Paul B. Conn

Spatial occupancy models for large data sets

Since its development, occupancy modeling has become a popular and useful tool for ecologists wishing to learn about the dynamics of species occurrence over time and space. Such models require presence–absence data to be collected at spatially indexed survey units. However, only recently have researchers recognized the need to correct for spatially induced overdisperison by explicitly accounting for spatial autocorrelation in occupancy probability. Previous efforts to incorporate such autocorrelation have largely focused on logit-normal formulations for occupancy, with spatial autocorrelation induced by a random effect within a hierarchical modeling framework. Although useful, computational time generally limits such an approach to relatively small data sets, and there are often problems with algorithm instability, yielding unsatisfactory results. Further, recent research has revealed a hidden form of multicollinearity in such applications, which may lead to parameter bias if not explicitly addressed. Com...

When can we reliably estimate the productivity of fish stocks

In modern fishery stock assessments, the productivity of exploited stocks is frequently summarized by a scale-invariant “steepness” parameter. This parameter, which describes the slope of the spawner–recruit curve, determines resilience of a stock to exploitation and is highly influential when estimating maximum sustainable yield. In this study, we examined conditions under which steepness can be estimated reliably. We applied a statistical catch-age model to data that were simulated over a broad range of stock characteristics and exploitation patterns and found that steepness is often estimated at its upper bound regardless of underlying productivity. The ability to estimate steepness reliably was most dependent on the true value of steepness, the exploitation history of the stock, natural mortality, duration of the time series, and quality of an index of abundance; this ability was relatively unaffected by levels of stochasticity in recruitment and sampling intensity of age compositions. We further expl...

marked: an R package for maximum likelihood and Markov Chain Monte Carlo analysis of capture–recapture data

Summary We describe an open-source r package, marked, for analysis of mark–recapture data to estimate survival and animal abundance. Currently, marked is capable of fitting Cormack–Jolly–Seber (CJS) and Jolly–Seber models with maximum likelihood estimation (MLE) and CJS models with Bayesian Markov Chain Monte Carlo methods. The CJS models can be fitted with MLE using optimization code in R or with Automatic Differentiation Model Builder. The latter allows incorporation of random effects. Some package features include: (i) individual-specific time intervals between sampling occasions, (ii) generation of optimization starting values from generalized linear model approximations and (iii) prediction of demographic parameters associated with unique combinations of individual and time-specific covariates. We demonstrate marked with a commonly analysed European dipper (Cinclus cinclus) data set. The package will be most useful to ecologists with large mark–recapture data sets and many individual covariates.

Integrated Population Modeling of Black Bears in Minnesota: Implications for Monitoring and Management

Background Wildlife populations are difficult to monitor directly because of costs and logistical challenges associated with collecting informative abundance data from live animals. By contrast, data on harvested individuals (e.g., age and sex) are often readily available. Increasingly, integrated population models are used for natural resource management because they synthesize various relevant data into a single analysis. Methodology/Principal Findings We investigated the performance of integrated population models applied to black bears (Ursus americanus) in Minnesota, USA. Models were constructed using sex-specific age-at-harvest matrices (1980–2008), data on hunting effort and natural food supplies (which affects hunting success), and statewide mark–recapture estimates of abundance (1991, 1997, 2002). We compared this approach to Downing reconstruction, a commonly used population monitoring method that utilizes only age-at-harvest data. We first conducted a large-scale simulation study, in which our integrated models provided more accurate estimates of population trends than did Downing reconstruction. Estimates of trends were robust to various forms of model misspecification, including incorrectly specified cub and yearling survival parameters, age-related reporting biases in harvest data, and unmodeled temporal variability in survival and harvest rates. When applied to actual data on Minnesota black bears, the model predicted that harvest rates were negatively correlated with food availability and positively correlated with hunting effort, consistent with independent telemetry data. With no direct data on fertility, the model also correctly predicted 2-point cycles in cub production. Model-derived estimates of abundance for the most recent years provided a reasonable match to an empirical population estimate obtained after modeling efforts were completed. Conclusions/Significance Integrated population modeling provided a reasonable framework for synthesizing age-at-harvest data, periodic large-scale abundance estimates, and measured covariates thought to affect harvest rates of black bears in Minnesota. Collection and analysis of these data appear to form the basis of a robust and viable population monitoring program.

Estimating multispecies abundance using automated detection systems: ice‐associated seals in the Bering Sea

Summary Automated detection systems employing advanced technology (e.g. infrared imagery, auditory recording systems, pattern recognition software) are compelling tools for gathering animal abundance and distribution data since investigators can often collect data more efficiently and reduce animal disturbance relative to surveys using human observers. Even with these improvements, analysing animal abundance with advanced technology can be challenging because of potential for incomplete detection, false positives and species misidentification. We argue that double sampling with an independent sampling method can provide the critical information needed to account for such errors. We present a hierarchical modelling framework for jointly analysing automated detection and double sampling data obtained during animal population surveys. Under our framework, observed counts in different sampling units are conceptualized as having arisen from a thinned log-Gaussian Cox process subject to spatial autocorrelation (where thinning accounts for incomplete detection). For multispecies surveys, our approach handles incomplete species observations owing to (i) structural uncertainties (e.g. in cases where the automatic detection data do not provide species observations) and (ii) species misclassification; the latter requires auxiliary information on the misclassification process. As an example of combining an automated detection system and a double sampling procedure, we consider the problem of estimating animal abundance from aerial surveys that use infrared imagery to detect animals, and independent, high-resolution digital photography to provide information on species composition and thermal detection accuracy. We illustrate our approach by analysing simulated data and data from a survey of four ice-associated seal species in the eastern Bering Sea. Our analysis indicated reasonable performance of our hierarchical modelling approach, but suggested a need to balance model complexity with the richness of the data set. For example, highly parameterized models can lead to spuriously high predictions of abundance in areas that are not sampled, especially when there are large gaps in spatial coverage. We recommend that ecologists employ double sampling when enumerating animal populations with automated detection systems to estimate and correct for detection errors. Combining multiple data sets within a hierarchical modelling framework provides a powerful approach for analysing animal abundance over large spatial domains.

Accounting for Transients When Estimating Abundance of Bottlenose Dolphins in Choctawhatchee Bay, Florida

ABSTRACT We investigated the potential for using mark—recapture models to estimate abundance of bottlenose dolphin populations in open systems (e.g., bays, estuaries). A major challenge in these systems is that immigration and emigration occur during sampling, thus violating one of the most basic assumptions of mark—recapture models. We assumed that dolphins using our study site were composed of both residents (those that used the study area almost exclusively during our study), and transients (those that passed through our study area but did not remain long), and examined several mark-recapture estimators for their ability to accurately and precisely estimate the abundance of residents and the superpopulation (i.e., residents + transients). Using simulated data, we found that a novel approach accounting for transients resulted in estimators with less bias, smaller absolute relative error, and confidence interval coverage closer to nominal than other approaches, but this novel approach required intensive sampling and that the “correct” transient pattern be specified. In contrast, classical mark—recapture estimators for closed populations often overestimated the number of residents and underestimated the superpopulation. Using photo-identification records, a model-averaged estimate of the superpopulation of bottlenose dolphins in and around Choctawhatchee Bay, Florida was 232 (SE = 13) animals. We estimated resident abundance at 179 (SE = 8), which was lower than the number of unique animals we encountered (188). Our results appear promising for developing monitoring programs for bottlenose dolphins and other taxa in open systems. Our estimators should prove useful to wildlife managers who wish to base conservation decisions on estimates of the number of animals that reside primarily in their study or management area.

Using spatiotemporal statistical models to estimate animal abundance and infer ecological dynamics from survey counts

Ecologists often fit models to survey data to estimate and explain variation in animal abundance. Such models typically require that animal density remains constant across the landscape where sampling is being conducted, a potentially problematic assumption for animals inhabiting dynamic landscapes or otherwise exhibiting considerable spatiotemporal variation in density. We review several concepts from the burgeoning literature on spatiotemporal statistical models, including the nature of the temporal structure (i.e., descriptive or dynamical) and strategies for dimension reduction to promote computational tractability. We also review several features as they specifically relate to abundance estimation, including boundary conditions, population closure, choice of link function, and extrapolation of predicted relationships to unsampled areas. We then compare a suite of novel and existing spatiotemporal hierarchical models for animal count data that permit animal density to vary over space and time, including formulations motivated by resource selection and allowing for closed populations. We gauge the relative performance (bias, precision, computational demands) of alternative spatiotemporal models when confronted with simulated and real data sets from dynamic animal populations. For the latter, we analyze spotted seal (Phoca largha) counts from an aerial survey of the Bering Sea where the quantity and quality of suitable habitat (sea ice) changed dramatically while surveys were being conducted. Simulation analyses suggested that multiple types of spatiotemporal models provide reasonable inference (low positive bias, high precision) about animal abundance, but have potential for overestimating precision. Analysis of spotted seal data indicated that several model formulations, including those based on a log-Gaussian Cox process, had a tendency to overestimate abundance. By contrast, a model that included a population closure assumption and a scale prior on total abundance produced estimates that largely conformed to our a priori expectation. Although care must be taken to tailor models to match the study population and survey data available, we argue that hierarchical spatiotemporal statistical models represent a powerful way forward for estimating abundance and explaining variation in the distribution of dynamical populations.

A Hierarchical Modeling Framework for Multiple Observer Transect Surveys

Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line), these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size). We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package, hierarchicalDS, to facilitate the building and fitting of these models.

On Extrapolating Past the Range of Observed Data When Making Statistical Predictions in Ecology

Ecologists are increasingly using statistical models to predict animal abundance and occurrence in unsampled locations. The reliability of such predictions depends on a number of factors, including sample size, how far prediction locations are from the observed data, and similarity of predictive covariates in locations where data are gathered to locations where predictions are desired. In this paper, we propose extending Cook’s notion of an independent variable hull (IVH), developed originally for application with linear regression models, to generalized regression models as a way to help assess the potential reliability of predictions in unsampled areas. Predictions occurring inside the generalized independent variable hull (gIVH) can be regarded as interpolations, while predictions occurring outside the gIVH can be regarded as extrapolations worthy of additional investigation or skepticism. We conduct a simulation study to demonstrate the usefulness of this metric for limiting the scope of spatial inference when conducting model-based abundance estimation from survey counts. In this case, limiting inference to the gIVH substantially reduces bias, especially when survey designs are spatially imbalanced. We also demonstrate the utility of the gIVH in diagnosing problematic extrapolations when estimating the relative abundance of ribbon seals in the Bering Sea as a function of predictive covariates. We suggest that ecologists routinely use diagnostics such as the gIVH to help gauge the reliability of predictions from statistical models (such as generalized linear, generalized additive, and spatio-temporal regression models).

Confronting preferential sampling when analysing population distributions: diagnosis and model-based triage

Summary Population surveys are often used to estimate the density, abundance, or distribution of natural populations. Recently, model-based approaches to analyzing survey data have become popular because one can more readily accommodate departures from pre-planned survey routes and construct more detailed maps than one can with design-based procedures. Spatial models for population distributions often make the implicit assumption that locations chosen for sampling and animal abundance at those locations are conditionally independent given modeled covariates. However, this assumption may be violated when survey effort is non-randomized, leading to preferential sampling. We develop a hierarchical statistical modeling framework for detecting and alleviating the biasing effects of preferential sampling in spatial distribution models fitted to count data. The approach works by specifying a joint model for population density and the locations selected for sampling, and specifying a dependent correlation structure between the two processes. Using simulation, we show that moderate levels of preferential sampling can lead to large (e.g. 40%) bias in estimates of animal density and that our modeling approach can considerably reduce this bias. In contrast, preferential sampling did not appear to bias inferences about parameters informing species-habitat relationships (i.e. slope parameters). We apply our approach to aerial survey counts of bearded seals (Erignathus barbatus) in the eastern Bering Sea. As expected, models with a preferential sampling effect led to lower abundance than those without. However, several lines of reasoning (better predictive performance, higher biological realism) led us to prefer models without a preferential sampling effect for this data set. When population surveys break from traditional scientific survey design principles, ecologists should recognize the potentially biasing effects of preferential sampling when estimating population density or occurrence. Joint models, such as those described in this paper, can be used to test and correct for such biases. However, such models can be unstable; ultimately the best way to avoid preferential sampling bias is to incorporate design-based principles such as randomization and/or systematic sampling into survey design. This article is protected by copyright. All rights reserved.