An open spatial capture–recapture model for estimating density,movement, and population dynamics from line‐transect surveys

The purpose of many wildlife population studies is to estimate density, movement, or demographic parameters. Linking these parameters to covariates, such as habitat features, provides additional ecological insight and can be used to make predictions for management purposes. Line‐transect surveys, combined with distance sampling methods, are often used to estimate density at discrete points in time, whereas capture–recapture methods are used to estimate movement and other demographic parameters. Recently, open population spatial capture–recapture models have been developed, which simultaneously estimate density and demographic parameters, but have been made available only for data collected from a fixed array of detectors and have not incorporated the effects of habitat covariates. We developed a spatial capture–recapture model that can be applied to line‐transect survey data by modeling detection probability in a manner analogous to distance sampling. We extend this model to a) estimate demographic parameters using an open population framework and b) model variation in density and space use as a function of habitat covariates. The model is illustrated using simulated data and aerial line‐transect survey data for North Atlantic right whales in the southeastern United States, which also demonstrates the ability to integrate data from multiple survey platforms and accommodate differences between strata or demographic groups. When individuals detected from line‐transect surveys can be uniquely identified, our model can be used to simultaneously make inference on factors that influence spatial and temporal variation in density, movement, and population dynamics.     

Exploring the drivers of wildlife population dynamics from insufficient data by Bayesian model averaging

A long-standing interest in ecology and wildlife management is to find drivers of wildlife population dynamics because it is crucial for implementing the effective wildlife management. Recent studies have demonstrated the usefulness of state-space modeling for this purpose, but we often confront the lack of the necessary time-series data. This is particularly common in wildlife management because of limited funds or early stage of data collection. In this study, we proposed a Bayesian model averaging technique in a state-space modeling framework for identifying the drivers of wildlife population dynamics from limited data. To exemplify the utility of Bayesian model averaging for wildlife management, we illustrate here the population dynamics of wild boars Sus scrofa in Chiba prefecture, central Japan. Despite the fact that our data are limited in both temporal and spatial resolution, Bayesian model averaging revealed the potential influence of bamboo forests and abandoned agricultural fields on wild boar population dynamics, and largely enhanced model predictability compared to the full model. Although Bayesian model averaging is not commonly used in ecology and wildlife management, our case study demonstrated that it may help to find influential drivers of wildlife population dynamics and develop a better management plan even from limited time-series data.     

A Bayesian hierarchical model for analyzing methylated RNA immunoprecipitation sequencing data

Background: The recently emerged technology of methylated RNA immunoprecipitation sequencing (MeRIP-seq) sheds light on the study of RNA epigenetics. This new bioinformatics question calls for effective and robust peaking calling algorithms to detect mRNA methylation sites from MeRIP-seq data. Methods: We propose a Bayesian hierarchical model to detect methylation sites from MeRIP-seq data. Our modeling approach includes several important characteristics. First, it models the zero-inflated and over-dispersed counts by deploying a zero-inflated negative binomial model. Second, it incorporates a hidden Markov model (HMM) to account for the spatial dependency of neighboring read enrichment. Third, our Bayesian inference allows the proposed model to borrow strength in parameter estimation, which greatly improves the model stability when dealing with MeRIP-seq data with a small number of replicates. We use Markov chain Monte Carlo (MCMC) algorithms to simultaneously infer the model parameters in a de novo fashion. The R Shiny demo is available at the authors' website and the R/C++ code is available at https://github.com/liqiwei2000/BaySeqPeak. Results: In simulation studies, the proposed method outperformed the competing methods exomePeak and MeTPeak, especially when an excess of zeros were present in the data. In real MeRIP-seq data analysis, the proposed method identified methylation sites that were more consistent with biological knowledge, and had better spatial resolution compared to the other methods. Conclusions: In this study, we develop a Bayesian hierarchical model to identify methylation peaks in MeRIP-seq data. The proposed method has a competitive edge over existing methods in terms of accuracy, robustness and spatial resolution.     

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

Monitoring temporal trends in spatially structured populations: how should sampling effort be allocated between space and time?

Estimating temporal trends in spatially structured populations has a critical role to play in understanding regional changes in biological populations and developing management strategies. Designing effective monitoring programmes to estimate these trends requires important decisions to be made about how to allocate sampling effort among spatial replicates (i.e. number of sites) and temporal replicates (i.e. how often to survey) to minimise uncertainty in trend estimates. In particular, the optimal mix of spatial and temporal replicates is likely to depend upon the spatial and temporal correlations in population dynamics. Although there has been considerable interest in the ecological literature on understanding spatial and temporal correlations in species’ population dynamics, little attention has been paid to its consequences for monitoring design. We address this issue using model‐based survey design to identify the optimal allocation of sampling effort among spatial and temporal replicates for estimating population trends under different levels of spatial and temporal correlation. Based on linear trends, we show that how we should allocate sampling effort among spatial and temporal replicates depends crucially on the spatial and temporal correlations in population dynamics, environmental variation, observation error and the spatial variation in temporal trends. When spatial correlation is low and temporal correlation is high, the best option is likely to be to sample many sites infrequently, particularly when observation error and/or spatial variation in temporal trends are high. When spatial correlation is high and temporal correlation is low, the best option is likely to be to sample few sites frequently, particularly when observation error and/or spatial variation in temporal trends are low. When abundances are spatially independent, it is always preferable to maximise spatial replication. This provides important insights into how spatio‐temporal monitoring programmes should be designed to estimate temporal trends in spatially structured populations.     

Open population maximum likelihood spatial capture‐recapture

Open population capture‐recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modeling with spatial capture‐recapture (SCR), allowing for estimation of the effective area sampled and population density. Here, open population SCR is formulated as a hidden Markov model (HMM), allowing inference by maximum likelihood for both Cormack‐Jolly‐Seber and Jolly‐Seber models, with and without activity center movement. The method is applied to a 12‐year survey of male jaguars (Panthera onca) in the Cockscomb Basin Wildlife Sanctuary, Belize, to estimate survival probability and population abundance over time. For this application, inference is shown to be biased when assuming activity centers are fixed over time, while including a model for activity center movement provides negligible bias and nominal confidence interval coverage, as demonstrated by a simulation study. The HMM approach is compared with Bayesian data augmentation and closed population models for this application. The method is substantially more computationally efficient than the Bayesian approach and provides a lower root‐mean‐square error in predicting population density compared to closed population models.     

Accounting for Errors in Data Improves Divergence Time Estimates in Single-cell Cancer Evolution

Single-cell sequencing provides a new way to explore the evolutionary history of cells. Compared to traditional bulk sequencing, where a population of heterogeneous cells is pooled to form a single observation, single-cell sequencing isolates and amplifies genetic material from individual cells, thereby preserving the information about the origin of the sequences. However, single-cell data are more error-prone than bulk sequencing data due to the limited genomic material available per cell. Here, we present error and mutation models for evolutionary inference of single-cell data within a mature and extensible Bayesian framework, BEAST2. Our framework enables integration with biologically informative models such as relaxed molecular clocks and population dynamic models. Our simulations show that modeling errors increase the accuracy of relative divergence times and substitution parameters. We reconstruct the phylogenetic history of a colorectal cancer patient and a healthy patient from single-cell DNA sequencing data. We find that the estimated times of terminal splitting events are shifted forward in time compared to models which ignore errors. We observed that not accounting for errors can overestimate the phylogenetic diversity in single-cell DNA sequencing data. We estimate that 30–50% of the apparent diversity can be attributed to error. Our work enables a full Bayesian approach capable of accounting for errors in the data within the integrative Bayesian software framework BEAST2.     

HiCImpute: A Bayesian hierarchical model for identifying structural zeros and enhancing single cell Hi-C data

Single cell Hi-C techniques enable one to study cell to cell variability in chromatin interactions. However, single cell Hi-C (scHi-C) data suffer severely from sparsity, that is, the existence of excess zeros due to insufficient sequencing depth. Complicating the matter further is the fact that not all zeros are created equal: some are due to loci truly not interacting because of the underlying biological mechanism (structural zeros); others are indeed due to insufficient sequencing depth (sampling zeros or dropouts), especially for loci that interact infrequently. Differentiating between structural zeros and dropouts is important since correct inference would improve downstream analyses such as clustering and discovery of subtypes. Nevertheless, distinguishing between these two types of zeros has received little attention in the single cell Hi-C literature, where the issue of sparsity has been addressed mainly as a data quality improvement problem. To fill this gap, in this paper, we propose HiCImpute, a Bayesian hierarchical model that goes beyond data quality improvement by also identifying observed zeros that are in fact structural zeros. HiCImpute takes spatial dependencies of scHi-C 2D data structure into account while also borrowing information from similar single cells and bulk data, when such are available. Through an extensive set of analyses of synthetic and real data, we demonstrate the ability of HiCImpute for identifying structural zeros with high sensitivity, and for accurate imputation of dropout values. Downstream analyses using data improved from HiCImpute yielded much more accurate clustering of cell types compared to using observed data or data improved by several comparison methods. Most significantly, HiCImpute-improved data have led to the identification of subtypes within each of the excitatory neuronal cells of L4 and L5 in the prefrontal cortex.     

Zero-inflated Poisson models with measurement error in the response

Zero-inflated count data arise frequently from genomics studies. Analysis of such data is often based on a mixture model which facilitates excess zeros in combination with a Poisson distribution, and various inference methods have been proposed under such a model. Those analysis procedures, however, are challenged by the presence of measurement error in count responses. In this article, we propose a new measurement error model to describe error-contaminated count data. We show that ignoring the measurement error effects in the analysis may generally lead to invalid inference results, and meanwhile, we identify situations where ignoring measurement error can still yield consistent estimators. Furthermore, we propose a Bayesian method to address the effects of measurement error under the zero-inflated Poisson model and discuss the identifiability issues. We develop a data-augmentation algorithm that is easy to implement. Simulation studies are conducted to evaluate the performance of the proposed method. We apply our method to analyze the data arising from a prostate adenocarcinoma genomic study.     

Spatially-explicit wildlife surveillance to prove freedom from diseases or pests

Surveillance undertaken to prove freedom from a disease has traditionally focussed on sampling a specified proportion of the population to determine the presence of the infective agent. Based on a sample of individuals testing negative for disease, standard probability theory using the binomial or hypergeometric distribution can be used to make inference about the probability of disease being absent. However, if the disease agent involves a wildlife host, then determining what proportion of the population was sampled becomes problematic as it requires an estimate of population abundance, which may be difficult and expensive to obtain. Surveillance during the eradication of pests such as feral ungulates often make use of the Judas technique, whereby radio-collared individuals are released and followed in the hope that the sociality of the individuals will betray the locations of conspecifics, which can then be dispatched. Data collected during such surveillance is explicitly spatial, containing information about the ‘search area’ of the Judas animal. However, there has been no attempt to use such data to make inference about the probability of the area being free of the pest, given Judas animals fail to detect any conspecifics. We present a framework for making specific use of the spatial nature of such wildlife surveillance data to make inference about the probability of freedom from the disease or pest. Underlying the sampling framework is a model of the detection process by sampled individuals. Estimates of individual detection probability are spatially smoothed using the extent of individual movements to produce a spatially- explicit detection surface. Bayes theorem is then used to combine this 2-dimensional surface with prior information on the probability of pest or disease presence, prior to sampling, to estimate the probability that the area is free from the disease or pest, given surveillance fails to detect evidence of their presence. We illustrate the method with examples of the detection of bovine Tb in wildlife in New Zealand and the detection of pigs (Sus scrofa) using the Judas technique during the feral pig eradication programme on Santa Cruz Island, California.     

Impacts of predator-mediated interactions along a climatic gradient on the population dynamics of an alpine bird

According to classic theory, species'' population dynamics and distributions are less influenced by species interactions under harsh climatic conditions compared to under more benign climatic conditions. In alpine and boreal ecosystems in Fennoscandia, the cyclic dynamics of rodents strongly affect many other species, including ground-nesting birds such as ptarmigan. According to the ‘alternative prey hypothesis’ (APH), the densities of ground-nesting birds and rodents are positively associated due to predator–prey dynamics and prey-switching. However, it remains unclear how the strength of these predator-mediated interactions change along a climatic harshness gradient in comparison with the effects of climatic variation. We built a hierarchical Bayesian model to estimate the sensitivity of ptarmigan populations to interannual variation in climate and rodent occurrence across Norway during 2007–2017. Ptarmigan abundance was positively linked with rodent occurrence, consistent with the APH. Moreover, we found that the link between ptarmigan abundance and rodent dynamics was strongest in colder regions. Our study highlights how species interactions play an important role in population dynamics of species at high latitudes and suggests that they can become even more important in the most climatically harsh regions.     

Cost-efficient selection of a marker panel in genetic studies

Genetic techniques are frequently used to sample and monitor wildlife populations. The goal of these studies is to maximize the ability to distinguish individuals for various genetic inference applications, a process which is often complicated by genotyping error. However, wildlife studies usually have fixed budgets, which limit the number of genetic markers available for inclusion in a study marker panel. Prior to our study, a formal algorithm for selecting a marker panel that included genotyping error, laboratory costs, and ability to distinguish individuals did not exist. We developed a constrained nonlinear programming optimization algorithm to determine the optimal number of markers for a marker panel, initially applied to a pilot study designed to estimate black bear abundance in central Georgia. We extend the algorithm to other genetic applications (e.g., parentage or population assignment) and incorporate possible null alleles. Our algorithm can be used in wildlife pilot studies to assess the feasibility of genetic sampling for multiple genetic inference applications. © 2011 The Wildlife Society.     

Disease‐structured N‐mixture models: A practical guide to model disease dynamics using count data

Obtaining inferences on disease dynamics (e.g., host population size, pathogen prevalence, transmission rate, host survival probability) typically requires marking and tracking individuals over time. While multistate mark–recapture models can produce high‐quality inference, these techniques are difficult to employ at large spatial and long temporal scales or in small remnant host populations decimated by virulent pathogens, where low recapture rates may preclude the use of mark–recapture techniques. Recently developed N‐mixture models offer a statistical framework for estimating wildlife disease dynamics from count data. N‐mixture models are a type of state‐space model in which observation error is attributed to failing to detect some individuals when they are present (i.e., false negatives). The analysis approach uses repeated surveys of sites over a period of population closure to estimate detection probability. We review the challenges of modeling disease dynamics and describe how N‐mixture models can be used to estimate common metrics, including pathogen prevalence, transmission, and recovery rates while accounting for imperfect host and pathogen detection. We also offer a perspective on future research directions at the intersection of quantitative and disease ecology, including the estimation of false positives in pathogen presence, spatially explicit disease‐structured N‐mixture models, and the integration of other data types with count data to inform disease dynamics. Managers rely on accurate and precise estimates of disease dynamics to develop strategies to mitigate pathogen impacts on host populations. At a time when pathogens pose one of the greatest threats to biodiversity, statistical methods that lead to robust inferences on host populations are critically needed for rapid, rather than incremental, assessments of the impacts of emerging infectious diseases.     

State-space model combining local camera data and regional administration data reveals population dynamics of wild boar

Recent increases in wildlife cause negative impacts on humans through both economic and ecological damage, as well as the spread of pathogens. Understanding the population dynamics of wildlife is crucial to develop effective management strategies. However, it is difficult to estimate accurate and precise population size over large spatial and temporal scales because of the limited data availability. We addressed these issues by first fitting a random encounter and staying time (REST) model based on camera trap data to construct an informative prior distribution for a capture rate parameter in a harvest-based Bayesian state-space model. We constructed a Bayesian state-space model that integrated administration data on the number of captured wild boar with the prior distribution of capture efficiency estimated by camera trap data. The model with informative prior distribution from the REST model successfully estimated population dynamics, whereas the model using only the administration data did not, owing to a lack of parameter convergence. We identified areas where (1) wild boars exhibit a high potential population growth rate and a high carrying capacity, (2) current trapping efforts are effectively suppressing local populations, and (3) trapping reinforcement is required to control populations in the whole region. The model could be used to predict future trends in populations under the assumptions of ongoing trapping pressure. This will help identify spatially explicit trapping efforts to achieve target population levels.     

Bayesian clustering algorithms ascertaining spatial population structure: a new computer program and a comparison study

On the basis of simulated data, this study compares the relative performances of the Bayesian clustering computer programs structure , geneland , geneclust and a new program named tess . While these four programs can detect population genetic structure from multilocus genotypes, only the last three ones include simultaneous analysis from geographical data. The programs are compared with respect to their abilities to infer the number of populations, to estimate membership probabilities, and to detect genetic discontinuities and clinal variation. The results suggest that combining analyses using tess and structure offers a convenient way to address inference of spatial population structure.     

Neural networks enable efficient and accurate simulation-based inference of evolutionary parameters from adaptation dynamics

The rate of adaptive evolution depends on the rate at which beneficial mutations are introduced into a population and the fitness effects of those mutations. The rate of beneficial mutations and their expected fitness effects is often difficult to empirically quantify. As these 2 parameters determine the pace of evolutionary change in a population, the dynamics of adaptive evolution may enable inference of their values. Copy number variants (CNVs) are a pervasive source of heritable variation that can facilitate rapid adaptive evolution. Previously, we developed a locus-specific fluorescent CNV reporter to quantify CNV dynamics in evolving populations maintained in nutrient-limiting conditions using chemostats. Here, we use CNV adaptation dynamics to estimate the rate at which beneficial CNVs are introduced through de novo mutation and their fitness effects using simulation-based likelihood–free inference approaches. We tested the suitability of 2 evolutionary models: a standard Wright–Fisher model and a chemostat model. We evaluated 2 likelihood-free inference algorithms: the well-established Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) algorithm, and the recently developed Neural Posterior Estimation (NPE) algorithm, which applies an artificial neural network to directly estimate the posterior distribution. By systematically evaluating the suitability of different inference methods and models, we show that NPE has several advantages over ABC-SMC and that a Wright–Fisher evolutionary model suffices in most cases. Using our validated inference framework, we estimate the CNV formation rate at the GAP1 locus in the yeast Saccharomyces cerevisiae to be 10^−4.7 to 10⁻⁴ CNVs per cell division and a fitness coefficient of 0.04 to 0.1 per generation for GAP1 CNVs in glutamine-limited chemostats. We experimentally validated our inference-based estimates using 2 distinct experimental methods—barcode lineage tracking and pairwise fitness assays—which provide independent confirmation of the accuracy of our approach. Our results are consistent with a beneficial CNV supply rate that is 10-fold greater than the estimated rates of beneficial single-nucleotide mutations, explaining the outsized importance of CNVs in rapid adaptive evolution. More generally, our study demonstrates the utility of novel neural network–based likelihood–free inference methods for inferring the rates and effects of evolutionary processes from empirical data with possible applications ranging from tumor to viral evolution.

This study shows that simulation-based inference of evolutionary dynamics using neural networks can yield parameter values for fitness and mutation rate that are difficult to determine experimentally, including those of copy number variants (CNVs) during experimental adaptive evolution of yeast.     

Phylodynamic Inference for Structured Epidemiological Models

Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.     

Extracting spatial networks from capture–recapture data reveals individual site fidelity patterns within a marine mammal’s spatial range

1. Estimating the impacts of anthropogenic disturbances requires an understanding of the habitat‐use patterns of individuals within a population. This is especially the case when disturbances are localized within a population''s spatial range, as variation in habitat use within a population can drastically alter the distribution of impacts.
2. Here, we illustrate the potential for multilevel binomial models to generate spatial networks from capture–recapture data, a common data source used in wildlife studies to monitor population dynamics and habitat use. These spatial networks capture which regions of a population''s spatial distribution share similar/dissimilar individual usage patterns, and can be especially useful for detecting structured habitat use within the population''s spatial range.
3. Using simulations and 18 years of capture–recapture data from St. Lawrence Estuary (SLE) beluga, we show that this approach can successfully estimate the magnitude of similarities/dissimilarities in individual usage patterns across sectors, and identify sectors that share similar individual usage patterns that differ from other sectors, that is, structured habitat use. In the case of SLE beluga, this method identified multiple clusters of individuals, each preferentially using restricted areas within their summer range of the SLE.
4. Multilevel binomial models can be effective at estimating spatial structure in habitat use within wildlife populations sampled by capture–recapture of individuals, and can be especially useful when sampling effort is not evenly distributed. Our finding of a structured habitat use within the SLE beluga summer range has direct implications for estimating individual exposures to localized stressors, such as underwater noise from shipping or other activities.

     

Postcatastrophe Population Dynamics and Density Dependence of an Endemic Island Duck

ABSTRACT Laysan ducks (Anas laysanensis) are restricted to approximately 9 km² in the Northwestern Hawaiian Islands, USA. To evaluate the importance of density dependence for Laysan ducks, we conducted a Bayesian analysis to estimate the parameters of a Gompertz model and the magnitude of process variation and observation error based on the fluctuations in Laysan duck abundance on Laysan Island from 1994 to 2007. This model described a stationary distribution for the population at carrying capacity that fluctuates around a long-term mean of 456 ducks and is between 316 to 636 ducks 95% of the time. This range of expected variability can be used to identify changes in population size that warn of catastrophic events. Density-dependent population dynamics may explain the recovery of Laysan duck from catastrophic declines and allow managers to identify population monitoring thresholds.     

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.