Geology topics

Perry J. Williams

Publications and source records attributed to Perry J. Williams.

17 recordsLinked to original sources

USGS2026

Ecological diffusion models are still useful in ecology

Context Connecting animal movement across scales—both among spatial scales and between individual and population level processes—is a central theme in ecology, including the sub-fields of movement and landscape ecology. However, most modeling frameworks operate at either the individual (Lagrangian) or population (Eulerian) level. Objectives We aimed to review how a partial differential equation (PDE) known as the ecological diffusion equation (EDE) offers connections among the scales of animal movement and how it can be embedded in commonly used statistical frameworks (e.g., hierarchical models) and fit to multiple types of data, such as count, presence-only, presence-absence, and telemetry data. In doing so, we also highlight emerging and promising avenues of research related to statistical EDE models. Methods We present how the EDE is derived from a simple set of first principles, can be used to represent both individual animal movement and spatiotemporal population dynamics, and can be fit to data by being applied in a hierarchical statistical framework. Finally, we review literature on recent applications and advances related to EDE models. Results In presenting the derivation of the EDE and reviewing recent advances and applications of EDE models, we established that the EDE can enable a mechanistic understanding of animal movement across scales, as well as the integration of multiple types of data. We also identified a number of topics where EDE models can be advanced to gain additional ecological insight. Conclusions Ecological diffusion is a process that emerges naturally from first principles governing animal movement and can be used to model both individual and population-level spatiotemporal dynamics. Statistical EDE models are related to other modeling frameworks, such as species distribution models, occupancy models, and step-selection analysis. The flexibility of hierarchical statistical modeling allows combining different types of data collected on movement and population dynamics, and the theoretical underpinnings of the EDE allow it to connect ecological processes occurring at fine and coarse spatial scales, as well as individual animal movement and population dynamics.

Landscape Ecology↗

USGS2025

The effects of breeding status on common raven movement, home range, and habitat selection

Anthropogenic infrastructure has contributed to increasing common raven ( Corvus corax ) abundance across the Great Basin region of the United States, particularly in sagebrush ecosystems, where high raven densities are correlated with reduced sage-grouse ( Centrocercus urophasianus ) nest survival. Our understanding of how raven reproductive behavior affects sage-grouse nest predation is limited, especially considering their overlapping breeding seasons. Understanding differences in space use and resource selection between breeding and non-breeding ravens could help identify high-use areas and corresponding predation risk for sage-grouse nests. We analyzed space use and resource selection of breeding ( n = 13) and non-breeding ( n = 32) global positioning system (GPS)-marked ravens in Nevada, USA (2017–2022) during the breeding season (1 March–31 June). We compared home-range size, core area size, step lengths, and resource selection within a Bayesian framework with inference made by comparing Bayesian credible intervals (CRI). We generated home range and core area estimates using autocorrelated kernel density methods. We did not find a difference in home range size between breeding (469.33 km 2 , 95% CRI = 228.79–709.45 km 2 ) and non-breeding (525.26 km 2 , 95% CRI = 410.71–654.10 km 2 ) ravens. However, breeding ravens had smaller core areas (10.77 km 2 , 95% CRI = 3.16–35.78 km 2 ) and shorter step lengths (1,160.33 m/hr, 95% CRI = 1,087.78–1,277.17 m/hr) than non-breeding ravens (core area = 279.50 km 2 , 95% CRI = 206.77–363.72 km 2 ; step length = 1,953.74 m/hr, 95% CRI = 1,898.42–2,009.56 m/hr). Ravens in both breeding classes selected high normalized difference vegetation index (NDVI) and low annual grass and shrub cover, but non-breeding ravens showed stronger selection for low annual grass and shrub cover areas. We found strong differences in selection between breeding classes for 6 of our 9 covariates: distance to road, solar radiation, distance to natural water, distance to forest edge, percent annual grass cover, and percent shrub cover. Non-breeding ravens concentrated activity near forest edges, natural water sources, and anthropogenic features, whereas breeding ravens focused activity close to their nests. Our findings suggest that raven management could be more effective if it targeted areas with high NDVI and low annual grass and shrub cover, especially in anthropogenically modified landscapes and near forest edges, and prevented raven nest establishment near prey populations of concern.

Nevada↗

USGS2025

Greater sage-grouse seasonal habitat associations: A review and considerations for interpretation and management applications

Habitat features needed by wildlife can change in composition throughout the year, particularly in temperate ecosystems, leading to distinct seasonal spatial-use patterns. Studies of species-habitat associations therefore often focus on understanding relationships within discrete seasonal periods with common goals of prediction (e.g., habitat mapping) and inference (e.g., interpreting model coefficients). Across the range of the greater sage-grouse ( Centrocercus urophasianus ) of western North America, the increasing use of high-frequency tracking devices has led to a surge in habitat association studies covering multiple temporal periods and spatial extents. We reviewed the literature for seasonal habitat association studies corresponding to the second and third orders of selection (Johnson 1980). Our objectives were to summarize the methodological approaches used to estimate habitat associations to aid understanding in cross-study comparisons and identify common habitat features reported as selected or avoided within different seasonal periods. We reviewed 71 second- and third-order studies published from 2007–2023 that evaluated covariates collected in a geographic information system (GIS) and modeled probability of selection or intensity of use. The most common study design evaluated a single level of selection (third-order) and was multi-scale (i.e., covariates were measured at varying spatial grains). The most common model approach estimated habitat associations using resource selection functions (RSFs) fit with logistic regression. Studies mostly focused on the breeding periods and winter, but all seasons throughout the annual cycle were covered. There was clear support for selection of sagebrush and avoidance of trees and rugged terrain across seasons, and strong selection of mesic conditions in summer. However, habitat associations for most covariates were mixed, with proportionally equivalent selection and avoidance reported, even within the same seasons. Different factors hampered cross-study comparisons, including variation in study design, but additional contributors likely included important context-dependent habitat associations, such as functional responses to changing habitat availability. We suggest collaborative studies leveraging multiple datasets can help improve seasonal habitat inference by removing the effects of variable study designs.

Journal of Wildlife Management↗

USGS2025

Estimating spatially explicit survival and mortality risk from telemetry data with thinned point process models

Mortality risk for animals often varies spatially and can be linked to how animals use landscapes. While numerous studies collect telemetry data on animals, the focus is typically on the period when animals are alive, even though there is important information that could be gleaned about mortality risk. We introduce a thinned spatial point process (SPP) modelling framework that couples relative abundance and space use with a mortality process to formally treat the occurrence of mortality events across the landscape as a spatial process. We show how this model can be embedded in a hierarchical statistical framework and fit to telemetry data to make inferences about how spatial covariates drive both space use and mortality risk. We apply the method to two data sets to study the effects of roads and habitat on spatially explicit mortality risk: (1) VHF telemetry data collected for willow ptarmigan in Alaska, and (2) hourly GPS telemetry data collected for black bears in Colorado. These case studies demonstrate the applicability of this method for different species and data types, making it broadly useful in enabling inferences about the mechanisms influencing animal survival and spatial population processes while formally treating survival as a spatial process, especially as the development and implementation of joint analyses continue to progress.

Ecology Letters↗

USGS2024

Rayleigh step-selection functions and connections to continuous-time mechanistic movement models

Background The process known as ecological diffusion emerges from a first principles view of animal movement, but ecological diffusion and other partial differential equation models can be difficult to fit to data. Step-selection functions (SSFs), on the other hand, have emerged as powerful practical tools for ecologists studying the movement and habitat selection of animals. Methods SSFs typically involve comparing resources between a set of used and available points at each step in a sequence of observed positions. We use change of variables to show that ecological diffusion implies certain distributions for available steps that are more flexible than others commonly used. We then demonstrate advantages of these distributions with SSF models fit to data collected for a mountain lion in Colorado, USA. Results We show that connections between ecological diffusion and SSFs imply a Rayleigh step-length distribution and uniform turning angle distribution, which can accommodate data collected at irregular time intervals. The results of fitting an SSF model with these distributions compared to a set of commonly used distributions revealed how precision and inference can vary between the two approaches. Conclusions Our new continuous-time step-length distribution can be integrated into various forms of SSFs, making them applicable to data sets with irregular time intervals between successive animal locations.

Movement Ecology↗

USGS2023

Informing management of recovering predators and their prey with ecological diffusion models

The reintroduction and recovery of predators can be ecologically beneficial as well as socially and economically controversial. However, the growth and expansion of predator populations, and thus their ecological, social, and economic impacts, are not static but rather they vary in space and time. We propose a spatiotemporal statistical modeling framework based on ecological diffusion to better inform the ecology and management of recovering predators and their prey. We demonstrate its utility by applying it to a recovering sea otter ( Enhydra lutris ) population in Southeast Alaska, where sea otters were reintroduced in the late 1960s and have exhibited unprecedented population growth. Estimated parameters yield inferences about movement and population ecology, and our approach provides useful derived quantities, such as local abundance and carrying capacity as well as a quantity we term the equilibrium differential. We used our model to examine how density dependence and carrying capacity of sea otters vary spatially across a region. The diffusion modeling approach we present can be generalized for use in other instances of (re)colonization across taxa to inform management and conservation efforts.

Alaska↗

USGS2023

A hierarchical modelling framework for estimating individual- and population-level reproductive success from movement data

Rapidly advancing animal telemetry technologies paired with new statistical models can provide insight into the behaviour of otherwise unobservable free-living animals. Changes in behaviour apparent from pairing telemetry with statistical models often occur as animals undertake key life-history activities, such as reproduction. For many species that are secretive or occupy remote areas, these life-history events are difficult to detect with conventional survey techniques, and consequently, vital rates are difficult to estimate. We present a hierarchical modelling framework, which integrates movement data observed via animal-borne telemetry and optional, infrequent survey data, to estimate individual- and population-level reproductive success. The approach combines a mechanistic movement model and survival model, and allows for assessing the effects of hypothesized individual and environmental covariates on reproductive success. We first tested our approach with simulated data, and then applied it to movement data from migratory golden eagles ( Aquila chrysaetos) breeding in southcentral Alaska across four breeding seasons. We show that results supported our biological hypotheses that changes in movement coincided with the timing of reproductive failures, and that changes in movement could be used to assess breeding success (and failure) at the individual and population levels. The analysis also provided evidence of inter-annual variation in population-level nest success and the timing of nesting failures. This new approach is adaptable to many species that care for young and can be tracked with telemetry devices, and can provide not only individual-level information useful for testing ecological hypotheses, but estimates of demographic parameters that can directly inform conservation and management if tagged animals are representative of the population.

Methods in Ecology and Evolution↗

USGS2021

Inter- and intra-annual effects of lethal removal on common raven abundance in Nevada and California, USA

Populations of common ravens ( Corvus corax ; ravens) have increased rapidly within sagebrush ( Artemisia spp.) ecosystems between 1960 and 2020. Although ravens are native to North America, their population densities have expanded to levels that negatively influence the population dynamics of other wildlife species of conservation concern, such as greater sage-grouse ( Centrocercus urophasianus ) and desert tortoises ( Gopherus agassizii ). For this reason, lethal removal, such as the application of the avicide DRC-1339, has been used to manage raven numbers at local scales and under certain circumstances. Because the relative effectiveness of DRC-1339 in reducing raven populations densities is not thoroughly understood, we completed 2 case studies using a before-after-control-impact experimental design of density estimates generated from point count data within a Bayesian hierarchical distance sampling framework. Specifically, we analyzed >16,000 point count surveys collected during 2009–2019 and split into 2 study designs covering multiple field sites within the Great Basin region. The first experiment evaluated intra-annual changes in density by comparing before and after treatment time periods within a single breeding season for multiple treatment regions compared to 2 control regions. The other experiment focused on inter-annual differences by comparing time periods across years before and after the onset of annual avicide application for a single treatment region compared to multiple control regions. Our models estimated a 100% probability of decline in density relative to control sites for both the intra- and inter-annual model designs. At treatment sites, expected densities of ravens varied but were reduced by 43% (95% CRI: 33–49%) and 54% (95% CRI: 24–71%) according to intra- and inter-annual analyses, respectively, whereas densities increased by 42% (95% CRI: 27–60%) and 15% (95% CRI: -17 to 58%) at control sites. Although population densities were reduced with treatments, trends indicated that sustained effort would likely be needed to maintain densities at acceptable levels within regions of interest. Effectively reducing the adverse effects of raven populations on other native species likely will depend on a variety of targeted management actions such as improving habitat quality for prey species, possibly reducing ravens’ population density, and treating the cause of increased raven abundance to reduce future carrying capacity and prevent rebounds.

California, Nevada↗

USGS2019

Nonlinear reaction–diffusion process models improve inference for population dynamics

Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long-term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a logistic reaction component instead of a Malthusian component when population growth demonstrates asymptotic behavior. As a case study, we demonstrated that our model improves spatiotemporal abundance forecasts of sea otters in Glacier Bay, Alaska. Furthermore, we predicted spatially varying local equilibrium abundances as a result of environmentally driven diffusion and density-regulated growth. Integrating equilibrium abundances over the study area in our application enabled us to infer the overall carrying capacity of sea otters in Glacier Bay, Alaska.

Alaska↗

USGS2019

Selecting ecological models using multi-objective optimization

Choices in ecological research and natural resource management require balancing multiple, often competing objectives. Examples include maximizing species persistence in a wildlife conservation context, while minimizing cost, or balancing opposing stakeholder objectives when managing wildlife populations. Multiple-objective optimization (MOO) provides a unifying framework for solving multiple objective problems. Model selection is a critical component of ecological inference and prediction and requires balancing the competing objectives of model fit and model complexity. The tradeoff between model fit and model complexity provides a basis for describing the model-selection problem within the MOO framework. We discuss MOO and two strategies for solving the MOO problem; modeling preferences pre-optimization and post-optimization. Most conventional model selection methods can be formulated as solutions of MOO problems via specification of pre-optimization preferences. We reconcile model selection within the MOO framework. We also consider model selection using post-optimization specification of preferences. That is, by first identifying Pareto optimal solutions, and then selecting among them. We demonstrate concepts with an ecological application of model selection using avian species richness data in the continental United States.

Ecological Modelling↗

USGS2018

A guide to Bayesian model checking for ecologists

Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously accounting for observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack of fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, Bayesian P values are relatively easy to compute, but are well known to be conservative, producing P values biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross‐validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness‐of‐fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack of fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies including (1) analysis of simulated spatiotemporal count data, (2) N‐mixture models for estimating abundance of sea otters from an aircraft, and (3) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictive P values detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross‐validation and pivot discrepancy measures (including the “sampled predictive P value”) appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is necessary to ensure that scientific inference is well founded. As an essential component of scientific discovery, it should accompany most Bayesian analyses presented in the literature.

Ecological Monographs↗

USGS2018

Monitoring dynamic spatio-temporal ecological processes optimally

Population dynamics vary in space and time. Survey designs that ignore these dynamics may be inefficient and fail to capture essential spatio‐temporal variability of a process. Alternatively, dynamic survey designs explicitly incorporate knowledge of ecological processes, the associated uncertainty in those processes, and can be optimized with respect to monitoring objectives. We describe a cohesive framework for monitoring a spreading population that explicitly links animal movement models with survey design and monitoring objectives. We apply the framework to develop an optimal survey design for sea otters in Glacier Bay. Sea otters were first detected in Glacier Bay in 1988 and have since increased in both abundance and distribution; abundance estimates increased from 5 otters to >5,000 otters, and they have spread faster than 2.7 km/yr. By explicitly linking animal movement models and survey design, we are able to reduce uncertainty associated with forecasting occupancy, abundance, and distribution compared to other potential random designs. The framework we describe is general, and we outline steps to applying it to novel systems and taxa.

Ecology↗

USGS2017

Estimating occupancy and abundance using aerial images with imperfect detection

Species distribution and abundance are critical population characteristics for efficient management, conservation, and ecological insight. Point process models are a powerful tool for modelling distribution and abundance, and can incorporate many data types, including count data, presence-absence data, and presence-only data. Aerial photographic images are a natural tool for collecting data to fit point process models, but aerial images do not always capture all animals that are present at a site. Methods for estimating detection probability for aerial surveys usually include collecting auxiliary data to estimate the proportion of time animals are available to be detected. We developed an approach for fitting point process models using an N -mixture model framework to estimate detection probability for aerial occupancy and abundance surveys. Our method uses multiple aerial images taken of animals at the same spatial location to provide temporal replication of sample sites. The intersection of the images provide multiple counts of individuals at different times. We examined this approach using both simulated and real data of sea otters ( Enhydra lutris kenyoni ) in Glacier Bay National Park, southeastern Alaska. Using our proposed methods, we estimated detection probability of sea otters to be 0.76, the same as visual aerial surveys that have been used in the past. Further, simulations demonstrated that our approach is a promising tool for estimating occupancy, abundance, and detection probability from aerial photographic surveys. Our methods can be readily extended to data collected using unmanned aerial vehicles, as technology and regulations permit. The generality of our methods for other aerial surveys depends on how well surveys can be designed to meet the assumptions of N -mixture models.

Methods in Ecology and Evolution↗

USGS2017

An integrated data model to estimate spatiotemporal occupancy, abundance, and colonization dynamics

Ecological invasions and colonizations occur dynamically through space and time. Estimating the distribution and abundance of colonizing species is critical for efficient management or conservation. We describe a statistical framework for simultaneously estimating spatiotemporal occupancy and abundance dynamics of a colonizing species. Our method accounts for several issues that are common when modeling spatiotemporal ecological data including multiple levels of detection probability, multiple data sources, and computational limitations that occur when making fine-scale inference over a large spatiotemporal domain. We apply the model to estimate the colonization dynamics of sea otters ( Enhydra lutris ) in Glacier Bay, in southeastern Alaska.

Ecology↗

USGS2017

A guide to multi-objective optimization for ecological problems with an application to cackling goose management

Choices in ecological research and management are the result of balancing multiple, often competing, objectives. Multi-objective optimization (MOO) is a formal decision-theoretic framework for solving multiple objective problems. MOO is used extensively in other fields including engineering, economics, and operations research. However, its application for solving ecological problems has been sparse, perhaps due to a lack of widespread understanding. Thus, our objective was to provide an accessible primer on MOO, including a review of methods common in other fields, a review of their application in ecology, and a demonstration to an applied resource management problem. A large class of methods for solving MOO problems can be separated into two strategies: modelling preferences pre-optimization (the a priori strategy), or modelling preferences post-optimization (the a posteriori strategy). The a priori strategy requires describing preferences among objectives without knowledge of how preferences affect the resulting decision. In the a posteriori strategy, the decision maker simultaneously considers a set of solutions (the Pareto optimal set) and makes a choice based on the trade-offs observed in the set. We describe several methods for modelling preferences pre-optimization, including: the bounded objective function method, the lexicographic method, and the weighted-sum method. We discuss modelling preferences post-optimization through examination of the Pareto optimal set. We applied each MOO strategy to the natural resource management problem of selecting a population target for cackling goose ( Branta hutchinsii minima ) abundance. Cackling geese provide food security to Native Alaskan subsistence hunters in the goose's nesting area, but depredate crops on private agricultural fields in wintering areas. We developed objective functions to represent the competing objectives related to the cackling goose population target and identified an optimal solution first using the a priori strategy, and then by examining trade-offs in the Pareto set using the a posteriori strategy. We used four approaches for selecting a final solution within the a posteriori strategy; the most common optimal solution, the most robust optimal solution, and two solutions based on maximizing a restricted portion of the Pareto set. We discuss MOO with respect to natural resource management, but MOO is sufficiently general to cover any ecological problem that contains multiple competing objectives that can be quantified using objective functions.

Ecological Modelling↗

USGS2016

Combining statistical inference and decisions in ecology

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation, and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem.

Ecological Applications↗

USGS2016

Factors affecting nest survival of Henslow's Sparrows ( Ammodramus henslowii ) in southern Indiana

Populations of Henslow’s Sparrows have declined dramatically in recent decades, coinciding with widespread loss of native grassland habitat. Prescribed burning is a primary tool for maintaining grassland patches, but its effects on nest survival of Henslow’s Sparrows remains largely unknown, especially in conjunction with other factors. We monitored 135 nests of Henslow’s Sparrows at Big Oaks National Wildlife Refuge in southern Indiana from 1998–2001 in an effort to understand factors influencing nest survival, including prescribed burning of habitat. We used a mixed-effects implementation of the logistic exposure model to predict daily nest survival in an information theoretic framework. We found that daily survival declined near the onset of hatching and increased with the height of standing dead vegetation, although this relationship was weak. We found only nominal support to suggest that time since burn influenced nest survival. Overall, nest age was the most important factor in estimating daily nest survival rates. Our daily survival estimate from our marginal model (0.937) was similar to that derived from the Mayfield method (0.944) suggesting that our results are comparable to previous studies using the Mayfield approach. Our results indicate that frequent burning to limit woody encroachment into grassland habitats might benefit Henslow’s Sparrow, but that a variety of factors ultimately influence daily nest survival. However, we note that burning too frequently can also limit occupancy by Henslow’s Sparrows. We suggest that additional research is needed to determine the population-level consequences of habitat alteration and if other extrinsic factors influence demographics of Henslow’s Sparrows.

Indiana↗