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Results for “Applied Mathematical Modelling”

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At least 37 records · Page 2Linked to original sources
USGS2018

N-mix for fish: estimating riverine salmonid habitat selection via N-mixture models

Models that formulate mathematical linkages between fish use and habitat characteristics are applied for many purposes. For riverine fish, these linkages are often cast as resource selection functions with variables including depth and velocity of water and distance to nearest cover. Ecologists are now recognizing the role that detection plays in observing organisms, and failure to account for imperfect detection can lead to spurious inference. Herein, we present a flexible N-mixture model to associate habitat characteristics with the abundance of riverine salmonids that simultaneously estimates detection probability. Our formulation has the added benefits of accounting for demographics variation and can generate probabilistic statements regarding intensity of habitat use. In addition to the conceptual benefits, model application to data from the Trinity River, California, yields interesting results. Detection was estimated to vary among surveyors, but there was little spatial or temporal variation. Additionally, a weaker effect of water depth on resource selection is estimated than that reported by previous studies not accounting for detection probability. N-mixture models show great promise for applications to riverine resource selection.

Canadian Journal of Fisheries and Aquatic Sciences↗
USGS2013

The SAFRR tsunami scenario-physical damage in California: Chapter E in The SAFRR (Science Application for Risk Reduction) Tsunami Scenario

his chapter attempts to depict a single realistic outcome of the SAFRR (Science Application for Risk Reduction) tsunami scenario in terms of physical damage to and recovery of various aspects of the built environment in California. As described elsewhere in this report, the tsunami is generated by a hypothetical magnitude 9.1 earthquake seaward of the Alaska Peninsula on the Semidi Sector of the Alaska–Aleutian Subduction Zone, 495 miles southwest of Anchorage, at 11:50 a.m. Pacific Daylight Time (PDT) on Thursday March 27, 2014, and arriving at the California coast between 4:00 and 5:40 p.m. (depending on location) the same day. Although other tsunamis could have locally greater impact, this source represents a substantial threat to the state as a whole. One purpose of this chapter is to help operators and users of coastal assets throughout California to develop emergency plans to respond to a real tsunami. Another is to identify ways that operators or owners of these assets can think through options for reducing damage before a future tsunami. A third is to inform the economic analyses for the SAFRR tsunami scenario. And a fourth is to identify research needs to better understand the possible consequences of a tsunami on these assets. The asset classes considered here include the following: Piers, cargo, buildings, and other assets at the Ports of Los Angeles and Long Beach Large vessels in the Ports of Los Angeles and Long Beach Marinas and small craft Coastal buildings Roads and roadway bridges Rail, railway bridges, and rolling stock Agriculture Fire following tsunami Each asset class is examined in a subsection of this chapter. In each subsection, we generally attempt to offer a historical review of damage. We characterize and quantify the assets exposed to loss and describe the modes of damage that have been observed in past tsunamis or are otherwise deemed likely to occur in the SAFRR tsunami scenario. Where practical, we offer a mathematical model of the damageability of assets exposed to loss. Then, applying the damageability model and the velocity, wave amplitude, and inundation models discussed in other SAFRR chapters we offer a single realistic depiction of damage. Other outcomes are of course possible for this hypothetical event. Where practical we estimate repair costs and estimate the duration required to restore the assets to their pre-tsunami condition. We identify opportunities to enhance the resiliency of the assets, either through making them less vulnerable to damage or able to recover more quickly in spite of the damage. Finally, we identify uncertainties in the modeling where research would improve our understanding of the underlying mechanisms of damage and loss or otherwise improve our ability to estimate the future impacts of tsunamis and inform risk-management decisions for tsunamis. However, it is certain that the kinds of damages discussed here have occurred in past tsunamis, even in developed nations, and in a sufficiently large event, will occur in California. Our uncertainties can operate in either direction, either leading to an overestimate of damage or an underestimate. Therefore, losses in an actual future tsunami could be greater than depicted here. Furthermore this evaluation is not intended to be an exhaustive depiction of what could happen in this or similar tsunamis. Other impacts could occur that are not presented here.

California↗
USGS2021

The application of ensemble wave forcing to quantify uncertainty of shoreline change predictions

Reliable predictions and accompanying uncertainty estimates of coastal evolution on decadal to centennial time scales are increasingly sought. So far, most coastal change projections rely on a single, deterministic realization of the unknown future wave climate, often derived from a global climate model. Yet, deterministic projections do not account for the stochastic nature of future wave conditions across a variety of temporal scales (e.g., daily, weekly, seasonally, and interannually). Here, we present an ensemble Kalman filter shoreline change model to predict coastal erosion and uncertainty due to waves at a variety of time scales. We compare shoreline change projections, simulated with and without ensemble wave forcing conditions by applying ensemble wave time series produced by a computationally efficient statistical downscaling method. We demonstrate a sizable (site-dependent) increase in model uncertainty compared with the unrealistic case of model projections based on a single, deterministic realization (e.g., a single time series) of the wave forcing. We support model-derived uncertainty estimates with a novel mathematical analysis of ensembles of idealized process models. Here, the developed ensemble modeling approach is applied to a well-monitored beach in Tairua, New Zealand. However, the model and uncertainty quantification techniques derived here are generally applicable to a variety of coastal settings around the world.

JGR Earth Surface↗
USGS2007

Biodegradation of PAHs and PCBs in soils and sludges

Results from a multi-year, pilot-scale land treatment project for PAHs and PCBs biodegradation were evaluated. A mathematical model, capable of describing sorption, sequestration, and biodegradation in soil/water systems, is applied to interpret the efficacy of a sequential active-passive biotreatment process of organic chemicals on remediation sites. To account for the recalcitrance of PAHs and PCBs in soils and sludges during long-term biotreatment, this model comprises a kinetic equation for organic chemical intraparticle sequestration process. Model responses were verified by comparison to measurements of biodegradation of PAHs and PCBs in land treatment units; a favorable match was found between them. Model simulations were performed to predict on-going biodegradation behavior of PAHs and PCBs in land treatment units. Simulation results indicate that complete biostabilization will be achieved when the concentration of reversibly sorbed chemical (S RA) reduces to undetectable levels, with a certain amount of irreversibly sequestrated residual chemical (S IA) remaining within the soil particle solid phase. The residual fraction (S IA) tends to lose its original chemical and biological activity, and hence, is much less available, toxic, and mobile than the "free" compounds. Therefore, little or no PAHs and PCBs will leach from the treatment site and constitutes no threat to human health or the environment. Biotreatment of PAHs and PCBs can be terminated accordingly. Results from the pilot-scale testing data and model calculations also suggest that a significant fraction (10-30%) of high-molecular-weight PAHs and PCBs could be sequestrated and become unavailable for biodegradation. Bioavailability (large K d , i.e., slow desorption rate) is the key factor limiting the PAHs degradation. However, both bioavailability and bioactivity (K in Monod kinetics, i.e., number of microbes, nutrients, and electron acceptor, etc.) regulate PCBs biodegradation. The sequential active-passive biotreatment can be a cost-effective approach for remediation of highly hydrophobic organic contaminants. The mathematical model proposed here would be useful in the design and operation of such organic chemical biodegradation processes on remediation sites. ?? 2007 Springer Science+Business Media B.V.

Water, Air, & Soil Pollution↗
USGS2011

The fate and transport of nitrate in shallow groundwater in northwestern Mississippi, USA

Agricultural contamination of groundwater in northwestern Mississippi, USA, has not been studied extensively, and subsurface fluxes of agricultural chemicals have been presumed minimal. To determine the factors controlling transport of nitrate-N into the Mississippi River Valley alluvial aquifer, a study was conducted from 2006 to 2008 to estimate fluxes of water and solutes for a site in the Bogue Phalia basin (1,250 km 2 ). Water-quality data were collected from a shallow water-table well, a vertical profile of temporary sampling points, and a nearby irrigation well. Nitrate was detected within 4.4 m of the water table but was absent in deeper waters with evidence of reducing conditions and denitrification. Recharge estimates from 6.2 to 10.9 cm/year were quantified using water-table fluctuations, a Cl – tracer method, and atmospheric age-tracers. A mathematical advection-reaction model predicted similar recharge to the aquifer, and also predicted that 15% of applied nitrogen is leached into the saturated zone. With current denitrification and application rates, the nitrate-N front is expected to remain in shallow groundwater, less than 6–9 m deep. Increasing application rates resulting from intensifying agricultural demands may advance the nitrate-N front to 16–23 m, within the zone of groundwater pumping.

Mississippi↗
USGS2013

Numerical flow models and their calibration using tracer based ages

Any estimate of ‘age’ of a groundwater sample based on environmental tracers requires some form of geochemical model to interpret the tracer chemistry (chapter 3) and is, therefore, referred to in this chapter as a tracer model age. the tracer model age of a groundwater sample can be useful for obtaining information on the residence time and replenishment rate of an aquifer system, but that type of data is most useful when it can be incorporated with all other information that is known about the groundwater system under study. groundwater fl ow models are constructed of aquifer systems because they are usually the best way of incorporating all of the known information about the system in the context of a mathematical framework that constrains the model to follow the known laws of physics and chemistry as they apply to groundwater flow and transport. It is important that the purpose or objective of the study be identified first before choosing the type and complexity of the model to be constructed, and to make sure such a model is necessary. The purpose of a modelling study is most often to characterize the system within a numerical framework, such that the hydrological responses of the system can be tested under potential stresses that might be imposed given future development scenarios. As this manual discusses dating as it applies to old groundwater, most readers are likely to be interested in studying regional groundwater flow systems and their water resource potential.

Book chapter↗
USGS2007

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model - that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable. ?? 2007 Society of Exploration Geophysicists.

Geophysics↗
USGS1980

The influences of land use and land cover on climate; an analysis of the Washington-Baltimore area that couples remote sensing with numerical simulation

The Sun drives the atmospheric heat engine by warming the terrestrial surface which in turn warms the atmosphere above. Climate, therefore, is significantly controlled by complex interaction of energy flows near and at the terrestrial surface. When man alters this delicate energy balance by his use of the land, he may alter his climatic environment as well. Land use climatology has emerged as a discipline in which these energy interactions are studied; first, by viewing the spatial distributions of their surface manifestations, and second, by analyzing the energy exchange processes involved. Two new tools for accomplishing this study are presented: one that can interpret surface energy exchange processes from space, and another that can simulate the complex of energy transfers by a numerical simulation model. Use of a satellite-borne multispectral scanner as an imaging radiometer was made feasible by devising a gray-window model that corrects measurements made in space for the effects of the atmosphere in the optical path. The simulation model is a combination of mathematical models of energy transfer processes at or near the surface. Integration of these two analytical approaches was applied to the Washington-Baltimore area to coincide with the August 5, 1973, Skylab 3 overpass which provided data for constructing maps of the energy characteristics of the Earth's surface. The use of the two techniques provides insights into the relationship of climate to land use and land cover and in predicting alterations of climate that may result from alterations of the land surface.

Professional Paper↗
USGS1962

Theory of aquifer tests

The development of water supplies from wells was placed on a rational basis with Darcy's development of the law governing the movement of fluids through sands and with Dupuit's application of that law to the problem of radial flow toward a pumped well. As field experience increased, confidence in the applicability of quantitative methods was gained and interest in developing solutions for more complex hydrologic problems was stimulated. An important milestone was Theis' development in 1935 of a solution for the nonsteady flow of ground water, which enabled hydrologists for the first time to predict future changes in ground-water levels resulting from pumping or recharging of wells. In the quarter century since, quantitative ground-water hydrology has been enlarging so rapidly as to discourage the preparation of comprehensive textbooks. This report surveys developments in fluid mechanics that apply to groundwater hydrology. It emphasizes concepts and principles, and the delineation of limits of applicability of mathematical models for analysis of flow systems in the field. It stresses the importance of the geologic variable and its role in governing the flow regimen. The report discusses the origin, occurrence, and motion of underground water in relation to the development of terminology and analytic expressions for selected flow systems. It describes the underlying assumptions necessary for mathematical treatment of these flow systems, with particular reference to the way in which the assumptions limit the validity of the treatment.

Water Supply Paper↗
USGS2011

Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

Eos, Earth and Space Science News↗
USGS1977

Digital model of the Arikaree Aquifer near Wheatland, southeastern Wyoming

A digital model that mathematically simulates the flow of ground water, approximating the flow system as two-dimensional, has been applied to predict the long-term effects of irrigation and proposed industrial pumping from the unconfined Arikaree aquifer in a 400 square-mile area in southeastern Wyoming. Three cases that represent projected maximum, mean, and minimum combined irrigation and industrial ground-water withdrawals at annual rates of 16,176, 11,168, and 6,749 acre-feet, respectively, were considered. Water-level declines of more than 5 feet over areas of 124, 120, and 98 square miles and depletions in streamflow of 14.4, 8.9, and 7.2 cfs from the Laramie and North Laramie Rivers were predicted to occur at the end of a 40-year simulation period for these maximum, mean, and minimum withdrawal rates, respectively. A tenfold incrase in the vertical hydraulic conductivity that was assumed for the streambeds results in smaller predicted drawdowns near the Laramie and North Laramie Rivers and a 36 percent increase in the predicted depletion in streamflow for the North Laramie River. (Woodard-USGS)

Open-File Report↗
USGS2017

A general modeling framework for describing spatially structured population dynamics

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network-based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life-history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network-based population is modeled with discrete time steps. Using both theoretical and real-world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network-based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles

Ecology and Evolution↗
USGS1992

Mass-conserving method of characteristics for streamflow modeling

A robust numerical model is presented for the computation of unsteady streamflow on steep river slopes. The one-dimensional model uses the method of characteristics on a specified space-time grid to solve the Saint-Venant equations. An additional continuity equation requirement on each space-time element provides greatly improved conservation of mass over traditional implementations of the method of characteristics on a fixed grid. The space-time geometry of the problem is described in a finite element setting. Hermite interpolation of channel parameters is used to avoid numerical difficulties that may occur with steep slopes due to discontinuities in the derivatives of data such as channel top width. Manning's equation for friction slope can be modified by a factor to make the slope more appropriate for steep rivers. The standard Manning's friction slope can also be used, if preferred. The computer model is not restricted to steep slopes, and applies as well to gently sloping streams. Two numerical examples support the mathematical approach and computational algorithm.

Water Supply Paper↗
USGS1998

Estimating formation properties from early-time recovery in wells subject to turbulent head losses

A mathematical model is developed to interpret the early-time recovering water level following the termination of pumping in wells subject to turbulent head losses. The model assumes that turbulent head losses dissipate immediately when pumping ends. In wells subject to both borehole storage and turbulent head losses, the early-time recovery exhibits a slope equal to 1/2 on log-log plots of the recovery versus time. This half-slope response should not be confused with the half-slope response associated with a linear flow regime during aquifer tests. The presence of a borehole skin due to formation damage or stimulation around the pumped well alters the early-time recovery in wells subject to turbulent head losses and gives the appearance of borehole storage, where the recovery exhibits a unit slope on log-log plots of recovery versus time. Type curves can be used to estimate the formation storafivity from the early-time recovery data. In wells that are suspected of having formation damage or stimulation, the type curves can be used to estimate the 'effective' radius of the pumped well, if an estimate of the formation storativity is available from observation wells or other information. Type curves for a homogeneous and isotropic dual-porosity aquifer are developed and applied to estimate formation properties and the effect of formation stimulation from a single-well test conducted in the Madison limestone near Rapid City, South Dakota.A mathematical model is developed to interpret the early-time recovering water level following the termination of pumping in wells subject to turbulent head losses. The model assumes that turbulent head losses dissipate immediately when pumping ends. In wells subject to both borehole storage and turbulent head losses, the early-time recovery exhibits a slope equal to 1/2 on log-log plots of the recovery versus time. This half-slope response should not be confused with the half-slope response associated with a linear flow regime during aquifer tests. The presence of a borehole skin due to formation damage or stimulation around the pumped well alters the early-time recovery in wells subject to turbulent head losses and gives the appearance of borehole storage, where the recovery exhibits a unit slope on log-log plots of recovery versus time. Type curves can be used to estimate the formation storativity from the early-time recovery data. In wells that are suspected of having formation damage or stimulation, the type curves can be used to estimate the `effective' radius of the pumped well, if an estimate of the formation storativity is available from observation wells or other information. Type curves for a homogeneous and isotropic dual-porosity aquifer are developed and applied to estimate formation properties and the effect of formation stimulation from a single-well test conducted in the Madison limestone near Rapid City, South Dakota.

Journal of Hydrology↗
USGS2009

Why are diverse relationships observed between phytoplankton biomass and transport time?

Transport time scales such as flushing time and residence time are often used to explain variability in phytoplankton biomass. In many cases, empirical data are consistent with a positive phytoplankton‐transport time relationship (i.e., phytoplankton biomass increases as transport time increases). However, negative relationships, varying relationships, or no significant relationship may also be observed. We present a simple conceptual model, in both mathematical and graphical form, to help explain why phytoplankton may have a range of relationships with transport time, and we apply it to several real systems. The phytoplankton growth‐loss balance determines whether phytoplankton biomass increases with, decreases with, or is insensitive to transport time. If algal growth is faster than loss (e.g., grazing, sedimentation), then phytoplankton biomass increases with increasing transport time. If loss is faster than growth, phytoplankton biomass decreases with increasing transport time. If growth and loss are approximately balanced, then phytoplankton biomass is relatively insensitive to transport time. In analyses of several systems, portions of an individual system, or time periods, apparent insensitivity of phytoplankton biomass to changes in transport time could arise due to the superposition of cases with different phytoplankton‐transport time relationships. Thus, in order to understand or predict responses of phytoplankton biomass to changes in transport time, the relative rates of algal growth and loss must be known.

Limnology and Oceanography↗
USGS2025

The transition from resistance to acceptance: Managing a marine invasive species in a changing world

Marine invasive species can transform coastal ecosystems, yet mitigating their effects can be difficult, and even impractical. Often, marine invasive species are managed at poorly matched spatial scales, and at the same time, rates of spread and establishment are increasing under climate change and can outpace resources available for population suppression. These circumstances challenge traditional conservation goals of maintaining a historic environmental state, especially for a species like the European green crab ( Carcinus maenas ), a formidable invader with few examples of successful long-term removal programs. A management paradigm where decision alternatives include resisting or accepting a new ecological trajectory may be needed. We apply mathematical concepts from decision theory to develop a quantitative framework for navigating management decisions in this new resist-accept paradigm. We develop a model of European green crab growth, removal and colonization, and we find optimal levels of removal effort that minimize both ecological change and removal cost. We establish a benchmark of colonization pressure at which green crab density becomes decoupled from a decision maker's actions, such that population control can no longer shape the invasion trajectory. For informing the decision boundary between resistance and acceptance, our results highlight that a decision maker's understanding of how removal cost scales with removal effort is more important than understanding the density-impact relationship. We show that assuming stationary system dynamics can result in sub-optimal levels of species removal effort, highlighting the importance of developing anticipatory management strategies by accounting for non-stationary dynamics. Policy implications . For marine invasive species that can disperse across long distances and recolonize rapidly after removal, the focus of conservation policy should shift away from understanding how to resist change to understanding when to stop resisting change. Navigating this decision problem involves trade-offs among competing objectives, highlighting the need for structured approaches to elicit objective weights that reflect the values of the decision maker. For natural resource managers facing possible ecosystem transformation, this decision framework can enable proactive and strategic decisions made under uncertainty in a changing world.

Journal of Applied Ecology↗
USGS2012

Modeling of multiphase multicontaminant transport in the subsurface

This review addresses modeling of subsurface hydrological systems in which contaminants are transported in more than one fluid phase. The primary focus is on problems involving nonaqueous-phase liquids (NAPLs), a dynamic gas phase, or both, so that the unsaturated and saturated zones are both discussed. Basic research in simpler settings is included if it develops concepts that could be applied in modeling of such problems. Recent developments in practical models are reviewed, along with experimental work and theoretical issues related to the formulation of mathematical models. It will be seen that the extent of validity of the local equilibrium assumption (LEA) for component partitioning among phases is a major question influencing the direction of these formulations. Also emphasized are upscaling to macroscopic and grid lengths, and the choice and coupling of primary variables in multicomponent systems. Relations to and possible use of developments in petroleum reservoir simulation are discussed.

Reviews of Geophysics↗
USGS2014

Using mark-recapture distance sampling methods on line transect surveys

Mark–recapture distance sampling (MRDS) methods are widely used for density and abundance estimation when the conventional DS assumption of certain detection at distance zero fails, as they allow detection at distance zero to be estimated and incorporated into the overall probability of detection to better estimate density and abundance. However, incorporating MR data in DS models raises survey and analysis issues not present in conventional DS. Conversely, incorporating DS assumptions in MR models raises issues not present in conventional MR. As a result, being familiar with either conventional DS methods or conventional MR methods does not on its own put practitioners in good a position to apply MRDS methods appropriately. This study explains the sometimes subtly different varieties of MRDS survey methods and the associated concepts underlying MRDS models. This is done as far as possible without giving mathematical details – in the hope that this will make the key concepts underlying the methods accessible to a wider audience than if we were to present the concepts via equations. We illustrate use of the two main types of MRDS model by using data collected on two different types of survey: a survey of ungulate faecal pellets where two observers searched independently of each other; and a cetacean survey that used a search protocol that could accommodate responsive movement, with only one observer searching independently and the other being aware of all detections. Synthesis and applications . Mark–recapture DS is a widely used method for estimating animal density and abundance when detection of animals at distance zero is not certain. Two observer configurations and three statistical models are described, and it is important to choose the most appropriate model for the observer configuration and target species in question. By way of making the methods more accessible to practicing ecologists, we describe the key ideas underlying MRDS methods, the sometimes subtle differences between them, and we illustrate these by applying different kinds of MRDS method to surveys of two different target species using different survey configurations.

Methods in Ecology and Evolution↗