Small Sample Estimators for Two-way Capture Recapture Experiments

The properties of the generalized Waring distribution defined on the non negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then we turn to the Petersen model for estimating the population size $N$ in a two-way capture recapture experiment. We construct a Bayesian model for $N$ by combining a Waring prior with the hypergeometric distribution for the number of units caught twice in the experiment. Confidence intervals for $N$ are obtained using quantiles of the posterior, a generalized Waring distribution. The standard confidence interval for the population size constructed using the asymptotic variance of Petersen estimator and .5 logit transformed interval are shown to be special cases of the generalized Waring confidence interval. The true coverage of this interval is shown to be bigger than or equal to its nominal converage in small populations, regardless of the capture probabilities. In addition, its length is substantially smaller than that of the .5 logit transformed interval. Thus a generalized Waring confidence interval appears to be the best way to quantify the uncertainty of the Petersen estimator for populations size

Tailoring Capture-Recapture Methods to Estimate Registry-Based Case Counts Based on Error-Prone Diagnostic Signals

Surveillance research is of great importance for effective and efficient epidemiological monitoring of case counts and disease prevalence. Taking specific motivation from ongoing efforts to identify recurrent cases based on the Georgia Cancer Registry, we extend recently proposed "anchor stream" sampling design and estimation methodology. Our approach offers a more efficient and defensible alternative to traditional capture-recapture (CRC) methods by leveraging a relatively small random sample of participants whose recurrence status is obtained through a principled application of medical records abstraction. This sample is combined with one or more existing signaling data streams, which may yield data based on arbitrarily non-representative subsets of the full registry population. The key extension developed here accounts for the common problem of false positive or negative diagnostic signals from the existing data stream(s). In particular, we show that the design only requires documentation of positive signals in these non-anchor surveillance streams, and permits valid estimation of the true case count based on an estimable positive predictive value (PPV) parameter. We borrow ideas from the multiple imputation paradigm to provide accompanying standard errors, and develop an adapted Bayesian credible interval approach that yields favorable frequentist coverage properties. We demonstrate the benefits of the proposed methods through simulation studies, and provide a data example targeting estimation of the breast cancer recurrence case count among Metro Atlanta area patients from the Georgia Cancer Registry-based Cancer Recurrence Information and Surveillance Program (CRISP) database

Contrasting abundance and residency patterns of two sympatric populations of transient killer whales (Orcinus orca) in the northern Gulf of Alaska

Two sympatric populations of “transient” (mammal-eating) killer whales were photo-identified over 27 years (1984–2010) in Prince William Sound and Kenai Fjords, coastal waters of the northern Gulf of Alaska (GOA). A total of 88 individuals were identified during 203 encounters with “AT1” transients (22 individuals) and 91 encounters with “GOA” transients (66 individuals). The median number of individuals identified annually was similar for both populations (AT1=7; GOA=8), but mark-recapture estimates showed the AT1 whales to have much higher fidelity to the study area, whereas the GOA whales had a higher exchange of individuals. Apparent survival estimates were generally high for both populations, but there was a significant reduction in the survival of AT1 transients after the Exxon Valdez oil spill in 1989, with an abrupt decline in estimated abundance from a high of 22 in 1989 to a low of seven whales at the end of 2010. There was no detectable decline in GOA population abundance or survival over the same period, but abundance ranged from just 6 to 18 whales annually. Resighting data from adjacent coastal waters and movement tracks from satellite tags further indicated that the GOA whales are part of a larger population with a more extensive range, whereas AT1 whales are resident to the study area

Non-invasive methods for obtaining occupancy probabilities and density estimates of Interior Alaska's mesocarnivore populations

Thesis (M.S.) University of Alaska Fairbanks, 2015Mesocarnivore species worldwide have been shown to be significant drivers of ecological communities. Changes in their abundance and distributions are known to cause cascading effects throughout ecosystems, and changes to the landscape and climate will likely lead to shifts in mesocarnivore population sizes and distributions. However, the current status of these species in some of the world's most susceptible landscapes is not known. I assessed the impacts of abiotic factors on the distributional patterns and abundance of boreal mesocarnivores and evaluated methods commonly used to estimate density and occupancy. I conducted non-invasive winter surveys of coyotes (Canis latrans), red foxes (Vulpes vulpes), lynx (Lynx canadensis), wolverines (Gulo gulo), and marten (Martes americana) in the interior of Alaska. Overall, mesocarnivore occupancy was most strongly influenced by snow depth and snow compaction as well as habitat type. Canid species used areas with shallow and compact snow while mustelid species used deeper and fluffier snow conditions most often, and lynx used areas with shallow and fluffy snow. Forested habitat types were used most commonly across all mesocarnivores. Prey abundance and the presence of human activity were less influential to mesocarnivore occupancy patterns than snow conditions and habitat, suggesting that a changing boreal climate may have a strong, direct influence on the distribution of these mesocarnivores. Estimating current population status of these species is particularly important in areas that are most susceptible to change, and I used two occupancy-modeling methods and a spatially explicit capture-recapture density estimator to assess coyote and red fox populations. Occupancy and density are two distinct parameters, however, the simplicity of occupancy (both in terms of sampling and modeling) makes its use as a proxy for density an appealing possibility. I found that occupancy and density estimates were not consistent and led to significantly different inference about coyote and red fox populations. Coyotes and red fox occupancy probabilities were similar to each other (range: 0.34-0.48), but red fox density was nearly four times greater than coyote density. While both methods produced precise parameter estimates, top-ranking occupancy and density models were different. I suggest that managers use caution when using occupancy as a proxy for density. Occupancy is best used to address questions related to spatial use, while density should be used to assess population size. Together, these findings provide valuable information about the current status of a previously unstudied mesocarnivore community and provide managers with useful insight into study design and management actions that should be taken to best protect this guild

Rcapture: Loglinear Models for Capture-Recapture in R

This article introduces Rcapture, an R package for capture-recapture experiments. The data for analysis consists of the frequencies of the observable capture histories over the t capture occasions of the experiment. A capture history is a vector of zeros and ones where one stands for a capture and zero for a miss. Rcapture can fit three types of models. With a closed population model, the goal of the analysis is to estimate the size N of the population which is assumed to be constant throughout the experiment. The estimator depends on the way in which the capture probabilities of the animals vary. Rcapture features several models for these capture probabilities that lead to different estimators for N. In an open population model, immigration and death occur between sampling periods. The estimation of survival rates is of primary interest. Rcapture can fit the basic Cormack-Jolly-Seber and Jolly-Seber model to such data. The third type of models fitted by Rcapture are robust design models. It features two levels of sampling; closed population models apply within primary periods and an open population model applies between periods. Most models in Rcapture have a loglinear form; they are fitted by carrying out a Poisson regression with the R function glm. Estimates of the demographic parameters of interest are derived from the loglinear parameter estimates; their variances are obtained by linearization. The novel feature of this package is the provision of several new options for modeling capture probabilities heterogeneity between animals in both closed population models and the primary periods of a robust design. It also implements many of the techniques developed by R. M. Cormack for open population models.

Model Averaging in Agriculture and Natural Resources: What Is It? When Is It Useful? When Is It a Distraction?

I use two examples to illustrate three methods for model averaging: using AIC weights, using BIC weights, and fully Bayesian analyses. The first example is a capture-recapture study that estimates the population size by averaging over 4 models for capture probabilities. The second is an analysis of a study of logging impacts on Curculionid weevils using a before-after-control-impact (BACI) study design. The estimated impact is averaged over 4 ecologically relevant models. Both examples demonstrate the sensitivity of model weights, or posterior model probabilities, to the choice of prior model probabilities and prior distributions for parameters. The model averaged estimates and their confidence intervals are less influenced by those choices. The BACI-design example also demonstrates the need to carefully choose the model parameterization so that the parameter of interest, the interaction, has the same interpretation for all models in the model set. I also briefly discuss three other frequentist approaches to model averaging: bagging, stacking, and model-averaged-tail-area confidence intervals

Estimation Problems in Complex Field Studies with Deep Interactions: Time-to-Event and Local Regression Models for Environmental Effects on Vital Rates

Field studies that measure vital rates in context over extended time periods are a cornerstone of our understanding of population processes. These studies inform us about the relationship between biological process and environmental noise in an irreplaceable way. These data sets bring ``big data\u27\u27 and ``big model\u27\u27 challenges, which limit the application of standard software (e.g., \textbf{BUGS}). The environmental sensitivity of vital rates is also expected to exhibit interactions and non-linearity, which typically result in difficult model selection questions in large data sets. Finally, long-term ecological data sets often contain complex temporal structure. In commonly applied discrete-time models complex temporal structure forces the analyst to make many competing decisions about discretizing time, which add complexity to any analysis and confuse the interpretation of parameters. I tackle these problems in three ways: 1) I apply and improve current state of the art statistical algorithms and software (Hamiltonian Monte Carlo with the NUTS sampler implemented in \textbf{Stan}) to implement the estimation of vital rates from mark-recapture data in a large Atlantic salmon data set; 2) I extend continuous-time time-to-event models with continuous estimated rate functions to mark-recapture and emigration data; and 3) I apply simple local regression to the estimation of vital rates to turn the model-selection problem resulting from interactions and non-linearity into an estimation problem, which is solved by the estimation algorithm. For each model I present methods for visualizing the results in biologically meaningful terms and use these for model criticism

Spring migration of Ruffs Philomachus pugnax in Fryslân: estimates of staging duration using resighting data

Seasonal bird migration involves long flights, but most time is actually spent at intermediate staging areas. The duration of stay at these sites can be evaluated with mark–recapture methods that employ day-to-day local encounters of individually marked birds. Estimates of staging duration are based on two probabilities: the immigration probability, the complement of a bird’s seniority to an area, and the emigration probability, the complement of the staying probability. Estimating total staging duration from seniority and staying probabilities requires validation for resighting data and here we compare three data categories of Ruffs Philomachus pugnax passing through The Netherlands during northward migration: (1) newly colour-ringed, (2) previously colour-ringed and (3) radio-tagged Ruffs (recorded by automated receiving stations). Between 2004 and 2008, 4363 resighting histories and 95 telemetry recording histories were collected. As sample sizes for females were low, only data for males were analysed. Possible catching effects affecting estimates of staging duration were explored. Staying probability was estimated for all data. Seniority however, could not be estimated for newly marked Ruffs; the assumption of equal ‘capture’ probability for reverse-time models applied to estimate seniority is violated for seasonal resighting histories starting with a catching event. Therefore, estimates of total staging duration were based on resightings of previously colour-marked birds only. For radio-tagged birds a minimal staging duration (time between tagging and last recording) was calculated. Modelling indicated that newly colour-ringed birds had a higher staying probability than previously colour-ringed birds, but the difference translated to a prolonged staging duration in newly ringed birds of only 0.4–0.5 d, suggesting a very small catching effect. The minimal staging duration of radio-tagged birds validated estimates of staging duration for colour-ringed birds in 2007 but not in 2005. In 2005 a low resighting probability resulted in underestimates of staging duration. We conclude that (1) estimates of staying probability can be affected by catching although effects on staging duration might be small, and that (2) low resighting probabilities can lead to underestimates in staging duration. In our study previously ringed Ruffs resighted in 2006–08 yielded reliable estimates of staging duration as data had sufficiently high resighting probabilities. Average staging durations varied between 19 d in 2008 and 23 d in 2006.