Under-reporting of COVID-19 in the Northern Health Authority region of British Columbia.

Asymptomatic and pauci-symptomatic presentations of COVID-19 along with restrictive testing protocols result in undetected COVID-19 cases. Estimating undetected cases is crucial to understanding the true severity of the outbreak. We introduce a new hierarchical disease dynamics model based on the N-mixtures hidden population framework. The new models make use of three sets of disease count data per region: reported cases, recoveries and deaths. Treating the first two as under-counted through binomial thinning, we model the true population state at each time point by partitioning the diseased population into the active, recovered and died categories. Both domestic spread and imported cases are considered. These models are applied to estimate the level of under-reporting of COVID-19 in the Northern Health Authority region of British Columbia, Canada, during 30 weeks of the provincial recovery plan. Parameter covariates are easily implemented and used to improve model estimates. We compare two distinct methods of model-fitting for this case study: (1) maximum likelihood estimation, and (2) Bayesian Markov chain Monte Carlo. The two methods agreed exactly in their estimates of under-reporting rate. When accounting for changes in weekly testing volumes, we found under-reporting rates varying from 60.2% to 84.2%.

Le recours à des protocoles de tests restrictifs et l'existence de formes asymptomatiques et paucisymptomatiques de la COVID­19 contribuent à la non détection de cas COVID­19. Pour comprendre la véritable gravité de l'épidémie, il est primordial d'estimer correctement le nombre de cas non détectés. A cette fin, les auteurs de ce travail proposent un nouveau modèle hiérarchique des dynamiques de la maladie basé sur l'approche de N­mélanges de population cachée. Ces modèles utilisent trois types de données régionales, à savoir, les nombres de cas déclarés, guéris et décédés. En faisant appel à l'amincissement binomial (binomial thinning) et en traitant les nombres de cas déclarés et guéris comme étant sous­évalués, les auteurs proposent une modélisation de l'état réel de l'épidémie basée sur une partition de la population malade en trois catégories : cas actifs, cas guéris et cas décédés. Cette partition tient compte des cas de propagation intérieure et des cas importés. Les auteurs ont utilisé les données recueillies durant les trente semaines du plan de rétablissement provincial de la région de l'Autorité sanitaire du Nord de la Colombie­Britannique, Canada pour illustrer leur approche et estimer le niveau de sous­déclaration COVID­19 associé. Des covariables peuvent être facilement incorporées au modèle proposé et améliorer la qualité des estimations. Deux méthodes d'ajustement sont retenues: (1) l'estimation par maximum de vraisemblance, et (2) la méthode de Monte Carlo par chaînes de Markov. Les estimations du taux de sous­déclaration obtenues par ces deux méthodes concordent exactement et varient entre 60,2% et 84,2% après ajustement des variations des volumes de tests hebdomadaires.

Lemur catta in small forest fragments: Which variables best predict population viability?

Habitat fragmentation is an increasingly serious issue affecting primates in most regions where they are found today. Populations of Lemur catta (ring-tailed lemur) in Madagascar's south-central region are increasingly restricted to small, isolated forest fragments, surrounded by grasslands or small-scale agriculture. Our aim was to evaluate the potential for population viability of L. catta in nine forest fragments of varying sizes (2-46 ha, population range: 6-210 animals) in south-central Madagascar, using a set of comparative, quantitative ecological measures. We used Poisson regression models with a log link function to examine the effects of fragment size, within-fragment food availability, and abundance of matrix resources (food and water sources) on L. catta population sizes and juvenile recruitment. We found a strong association between overall population size and (a) fragment size and (b) abundance of key food resources Melia azedarach and Ficus spp. (per 100 m along transect lines). Juvenile recruitment was also associated with fragment size and abundance of the two above-mentioned food resources. When the largest population, an outlier, was removed from the analysis, again, the model containing fragment size and abundance of M. azedarach and Ficus spp. was the best fitting, but the model that best predicted juvenile recruitment contained only fragment size. While our results are useful for predicting population presence and possible persistence in these fragments, both the potential for male dispersal and the extent of human disturbance within most fragments play crucial roles regarding the likelihood of long-term L. catta survival. While seven of the nine fragments were reasonably protected from human disturbance, only three offered the strong potential for male dispersal, thus the long-term viability of many of these populations is highly uncertain.

Hidden Markov models for extended batch data.

Batch marking provides an important and efficient way to estimate the survival probabilities and population sizes of wild animals. It is particularly useful when dealing with animals that are difficult to mark individually. For the first time, we provide the likelihood for extended batch-marking experiments. It is often the case that samples contain individuals that remain unmarked, due to time and other constraints, and this information has not previously been analyzed. We provide ways of modeling such information, including an open N-mixture approach. We demonstrate that models for both marked and unmarked individuals are hidden Markov models; this provides a unified approach, and is the key to developing methods for fast likelihood computation and maximization. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modeling. This allows the simultaneous estimation of population size and immigration, in addition to survival, as well as efficient estimation of standard errors and methods of model selection and evaluation, using standard likelihood techniques. Alternative methods for estimating population size are presented and compared. An illustration is provided by a weather-loach data set, previously analyzed by means of a complex procedure of constructing a pseudo likelihood, the formation of estimating equations, the use of sandwich estimates of variance, and piecemeal estimation of population size. Simulation provides general validation of the hidden Markov model methods developed and demonstrates their excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically required.

Estimating the number of injection drug users in greater Victoria, Canada using capture-recapture methods.

BACKGROUND: Population size estimation is critical for planning public health programmes for injection drug users. Estimation is difficult, as these populations are considered 'hidden' or 'hard to reach'. The currently accepted population size estimate for greater Victoria, Canada is between 1,500 and 2,000 individuals, which is dated prior to the year 2000, and is likely an underestimate. METHODS: We used three mark-recapture methods (the Lincoln-Petersen estimator, Huggins' model, and Pledger's model) to estimate population size using cross-sectional survey data collected in 2003 and 2005. Data come from a closed population with two time-ordered samples from the same source. We compare our estimates with the currently accepted estimate that is based on the registry of a Victoria needle exchange. RESULTS: All methods provided population size estimates that were higher than the currently accepted estimate. Huggins' method produced wider confidence intervals. Point estimates of population size from the three methods ranged from 3,329 to 3,342. CONCLUSIONS: Our estimates will aid health authorities in planning for harm reduction programmes. Repeating the methods as further phases of I-Track data become available will ensure that the population estimates remain up to date.

New proteins for a new perspective on syphilis diagnosis.

Syphilis is a sexually transmitted disease caused by Treponema pallidum subsp. pallidum; it can be effectively treated with penicillin yet remains prevalent worldwide, due in part to the shortcomings of current diagnostic tests. Here we report the production of soluble recombinant versions of three novel diagnostic candidate proteins, Tp0326, Tp0453, and a Tp0453-Tp0326 chimera. The sensitivities of these recombinant proteins were assessed by screening characterized serum samples from primary, secondary, and latent stages of infection (n = 169). The specificities were assessed by screening false positives identified with the standard diagnostic testing algorithm (n = 21), samples from patients with potentially cross-reactive infections (Leptospira spp., Borrelia burgdorferi, Helicobacter pylori, Epstein-Barr virus, hepatitis B virus, hepatitis C virus, or cytomegalovirus) (n = 38), and samples from uninfected individuals (n = 11). The sensitivities of Tp0326, Tp0453, and the Tp0453-Tp0326 chimera were found to be 86%, 98%, and 98%, respectively, and the specificities were 99%, 100%, and 99%. In a direct comparison, the Captia syphilis (T. pallidum)-G enzyme immunoassay (Trinity Biotech) was used to screen the same serum samples and was found to have a sensitivity of 98% and a specificity of 90%. In particular, Tp0453 and the chimera exhibited superior accuracy in classifying analytical false-positive samples (100%, compared to 43% for the Captia assay). These findings identify Tp0453 and the Tp0453-Tp0326 chimera as novel syphilis-specific diagnostic candidates that surpass the performance of a currently available diagnostic enzyme immunoassay test for syphilis and that allow accurate detection of all stages of infection.

Minimum chi-square method for estimating population size in capture-recapture experiments.

Closed population capture-recapture estimation of population size is difficult under heterogeneous capture probabilities. We introduce the minimum chi-square method which can handle multi-occasion capture-recapture data. It complements likelihood methods with elements that can lead to confidence intervals and assessment of goodness-of-fit. We conduct a comprehensive study on the minimum chi-square method for estimating the size of a closed population using multiple-occasion capture-recapture data under heterogeneous capture probability. We also develop two different bootstrap techniques that can be combined with any underlying estimator, be it the minimum chi-square estimator or a likelihood estimator, to perform useful inference for estimating population size. We present a simulation study on the minimum chi-square method and apply it to analyze white stork multiple capture-recapture data. Under certain conditions, the chi-square method outperforms the likelihood based methods.

Computational Efficiency and Precision for Replicated-Count and Batch-Marked Hidden Population Models.

We address two computational issues common to open-population N-mixture models, hidden integer-valued autoregressive models, and some hidden Markov models. The first issue is computation time, which can be dramatically improved through the use of a fast Fourier transform. The second issue is tractability of the model likelihood function for large numbers of hidden states, which can be solved by improving numerical stability of calculations. As an illustrative example, we detail the application of these methods to the open-population N-mixture models. We compare computational efficiency and precision between these methods and standard methods employed by state-of-the-art ecological software. We show faster computing times (a ∼ 6 to ∼ 30 times speed improvement for population size upper bounds of 500 and 1000, respectively) over state-of-the-art ecological software for N-mixture models. We also apply our methods to compute the size of a large elk population using an N-mixture model and show that while our methods converge, previous software cannot produce estimates due to numerical issues. These solutions can be applied to many ecological models to improve precision when logs of sums exist in the likelihood function and to improve computational efficiency when convolutions are present in the likelihood function. Supplementary materials accompanying this paper appear online. Supplementary materials for this article are available at 10.1007/s13253-022-00509-y.

Integrating technologies provides insight into the subsurface foraging behaviour of a humpback whale (Megaptera novaeangliae) feeding on walleye pollock (Gadus chalcogrammus) in Juan de Fuca Strait, Canada.

Subsurface foraging is an important proportion of the activity budget of rorqual whales, yet information on their behaviour underwater remains challenging to obtain. Rorquals are assumed to feed throughout the water column and to select prey as a function of depth, availability and density, but there remain limitations in the precise identification of targeted prey. Current data on rorqual foraging in western Canadian waters have thus been limited to observations of prey species amenable to surface feeding, such as euphausiids and Pacific herring (Clupea pallasii), with no information on deeper alternative prey sources. We measured the foraging behaviour of a humpback whale (Megaptera novaeangliae) in Juan de Fuca Strait, British Columbia, using three complimentary methods: whale-borne tag data, acoustic prey mapping, and fecal sub-sampling. Acoustically detected prey layers were near the seafloor and consistent with dense schools of walleye pollock (Gadus chalcogrammus) distributed above more diffuse aggregations of pollock. Analysis of a fecal sample from the tagged whale confirmed that it had been feeding on pollock. Integrating the dive profile with the prey data revealed that the whale's foraging effort followed the general pattern of areal prey density, wherein the whale had a higher lunge-feeding rate at the highest prey abundance and stopped feeding when prey became limited. Our findings of a humpback whale feeding on seasonally energy-dense fish like walleye pollock, which are potentially abundant in British Columbia, suggests that pollock may be an important prey source for this rapidly growing whale population. This result is informative when assessing regional fishing activities for semi-pelagic species as well as the whales' vulnerability to fishing gear entanglements and feeding disturbances during a narrow window of prey acquisition.

A contact tracing SIR model for randomly mixed populations.

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.

Fine-scale diversity of prey detected in humpback whale feces.

Predator diets are largely influenced by prey availability and abundance. Yet, in heterogenous marine environments, identifying the prey species consumed by diving mammals remains a fundamental challenge. For rorqual whales, the energetic constraints of prey engulfment require that the whales seek areas of high prey abundance and execute discrete lunge feeding events on patches of high-density prey. Prey occurrences in feces should therefore provide meaningful insight into the dominant taxa in food patches selected by the animal. We investigated the prey consumed by humpback whales in three regions in southern British Columbia (BC), Canada, using opportunistic fecal sampling, microscopy, and DNA metabarcoding of 14 fecal samples. Fish including Pacific herring (Clupea pallasii), hake (Merluccius productus), and eulachon (Thaleichthys pacificus) were the most common fish species potentially targeted by humpback whales in two regions. The krill Euphausia pacifica was the most prevalent invertebrate DNA detected in all three regions, while sergestid and mysid shrimp may also be important. High DNA read abundances from walleye pollock (Gadus chalcogrammus) and sablefish (Anoplopoma fimbria) were also recovered in one sample each, suggesting that juveniles of these semi-pelagic species may occasionally be targeted. In general, we observed heavily digested fecal material that drove substantial dissimilarities in taxonomic resolution between polymerase chain reaction-based and morphological analyses of the feces. Pacific herring and walleye pollock were the only prey species confirmed by both methods. Our results highlight that molecular and visual analyses of fecal samples provide a complementary approach to diet analysis, with each method providing unique insight into prey diversity.

Parameter redundancy in Jolly-Seber tag loss models.

Capture-recapture experiments are conducted to estimate population parameters such as population size, survival rates, and capture rates. Typically, individuals are captured and given unique tags, then recaptured over several time periods with the assumption that these tags are not lost. However, for some populations, tag loss cannot be assumed negligible. The Jolly-Seber tag loss model is used when the no-tag-loss assumption is invalid. Further, the model has been extended to incorporate group heterogeneity, which allows parameters to vary by group membership. Many mark-recapture models become overparameterized resulting in the inability to independently estimate parameters. This is known as parameter redundancy.We investigate parameter redundancy using symbolic methods. Because of the complex structure of some tag loss models, the methods cannot always be applied directly. Instead, we develop a simple combination of parameters that can be used to investigate parameter redundancy in tag loss models.The incorporation of tag loss and group heterogeneity into Jolly-Seber models does not result in further parameter redundancies. Furthermore, using hybrid methods we studied the parameter redundancy caused by data through case studies and generated tag histories with different parameter values.Smaller capture and survival rates are found to cause parameter redundancy in these models. These problems resolve when applied to large populations.

Complete tag loss in capture-recapture studies affects abundance estimates: An elephant seal case study.

In capture-recapture studies, recycled individuals occur when individuals lose all of their tags and are recaptured as though they were new individuals. Typically, the effect of these recycled individuals is assumed negligible.Through a simulation-based study of double-tagging experiments, we examined the effect of recycled individuals on parameter estimates in the Jolly-Seber model with tag loss (Cowen & Schwarz, 2006). We validated the simulation framework using long-term census data of elephant seals.Including recycled individuals did not affect estimates of capture, survival, and tag-retention probabilities. However, with low tag-retention rates, high capture rates, and high survival rates, recycled individuals produced overestimates of population size. For the elephant seal case study, we found population size estimates to be between 8% and 53% larger when recycled individuals were ignored.Ignoring the effects of recycled individuals can cause large biases in population size estimates. These results are particularly noticeable in longer studies.

A comparison of abundance estimates from extended batch-marking and Jolly-Seber-type experiments.

Little attention has been paid to the use of multi-sample batch-marking studies, as it is generally assumed that an individual's capture history is necessary for fully efficient estimates. However, recently, Huggins et al. (2010) present a pseudo-likelihood for a multi-sample batch-marking study where they used estimating equations to solve for survival and capture probabilities and then derived abundance estimates using a Horvitz-Thompson-type estimator. We have developed and maximized the likelihood for batch-marking studies. We use data simulated from a Jolly-Seber-type study and convert this to what would have been obtained from an extended batch-marking study. We compare our abundance estimates obtained from the Crosbie-Manly-Arnason-Schwarz (CMAS) model with those of the extended batch-marking model to determine the efficiency of collecting and analyzing batch-marking data. We found that estimates of abundance were similar for all three estimators: CMAS, Huggins, and our likelihood. Gains are made when using unique identifiers and employing the CMAS model in terms of precision; however, the likelihood typically had lower mean square error than the pseudo-likelihood method of Huggins et al. (2010). When faced with designing a batch-marking study, researchers can be confident in obtaining unbiased abundance estimators. Furthermore, they can design studies in order to reduce mean square error by manipulating capture probabilities and sample size.