Review of the book Handbook of spatial point-pattern analysis in Ecology, by Thorsten Wiegand and Kirk A. Moloney
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Journal of Agricultural, Biological, and Environme↗
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Book review: Analysis of capture–recapture data
Analysis of Capture–Recapture Data by McCrea and Morgan is an excellent, easy to read monograph about capture–recapture models. In this book, the authors provide a concise overview of traditional closed population capture–recapture models (Models M0, Mb, Mh, etc.), individual covariate models, and open population models such as the Cormack–Jolly–Seber, Jolly–Seber models, multi-state models, and more recent developments such as occupancy models, state-space models, and integrated population models. The authors write “In this book we aim to cover the many modern developments in the area of capture–recapture and related models, and to set them in historical context of relevant research over the past 100 years.” The book does a good job of achieving this objective. And it is a very easy to read because it is well organized and the writing is clear and concise. I would recommend this book as a reference for the quantitative ecologist or statistician interested in knowing what’s out there. Review info: Analysis of Capture–Recapture Data. By Rachel S. McCrea and Byron J. T. Morgan, 2015. ISBN: 978-14398-6590, xx+292 pp.
Journal of Agricultural, Biological, and Environme↗
Individual heterogeneity in growth and age at sexual maturity: A gamma process analysis of capture–mark–recapture data
Knowledge of organisms’ growth rates and ages at sexual maturity is important for conservation efforts and a wide variety of studies in ecology and evolutionary biology. However, these life history parameters may be difficult to obtain from natural populations: individuals encountered may be of unknown age, information on age at sexual maturity may be uncertain and interval-censored, and growth data may include both individual heterogeneity and measurement errors. We analyzed mark–recapture data for Red-backed Salamanders ( Plethodon cinereus ) to compare sex-specific growth rates and ages at sexual maturity. Aging of individuals was made possible by the use of a von Bertalanffy model of growth, complemented with models for interval-censored and imperfect observations at sexual maturation. Individual heterogeneity in growth was modeled through the use of Gamma processes. Our analysis indicates that female P. cinereus mature earlier and grow more quickly than males, growing to nearly identical asymptotic size distributions as males.
Journal of Agricultural, Biological, and Environme↗
Extending ordinal regression with a latent zero-augmented beta distribution
Ecological abundance data are often recorded on an ordinal scale in which the lowest category represents species absence. One common example is when plant species cover is visually assessedwithin bounded quadrats and then assigned to pre-defined cover class categories.We present an ordinal beta hurdle model that directly models ordinal category probabilitieswith a biologically realistic beta-distributed latent variable.Ahurdle-at-zero model allows ecologists to explore distribution (absence) and abundance processes in an integrated framework. This provides an alternative to cumulative link models when data are inconsistent with the assumption that the odds ofmoving into a higher category are the same for all categories (proportional odds). Graphical tools and a deviance information criterion were developed to assess whether a hurdle-at-zero model should be used for inferences rather than standard ordinal methods. Hurdle-at-zero and non-hurdle ordinal models fit to vegetation cover class data produced substantially different conclusions.The ordinal beta hurdle model yielded more precise parameter estimates than cumulative logit models, although out-of-sample predictions were similar. The ordinal beta hurdle model provides inferences directly on the latent biological variable of interest, percent cover, and supports exploration of more realistic ecological patterns and processes through the hurdle-at-zero or two-part specification.We provide JAGS code as an on-line supplement. Supplementary materials accompanying this paper appear on-line.
Journal of Agricultural, Biological, and Environme↗
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↗
Agent-based models for collective animal movement: Proximity-induced state switching
Animal movement is a complex phenomenon where individual movement patterns can be influenced by a variety of factors including the animal’s current activity, available terrain and habitat, and locations of other animals. Motivated by modeling grizzly bear movement in the Greater Yellowstone Ecosystem, this article presents an agent-based model represented in a state-space framework for collective animal movement. The novel contribution of this work is a collective animal movement model that captures interactions between animals that can trigger changes in movement patterns, such as when a dominant grizzly bear may cause another subordinate bear to temporarily leave an area. The modeling framework enables learning different movement patterns through a state-space representation with particle-MCMC methods for fully Bayesian model fitting and the prediction of future animal movement behaviors.
Journal of Agricultural, Biological and Environmen↗
Greater than the sum of its parts: Computationally flexible Bayesian hierarchical modeling
We propose a multistage method for making inference at all levels of a Bayesian hierarchical model (BHM) using natural data partitions to increase efficiency by allowing computations to take place in parallel form using software that is most appropriate for each data partition. The full hierarchical model is then approximated by the product of independent normal distributions for the data component of the model. In the second stage, the Bayesian maximum a posteriori (MAP) estimator is found by maximizing the approximated posterior density with respect to the parameters. If the parameters of the model can be represented as normally distributed random effects, then the second-stage optimization is equivalent to fitting a multivariate normal linear mixed model. We consider a third stage that updates the estimates of distinct parameters for each data partition based on the results of the second stage. The method is demonstrated with two ecological data sets and models, a generalized linear mixed effects model (GLMM) and an integrated population model (IPM). The multistage results were compared to estimates from models fit in single stages to the entire data set. In both cases, multistage results were very similar to a full MCMC analysis. Supplementary materials accompanying this paper appear online.
Journal of Agricultural, Biological and Environmen↗
Dynamic population models with temporal preferential sampling to infer phenology
To study population dynamics, ecologists and wildlife biologists typically use relative abundance data, which may be subject to temporal preferential sampling. Temporal preferential sampling occurs when the times at which observations are made and the latent process of interest are conditionally dependent. To account for preferential sampling, we specify a Bayesian hierarchical abundance model that considers the dependence between observation times and the ecological process of interest. The proposed model improves relative abundance estimates during periods of infrequent observation and accounts for temporal preferential sampling in discrete time. Additionally, our model facilitates posterior inference for population growth rates and mechanistic phenometrics. We apply our model to analyze both simulated data and mosquito count data collected by the National Ecological Observatory Network. In the second case study, we characterize the population growth rate and relative abundance of several mosquito species in the Aedes genus. Supplementary materials accompanying this paper appear on-line.
Journal of Agricultural, Biological, and Environme↗
Melded integrated population models
Integrated population models provide a framework for assimilating multiple datasets to understand population dynamics. Understanding drivers of demography is key to improving wildlife management, and integrated population models have informed conservation practices for many species of conservation concern. Motivated by multiple surveys of lesser prairie-chicken ( Tympanuchus pallidicinctus ), we developed a flexible integrated population modeling framework for assimilating demographic data with multiple surveys of abundance. Measurements of abundance are derived from aerial and ground surveys that vary in their observational uncertainty, sampling design, temporal coverage, and survey effort. Our proposed integrated population model draws from the strengths of each survey and prevents their sampling biases from compromising inference. We facilitate posterior inference for our integrated population model using chained Markov melding, which induces the joint distribution for all data sources by linking inference across several submodels. Using Markov melding, we extend the modeling framework previously proposed for analyzing the individual data sources while still obtaining joint Bayesian inference. We fit the melded model with a multistage Markov chain Monte Carlo algorithm that decreases run time and improves mixing. We assimilate data from several state and federal wildlife agencies and over a dozen independent researchers to infer lesser prairie-chicken abundance and vital rates across its entire range over the last 18 years. Supplementary materials accompanying this paper appear online.
Colorado, Kansas, New Mexico, Oklahoma, Texas↗
Estimating submersed aquatic vegetation biomass using a hierarchical Bayesian model of ordinal measurements and structural zeros
This study explores the prediction of a continuous target variable that is primarily measured as an ordinal outcome. Interest in such prediction may occur given data from double- or two-phase sampling designs, where an auxiliary variable is measured at all sampling units and a target and predictor variable, X , at a subset of those units. This study focuses on the case where X is nonnegative, is conditional on a zero process, and is sampled using a cluster sampling design. We model the ordinal outcome using cumulative logistic regression and the conditional regressor X , following log transformation, in a Bayesian setting. Estimation of model parameters and prediction of missing X is generally accurate and precise, particularly with sufficiently large Pr(X > 0) and associated variances. This study is motivated by a need to accurately estimate the biomass of submersed aquatic vegetation on the Upper Mississippi River, where two types of measurements for biomass are available: inexpensive, ordinal biomass scores and expensive, continuous diver-harvested biomass data. Here, X represents plant biomass and Pr(X > 0) is the usual species site occupancy measure. When fit using biomass data from the submerged aquatic vegetation species Vallisneria americana Michx, our model estimates parameters within the parameter space region where the model performed acceptably using synthetic data. We expect this model to appeal to investigators with ordered outcomes, cluster designs, and one or more continuous, positive predictors.
Journal of Agricultural, Biological and Environmen↗
Estimation of population size using open capture-recapture models
One of the most important needs for wildlife managers is an accurate estimate of population size. Yet, for many species, including most marine species and large mammals, accurate and precise estimation of numbers is one of the most difficult of all research challenges. Open-population capture-recapture models have proven useful in many situations to estimate survival probabilities but typically have not been used to estimate population size. We show that open-population models can be used to estimate population size by developing a Horvitz-Thompson-type estimate of population size and an estimator of its variance. Our population size estimate keys on the probability of capture at each trap occasion and therefore is quite general and can be made a function of external covariates measured during the study. Here we define the estimator and investigate its bias, variance, and variance estimator via computer simulation. Computer simulations make extensive use of real data taken from a study of polar bears (Ursus maritimus) in the Beaufort Sea. The population size estimator is shown to be useful because it was negligibly biased in all situations studied. The variance estimator is shown to be useful in all situations, but caution is warranted in cases of extreme capture heterogeneity.
Journal of Agricultural, Biological, and Environme↗
Polar bears in the Beaufort Sea: A 30-year mark-recapture case history
Knowledge of population size and trend is necessary to manage anthropogenic risks to polar bears ( Ursus maritimus ). Despite capturing over 1,025 females between 1967 and 1998, previously calculated estimates of the size of the southern Beaufort Sea (SBS) population have been unreliable. We improved estimates of numbers of polar bears by modeling heterogeneity in capture probability with covariates. Important covariates referred to the year of the study, age of the bear, capture effort, and geographic location. Our choice of best approximating model was based on the inverse relationship between variance in parameter estimates and likelihood of the fit and suggested a growth from ≈ 500 to over 1,000 females during this study. The mean coefficient of variation on estimates for the last decade of the study was 0.16—the smallest yet derived. A similar model selection approach is recommended for other projects where a best model is not identified by likelihood criteria alone.
Beaufort Sea↗
A permutation test for quantile regression
A drop in dispersion, F -ratio like, permutation test ( D ) for linear quantile regression estimates (0≤τ≤1) had relative power ≥1 compared to quantile rank score tests ( T ) for hypotheses on parameters other than the intercept. Power was compared for combinations of sample sizes ( n =20−300) and quantiles (τ=0.50−0.99) where both tests maintained valid Type I error rates in simulations with p =2 and 6 parameters in homogeneous and heterogeneous error models. The D test required two modifications of permuting residuals from null, reduced parameter models to maintain correct Type I error rates when null models were constrained through the origin or included multiple parameters. A double permutation scheme was used when null models were constrained through the origin and all but 1 of the zero residuals were deleted for null models with multiple parameters. Although there was considerable overlap in sample size, quantiles, and hypotheses where both the D and rank score tests maintained correct Type I error rates, we identified regions at smaller n and more extreme quantiles where one or the other maintained better error rates. Confidence intervals on parameters for an ecological application relating Lahontan cutthroat trout densities to stream channel width:depth were estimated by test inversion, demonstrating a smoother pattern of slightly narrower intervals across quantiles than those provided by the rank score test.
Journal of Agricultural, Biological, and Environme↗
Evaluating estimators for numbers of females with cubs-of-the-year in the Yellowstone grizzly bear population
Current management of the grizzly bear ( Ursus arctos ) population in Yellowstone National Park and surrounding areas requires annual estimation of the number of adult female bears with cubs-of-the-year. We examined the performance of nine estimators of population size via simulation. Data were simulated using two methods for different combinations of population size, sample size, and coefficient of variation of individual sighting probabilities. We show that the coefficient of variation does not, by itself, adequately describe the effects of capture heterogeneity, because two different distributions of capture probabilities can have the same coefficient of variation. All estimators produced biased estimates of population size with bias decreasing as effort increased. Based on the simulation results we recommend the Chao estimator for model M h be used to estimate the number of female bears with cubs of the year; however, the estimator of Chao and Shen may also be useful depending on the goals of the research.
Wyoming↗
Spatial design and strength of spatial signal: Effects on covariance estimation
In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling ( n =144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.
Journal of Agricultural, Biological, and Environme↗
Use of generalized linear models and digital data in a forest inventory of northern Utah
Forest inventories, like those conducted by the Forest Service's Forest Inventory and Analysis Program (FIA) in the Rocky Mountain Region, are under increased pressure to produce better information at reduced costs. Here we describe our efforts in Utah to merge satellite-based information with forest inventory data for the purposes of reducing the costs of estimates of forest population totals and providing spatial depiction of forest resources. We illustrate how generalized linear models can be used to construct approximately unbiased and efficient estimates of population totals while providing a mechanism for prediction in space for mapping of forest structure. We model forest type and timber volume of five tree species groups as functions of a variety of predictor variables in the northern Utah mountains. Predictor variables include elevation, aspect, slope, geographic coordinates, as well as vegetation cover types based on satellite data from both the Advanced Very High Resolution Radiometer (AVHRR) and Thematic Mapper (TM) platforms. We examine the relative precision of estimates of area by forest type and mean cubic-foot volumes under six different models, including the traditional double sampling for stratification strategy. Only very small gains in precision were realized through the use of expensive photointerpreted or TM-based data for stratification, while models based on topography and spatial coordinates alone were competitive. We also compare the predictive capability of the models through various map accuracy measures. The models including the TM-based vegetation performed best overall, while topography and spatial coordinates alone provided substantial information at very low cost.
Utah↗
Hierarchical models of animal abundance and occurrence
Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.
Journal of Agricultural, Biological, and Environme↗
Hierarchical modeling of cluster size in wildlife surveys
Clusters or groups of individuals are the fundamental unit of observation in many wildlife sampling problems, including aerial surveys of waterfowl, marine mammals, and ungulates. Explicit accounting of cluster size in models for estimating abundance is necessary because detection of individuals within clusters is not independent and detectability of clusters is likely to increase with cluster size. This induces a cluster size bias in which the average cluster size in the sample is larger than in the population at large. Thus, failure to account for the relationship between delectability and cluster size will tend to yield a positive bias in estimates of abundance or density. I describe a hierarchical modeling framework for accounting for cluster-size bias in animal sampling. The hierarchical model consists of models for the observation process conditional on the cluster size distribution and the cluster size distribution conditional on the total number of clusters. Optionally, a spatial model can be specified that describes variation in the total number of clusters per sample unit. Parameter estimation, model selection, and criticism may be carried out using conventional likelihood-based methods. An extension of the model is described for the situation where measurable covariates at the level of the sample unit are available. Several candidate models within the proposed class are evaluated for aerial survey data on mallard ducks (Anas platyrhynchos).
Journal of Agricultural, Biological, and Environme↗