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USGS2004

N-mixture models for estimating population size from spatially replicated counts

Spatial replication is a common theme in count surveys of animals. Such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability. In this article, I describe a class of models (n-mixture models) which allow for estimation of population size from such data. The key idea is to view site-specific population sizes, n, as independent random variables distributed according to some mixing distribution (e.g., Poisson). Prior parameters are estimated from the marginal likelihood of the data, having integrated over the prior distribution for n. Carroll and Lombard (1985, Journal of American Statistical Association 80, 423-426) proposed a class of estimators based on mixing over a prior distribution for detection probability. Their estimator can be applied in limited settings, but is sensitive to prior parameter values that are fixed a priori. Spatial replication provides additional information regarding the parameters of the prior distribution on n that is exploited by the n-mixture models and which leads to reasonable estimates of abundance from sparse data. A simulation study demonstrates superior operating characteristics (bias, confidence interval coverage) of the n-mixture estimator compared to the Caroll and Lombard estimator. Both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence.

Biometrics↗

USGS1995

Estimation and confidence intervals for empirical mixing distributions

Questions regarding collections of parameter estimates can frequently be expressed in terms of an empirical mixing distribution (EMD). This report discusses empirical Bayes estimation of an EMD, with emphasis on the construction of interval estimates. Estimation of the EMD is accomplished by substitution of estimates of prior parameters in the posterior mean of the EMD. This procedure is examined in a parametric model (the normal-normal mixture) and in a semi-parametric model. In both cases, the empirical Bayes bootstrap of Laird and Louis (1987, Journal of the American Statistical Association 82, 739-757) is used to assess the variability of the estimated EMD arising from the estimation of prior parameters. The proposed methods are applied to a meta-analysis of population trend estimates for groups of birds.

Biometrics↗

USGS2013

Computationally efficient statistical differential equation modeling using homogenization

Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.

Journal of Agricultural, Biological, and Environme↗

USGS2016

Climate adaption and post-fire restoration of a foundational perennial in cold desert: Insights from intraspecific variation in response to weather

1.The loss of foundational but fire-intolerant perennials such as sagebrush due to increases in fire size and frequency in semiarid regions has motivated efforts to restore them, often with mixed or even no success. Seeds of sagebrush Artemisia tridentata and related species must be moved considerable distances from seed source to planting sites, but such transfers have not been guided by an understanding of local climate adaptation. Initial seedling establishment and its response to weather are a key demographic bottleneck that likely varies among subspecies and populations of sagebrush. 2.We assessed differences in survival, growth, and physiological responses of sagebrush to weather among eleven seed sources that varied in subspecies, cytotype, and climates-of-origin over 18 months following outplanting. Diploid or polyploid populations of mountain, Wyoming, and basin big sagebrush ( A.tridentata ssp. vaseyana, A.tridentata ssp. wyomingensis, and A.tridentata ssp. tridentata , respectively) were planted onto five burned sites that normally support A.t.wyomingensis with some A.t.tridentata . 3.A.t.wyomingensis had the most growth and survival, and tetraploid populations had greater survival and height than diploids. Seasonal timing of mortality varied among the subspecies/cytotypes and was more closely related to minimum temperatures than water deficit. 4.Temperatures required to induce ice formation were up to 6°C more negative in 4n- A.t.tridentata and A.t.wyomingensis than other subspecies/cytotypes, indicating greater freezing avoidance. In contrast, freezing resistance of photosynthesis varied only 1°C among subspecies/cytotypes, being greatest in A.t.wyomingensis and least in the subspecies normally considered most cold-adapted, A.t.vaseyana . A large spectrum of reliance on freezing-avoidance vs. freezing-tolerance was observed and corresponded to differences in post-fire survivorship among subspecies/cytotypes. Differences in water deficit responses among subspecies/cytotypes were not as strong and did not relate to survival patterns. 5. Synthesis and applications. Low temperature responses are a key axis defining climate adaptation in young sagebrush seedlings and vary more with cytotype than with subspecies, which contrasts with the traditional emphases on (i) water limitations to explain establishment in these deserts, and (ii) subspecies in selecting restoration seedings. These important and novel insights on climate adaptation are critical for seed selection and parameterizing seed transfer zones, and were made possible by incorporating weather data with survival statistics. The survival/weather statistics used here could be applied to any restoration planting or seeding to help elucidate factors contributing to success and enable adaptive management.

Journal of Applied Ecology↗

USGS2011

Has the magnitude of floods across the USA changed with global CO2 levels?

Statistical relationships between annual floods at 200 long-term (85–127 years of record) streamgauges in the coterminous United States and the global mean carbon dioxide concentration (GMCO2) record are explored. The streamgauge locations are limited to those with little or no regulation or urban development. The coterminous US is divided into four large regions and stationary bootstrapping is used to evaluate if the patterns of these statistical associations are significantly different from what would be expected under the null hypothesis that flood magnitudes are independent of GMCO2. In none of the four regions defined in this study is there strong statistical evidence for flood magnitudes increasing with increasing GMCO2. One region, the southwest, showed a statistically significant negative relationship between GMCO2 and flood magnitudes. The statistical methods applied compensate both for the inter-site correlation of flood magnitudes and the shorter-term (up to a few decades) serial correlation of floods.

Hydrological Sciences Journal↗

USGS2017

A multimodal wave spectrum-based approach for statistical downscaling of local wave climate

Characterization of wave climate by bulk wave parameters is insufficient for many coastal studies, including those focused on assessing coastal hazards and long-term wave climate influences on coastal evolution. This issue is particularly relevant for studies using statistical downscaling of atmospheric fields to local wave conditions, which are often multimodal in large ocean basins (e.g. the Pacific). Swell may be generated in vastly different wave generation regions, yielding complex wave spectra that are inadequately represented by a single set of bulk wave parameters. Furthermore, the relationship between atmospheric systems and local wave conditions is complicated by variations in arrival time of wave groups from different parts of the basin. Here, we address these two challenges by improving upon the spatiotemporal definition of the atmospheric predictor used in statistical downscaling of local wave climate. The improved methodology separates the local wave spectrum into “wave families,” defined by spectral peaks and discrete generation regions, and relates atmospheric conditions in distant regions of the ocean basin to local wave conditions by incorporating travel times computed from effective energy flux across the ocean basin. When applied to locations with multimodal wave spectra, including Southern California and Trujillo, Peru, the new methodology improves the ability of the statistical model to project significant wave height, peak period, and direction for each wave family, retaining more information from the full wave spectrum. This work is the base of statistical downscaling by weather types, which has recently been applied to coastal flooding and morphodynamic applications.

Journal of Physical Oceanography↗

USGS2017

Imputation approaches for animal movement modeling

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals ( Callorhinus ursinus ) in the Bering Sea. Supplementary materials accompanying this paper appear online.

Journal of Agricultural, Biological, and Environme↗

USGS2019

Balancing sampling intensity against spatial coverage for a community science monitoring programme

Community science is an increasingly integral part of biodiversity research and monitoring, often achieving broad spatial and temporal coverage but lower sampling intensity than studies conducted by professional scientists. When designing a community‐science monitoring programme, careful assessment of sampling designs that could be both feasible and successful at meeting programme goals is essential. Monarch butterflies ( Danaus plexippus ) are the focus of several successful community‐science projects in the U.S., but broader coverage is needed to monitor breeding areas and explain population declines observed in overwintering areas. The U.S. Monarch Conservation Science Partnership's Integrated Monarch Monitoring Program (IMMP) will representatively monitor monarchs and milkweed across North America. We performed a simulation‐based power analysis to predict trade‐offs between sampling breadth (number of sites and years) and sampling intensity (number of visits or subplots per site and year) for the IMMP. We evaluated whether each sampling design would produce sufficient statistical power to detect population trends and differences among land‐use sectors in densities of milkweed, monarch eggs, and adult monarchs. Sampling breadth had much stronger effects than sampling intensity on statistical power for all three monitoring targets. Depending on land‐use sector, monitoring 400–800 sites over 10–15 years would detect trends in densities of milkweed and adult monarchs, but no scenarios were successful for monarch eggs. Sampling 400–800 sites would also detect small (for adult monarchs) to large (for milkweed) differences among land‐use sectors in density of all three monitoring targets within the first 2–5 years. As more data become available from the IMMP, the sampling goals can be updated. Synthesis and applications . Careful sample design is an essential step in developing a successful monitoring programme. For monarchs and milkweed, we found that sampling breadth (number of sites and years) had a much stronger effect on statistical power than sampling intensity (number of visits or subsamples per site), suggesting field protocols could be tailored to maximize recruitment and retention of volunteers by minimizing the effort required to monitor each site. Many long‐term monitoring programmes might similarly benefit from evaluating the statistical trade‐offs between sampling breadth and intensity in their sampling designs.

Journal of Applied Ecology↗

USGS2009

A cautionary note on substituting spatial subunits for repeated temporal sampling in studies of site occupancy

1. Assessing the probability that a given site is occupied by a species of interest is important to resource managers, as well as metapopulation or landscape ecologists. Managers require accurate estimates of the state of the system, in order to make informed decisions. Models that yield estimates of occupancy, while accounting for imperfect detection, have proven useful by removing a potentially important source of bias. To account for detection probability, multiple independent searches per site for the species are required, under the assumption that the species is available for detection during each search of an occupied site. 2. We demonstrate that when multiple samples per site are defined by searching different locations within a site, absence of the species from a subset of these spatial subunits induces estimation bias when locations are exhaustively assessed or sampled without replacement. 3. We further demonstrate that this bias can be removed by choosing sampling locations with replacement, or if the species is highly mobile over a short period of time. 4. Resampling an existing data set does not mitigate bias due to exhaustive assessment of locations or sampling without replacement. 5. Synthesis and applications. Selecting sampling locations for presence/absence surveys with replacement is practical in most cases. Such an adjustment to field methods will prevent one source of bias, and therefore produce more robust statistical inferences about species occupancy. This will in turn permit managers to make resource decisions based on better knowledge of the state of the system.

Journal of Applied Ecology↗

USGS2021

Assessment of a claimed ultra-low frequency electromagnetic (ULFEM) earthquake precursor

The rate of occurrence of anomalous ultra-low frequency electromagnetic (ULFEM) pulses has been claimed to have increased days to weeks prior to the M5.4 2007 and M4.0 2010 Alum Rock earthquakes. We re-examine the previously reported ultra-low frequency (ULF: 0.01–10 Hz) magnetic data recorded at a QuakeFinder site located 9 km from the earthquake hypocentre, and compare to data from a nearby Stanford-USGS site located 42 km from the hypocentre, to analyse the characteristics of the pulses and assess their origin. Using pulse definitions and pulse-counting algorithms analogous to those previously reported, we corroborate the increase in pulse counts before the 2007 Alum Rock earthquake at the QuakeFinder station, but we note that the number of pulses depends on chosen temporal and amplitude detection thresholds. These thresholds are arbitrary because we lack a clear physical model or basis for their selection. We do not see the same increase in pulse counts before the 2010 Alum Rock earthquake at the QuakeFinder or Stanford-USGS stations. In addition, the majority of pulses in the QuakeFinder data and Stanford-USGS data do not match temporally, indicating the pulses lack a common origin and are not from lightning or solar-driven ionospheric/magnetospheric disturbances. Our assessment of the temporal distribution of pulse counts shows pulse counts increase during peak human activity hours, suggesting these pulses result from local cultural noise and are not tectonic in origin. The many unknowns about the character and even existence of precursory earthquake pulses means that standard numerical and statistical tests cannot easily be applied. Yet here we show that exhaustive investigation of many different aspects of ULFEM signals can be used to properly characterize their origin.

California↗

USGS1988

A field test for differences in condition among trapped and shot mallards

We tested predictions from the condition bias hypothesis (Weatherland and Greenwood 1981) regarding the effects of sampling methods of body weights of mallards ( Anas platyrhynchos ) at White River National Wildlife Refuge (WRNWR), Arkansas, during 24 November-8 December 1985. Body weights of 84 mallards caught with unbaited rocket nets in a natural wetland were used as experimental controls and compared to the body weights of 70 mallards captured with baited rocket nets, 86 mallards captured with baited swim-in traps, and 130 mallards killed by hunters. We found no differences (P > 0.27) in body weight among sampling methods, but body condition (wt/wing length) of the birds killed by hunters was less (P < 0.02) than that of the controls. Power of the test statistics to reject the null hypothesis of equal body weights among sampling methods was > 0.75 for differences > 50 g. The condition bias hypothesis probably applies to ducks killed by hunters but not to trapping operations when substantial (> 20 at 1 time) numbers of birds are captured.

Arkansas↗

USGS1978

Low-cost computer classification of land cover in the Portland area, Oregon, by signature extension techniques

Computer-aided techniques for interpreting multispectral data acquired by Landsat offer economies in the mapping of land cover. Even so, the actual establishment of the statistical classes, or "signatures," is one of the relatively more costly operations involved. Analysts have, therefore, been seeking cost-saving signature extension techniques that would accept training data acquired at one time or place and apply them to another. Signatures may be extended in preprocessing steps or in the classification steps that follow. In the present example, land cover classes were derived by the simplest and most direct form of signature extension: Classes statistically derived from a Landsat scene of the Puget Sound area, Wash., were applied to the adjacent Landsat scene of the Portland area, Oreg., acquired during the next 25 seconds down orbit. Many features can be recognized on the reduced-scale version of the Portland land cover map shown in this report although no statistical assessment of its accuracy is available.

Oregon, Washington↗

USGS2002

Yellowstone grizzly bear investigations: Annual report of the Interagency Grizzly Bear Study Team, 2001

The contents of this Annual Report summarize results of monitoring and research from the 2001 field season. The report also contains a summary of nuisance grizzly bear ( Ursus arctos horribilis ) management actions. In addition to our normal monitoring, we completed an array of studies addressing the potential impacts of winter recreation on denning grizzly bears. This research was in response to a lawsuit filed against the Gallatin National Forest and subsequent need to develop a biological assessment addressing effects of snowmobile use on grizzly bears (Chemy 2001). Research results were also used by the National Park Service for a biological assessment and winter use plan (U.S. Department of the Interior 2001). The Interagency Grizzly Bear Study Team (IGBST) was able to use existing data collected from collared bears to address several issues and data needs for both agencies. Denning chronology (Haroldson et al. 2002), denning areas (Podruzny et al. 2002), and grizzly distribution (Schwartz et al. 2002) were all addressed. Information from these studies was presented at the International Association for Bear Research and Management (IBA) in Jackson Hole, Wyoming in 2001, and all 3 manuscripts have been officially accepted for publication in the journal Ursus . Abstracts are attached to this report (Appendices A, B. and C). Additionally, members of the study team participated in a workshop held by the National Park Service to develop monitoring protocols addressing the impacts of snowmobiles on wildlife (Graves and Reams 2001). The study team has also been working on issues associated with counts of unduplicated females with cubs-of-the-year (COY). These counts are used to establisha minimum population size, which is then used to establish mortality thresholds for the Recovery Plan (U.S. Fish and Wildlife Service [USFWS) 1993). Efforts by the Study Team to calculate more statistically sound estimates of population size have been underway for sometime. Eberhardt and Knight (1996) applied a Peterson-type capturemark-recapture estimator to unduplicated counts, and Boyce et al. (1999) recommended a maximum likelihood method. These methods assumed equal sightability of families, which was unrealistic for the Yellowstone population. Consequently, Boyce et al. (2001) recommended using a negative binomial distribution but found that they obtained reasonable results only when the coefficient of variation among sightings was assumed to be constant overtime. This assumption is also difficult to justify. Recent work by the study team (Keating et al. 2002) evaluated the application of 7 nonparametric estimators to assess their performance in determining the number of females with COY in a given year. This work identified 2 estimators that performed well using Monte Carlo simulations over a range of sampling conditions deemed plausible for the Yellowstone population: Chao's estimator (Chao 1984) and the sample coverage estimator (Chao and Lee 1992, Lee and Chao 1994). This work was presented at the IBA meeting in Jackson and the manuscript has been accepted in the journal Ursus . An abstract of this work is attached to this annual report (Appendix D). We are currently refining the application of these techniques to expand the predicted number of females with COY into a total population estimate. We anticipate completion of that work in 2002 or 2003.

Idaho, Montana, Wyoming↗

USGS2025

Valuing recreational fishing using creel survey statistics

Recreation demand analysis has relied on mail and internet surveys to collect information on individual recreators. However, conducting these surveys is costly and time-consuming. Alternative sources that report aggregate visitation may go unused due to a lack of information about trip starting points. We set up and solve a system of equations that predict reservoir visits and the home locations of recreational anglers. Using mode-level effort statistics from Nebraska creel surveys, we separate the effects of travel cost and site attributes between bank and boat anglers, which allows us to measure heterogenous values for public reservoir access.

Nebraska↗

USGS2018

Analysis of population change and movement using robust design removal data

In capture-mark-reencounter studies, Pollock’s robust design combines methods for open populations with methods for closed populations. Open population features of the robust design allow for estimation of rates of death or permanent emigration, and closed population features enhance estimation of population sizes. We describe a similar design, but for use with removal data. Data collection occurs on secondary sampling occasions clustered within primary sampling periods. Primary sampling periods are intervals of brief enough duration that it can be safely assumed that the population is unchanged by births, deaths, immigration or emigration during them; all population change and movement occurs between primary sampling periods. Our model provides a basis for inference about population size, changes in population size, and movement rates among sample locations between primary sampling periods. Movement rates are modeled as functions of distance and time. Capture probabilities are modeled as a function of effort. We apply the model to data obtained in attempting to eradicate an introduced population of veiled chameleons ( Chamaeleo calyptratus ) on the island of Maui in Hawaii.

Journal of Agricultural, Biological, and Environme↗

USGS2024

Cross-fade sampling: Extremely efficient Bayesian inversion for a variety of geophysical problems

This paper introduces cross-fade sampling, a computationally efficient Markov Chain Monte Carlo simulation method that uses a semi-analytical approach to quickly solve Bayesian inverse problems that do not themselves have an analytical solution. Cross-fading is efficient in two ways. First, it requires fewer samples to obtain the same quality simulation of the target probability density function (PDF). Secondly, it is much faster to evaluate the posterior probability of each sample than conventional sampling methods for simulating Bayesian posterior PDFs. Conventional methods require evaluating the prior probability (which describes your a priori constraints) and data likelihood (which describes the fit between the observations and the predictions of the model) for each sample model. However, cross-fading does not require evaluating the data likelihood, meaning that ‘big data’ can be fit with zero additional computational cost. Further, the cross-fading approach can be used to calculate the marginal likelihood associated with a model design, facilitating model comparison and Bayesian model averaging. Topics covered in this paper include derivation of the cross-fade approach and how it can be used to simulate Bayesian posterior PDFs and compute the marginal likelihood, discussion of the class of problems to which cross-fading can be applied (with examples from earthquake statistics, earthquake ground motion modelling, volcanic eruption forecasting, and finite fault slip modelling), demonstration of efficiency relative to existing sampling methods and discussion of how cross-fading can be used to account for prediction errors (i.e. epistemic errors) as part of the geophysical inverse problem.

Geophysical Journal International↗

USGS2023

Bridging the gap between mathematical biology and undergraduate education using applicable natural resource modeling

Mathematical biology is a wide field of study with many venues that undergraduate students can access through research. However, the topics of study for these students can be overwhelming, and many topics of study yield either only trivial results or abstract outcomes that are nonintuitive and diffcult to understand. We have used natural resource modeling, and more specifically, a partnership between academic researchers and federal scientists, as a bridge between undergraduate research and mathematical biology. Our collaboration is an interdisciplinary team that combines biology, mathematics, and statistics professors with government research scientists. As a team, we have mentored students through opportunities such as a Research Experiences for Undergraduates and other projects. In this article, we provide an overview of how we develop questions for undergraduates and outline two case studies, both of which resulted in peer reviewed journal articles. Last, we describe how we also transfer the results from these undergraduate projects to resource managers so the results may be applied to real world problems.

Letters in Biomathematics↗

USGS2015

Spatial occupancy models for predicting metapopulation dynamics and viability following reintroduction

The reintroduction of a species into its historic range is a critical component of conservation programmes designed to restore extirpated metapopulations. However, many reintroduction efforts fail, and the lack of rigorous monitoring programmes and statistical models have prevented a general understanding of the factors affecting metapopulation viability following reintroduction. Spatially explicit metapopulation theory provides the basis for understanding the dynamics of fragmented populations linked by dispersal, but the theory has rarely been used to guide reintroduction programmes because most spatial metapopulation models require presence–absence data from every site in the network, and they do not allow for observation error such as imperfect detection. We develop a spatial occupancy model that relaxes these restrictive assumptions and allows for inference about metapopulation extinction risk and connectivity. We demonstrate the utility of the model using six years of data on the Chiricahua leopard frog Lithobates chiricahuensis , a threatened desert-breeding amphibian that was reintroduced to a network of sites in Arizona USA in 2003. Our results indicate that the model can generate precise predictions of extinction risk and produce connectivity maps that can guide conservation efforts following reintroduction. In the case of L. chiricahuensis , many sites were functionally isolated, and 82% of sites were characterized by intermittent water availability and high local extinction probabilities (0·84, 95% CI: 0·64–0·99). However, under the current hydrological conditions and spatial arrangement of sites, the risk of metapopulation extinction is estimated to be <3% over a 50-year time horizon. Low metapopulation extinction risk appears to result from the high dispersal capability of the species, the high density of sites in the region and the existence of predator-free permanent wetlands with low local extinction probabilities. Should management be required, extinction risk can be reduced by either increasing the hydroperiod of existing sites or by creating new sites to increase connectivity. Synthesis and applications . This work demonstrates how spatio-temporal statistical models based on ecological theory can be applied to forecast the outcomes of conservation actions such as reintroduction. Our spatial occupancy model should be particularly useful when management agencies lack the funds to collect intensive individual-level data.

Arizona, New Mexico↗