A Design and Analytical Strategy for Monitoring Disease Positivity and Biomarker Levels in Accessible Closed Populations.

In this paper, we advocate and expand upon a previously described monitoring strategy for efficient and robust estimation of disease prevalence and case numbers within closed and enumerated populations such as schools, workplaces, or retirement communities. The proposed design relies largely on voluntary testing, which is notoriously biased (e.g., in the case of coronavirus disease 2019) due to nonrepresentative sampling. The approach yields unbiased and comparatively precise estimates with no assumptions about factors underlying selection of individuals for voluntary testing, building on the strength of what can be a small random sampling component. This component enables the use of a recently proposed "anchor stream" estimator, a well-calibrated alternative to classical capture-recapture (CRC) estimators based on 2 data streams. We show that this estimator is equivalent to a direct standardization based on "capture," that is, selection (or not) by the voluntary testing program, made possible by means of a key parameter identified by design. This equivalency simultaneously allows for novel 2-stream CRC-like estimation of general mean values (e.g., means of continuous variables like antibody levels or biomarkers). For inference, we propose adaptations of Bayesian credible intervals when estimating case counts and bootstrapping when estimating means of continuous variables. We use simulations to demonstrate significant precision benefits relative to random sampling alone.

Evaluating a Targeted Minimum Loss-Based Estimator for Capture-Recapture Analysis: An Application to HIV Surveillance in San Francisco, California.

The capture-recapture method is a common tool used in epidemiology to estimate the size of "hidden" populations and correct the underascertainment of cases, based on incomplete and overlapping lists of the target population. Log-linear models are often used to estimate the population size yet may produce implausible and unreliable estimates due to model misspecification and small cell sizes. A novel targeted minimum loss-based estimation (TMLE) model developed for capture-recapture makes several notable improvements to conventional modeling: "targeting" the parameter of interest, flexibly fitting the data to alternative functional forms, and limiting bias from small cell sizes. Using simulations and empirical data from the San Francisco, California, Department of Public Health's human immunodeficiency virus (HIV) surveillance registry, we evaluated the performance of the TMLE model and compared results with those of other common models. Based on 2,584 people observed on 3 lists reportable to the surveillance registry, the TMLE model estimated the number of San Francisco residents living with HIV as of December 31, 2019, to be 13,523 (95% confidence interval: 12,222, 14,824). This estimate, compared with a "ground truth" of 12,507, was the most accurate and precise of all models examined. The TMLE model is a significant advancement in capture-recapture studies, leveraging modern statistical methods to improve estimation of the sizes of hidden populations.

The central role of the identifying assumption in population size estimation.

The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the population size should be produced based on that data set, as models with different identifying assumptions can produce arbitrarily different population size estimates-even with identical observed data fits. Approaches to multiple-systems estimation often do not explicitly specify identifying assumptions. This makes it difficult to decouple the specification of the model for the observed data from the identifying assumption and to provide justification for the identifying assumption. We present a re-framing of the multiple-systems estimation problem that leads to an approach that decouples the specification of the observed-data model from the identifying assumption, and discuss how common models fit into this framing. This approach takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study estimating the number of civilian casualties in the Kosovo war.

That's not the Mona Lisa! How to interpret spatial capture-recapture density surface estimates.

Spatial capture-recapture methods are often used to produce density surfaces, and these surfaces are often misinterpreted. In particular, spatial change in density is confused with spatial change in uncertainty about density. We illustrate correct and incorrect inference visually by treating a grayscale image of the Mona Lisa as an activity center intensity or density surface and simulating spatial capture-recapture survey data from it. Inferences can be drawn about the intensity of the point process generating activity centers, and about the likely locations of activity centers associated with the capture histories obtained from a single survey of a single realization of this process. We show that treating probabilistic predictions of activity center locations as estimates of the intensity of the process results in invalid and misleading ecological inferences, and that predictions are highly dependent on where the detectors are placed and how much survey effort is used. Estimates of the activity center density surface should be obtained by estimating the intensity of a point process model for activity centers. Practitioners should state explicitly whether they are estimating the intensity or making predictions of activity center location, and predictions of activity center locations should not be confused with estimates of the intensity.

Estimating the size of a closed population by modeling latent and observed heterogeneity.

The paper extends the empirical likelihood (EL) approach of Liu et al. to a new and very flexible family of latent class models for capture-recapture data also allowing for serial dependence on previous capture history, conditionally on latent type and covariates. The EL approach allows to estimate the overall population size directly rather than by adding estimates conditional to covariate configurations. A Fisher-scoring algorithm for maximum likelihood estimation is proposed and a more efficient alternative to the traditional EL approach for estimating the non-parametric component is introduced; this allows us to show that the mapping between the non-parametric distribution of the covariates and the probabilities of being never captured is one-to-one and strictly increasing. Asymptotic results are outlined, and a procedure for constructing profile likelihood confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach and a simulation study indicates that, when estimating the overall undercount, the method proposed here is substantially more efficient than the one based on conditional maximum likelihood estimation, especially when the sample size is not sufficiently large.

Relationship between wintering site and survival in a migratory waterbird using different migration routes.

When wintering at different sites, individuals from the same breeding population can experience different conditions, with costs and benefits that may have implications throughout their lifetime. Using a dataset from a longitudinal study on Eurasian Spoonbills from southern France, we explored whether survival rate varied among individuals using different wintering sites. In the last 13 years, more than 3000 spoonbills have been ringed as chicks in Camargue. These birds winter in five main regions that vary in both migratory flyway (East Atlantic vs. Central European) and migration distance (long-distance vs. short-distance vs. resident). We applied Cormack-Jolly-Seber models and found evidence for apparent survival to correlate with migration distance, but not with flyway. During the interval between the first winter sighting and the next breeding period, long-distance migrants had the lowest survival, independently of the flyway taken. Additionally, as they age, spoonbills seem to better cope with migratory challenges and wintering conditions as no differences in apparent survival among wintering strategies were detected during subsequent years. As dispersal to other breeding colonies was rarely observed, the lower apparent survival during this period is likely to be partly driven by lower true survival. This supports the potential role of crossing of natural barriers and degradation of wintering sites in causing higher mortality rates as recorded for a variety of long-distance migrants. Our work confirms variation in demographic parameters across winter distribution ranges and reinforces the importance of longitudinal studies to better understand the complex demographics of migratory species.

Population mortality before and during the COVID-19 epidemic in two Sudanese settings: a key informant study.

BACKGROUND: Population mortality is an important metric that sums information from different public health risk factors into a single indicator of health. However, the impact of COVID-19 on population mortality in low-income and crisis-affected countries like Sudan remains difficult to measure. Using a community-led approach, we estimated excess mortality during the COVID-19 epidemic in two Sudanese communities. METHODS: Three sets of key informants in two study locations, identified by community-based research teams, were administered a standardised questionnaire to list all known decedents from January 2017 to February 2021. Based on key variables, we linked the records before analysing the data using a capture-recapture statistical technique that models the overlap among lists to estimate the true number of deaths. RESULTS: We estimated that deaths per day were 5.5 times higher between March 2020 and February 2021 compared to the pre-pandemic period in East Gezira, while in El Obeid City, the rate was 1.6 times higher. CONCLUSION: This study suggests that using a community-led capture-recapture methodology to measure excess mortality is a feasible approach in Sudan and similar settings. Deploying similar community-led estimation methodologies should be considered wherever crises and weak health infrastructure prevent an accurate and timely real-time understanding of epidemics' mortality impact in real-time.

Where the small things are: Modelling edge effects on mouse lemur population density and distribution in northwestern Madagascar.

Edge effects result from the penetration to varying depths and intensities, of abiotic and biotic conditions from the surrounding non-forest matrix into the forest interior. Although 70% of the world's forests are within 1 km of a forest edge, making edge effects a dominant feature of most forest habitats, there are few empirical data on inter-site differences in edge responses in primates. We used spatially explicit capture-recapture (SECR) models to determine spatial patterns of density for two species of mouse lemurs (Microcebus murinus and Microcebus ravelobensis) in two forest landscapes in northwestern Madagascar. The goal of our study was to determine if mouse lemurs displayed spatially variable responses to edge effects. We trapped animals using Sherman live traps in the Mariarano Classified Forest (MCF) and in the Ambanjabe Forest Fragment Site (AFFS) site within Ankarafantsika National Park. We trapped 126 M. murinus and 79 M. ravelobensis at MCF and 78 M. murinus and 308 M. ravelobensis at AFFS. For M. murinus, our top model predicted a positive edge response, where density increased towards edge habitats. In M. ravelobensis, our top model predicted a negative edge response, where density was lower near the forest edges and increased towards the forest interior. At regional and landscape-specific scales, SECR models estimated different density patterns between M. murinus and M. ravelobensis as a result of variation in edge distance. The spatial variability of our results using SECR models indicate the importance of studying the population ecology of primates at varying scales that are appropriate to the processes of interest. Our results lend further support to the theory that some lemurs exhibit a form of ecological flexibility in their responses to forest loss, forest fragmentation, and associated edge effects.

Finite mixtures in capture-recapture surveys for modeling residency patterns in marine wildlife populations.

This work aims to show how prior knowledge about the structure of a heterogeneous animal population can be leveraged to improve the abundance estimation from capture-recapture survey data. We combine the Open Jolly-Seber model with finite mixtures and propose a parsimonious specification tailored to the residency patterns of the common bottlenose dolphin. We employ a Bayesian framework for our inference, discussing the appropriate choice of priors to mitigate label-switching and nonidentifiability issues, commonly associated with finite mixture models. We conduct a series of simulation experiments to illustrate the competitive advantage of our proposal over less specific alternatives. The proposed approach is applied to data collected on the common bottlenose dolphin population inhabiting the Tiber River estuary (Mediterranean Sea). Our results provide novel insights into this population's size and structure, shedding light on some of the ecological processes governing its dynamics.

Estimating the Burden of Influenza Hospitalizations Across Multiple Seasons Using Capture-Recapture.

INTRODUCTION: Influenza remains an important cause of hospitalizations in the United States. Estimating the number of influenza hospitalizations is vital for public health decision making. Combining existing surveillance systems through capture-recapture methods allows for more comprehensive burden estimations. METHODS: Data from independent surveillance systems were combined using capture-recapture methods to estimate influenza hospitalization rates for children and adults in Middle Tennessee during consecutive influenza seasons from 2016-17 through 2019-20. EIP identified cases through surveillance of laboratory results for hospitalized children and adults. HAIVEN and NVSN recruited hospitalized patients with respiratory symptoms or fever. Population-based influenza rates and the proportion of cases detected by each surveillance system were calculated. RESULTS: Estimated overall influenza hospitalization rates ranged from 23 influenza-related hospitalizations per 10,000 persons in 2016-17 to 40 per 10,000 persons in 2017-18. Adults age ≥65 years had the highest hospitalization rates across seasons and experienced a rate of 170 hospitalizations per 10,000 persons during the 2017-18 season. EIP consistently identified a higher proportion of influenza cases for adults and children compared with HAIVEN and NVSN, respectively. CONCLUSION: Current surveillance systems underestimate the influenza burden. Capture-recapture provides an alternative approach to use data from independent surveillance systems and complement population-based burden estimates.

Hierarchical Variation in Phenotypic Flexibility across Timescales and Associated Survival Selection Shape the Dynamics of Partial Seasonal Migration.

AbstractPopulation responses to environmental variation ultimately depend on within-individual and among-individual variation in labile phenotypic traits that affect fitness and resulting episodes of selection. Yet complex patterns of individual phenotypic variation arising within and between time periods, as well as associated variation in selection, have not been fully conceptualized or quantified. We highlight how structured patterns of phenotypic variation in dichotomous threshold traits can theoretically arise and experience varying forms of selection, shaping overall phenotypic dynamics. We then fit novel multistate models to 10 years of band-resighting data from European shags to quantify phenotypic variation and selection in a key threshold trait underlying spatioseasonal population dynamics: seasonal migration versus residence. First, we demonstrate substantial among-individual variation alongside substantial between-year individual repeatability in within-year phenotypic variation ("flexibility"), with weak sexual dimorphism. Second, we demonstrate that between-year individual variation in within-year phenotypes ("supraflexibility") is structured and directional, consistent with the threshold trait model. Third, we demonstrate strong survival selection on within-year phenotypes-and hence on flexibility-that varies across years and sexes, including episodes of disruptive selection representing costs of flexibility. By quantitatively combining these results, we show how supraflexibility and survival selection on migratory flexibility jointly shape population-wide phenotypic dynamics of seasonal movement.

Estimating the undetected infections in the Monkeypox outbreak.

While the number of detected Monkeypox infections are widely available, an understanding of the extent of undetected cases is urgently needed for an effective tackling of its spread. The aim of this study is to estimate the true number of Monkeypox (detected and undetected) infections in most affected countries. The question being asked is: How many cases have actually occurred? We propose a lower bound estimator for the true number of Monkeypox cases. The estimator is data-driven and can be easily computed from the cumulative distributions of weekly cases. We focused on the ratio of the total estimated cases to the observed cases on July 31, 2022: The proportion of undetected cases was relevant in all countries, with countries whose estimated true number of infections could be more than three times the observed one. We provided a practical contribution to the understanding of the current Monkeypox wave and reliable estimates on how many undetected cases are going around in several countries, where the epidemic spreads differently.

Climate change and commercial fishing practices codetermine survival of a long-lived seabird.

Understanding the environmental mechanisms that govern population change is a fundamental objective in ecology. Although the determination of how top-down and bottom-up drivers affect demography is important, it is often equally critical to understand the extent to which, environmental conditions that underpin these drivers fluctuate across time. For example, associations between climate and both food availability and predation risk may suggest the presence of trophic interactions that may influence inferences made from patterns in ecological data. Analytical tools have been developed to account for these correlations, while providing opportunities to ask novel questions regarding how populations change across space and time. Here, we combine two modeling disciplines-path analysis and mark-recapture-recovery models-to explore whether shifts in sea-surface temperatures (SSTs) influenced top-down (entanglement in fishing equipment) or bottom-up (forage fish production) population constraints over 60 years, and the extent to which these covarying processes shaped the survival of a long-lived seabird, the Royal tern. We found that hemispheric trends in SST were associated with variation in the amount of fish harvested along the Atlantic coast of North America and in the Caribbean, whereas reductions in forage fish production were mostly driven by shifts in the amount of fish harvested by commercial fisheries throughout the North Atlantic the year prior. Although the indirect (i.e., stock depletion) and direct (i.e., entanglement) impacts of commercial fishing on Royal tern mortality has declined over the last 60 years, increased SSTs during this time period has resulted in a comparable increase in mortality risk, which disproportionately impacted the survival of the youngest age-classes of Royal terns. Given climate projections for the North Atlantic, our results indicate that threats to Royal tern population persistence in the Mid-Atlantic will most likely be driven by failures to recruit juveniles into the breeding population.

Male fertility advantage within and between seasons in the perennial androdioecious plant Phillyrea angustifolia.

BACKGROUND AND AIMS: Androdioecy, the co-occurrence of males and hermaphrodites, is a rare reproductive system. Males can be maintained if they benefit from a higher male fitness than hermaphrodites, referred to as male advantage. Male advantage can emerge from increased fertility owing to resource reallocation. However, empirical studies usually compare sexual phenotypes over a single flowering season, thus ignoring potential cumulative effects over successive seasons in perennials. In this study, we quantify various components of male fertility advantage, both within and between seasons, in the long-lived perennial shrub Phillyrea angustifolia (Oleaceae). Although, owing to a peculiar diallelic self-incompatibility system and female sterility mutation strictly associated with a breakdown of incompatibility, males do not need fertility advantage to persist in this species, this advantage remains an important determinant of their equilibrium frequency. METHODS: A survey of >1000 full-sib plants allowed us to compare males and hermaphrodites for several components of male fertility. Individuals were characterized for proxies of pollen production and vegetative growth. By analysing maternal progeny, we compared the siring success of males and hermaphrodites. Finally, using a multistate capture-recapture model we assessed, for each sexual morph, how the intensity of flowering in one year impacts next-year growth and reproduction. KEY RESULTS: Males benefitted from a greater vegetative growth and flowering intensity. Within one season, males sired twice as many seeds as equidistant, compatible hermaphroditic competitors. In addition, males more often maintained intense flowering over successive years. Finally, investment in male reproductive function appeared to differ between the two incompatibility groups of hermaphrodites. CONCLUSION: Males, by sparing the cost of female reproduction, have a higher flowering frequency and vegetative growth, both of which contribute to male advantage over an individual lifetime. This suggests that studies analysing sexual phenotypes during only single reproductive periods are likely to provide inadequate estimates of male advantage in perennials.

Estimating population size: The importance of model and estimator choice.

We consider estimator and model choice when estimating abundance from capture-recapture data. Our work is motivated by a mark-recapture distance sampling example, where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences, we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effects models.

A general modeling framework for open wildlife populations based on the Polya tree prior.

Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been developed for analyzing these data. Although these models have been parameterized and fitted using different approaches, they have all been designed to either model the pattern with which individuals enter and/or exit the population, or to estimate the population size by accounting for the corresponding observation process, or both. However, existing approaches rely on a predefined model structure and complexity, either by assuming that parameters linked to the entry and exit pattern (EEP) are specific to sampling occasions, or by employing parametric curves to describe the EEP. Instead, we propose a novel Bayesian nonparametric framework for modeling EEPs based on the Polya tree (PT) prior for densities. Our Bayesian nonparametric approach avoids overfitting when inferring EEPs, while simultaneously allowing more flexibility than is possible using parametric curves. Finally, we introduce the replicate PT prior for defining classes of models for these data allowing us to impose constraints on the EEPs, when required. We demonstrate our new approach using capture-recapture, count, and ring-recovery data for two different case studies.

Latent multinomial models for extended batch-mark data.

Batch marking is common and useful for many capture-recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture-recapture models to such data requires one to identify all possible sets of capture-recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.

Continuous time-interaction processes for population size estimation, with an application to drug dealing in Italy.

We introduce a time-interaction point process where the occurrence of an event can increase (self-excitement) or reduce (self-correction) the probability of future events. Self-excitement and self-correction are allowed to be triggered by the same event, at different timescales; other effects such as those of covariates, unobserved heterogeneity, and temporal dependence are also allowed in the model. We focus on capture-recapture data, as our work is motivated by an original example about the estimation of the total number of drug dealers in Italy. To do so, we derive a conditional likelihood formulation where only subjects with at least one capture are involved in the inference process. The result is a novel and flexible continuous-time population size estimator. A simulation study and the analysis of our motivating example illustrate the validity of our approach in several scenarios.

Counting the Capital's cats: Estimating drivers of abundance of free-roaming cats with a novel hierarchical model.

Free-roaming cats are a conservation concern in many areas but identifying their impacts and developing mitigation strategies requires a robust understanding of their distribution and density patterns. Urban and residential areas may be especially relevant in this process because free-roaming cats are abundant in these anthropogenic landscapes. Here, we estimate the occupancy and density of free-roaming cats in Washington D.C. and relate these metrics to known landscape and social factors. We conducted an extended camera trap survey of public and private spaces across D.C. and analyzed data collected from 1483 camera deployments from 2018 to 2020. We estimated citywide cat distribution by fitting hierarchical occupancy models and further estimated cat abundance using a novel random thinning spatial capture-recapture model that allows for the use of photos that can and cannot be identified to individual. Within this model, we utilized individual covariates that provided identity exclusions between photos of unidentifiable cats with inconsistent coat patterns, thus increasing the precision of abundance estimates. This combined model also allowed for unbiased estimation of density when animals cannot be identified to individual at the same rate as for free-roaming cats whose identifiability depended on their coat characteristics. Cat occupancy and abundance declined with increasing distance from residential areas, an effect that was more pronounced in wealthier neighborhoods. There was noteworthy absence of cats detected in larger public spaces and forests. Realized densities ranged from 0.02 to 1.75 cats/ha in sampled areas, resulting in a district-wide estimate of ~7296 free-roaming cats. Ninety percent of cat detections lacked collars and nearly 35% of known individuals were ear-tipped, indicative of district Trap-Neuter-Return (TNR) programs. These results suggest that we mainly sampled and estimated the unowned cat subpopulation, such that indoor/outdoor housecats were not well represented. The precise estimation of cat population densities is difficult due to the varied behavior of subpopulations within free-roaming cat populations (housecats, stray and feral cats), but our methods provide a first step in establishing citywide baselines to inform data-driven management plans for free-roaming cats in urban environments.

Avoiding bias in estimates of population size for translocation management.

Mark-recapture surveys are commonly used to monitor translocated populations globally. Data gathered are then used to estimate demographic parameters, such as abundance and survival, using Jolly-Seber (JS) models. However, in translocated populations initial population size is known and failure to account for this may bias parameter estimates, which are important for informing conservation decisions during population establishment. Here, we provide methods to account for known initial population size in JS models by incorporating a separate component likelihood for translocated individuals, using a maximum-likelihood estimation, with models that can be fitted using either R or MATLAB. We use simulated data and a case study of a threatened lizard species with low capture probability to demonstrate that unconstrained JS models may overestimate the size of translocated populations, especially in the early stages of post-release monitoring. Our approach corrects this bias; we use our simulations to demonstrate that overestimates of population size between 78% and 130% can occur in the unconstrained JS models when the detection probability is below 0.3 compared to 1%-8.9% for our constrained model. Our case study did not show an overestimate; however accounting for the initial population size greatly reduced error in all parameter estimates and prevented boundary estimates. Adopting the corrected JS model for translocations will help managers to obtain more robust estimates of the population sizes of translocated animals, better informing future management including reinforcement decisions, and ultimately improving translocation success.