multimark: an R package for analysis of capture–recapture data consisting of multiple “noninvasive” marks

I describe an open‐source R package, multimark , for estimation of survival and abundance from capture–mark–recapture data consisting of multiple “noninvasive” marks. Noninvasive marks include natural pelt or skin patterns, scars, and genetic markers that enable individual identification in lieu of physical capture. multimark provides a means for combining and jointly analyzing encounter histories from multiple noninvasive sources that otherwise cannot be reliably matched (e.g., left‐ and right‐sided photographs of bilaterally asymmetrical individuals). The package is currently capable of fitting open population Cormack–Jolly–Seber (CJS) and closed population abundance models with up to two mark types using Bayesian Markov chain Monte Carlo (MCMC) methods. multimark can also be used for Bayesian analyses of conventional capture–recapture data consisting of a single‐mark type. Some package features include (1) general model specification using formulas already familiar to most R users, (2) ability to include temporal, behavioral, age, cohort, and individual heterogeneity effects in detection and survival probabilities, (3) improved MCMC algorithm that is computationally faster and more efficient than previously proposed methods, (4) Bayesian multimodel inference using reversible jump MCMC, and (5) data simulation capabilities for power analyses and assessing model performance. I demonstrate use of multimark using left‐ and right‐sided encounter histories for bobcats (Lynx rufus) collected from remote single‐camera stations in southern California. In this example, there is evidence of a behavioral effect (i.e., trap “happy” response) that is otherwise indiscernible using conventional single‐sided analyses. The package will be most useful to ecologists seeking stronger inferences by combining different sources of mark–recapture data that are difficult (or impossible) to reliably reconcile, particularly with the sparse datasets typical of rare or elusive species for which noninvasive sampling techniques are most commonly employed. Addressing deficiencies in currently available software, multimark also provides a user‐friendly interface for performing Bayesian multimodel inference using capture–recapture data consisting of a single conventional mark or multiple noninvasive marks.     

Combining capture–recapture data and pedigree information to assess heritability of demographic parameters in the wild

Quantitative genetic analyses have been increasingly used to estimate the genetic basis of life‐history traits in natural populations. Imperfect detection of individuals is inherent to studies that monitor populations in the wild, yet it is seldom accounted for by quantitative genetic studies, perhaps leading to flawed inference. To facilitate the inclusion of imperfect detection of individuals in such studies, we develop a method to estimate additive genetic variance and assess heritability for binary traits such as survival, using capture–recapture (CR) data. Our approach combines mixed‐effects CR models with a threshold model to incorporate discrete data in a standard ‘animal model’ approach. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters. We illustrate our approach using data from a wild population of blue tits (Cyanistes caeruleus) and present the first estimate of heritability of adult survival in the wild. In agreement with the prediction that selection should deplete additive genetic variance in fitness, we found that survival had low heritability. Because the detection process is incorporated, capture–recapture animal models (CRAM) provide unbiased quantitative genetics analyses of longitudinal data collected in the wild.     

Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis

Summary With increasing frequency, epidemiologic studies are addressing hypotheses regarding gene‐environment interaction. In many well‐studied candidate genes and for standard dietary and behavioral epidemiologic exposures, there is often substantial prior information available that may be used to analyze current data as well as for designing a new study. In this article, first, we propose a proper full Bayesian approach for analyzing studies of gene–environment interaction. The Bayesian approach provides a natural way to incorporate uncertainties around the assumption of gene–environment independence, often used in such an analysis. We then consider Bayesian sample size determination criteria for both estimation and hypothesis testing regarding the multiplicative gene–environment interaction parameter. We illustrate our proposed methods using data from a large ongoing case–control study of colorectal cancer investigating the interaction of N‐acetyl transferase type 2 (NAT2) with smoking and red meat consumption. We use the existing data to elicit a design prior and show how to use this information in allocating cases and controls in planning a future study that investigates the same interaction parameters. The Bayesian design and analysis strategies are compared with their corresponding frequentist counterparts.     

A local evaluation of the individual state‐space to scale up Bayesian spatial capture–recapture

Spatial capture–recapture models (SCR) are used to estimate animal density and to investigate a range of problems in spatial ecology that cannot be addressed with traditional nonspatial methods. Bayesian approaches in particular offer tremendous flexibility for SCR modeling. Increasingly, SCR data are being collected over very large spatial extents making analysis computational intensive, sometimes prohibitively so. To mitigate the computational burden of large‐scale SCR models, we developed an improved formulation of the Bayesian SCR model that uses local evaluation of the individual state‐space (LESS). Based on prior knowledge about a species’ home range size, we created square evaluation windows that restrict the spatial domain in which an individual's detection probability (detector window) and activity center location (AC window) are estimated. We used simulations and empirical data analyses to assess the performance and bias of SCR with LESS. LESS produced unbiased estimates of SCR parameters when the AC window width was ≥5σ (σ: the scale parameter of the half‐normal detection function), and when the detector window extended beyond the edge of the AC window by 2σ. Importantly, LESS considerably decreased the computation time needed for fitting SCR models. In our simulations, LESS increased the computation speed of SCR models up to 57‐fold. We demonstrate the power of this new approach by mapping the density of an elusive large carnivore—the wolverine (Gulo gulo)—with an unprecedented resolution and across the species’ entire range in Norway (> 200,000 km²). Our approach helps overcome a major computational obstacle to population and landscape‐level SCR analyses. The LESS implementation in a Bayesian framework makes the customization and fitting of SCR accessible for practitioners working at scales that are relevant for conservation and management.     

Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

In capture–recapture models, survival and capture probabilities can be modelled as functions of time‐varying covariates, such as temperature or rainfall. The Cormack–Jolly–Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi‐parametrically modelling capture and survival probabilities using a frequentist approach via P‐splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi‐parametric Bayesian approaches on simulated and real data sets.     

Predictive Model Assessment for Count Data

Summary We discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data. Our proposals include a nonrandomized version of the probability integral transform, marginal calibration diagrams, and proper scoring rules, such as the predictive deviance. In case studies, we critique count regression models for patent data, and assess the predictive performance of Bayesian age‐period‐cohort models for larynx cancer counts in Germany. The toolbox applies in Bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes.     

Multistate Mark–Recapture Model Selection Using Score Tests

Summary Although multistate mark–recapture models are recognized as important, they lack a simple model‐selection procedure. This article proposes and evaluates a step‐up approach to select appropriate models for multistate mark–recapture data using score tests. Only models supported by the data require fitting, so that over‐complicated model structures with too many parameters do not need to be considered. Typically only a small number of models are fitted, and the procedure is also able to identify parameter‐redundant and near‐redundant models. The good performance of the technique is demonstrated using simulation, and the approach is illustrated on a three‐region Canada goose data set. In this case, it identifies a new model that is much simpler than the best model previously considered for this application.     

Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension

Summary Reversible jump Markov chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture–recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models, in contrast to likelihood‐based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set.     

Divergence time uncertainty and historical biogeography reconstruction – an example from Urophylleae (Rubiaceae)

Aim When hypotheses of historical biogeography are evaluated, age estimates of individual nodes in a phylogeny often have a direct impact on what explanation is concluded to be most likely. Confidence intervals of estimated divergence times obtained in molecular dating analyses are usually very large, but the uncertainty is rarely incorporated in biogeographical analyses. The aim of this study is to use the group Urophylleae, which has a disjunct pantropical distribution, to explore how the uncertainty in estimated divergence times affects conclusions in biogeographical analysis. Two hypotheses are evaluated: (1) long‐distance dispersal from Africa to Asia and the Neotropics, and (2) a continuous distribution in the boreotropics, probably involving migration across the North Atlantic Land Bridge, followed by isolation in equatorial refugia. Location Tropical and subtropical Asia, tropical Africa, and central and southern tropical America. Methods This study uses parsimony and Bayesian phylogenetic analyses of chloroplast DNA and nuclear ribosomal DNA data from 56 ingroup species, beast molecular dating and a Bayesian approach to dispersal–vicariance analysis (Bayes‐DIVA) to reconstruct the ancestral area of the group, and the dispersal–extinction–cladogenesis method to test biogeographical hypotheses. Results When the two models of geographic range evolution were compared using the maximum likelihood (ML) tree with mean estimates of divergence times, boreotropical migration was indicated to be much more likely than long‐distance dispersal. Analyses of a large sample of dated phylogenies did, however, show that this result was not consistent. The age estimate of one specific node had a major impact on likelihood values and on which model performed best. The results show that boreotropical migration provides a slightly better explanation of the geographical distribution patterns of extant Urophylleae than long‐distance dispersal. Main conclusions This study shows that results from biogeographical analyses based on single phylogenetic trees, such as a ML or consensus tree, can be misleading, and that it may be very important to take the uncertainty in age estimates into account. Methods that account for the uncertainty in topology, branch lengths and estimated divergence times are not commonly used in biogeographical inference today but should definitely be preferred in order to avoid unwarranted conclusions.     

A Composite Gel–Polymer/Glass–Fiber Electrolyte for Sodium‐Ion Batteries

An integrated preparation of a low‐cost composite gel–polymer/glass–fiber electrolyte with poly(vinylidene fluoride‐co‐hexafluoropropylene) (PVDF‐HFP) reinforced by a glass–fiber paper and modified by a polydopamine coating to tune the mechanical and surface properties of PVDF‐HFP is shown to be applicable to a sodium‐ion battery. The composite polymer matrix exhibits excellent mechanical strength and thermal stability up to 200 °C. After saturating with a liquid electrolyte, a wide electrochemical window and high ionic conductivity is obtained for the composite gel–polymer/glass–fiber electrolyte. When tested in a sodium‐ion battery with Na₂MnFe(CN)₆ as cathode, the rate capability, cycling performance, and coulombic efficiency are significantly improved. The results suggest that the composite polymer electrolyte is a very attractive separator for a large‐scale battery system where safety and cost are the main concerns.     

Predicted residue–residue contacts can help the scoring of 3D models

During the 7th Critical Assessment of Protein Structure Prediction (CASP7) experiment, it was suggested that the real value of predicted residue–residue contacts might lie in the scoring of 3D model structures. Here, we have carried out a detailed reassessment of the contact predictions made during the recent CASP8 experiment to determine whether predicted contacts might aid in the selection of close‐to‐native structures or be a useful tool for scoring 3D structural models. We used the contacts predicted by the CASP8 residue–residue contact prediction groups to select models for each target domain submitted to the experiment. We found that the information contained in the predicted residue–residue contacts would probably have helped in the selection of 3D models in the free modeling regime and over the harder comparative modeling targets. Indeed, in many cases, the models selected using just the predicted contacts had better GDT‐TS scores than all but the best 3D prediction groups. Despite the well‐known low accuracy of residue–residue contact predictions, it is clear that the predictive power of contacts can be useful in 3D model prediction strategies. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Bayesian model selection for spatial capture–recapture models

A vast amount of ecological knowledge generated over the past two decades has hinged upon the ability of model selection methods to discriminate among various ecological hypotheses. The last decade has seen the rise of Bayesian hierarchical models in ecology. Consequently, commonly used tools, such as the AIC, become largely inapplicable and there appears to be no consensus about a particular model selection tool that can be universally applied. We focus on a specific class of competing Bayesian spatial capture–recapture (SCR) models and apply and evaluate some of the recommended Bayesian model selection tools: (1) Bayes Factor—using (a) Gelfand‐Dey and (b) harmonic mean methods, (2) Deviance Information Criterion (DIC), (3) Watanabe‐Akaike's Information Criterion (WAIC) and (4) posterior predictive loss criterion. In all, we evaluate 25 variants of model selection tools in our study. We evaluate these model selection tools from the standpoint of selecting the “true” model and parameter estimation. In all, we generate 120 simulated data sets using the true model and assess the frequency with which the true model is selected and how well the tool estimates N (population size), a parameter of much importance to ecologists. We find that when information content is low in the data, no particular model selection tool can be recommended to help realize, simultaneously, both the goals of model selection and parameter estimation. But, in general (when we consider both the objectives together), we recommend the use of our application of the Bayes Factor (Gelfand‐Dey with MAP approximation) for Bayesian SCR models. Our study highlights the point that although new model selection tools are emerging (e.g., WAIC) in the applied statistics literature, those tools based on sound theory even under approximation may still perform much better.     

Occupancy versus colonization–extinction models for projecting population trends at different spatial scales

Understanding spatiotemporal population trends and their drivers is a key aim in population ecology. We further need to be able to predict how the dynamics and sizes of populations are affected in the long term by changing landscapes and climate. However, predictions of future population trends are sensitive to a range of modeling assumptions. Deadwood‐dependent fungi are an excellent system for testing the performance of different predictive models of sessile species as these species have different rarity and spatial population dynamics, the populations are structured at different spatial scales, and they utilize distinct substrates. We tested how the projected large‐scale occupancies of species with differing landscape‐scale occupancies are affected over the coming century by different modeling assumptions. We compared projections based on occupancy models against colonization–extinction models, conducting the modeling at alternative spatial scales and using fine‐ or coarse‐resolution deadwood data. We also tested effects of key explanatory variables on species occurrence and colonization–extinction dynamics. The hierarchical Bayesian models applied were fitted to an extensive repeated survey of deadwood and fungi at 174 patches. We projected higher occurrence probabilities and more positive trends using the occupancy models compared to the colonization–extinction models, with greater difference for the species with lower occupancy, colonization rate, and colonization:extinction ratio than for the species with higher estimates of these statistics. The magnitude of future increase in occupancy depended strongly on the spatial modeling scale and resource resolution. We encourage using colonization–extinction models over occupancy models, modeling the process at the finest resource‐unit resolution that is utilizable by the species, and conducting projections for the same spatial scale and resource resolution at which the model fitting is conducted. Further, the models applied should include key variables driving the metapopulation dynamics, such as the availability of suitable resource units, habitat quality, and spatial connectivity.     

An integrated population model for a long‐lived ungulate: more efficient data use with Bayesian methods

We develop an integrated population model for Svalbard reindeer Rangifer tarandus platyrhynchus, and demonstrate how this type of model can be used to extract more information from the data and separate different sources of variability in population estimates. Our model combines individual mark–recapture data with population counts and harvesting data within a Bayesian model framework, and accounts for observation error, environmental and demographic stochasticity, and age structure. From this model we obtain annual estimates of age‐specific population size, survival and fecundity. The model provides estimates of age structure at a finer scale than that found in the census data, and enables us to estimate survival for the period before calves are first caught and marked, i.e. before they enter the individual mark–recapture data. The modeling framework provides an improved approach to studying age‐structured populations that are imperfectly censused and where the demography of only a sample of individuals is known. We use data from independent censuses of the same population to evaluate population estimates obtained from the model, and show that it is successful at correcting for different types of observation error. Based on our model results, we suggest that allocating resources to the collection of supplementary mark–recapture data could improve the reliability of population projections more than making regular population censuses as exhaustive as possible. Our work demonstrates how integrated Bayesian population modeling can be used to increase the amount of information extracted from collections of data, identifying and disentangling sources of variation in individual performance and population size. This represents an important step towards increasing the predictive ability of population growth models for long‐lived species experiencing changes in environmental conditions and harvesting regimes.     

sars: an R package for fitting,evaluating and comparing species–area relationship models

The species–area relationship (SAR) constitutes one of the most general ecological patterns globally. A number of different SAR models have been proposed. Recent work has shown that no single model universally provides the best fit to empirical SAR datasets: multiple models may be of practical and theoretical interest. However, there are no software packages available that a) allow users to fit the full range of published SAR models, or b) provide functions to undertake a range of additional SAR‐related analyses. To address these needs, we have developed the R package ‘sars’ that provides a wide variety of SAR‐related functionality. The package provides functions to: a) fit 20 SAR models using non‐linear and linear regression, b) calculate multi‐model averaged curves using various information criteria, and c) generate confidence intervals using bootstrapping. Plotting functions allow users to depict and scrutinize the fits of individual models and multi‐model averaged curves. The package also provides additional SAR functionality, including functions to fit, plot and evaluate the random placement model using a species–sites abundance matrix, and to fit the general dynamic model of oceanic island biogeography. The ‘sars’ R package will aid future SAR research by providing a comprehensive set of simple to use tools that enable in‐depth exploration of SARs and SAR‐related patterns. The package has been designed to allow other researchers to add new functions and models in the future and thus the package represents a resource for future SAR work that can be built on and expanded by workers in the field.     

Population size estimates based on the frequency of genetically assigned parent–offspring pairs within a subsample

Estimating population density as precise as possible is a key premise for managing wild animal species. This can be a challenging task if the species in question is elusive or, due to high quantities, hard to count. We present a new, mathematically derived estimator for population size, where the estimation is based solely on the frequency of genetically assigned parent–offspring pairs within a subsample of an ungulate population. By use of molecular markers like microsatellites, the number of these parent–offspring pairs can be determined. The study's aim was to clarify whether a classical capture–mark–recapture (CMR) method can be adapted or extended by this genetic element to a genetic‐based capture–mark–recapture (g‐CMR). We numerically validate the presented estimator (and corresponding variance estimates) and provide the R‐code for the computation of estimates of population size including confidence intervals. The presented method provides a new framework to precisely estimate population size based on the genetic analysis of a one‐time subsample. This is especially of value where traditional CMR methods or other DNA‐based (fecal or hair) capture–recapture methods fail or are too difficult to apply. The DNA source used is basically irrelevant, but in the present case the sampling of an annual hunting bag is to serve as data basis. In addition to the high quality of muscle tissue samples, hunting bags provide additional and essential information for wildlife management practices, such as age, weight, or sex. In cases where a g‐CMR method is ecologically and hunting‐wise appropriate, it enables a wide applicability, also through its species‐independent use.     

Few multiyear precipitation–reduction experiments find a shift in the productivity–precipitation relationship

Well‐defined productivity–precipitation relationships of ecosystems are needed as benchmarks for the validation of land models used for future projections. The productivity–precipitation relationship may be studied in two ways: the spatial approach relates differences in productivity to those in precipitation among sites along a precipitation gradient (the spatial fit, with a steeper slope); the temporal approach relates interannual productivity changes to variation in precipitation within sites (the temporal fits, with flatter slopes). Precipitation–reduction experiments in natural ecosystems represent a complement to the fits, because they can reduce precipitation below the natural range and are thus well suited to study potential effects of climate drying. Here, we analyse the effects of dry treatments in eleven multiyear precipitation–manipulation experiments, focusing on changes in the temporal fit. We expected that structural changes in the dry treatments would occur in some experiments, thereby reducing the intercept of the temporal fit and displacing the productivity–precipitation relationship downward the spatial fit. The majority of experiments (72%) showed that dry treatments did not alter the temporal fit. This implies that current temporal fits are to be preferred over the spatial fit to benchmark land‐model projections of productivity under future climate within the precipitation ranges covered by the experiments. Moreover, in two experiments, the intercept of the temporal fit unexpectedly increased due to mechanisms that reduced either water loss or nutrient loss. The expected decrease of the intercept was observed in only one experiment, and only when distinguishing between the late and the early phases of the experiment. This implies that we currently do not know at which precipitation–reduction level or at which experimental duration structural changes will start to alter ecosystem productivity. Our study highlights the need for experiments with multiple, including more extreme, dry treatments, to identify the precipitation boundaries within which the current temporal fits remain valid.     

One size does not fit all: Customizing MCMC methods for hierarchical models using NIMBLE

Improved efficiency of Markov chain Monte Carlo facilitates all aspects of statistical analysis with Bayesian hierarchical models. Identifying strategies to improve MCMC performance is becoming increasingly crucial as the complexity of models, and the run times to fit them, increases. We evaluate different strategies for improving MCMC efficiency using the open‐source software NIMBLE (R package nimble) using common ecological models of species occurrence and abundance as examples. We ask how MCMC efficiency depends on model formulation, model size, data, and sampling strategy. For multiseason and/or multispecies occupancy models and for N‐mixture models, we compare the efficiency of sampling discrete latent states vs. integrating over them, including more vs. fewer hierarchical model components, and univariate vs. block‐sampling methods. We include the common MCMC tool JAGS in comparisons. For simple models, there is little practical difference between computational approaches. As model complexity increases, there are strong interactions between model formulation and sampling strategy on MCMC efficiency. There is no one‐size‐fits‐all best strategy, but rather problem‐specific best strategies related to model structure and type. In all but the simplest cases, NIMBLE's default or customized performance achieves much higher efficiency than JAGS. In the two most complex examples, NIMBLE was 10–12 times more efficient than JAGS. We find NIMBLE is a valuable tool for many ecologists utilizing Bayesian inference, particularly for complex models where JAGS is prohibitively slow. Our results highlight the need for more guidelines and customizable approaches to fit hierarchical models to ensure practitioners can make the most of occupancy and other hierarchical models. By implementing model‐generic MCMC procedures in open‐source software, including the NIMBLE extensions for integrating over latent states (implemented in the R package nimbleEcology), we have made progress toward this aim.     

A non‐redundant protein–RNA docking benchmark version 2.0

We present an updated version of the protein–RNA docking benchmark, which we first published four years back. The non‐redundant protein–RNA docking benchmark version 2.0 consists of 126 test cases, a threefold increase in number compared to its previous version. The present version consists of 21 unbound–unbound cases, of which, in 12 cases, the unbound RNAs are taken from another complex. It also consists of 95 unbound–bound cases where only the protein is available in the unbound state. Besides, we introduce 10 new bound–unbound cases where only the RNA is found in the unbound state. Based on the degree of conformational change of the interface residues upon complex formation the benchmark is classified into 72 rigid‐body cases, 25 semiflexible cases and 19 full flexible cases. It also covers a wide range of conformational flexibility including small side chain movement to large domain swapping in protein structures as well as flipping and restacking in RNA bases. This benchmark should provide the docking community with more test cases for evaluating rigid‐body as well as flexible docking algorithms. Besides, it will also facilitate the development of new algorithms that require large number of training set. The protein–RNA docking benchmark version 2.0 can be freely downloaded from http://www.csb.iitkgp.ernet.in/applications/PRDBv2 . Proteins 2017; 85:256–267. © 2016 Wiley Periodicals, Inc.     

Optimal design of the Wilcoxon–Mann–Whitney‐test

In scientific research, many hypotheses relate to the comparison of two independent groups. Usually, it is of interest to use a design (i.e., the allocation of sample sizes m and n for fixed ) that maximizes the power of the applied statistical test. It is known that the two‐sample t‐tests for homogeneous and heterogeneous variances may lose substantial power when variances are unequal but equally large samples are used. We demonstrate that this is not the case for the nonparametric Wilcoxon–Mann–Whitney‐test, whose application in biometrical research fields is motivated by two examples from cancer research. We prove the optimality of the design in case of symmetric and identically shaped distributions using normal approximations and show that this design generally offers power only negligibly lower than the optimal design for a wide range of distributions.