A cautionary note on Bayesian estimation of population size by removal sampling with diffuse priors

We consider the problem of estimating a population size by removal sampling when the sampling rate is unknown. Bayesian methods are now widespread and allow to include prior knowledge in the analysis. However, we show that Bayes estimates based on default improper priors lead to improper posteriors or infinite estimates. Similarly, weakly informative priors give unstable estimators that are sensitive to the choice of hyperparameters. By examining the likelihood, we show that population size estimates can be stabilized by penalizing small values of the sampling rate or large value of the population size. Based on theoretical results and simulation studies, we propose some recommendations on the choice of the prior. Then, we applied our results to real datasets.     

A means of estimating the completeness of haplotype sampling using the Stirling probability distribution

I present a tool for use in phylogeography that helps estimate the completeness of haplotype sampling, based on the number of individuals analysed and the number of different haplotypes they show. Applying the Stirling probability distribution and Bayes’ theorem, a posterior probability distribution of the total number of haplotypes, including those yet to be observed, may be obtained. This enables one to deduce if the data are complete enough for further analysis. A program for calculating the posterior probabilities is available at http://www.botanik.univie.ac.at/plantchorology/haplo.htm .     

Bayesian analysis for nonlinear regression model under skewed errors,with application in growth curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew‐t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.     

Capwire: a R package for estimating population census size from non‐invasive genetic sampling

Non‐invasive genetic sampling is an increasingly popular approach for investigating the demographics of natural populations. This has also become a useful tool for managers and conservation biologists, especially for those species for which traditional mark–recapture studies are not practical. However, the consequence of collecting DNA indirectly is that an individual may be sampled multiple times per sampling session. This requires alternative statistical approaches to those used in traditional mark–recapture studies. Here we present the R package capwire , an implementation of the population size estimators of Miller et al. (Molecular Ecology 2005; 14 : 1991), which were designed to deal specifically with this type of sampling. The aim of this project is to enable users across platforms to easily manipulate their data and interact with existing R packages. We have also provided functions to simulate data under a variety of scenarios to allow for rigorous testing of the robustness of the method and to facilitate further development of this approach.     

BMA‐Mod: A Bayesian model averaging strategy for determining dose‐response relationships in the presence of model uncertainty

Successful pharmaceutical drug development requires finding correct doses. The issues that conventional dose‐response analyses consider, namely whether responses are related to doses, which doses have responses differing from a control dose response, the functional form of a dose‐response relationship, and the dose(s) to carry forward, do not need to be addressed simultaneously. Determining if a dose‐response relationship exists, regardless of its functional form, and then identifying a range of doses to study further may be a more efficient strategy. This article describes a novel estimation‐focused Bayesian approach (BMA‐Mod) for carrying out the analyses when the actual dose‐response function is unknown. Realizations from Bayesian analyses of linear, generalized linear, and nonlinear regression models that may include random effects and covariates other than dose are optimally combined to produce distributions of important secondary quantities, including test‐control differences, predictive distributions of possible outcomes from future trials, and ranges of doses corresponding to target outcomes. The objective is similar to the objective of the hypothesis‐testing based MCP‐Mod approach, but provides more model and distributional flexibility and does not require testing hypotheses or adjusting for multiple comparisons. A number of examples illustrate the application of the method.     

A parametric model for estimating prevalence,incidence, and mean bout duration from point sampling

Point or instantaneous sampling refers to the scoring of presence or absence of behavior at the end of equally spaced intervals of time and is used to estimate prevalence. The literature cited demonstrates that point sampling does not adequately estimate frequency or mean bout duration. A parametric model is developed based on exponentially distributed times of behavior and intervening nonbehavior, thus enabling estimators of mean bout length and incidence. Variance estimators are provided and a method is suggested for designing sample situations which control the variance of the prevalence estimator. The paper concludes the theoretical investigation with a thorough Monte Carlo investigation and application to a “real-life” problem. The point sample estimators compare favorably with continuous observation under appropriate choice of sampling interval and under approximately exponential assumptions.     

On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty

Summary .   We consider the estimation of the size of a closed population, often of interest for wild animal populations, using a capture–recapture study. The estimate of the total population size can be very sensitive to the choice of model used to fit to the data. We consider a Bayesian approach, in which we consider all eight plausible models initially described by Otis et al. (1978, Wildlife Monographs 62, 1–135) within a single framework, including models containing an individual heterogeneity component. We show how we are able to obtain a model-averaged estimate of the total population, incorporating both parameter and model uncertainty. To illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known, before considering a real example relating to a population of dolphins off northeast Scotland.     

Challenges and opportunities for estimating abundance of a low-density moose population

Monitoring large herbivores across their core range has been readily accomplished using aerial surveys and traditional distance sampling. But for peripheral populations, where individuals may occur in patchy, low-density populations, precise estimation of population size and trend remains logistically and statistically challenging. For moose (Alces alces) along their southern range margin in northern New York, USA, we sought robust estimates of moose distribution, abundance, and population trend (2016–2019) using a combination of aerial surveys (line transect distance-sampling), repeated surveys in areas where moose were known to occur to boost the number of detections, and density surface modeling (DSM) with spatial covariates. We achieved a precise estimate of density (95% CI = 0.00–0.29 moose/km²) for this small population (656 moose, 95% CI = 501–859), which was patchily distributed across a large and heavily forested region (the 24,280-km² Adirondack Park). Local moose abundance was positively related to active timber management, elevation, and snow cover, and negatively related to large bodies of water. As expected, moose abundance in this peripheral population was low relative to its core range in other northern forest states. Yet, in areas where abundance was greatest, moose densities in New York approached those where epizootics of winter tick (Dermacentor albipictus) have been reported, underscoring the need for effective and efficient monitoring. By incorporating autocorrelation in observations and landscape covariates, DSM provided spatially explicit estimates of moose density with greater precision and no additional field effort over traditional distance sampling. Combined with repeated surveys of areas with known moose occurrence to achieve viable sample sizes, DSM is a useful tool for effectively monitoring low density and patchy populations.     

A Bayesian joint model of recurrent events and a terminal event

Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. In this situation, dependent censoring is encountered because of potential dependence between these two event processes, leading to invalid inference if analyzing recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject‐level frailty; however, this could be violated when the dependency may also depend on time‐varying covariates across recurrences. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation with vague interpretation. In order to fill these gaps, we propose a novel joint frailty‐copula approach to model recurrent events and a terminal event with relaxed assumptions. Metropolis–Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness, and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error of the proposal is smaller when the conditional independence assumption is violated. Finally, we apply our method into a real example extracted from the MarketScan database to study the association between recurrent strokes and mortality.     

A method for estimating population sex ratio for sage‐grouse using noninvasive genetic samples

Population sex ratio is an important metric for wildlife management and conservation, but estimates can be difficult to obtain, particularly for sexually monomorphic species or for species that differ in detection probability between the sexes. Noninvasive genetic sampling (NGS) using polymerase chain reaction (PCR) has become a common method for identifying sex from sources such as hair, feathers or faeces, and is a potential source for estimating sex ratio. If, however, PCR success is sex‐biased, naively using NGS could lead to a biased sex ratio estimator. We measured PCR success rates and error rates for amplifying the W and Z chromosomes from greater sage‐grouse (Centrocercus urophasianus) faecal samples, examined how success and error rates for sex identification changed in response to faecal sample exposure time, and used simulation models to evaluate precision and bias of three sex assignment criteria for estimating population sex ratio with variable sample sizes and levels of PCR replication. We found PCR success rates were higher for females than males and that choice of sex assignment criteria influenced the bias and precision of corresponding sex ratio estimates. Our simulations demonstrate the importance of considering the interplay between the sex bias of PCR success, number of genotyping replicates, sample size, true population sex ratio and accuracy of assignment rules for designing future studies. Our results suggest that using faecal DNA for estimating the sex ratio of sage‐grouse populations has great potential and, with minor adaptations and similar marker evaluations, should be applicable to numerous species.     

A mathematical model of a crocodilian population using delay-differential equations

The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.     

A partial linear model in the outcome-dependent sampling setting to evaluate the effect of prenatal PCB exposure on cognitive function in children

Outcome-dependent sampling (ODS) has been widely used in biomedical studies because it is a cost-effective way to improve study efficiency. However, in the setting of a continuous outcome, the representation of the exposure variable has been limited to the framework of linear models, due to the challenge in terms of both theory and computation. Partial linear models (PLM) are a powerful inference tool to nonparametrically model the relation between an outcome and the exposure variable. In this article, we consider a case study of a PLM for data from an ODS design. We propose a semiparametric maximum likelihood method to make inferences with a PLM. We develop the asymptotic properties and conduct simulation studies to show that the proposed ODS estimator can produce a more efficient estimate than that from a traditional simple random sampling design with the same sample size. Using this newly developed method, we were able to explore an open question in epidemiology: whether in utero exposure to background levels of polychlorinated biphenyls (PCBs) is associated with children's intellectual impairment. Our model provides further insights into the relation between low-level PCB exposure and children's cognitive function. The results shed new light on a body of inconsistent epidemiologic findings.     

A Beta-mixture model for assessing genetic population structure

Summary An important fraction of recently generated molecular data is dominant markers. They contain substantial information about genetic variation but dominance makes it impossible to apply standard techniques to calculate measures of genetic differentiation, such as F‐statistics. In this article, we propose a new Bayesian beta‐mixture model that more accurately describes the genetic structure from dominant markers and estimates multiple F_ST s from the sample. The model also has important application for codominant markers and single‐nucleotide polymorphism (SNP) data. The number of F_ST is assumed unknown beforehand and follows a random distribution. The reversible jump algorithm is used to estimate the unknown number of multiple F_ST s. We evaluate the performance of three split proposals and the overall performance of the proposed model based on simulated dominant marker data. The model could reliably identify and estimate a spectrum of degrees of genetic differentiation present in multiple loci. The estimates of F_ST s also incorporate uncertainty about the magnitude of within‐population inbreeding coefficient. We illustrate the method with two examples, one using dominant marker data from a rare orchid and the other using codominant marker data from human populations.