on the evaluation of model-parameter and predictive uncertainty. As a complement to functionality that it provides for highly parameterized inversion (calibration) by means of formal mathematical regularization techniques, the PEST suite provides utilities for linear and nonlinear error-variance and uncertainty analysis in these highly parameterized modeling contexts. Availability of these utilities is particularly important because, in many cases, a significant proportion of the uncertainty associated with model parameters-and the predictions that depend on them-arises from differences between the complex properties of the real world and the simplified representation of those properties that is expressed by the calibrated model. This report is intended to guide intermediate to advanced modelers in the use of capabilities available with the PEST suite of programs for evaluating model predictive error and uncertainty. A brief theoretical background is presented on sources of parameter and predictive uncertainty and on the means for evaluating this uncertainty. Applications of PEST tools are then discussed for overdetermined and underdetermined problems, both linear and nonlinear. PEST tools for calculating contributions to model predictive uncertainty, as well as optimization of data acquisition for reducing parameter and predictive uncertainty, are presented. The appendixes list the relevant PEST variables, files, and utilities required for the analyses described in the document.

Michigan