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USGS2021

Bayesian modeling can facilitate adaptive management in restoration

There is an urgent need for near-term predictions of ecological restoration outcomes despite imperfect knowledge of ecosystems. Restoration outcomes are always uncertain but integrating Bayesian modeling into the process of adaptive management allows researchers and practitioners to explicitly incorporate prior knowledge of ecosystems into future predictions. Although barriers exist, employing qualitative expert knowledge and previous case studies can help narrow the range of uncertainty in forecasts. Software and processes that allow for repeatable methodologies can help bridge the existing gap between theory and application of Bayesian methods in adaptive management.

Restoration Ecology↗

USGS2012

An accessible method for implementing hierarchical models with spatio-temporal abundance data

A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.

PLoS ONE↗

USGS2002

Hierarchical modeling of population stability and species group attributes from survey data

Many ecological studies require analysis of collections of estimates. For example, population change is routinely estimated for many species from surveys such as the North American Breeding Bird Survey (BBS), and the species are grouped and used in comparative analyses. We developed a hierarchical model for estimation of group attributes from a collection of estimates of population trend. The model uses information from predefined groups of species to provide a context and to supplement data for individual species; summaries of group attributes are improved by statistical methods that simultaneously analyze collections of trend estimates. The model is Bayesian; trends are treated as random variables rather than fixed parameters. We use Markov Chain Monte Carlo (MCMC) methods to fit the model. Standard assessments of population stability cannot distinguish magnitude of trend and statistical significance of trend estimates, but the hierarchical model allows us to legitimately describe the probability that a trend is within given bounds. Thus we define population stability in terms of the probability that the magnitude of population change for a species is less than or equal to a predefined threshold. We applied the model to estimates of trend for 399 species from the BBS to estimate the proportion of species with increasing populations and to identify species with unstable populations. Analyses are presented for the collection of all species and for 12 species groups commonly used in BBS summaries. Overall, we estimated that 49% of species in the BBS have positive trends and 33 species have unstable populations. However, the proportion of species with increasing trends differs among habitat groups, with grassland birds having only 19% of species with positive trend estimates and wetland birds having 68% of species with positive trend estimates.

Ecology↗

USGS2005

Assessing uncertainty in ecological systems using global sensitivity analyses: A case example of simulated wolf reintroduction effects on elk

Often landmark conservation decisions are made despite an incomplete knowledge of system behavior and inexact predictions of how complex ecosystems will respond to management actions. For example, predicting the feasibility and likely effects of restoring top-level carnivores such as the gray wolf ( Canis lupus ) to North American wilderness areas is hampered by incomplete knowledge of the predator-prey system processes and properties. In such cases, global sensitivity measures, such as Sobol’ indices, allow one to quantify the effect of these uncertainties on model predictions. Sobol’ indices are calculated by decomposing the variance in model predictions (due to parameter uncertainty) into main effects of model parameters and their higher order interactions. Model parameters with large sensitivity indices can then be identified for further study in order to improve predictive capabilities. Here, we illustrate the use of Sobol’ sensitivity indices to examine the effect of parameter uncertainty on the predicted decline of elk ( Cervus elaphus ) population sizes following a hypothetical reintroduction of wolves to Olympic National Park, Washington, USA. The strength of density dependence acting on survival of adult elk and magnitude of predation were the most influential factors controlling elk population size following a simulated wolf reintroduction. In particular, the form of density dependence in natural survival rates and the per-capita predation rate together accounted for over 90% of variation in simulated elk population trends. Additional research on wolf predation rates on elk and natural compensations in prey populations is needed to reliably predict the outcome of predator–prey system behavior following wolf reintroductions.

Ecological Modelling↗

USGS2016

Creating a Coastal National Elevation Database (CoNED) for science and conservation applications

The U.S. Geological Survey is creating the Coastal National Elevation Database, an expanding set of topobathymetric elevation models that extend seamlessly across coastal regions of high societal or ecological significance in the United States that are undergoing rapid change or are threatened by inundation hazards. Topobathymetric elevation models are raster datasets useful for inundation prediction and other earth science applications, such as the development of sediment-transport and storm surge models. These topobathymetric elevation models are being constructed by the broad regional assimilation of numerous topographic and bathymetric datasets, and are intended to fulfill the pressing needs of decision makers establishing policies for hazard mitigation and emergency preparedness, coastal managers tasked with coastal planning compatible with predictions of inundation due to sea-level rise, and scientists investigating processes of coastal geomorphic change. A key priority of this coastal elevation mapping effort is to foster collaborative lidar acquisitions that meet the standards of the USGS National Geospatial Program's 3D Elevation Program, a nationwide initiative to systematically collect high-quality elevation data. The focus regions are located in highly dynamic environments, for example in areas subject to shoreline change, rapid wetland loss, hurricane impacts such as overwash and wave scouring, and/or human-induced changes to coastal topography.

Journal of Coastal Research↗

USGS2024

Viability modeling for decision support with limited data: A lizard case study

Plateau spot-tailed earless lizards, Holbrookia lacerata, are a species of ground lizard in central Texas that are under review for listing as endangered under the US Endangered Species Act, but heretofore no predictive models of population dynamics or viability have been developed. We used limited available data and published demographic rates in a PVA model to predict future status of these lizards under parametric and ecological uncertainty and temporal variability. Even in cases where data are sparse and life history information are limited, viability models can help clarify the consequences of management choices given the uncertainty. Our model predicted that on average populations will decline in in the future. Quasi-extinction probability was low 20 years into the future but up to 0.60. Extinction risk was highly dependent on the road mortality effect and the proportion of the population exposed to roadways, both of which are currently uncertain quantities. Despite these unknowns, our model enables managers to consider the future abundance and extinction risk for the species and make decisions about management to project the populations and also identifies key uncertainties for future research and monitoring.

Texas↗

USGS2018

The ecology of movement and behaviour: a saturated tripartite network for describing animal contacts

Ecologists regularly use animal contact networks to describe interactions underlying pathogen transmission, gene flow, and information transfer. However, empirical descriptions of contact often overlook some features of individual movement, and decisions about what kind of network to use in a particular setting are commonly ad hoc . Here, we relate individual movement trajectories to contact networks through a tripartite network model of individual, space, and time nodes. Most networks used in animal contact studies (e.g. individual association networks, home range overlap networks, and spatial networks) are simplifications of this tripartite model. The tripartite structure can incorporate a broad suite of alternative ecological metrics like home range sizes and patch occupancy patterns into inferences about contact network metrics such as modularity and degree distribution. We demonstrate the model's utility with two simulation studies using alternative forms of ecological data to constrain the tripartite network's structure and inform expectations about the harder-to-measure metrics related to contact.

Proceedings of the Royal Society B: Biological Sci↗

USGS2010

Spatial and stage-structured population model of the American crocodile for comparison of comprehensive Everglades Restoration Plan (CERP) alternatives

As part of the U.S. Geological Survey Priority Ecosystems Science (PES) initiative to provide the ecological science required during Everglades restoration, we have integrated current regional hydrologic models with American crocodile (Crocodylus acutus) research and monitoring data to create a model that assesses the potential impact of Comprehensive Everglades Restoration Plan (CERP) efforts on the American crocodile. A list of indicators was created by the Restoration Coordination and Verification (RECOVER) component of CERP to help determine the success of interim restoration goals. The American crocodile was established as an indicator of the ecological condition of mangrove estuaries due to its reliance upon estuarine environments characterized by low salinity and adequate freshwater inflow. To gain a better understanding of the potential impact of CERP restoration efforts on the American crocodile, a spatially explicit crocodile population model has been created that has the ability to simulate the response of crocodiles to various management strategies for the South Florida ecosystem. The crocodile model uses output from the Tides and Inflows in the Mangroves of the Everglades (TIME) model, an application of the Flow and Transport in a Linked Overland/Aquifer Density Dependent System (FTLOADDS) simulator. TIME has the capability to link to the South Florida Water Management Model (SFWMM), which is the primary regional tool used to assess CERP restoration scenarios. A crocodile habitat suitability index and spatial parameter maps that reflect salinity, water depth, habitat, and nesting locations are used as driving functions to construct crocodile finite rate of increase maps under different management scenarios. Local stage-structured models are integrated with a spatial landscape grid to display crocodile movement behavior in response to changing environmental conditions. Restoration efforts are expected to affect salinity levels throughout the habitat of the American crocodile. This modeling effort examines how CERP restoration alternatives will affect growth and survival rates of hatchling and juvenile crocodiles, hatchling dispersal to suitable nursery habitat, and relative abundance and distribution in response to changing salinity and water depth for all stage classes of crocodiles. The response of the American crocodile to restoration efforts will provide a quantifiable measure of restoration success. By applying the crocodile model to proposed restoration alternatives and predicting population responses, we can choose alternatives that approximate historical conditions, enhance habitat for multiple species, and identify future research needs.

Open-File Report↗

USGS2026

Assessing the state of hydrologic science in the Upper Klamath Basin—A comprehensive review of data, tools, and models

Water demand in the Upper Klamath Basin (UKB) from various stakeholders and ecological needs often outstrips available supply, leading to persistent management challenges. This study reviews the state of hydrologic science within the UKB as of 2025—specifically, the tools, data, and models available for assessing five key components of the water system: (1) surface water; (2) precipitation; (3) evapotranspiration; (4) groundwater; and (5) water use. The UKB water supply is critical for Native American communities, regional agriculture, and federally listed fishes and faces challenges from competing needs, climate variability, and operational/regulatory requirements. We assess existing datasets, regional and national models, and historical studies to understand the available resources and identify gaps that may hinder integrated water assessments and management. Our findings indicate areas where improvements in data collection and model precision could improve the accuracy of water-availability forecasts and support water-management practices. This review can inform near-term forecasting, assist in optimizing water-resource data collection and management strategies, and support regional water-availability assessments of the basin.

Oregon↗

USGS2025

A comparison of deep-sea coral and sponge species distribution models and the impact of ocean currents in the Southern California Bight

Deep-sea corals and sponges (DSCS) are signature taxa of deep-water habitats, but ecological mechanisms that drive their geographic distributions can be difficult to uncover due to the challenges of surveying deep-water ecosystems and limited oceanographic data. A comparison of species distribution models was made for three DSCS ( Antipathes dendochristos, Plumarella longispina, and an unidentified sponge morphotype known as Porifera #2), two of which are associated with young-of-the-year and adult rockfish taxa ( Sebastes spp.). Models were built using generalized additive models (GAMs) that accounted for spatial autocorrelation. These models were compared to Maxent models, a commonly used method. All models utilized bathymetrically derived variables (including depth, slope, and Bathymetric Position Index) and output from a coupled physical-biogeochemical ocean model (including current direction and magnitude, food abundance, and dissolved oxygen). Direction of benthic ocean currents played an important role in predictions, pointing to large-scale ecological processes that may determine presence of DSCS. GAMs outperformed Maxent models and predicted more ecologically interpretable patterns. Additionally we quantified the predicted amount of suitable habitat that is currently located within some protected areas of the Southern California Bight and show that many hot spots occur outside protected areas. Given the importance of DSCS for multiple demersal fish species of commercial or conservation concerns, this research provides valuable information that natural resource managers can use as a tool in the Southern California Bight.

California↗

USGS2009

Comparison of mid-Pliocene climate predictions produced by the HadAM3 and GCMAM3 General Circulation Models

The mid-Pliocene warm period (ca. 3 to 3.3??million years ago) has become an important interval of time for palaeoclimate modelling exercises, with a large number of studies published during the last decade. However, there has been no attempt to assess the degree of model dependency of the results obtained. Here we present an initial comparison of mid-Pliocene climatologies produced by the Goddard Institute for Space Studies and Hadley Centre for Climate Prediction and Research atmosphere-only General Circulation Models (GCMAM3 and HadAM3). Whilst both models are consistent in the simulation of broad-scale differences in mid-Pliocene surface air temperature and total precipitation rates, significant variation is noted on regional and local scales. There are also significant differences in the model predictions of total cloud cover. A terrestrial data/model comparison, facilitated by the BIOME 4 model and a new data set of Piacenzian Stage land cover [Salzmann, U., Haywood, A.M., Lunt, D.J., Valdes, P.J., Hill, D.J., (2008). A new global biome reconstruction and data model comparison for the Middle Pliocene. Global Ecology and Biogeography 17, 432-447, doi:10.1111/j.1466-8238.2007.00381.x] and combined with the use of Kappa statistics, indicates that HadAM3-based biome predictions provide a closer fit to proxy data in the mid to high-latitudes. However, GCMAM3-based biomes in the tropics provide the closest fit to proxy data. ?? 2008 Elsevier B.V.

Global and Planetary Change↗

USGS2024

Estimating migration timing and abundance in partial migratory systems by integrating continuous antenna detections with physical captures

Many populations migrate between two different habitats (e.g. wintering/foraging to breeding area, mainstem–tributary, river–lake, river–ocean, river–side channel) as part of their life history. Detection technologies, such as passive integrated transponder (PIT) antennas or sonic receivers, can be placed at boundaries between habitats (e.g. near the confluence of rivers) to detect migratory movements of marked animals. Often, these detection systems have high detection probabilities and detect many individuals but are limited in their ability to make inferences about abundance because only marked individuals can be detected. Here, we introduce a mark–recapture modelling approach that uses detections from a double-array PIT antenna system to imply movement directionality from arrays and estimate migration timing. Additionally, when combined with physical captures, the model can be used to estimate abundances for both migratory and non-migratory groups and help quantify partial migration. We first test our approach using simulation, and results indicate our approach displayed negligible bias for total abundance (less than ±1%) and slight biases for state-specific abundance estimates (±1%–6%). We fit our model to array detections and physical captures of three native fishes (humpback chub [ Gila cypha ], flannelmouth sucker [ Catostomus latipinnis ] and bluehead sucker [ Catostomus discobolus ]) in the Little Colorado River (LCR) in Grand Canyon, AZ, a system that exhibits partial migration (i.e. includes residents and migrants). Abundance estimates from our model confirm that, for all three species, migratory individuals are much more numerous than residents. There was little difference in movement timing between 2021 (a year without preceding winter/spring floods) and 2022 (a year with a small flood occurring in early April). In both years, flannelmouth sucker arrived in mid-March whereas humpback chub and bluehead sucker arrivals occurred early- to mid-April. With humpback chub and flannelmouth sucker, movement timing was influenced by body size so that large individuals were more likely to arrive early compared to smaller individuals. With more years of data, this model framework could be used to evaluate ecological questions pertaining to flow cues and movement timing or intensity, relative trends in migrants versus residents and ecological drivers of skipped spawning.

Journal of Animal Ecology↗

USGS2019

Reserve design to optimize functional connectivity and animal density

Ecological distance-based spatial capture–recapture models (SCR) are a promising approach for simultaneously estimating animal density and connectivity, both of which affect spatial population processes and ultimately species persistence. We explored how SCR models can be integrated into reserve-design frameworks that explicitly acknowledge both the spatial distribution of individuals and their space use resulting from landscape structure. We formulated the design of wildlife reserves as a budget-constrained optimization problem and conducted a simulation to explore 3 different SCR-informed optimization objectives that prioritized different conservation goals by maximizing the number of protected individuals, reserve connectivity, and density-weighted connectivity. We also studied the effect on our 3 objectives of enforcing that the space-use requirements of individuals be met by the reserve for individuals to be considered conserved (referred to as home-range constraints). Maximizing local population density resulted in fragmented reserves that would likely not aid long-term population persistence, and maximizing the connectivity objective yielded reserves that protected the fewest individuals. However, maximizing density-weighted connectivity or preemptively imposing home-range constraints on reserve design yielded reserves of largely spatially compact sets of parcels covering high-density areas in the landscape with high functional connectivity between them. Our results quantify the extent to which reserve design is constrained by individual home-range requirements and highlight that accounting for individual space use in the objective and constraints can help in the design of reserves that balance abundance and connectivity in a biologically relevant manner.

Conservation Biology↗

USGS2021

Age-structured Jolly-Seber model expands inference and improves parameter estimation from capture-recapture data

Understanding the influence of individual attributes on demographic processes is a key objective of wildlife population studies. Capture-recapture and age data are commonly collected to investigate hypotheses about survival, reproduction, and viability. We present a novel age-structured Jolly-Seber model that incorporates age and capture-recapture data to provide comprehensive information on population dynamics, including abundance, age-dependent survival, recruitment, age structure, and population growth rates. We applied our model to a multi-year capture-recapture study of polar bears (Ursus maritimus) in western Hudson Bay, Canada (20122018), where management and conservation require a detailed understanding of how polar bears respond to climate change and other factors. In simulation studies, the age-structured Jolly-Seber model improved precision of survival, recruitment, and annual abundance estimates relative to standard Jolly-Seber models that omit age information. Furthermore, incorporating age information improved precision of population growth rates, increased power to detect trends in abundance, and allowed direct estimation of age-dependent survival and changes in annual age structure. Our case study provided detailed evidence for senescence in polar bear survival. Median survival estimates were lower (<0.95) for individuals aged <5 years, remained high (>0.95) for individuals aged 722 years, and subsequently declined to near zero for individuals >30 years. We also detected cascading effects of large recruitment classes on population age structure, which created major shifts in age structure when these classes entered the population and then again when they reached prime breeding ages (1015 years old). Overall, age-structured Jolly-Seber models provide a flexible means to investigate ecological and evolutionary processes that shape populations (e.g., via senescence, life expectancy, and lifetime reproductive success) while improving our ability to investigate population dynamics and forecast population changes from capture-recapture data.

PLoS ONE↗

USGS2011

Estimating equivalence with quantile regression

Equivalence testing and corresponding confidence interval estimates are used to provide more enlightened statistical statements about parameter estimates by relating them to intervals of effect sizes deemed to be of scientific or practical importance rather than just to an effect size of zero. Equivalence tests and confidence interval estimates are based on a null hypothesis that a parameter estimate is either outside (inequivalence hypothesis) or inside (equivalence hypothesis) an equivalence region, depending on the question of interest and assignment of risk. The former approach, often referred to as bioequivalence testing, is often used in regulatory settings because it reverses the burden of proof compared to a standard test of significance, following a precautionary principle for environmental protection. Unfortunately, many applications of equivalence testing focus on establishing average equivalence by estimating differences in means of distributions that do not have homogeneous variances. I discuss how to compare equivalence across quantiles of distributions using confidence intervals on quantile regression estimates that detect differences in heterogeneous distributions missed by focusing on means. I used one-tailed confidence intervals based on inequivalence hypotheses in a two-group treatment-control design for estimating bioequivalence of arsenic concentrations in soils at an old ammunition testing site and bioequivalence of vegetation biomass at a reclaimed mining site. Two-tailed confidence intervals based both on inequivalence and equivalence hypotheses were used to examine quantile equivalence for negligible trends over time for a continuous exponential model of amphibian abundance. ?? 2011 by the Ecological Society of America.

Ecological Applications↗

USGS2023

Viewing river corridors through the lens of critical zone science

River corridors integrate the active channels, geomorphic floodplain and riparian areas, and hyporheic zone while receiving inputs from the uplands and groundwater and exchanging mass and energy with the atmosphere. Here, we trace the development of the contemporary understanding of river corridors from the perspectives of geomorphology, hydrology, ecology, and biogeochemistry. We then summarize contemporary models of the river corridor along multiple axes including dimensions of space and time, disturbance regimes, connectivity, hydrochemical exchange flows, and legacy effects of humans. We explore how river corridor science can be advanced with a critical zone framework by moving beyond a primary focus on discharge-based controls toward multi-factor models that identify dominant processes and thresholds that make predictions that serve society. We then identify opportunities to investigate relationships between large-scale spatial gradients and local-scale processes, embrace that riverine processes are temporally variable and interacting, acknowledge that river corridor processes and services do not respect disciplinary boundaries and increasingly need integrated multidisciplinary investigations, and explicitly integrate humans and their management actions as part of the river corridor. We intend our review to stimulate cross-disciplinary research while recognizing that river corridors occupy a unique position on the Earth's surface.

Frontiers in Water↗

USGS2021

Determination of burn severity models ranging from regional to continental scales for the conterminous United States

Identifying meaningful measures of ecological change over large areas is dependent on the quantification of robust relationships between ecological metrics and remote sensing products. Over the past several decades, ground observations of wildfire and prescribed fire severity have been acquired across hundreds of wildland fires in the United States, primarily utilizing the Composite Burn Index (CBI) plot protocol. These observations have been coupled to spaceborne passive spectral reflectance indices (e.g. Landsat-derived variations of the Normalized Burn Ratio [NBR]) to produce regression models describing their relationship. Here we develop regression models by vegetation type for multiple vegetation classification systems representing a range of spatial scales, and a decision tree framework for evaluating these regression models. Our overall goals were to determine which scale of ecological classifications provided the best estimate of burn severity from Landsat data and how to choose the best regression model. We aggregated a total of 6280 CBI plots for 234 wildland fires that burned between 1994 and 2017 and produced Landsat-derived NBR and differenced NBR (dNBR) values for each plot. We then calculated best fit linear or higher order regression equations between CBI and NBR/dNBR for each landcover classification system from smallest to largest scale: LANDFIRE Biophysical Settings (BPS), National Vegetation Classification macrogroup (NVC) landcover classifications, Omernick III, II, and I ecoregions, LANDFIRE Fire Regime Groups (FRG), and the entire conterminous United States (CONUS) dataset. The CONUS regression model goodness of fit was moderate (R 2 = 0.55, P < 0.001) for dNBR and poor (R 2 = 0.30, P < 0.001) for NBR. Within landcover classifications, CBI was better fit by dNBR than NBR. Finer scale regional regression models including BPS (dNBR R 2 ¯ "> R2¯ = 0.56 and 0.00–0.83 R 2 range; NBR R 2 ¯ "> R(bar) 2 = 0.43 and 0.00–0.82 R 2 range) and NVC (dNBR R 2 ¯ "> R(bar) 2 = 0.55 and 0.15–0.78 R 2 range; NBR R 2 ¯ "> R(bar) 2 = 0.41 and 0.00–0.79 R 2 range) were on average the same or better than the CONUS models for dNBR and NBR, with the strongest fit models exhibiting R 2 ≥ 0.70, whereas larger scale regional models R 2 ¯ "> R(bar) 2 ranged from 0.28 to 0.5. However, variation in accuracy among landcover types indicate that dNBR and NBR regression models could be used to effectively estimate CBI for future fires in certain regions, while for other regions models may require additional field observations or alternative spectral transformations. Our decision tree schema can be used to help users determine which scale is likely to produce the most accurate results using our models. The CBI regression models developed here, paired with the decision tree, provide users with a simple method to estimate burn severity in units of CBI for any fire within CONUS with moderate to high levels of confidence and provide a template for further development of models with new data going forward.

Conterminous United States↗

USGS2024

A hierarchical model for eDNA fate and transport dynamics accommodating low concentration samples

Environmental DNA (eDNA) sampling is an increasingly important tool for answering ecological questions and informing aquatic species management; however, several factors currently limit the reliability of ecological inference from eDNA sampling. Two particular challenges are 1) determining species source location(s) and 2) accurately and precisely measuring low concentration eDNA samples in the presence of multiple sources of ecological and measurement variability. The recently introduced eDNA Integrating Transport and Hydrology (eDITH) model provides a framework for relating eDNA measurements to source locations in riverine networks, but little empirical work has been done to test and refine model assumptions or accommodate low concentration samples, that can be systematically undermeasured. To better understand eDNA fate and transport dynamics and our ability to reliably quantify low concentration samples, we developed a hierarchical model and used it to evaluate a fate and transport experiment. Our model addresses several low concentration challenges by modeling the number of copies in each PCR replicate as a latent variable with a count distribution and conditioning detection and quantification on replicate copy number. We provide evidence that the eDNA removal rate declined through time, estimating that over 80% of eDNA was removed over the first 10 meters, traversed in 41 seconds. After this initial period of rapid decay, eDNA decayed slowly with consistent detection through our farthest site 1km from the release location, traversed in 250 seconds. Our model further allowed us to detect extra-Poisson variation in the allocation of copies to replicates. We extended our hierarchical model to accommodate a continuous effect of inhibitors and used our model to provide evidence for the inhibitor hypothesis and explore the potential implications. While our model is not a panacea for all challenges faced when quantifying low-concentration eDNA samples, it provides a framework for a more complete accounting of uncertainty.

BioRxiv↗