Applications and extensions of Chao's moment estimator for the size of a closed population

This article revisits Chao's (1989, Biometrics45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model M(h)). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (M(th)) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for M(th). Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment.     

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.     

Loglinear models for the robust design in mark-recapture experiments

The robust design is a method for implementing a mark-recapture experiment featuring a nested sampling structure. The first level consists of primary sampling sessions; the population experiences mortality and immigration between primary sessions so that open population models apply at this level. The second level of sampling has a short mark-recapture study within each primary session. Closed population models are used at this stage to estimate the animal abundance at each primary session. This article suggests a loglinear technique to fit the robust design. Loglinear models for the analysis of mark-recapture data from closed and open populations are first reviewed. These two types of models are then combined to analyze the data from a robust design. The proposed loglinear approach to the robust design allows incorporating parameters for a heterogeneity in the capture probabilities of the units within each primary session. Temporary emigration out of the study area can also be accounted for in the loglinear framework. The analysis is relatively simple; it relies on a large Poisson regression with the vector of frequencies of the capture histories as dependent variable. An example concerned with the estimation of abundance and survival of the red-back vole in an area of southeastern Québec is presented.     

Ecological and methodological factors affecting detectability and population estimation in elusive species

Although mark-recapture methods are among the most powerful tools for monitoring wildlife populations, the secretive nature of some species requires a comprehensive understanding of the factors that affect capture probability to maximize accuracy and precision of population parameter estimates (e.g., population size and survivorship). Here, we used aquatic snakes as a case study in applying rigorous mark-recapture methods to estimate population parameters for secretive species. Specifically, we used intensive field sampling and robust design mark-recapture analyses in Program MARK to test specific hypotheses about ecological and methodological factors influencing detectability of two species of secretive aquatic snakes, the banded watersnake (Nerodia fasciata), and the black swamp snake (Seminatrix pygaea). We constructed a candidate set of a priori mark-recapture models incorporating various combinations of time- and sex-varying capture and recapture probabilities, behavioral responses to traps (i.e., trap-happiness or trap-shyness), and temporary emigration, and we ranked models for each species using Akaike's Information Criterion. For both banded watersnakes and black swamp snakes we found strong support for time-varying capture and recapture probabilities and strong trap-happy responses, factors that can bias population estimation if not accommodated in the models. We also found evidence of sex-dependent temporary emigration in black swamp snakes. Our study is among the first comprehensive assessments of factors affecting detectability in snakes and provides a framework for studies aimed at monitoring populations of other secretive species. © 2010 The Wildlife Society.     

Population size estimation of an Asian elephant population in eastern Cambodia through non-invasive mark-recapture sampling

The Asian elephant is a flagship species for conservation in tropical Asia, but reliable population estimates are available only from a few populations. This is because the species can be elusive and occurs at low densities in dense habitat over a large part of its range. Phnom Prich Wildlife Sanctuary in the Eastern Plains, Cambodia, which is part of one of the largest protected area complexes in South-East Asia, is one such habitat that had not been systematically censused for elephants. We, therefore, used fecal-DNA based capture-mark-recapture sampling to estimate the population size for establishing a monitoring baseline. Five sampling sessions targeted all areas in and adjacent to Phnom Prich Wildlife Sanctuary believed to be used by elephants. Fresh dung was collected as the source of DNA and genotyping was carried out based on nine microsatellite loci. The 224 samples collected yielded 78 unique genotypes. Using model averaging of closed population capture-mark-recapture models, the elephant population in Phnom Prich Wildlife Sanctuary was estimated to number 136 ± 18 (SE) individuals. Our results suggest that eastern Cambodia supports a regionally important Asian elephant population.     

Comparing data of different survey methods for sustainable wildlife management in hunting areas: the case of Tarangire–Manyara ecosystem,northern Tanzania

Cost–benefit considerations of wildlife monitoring are essential, particularly, in areas outside national park boundaries, where resources for conducting wildlife censuses are scarce, but that, at the same time, are subject to high pressure for wildlife utilization, such as hunting. Large mammal survey data from various sources were collated and analyzed to investigate which methods are best suited for monitoring purposes at low cost in the Tarangire–Manyara ecosystem, northern Tanzania. Our results indicate that primary data (from aerial and road transects counts) that involve direct species observations, although sometimes very expensive, are required for establishing the status of the target species in terms of density or population size. Concomitantly, secondary data from various sources, such as interviews, hunting quota, and damage reports, obtained over wide areas and over longer periods of time, can provide important information on presence/absence and distribution of species within an area. In addition, the study revealed that hunting quotas set did not correlate with species abundance/numbers from the primary data surveys for most of the large mammals hunted within the ecosystem. For a better conservation and management of wildlife, in particular with respect to the forthcoming formation of Wildlife Management Areas, we propose an integrated approach to wildlife monitoring using primary and secondary data sources through the involvement of local people’s knowledge.     

Survival and population persistence in the critically endangered Tuamotu kingfisher

A wide range of threats affect populations of Pacific island birds and conservationists have been challenged to identify factors upon which to focus management. The Tuamotu kingfisher (Todiramphus gambieri) is one of the most endangered vertebrate species in the world, yet little has been published about basic biology or causes of the population decline. We used 4 years of mark-resight and territory resource information to model survival in juvenile and adult Tuamotu kingfishers. Annual survival of adult males (ϕ = 0.77) was similar to congeneric species, whereas survival of adult females (ϕ = 0.40) and juveniles (ϕ = 0.12) was much lower. The best-supported survival model indicated adult female survival was positively related to territory size, whereas adult male survival was negatively related to atoll forest within territories. We used parameter estimates from survival models in a life-stage simulation analysis to evaluate the relative influence of vital rates and territory habitats on population processes. Results indicated that adult female and juvenile survival had the greatest impact on Tuamotu kingfisher populations, accounting for 58% and 32% of variation in the finite rate of population increase, respectively. Nocturnal predation by rats (Rattus spp.) on incubating kingfishers may explain the lower survival of females than males, whereas juvenile birds may be especially vulnerable to predation by cats (Felis catus). Thus, conservation management for Tuamotu kingfishers should include use of metal guards on cavity trees to protect nests and incubating females, and control predator access during fledging periods. © 2012 The Wildlife Society.     

Variations in age‐ and sex‐specific survival rates help explain population trend in a discrete marine mammal population

Understanding the drivers underlying fluctuations in the size of animal populations is central to ecology, conservation biology, and wildlife management. Reliable estimates of survival probabilities are key to population viability assessments, and patterns of variation in survival can help inferring the causal factors behind detected changes in population size. We investigated whether variation in age‐ and sex‐specific survival probabilities could help explain the increasing trend in population size detected in a small, discrete population of bottlenose dolphins Tursiops truncatus off the east coast of Scotland. To estimate annual survival probabilities, we applied capture–recapture models to photoidentification data collected from 1989 to 2015. We used robust design models accounting for temporary emigration to estimate juvenile and adult survival, multistate models to estimate sex‐specific survival, and age models to estimate calf survival. We found strong support for an increase in juvenile/adult annual survival from 93.1% to 96.0% over the study period, most likely caused by a change in juvenile survival. Examination of sex‐specific variation showed weaker support for this trend being a result of increasing female survival, which was overall higher than for males and animals of unknown sex. Calf survival was lower in the first than second year; a bias in estimating third‐year survival will likely exist in similar studies. There was some support first‐born calf survival being lower than for calves born subsequently. Coastal marine mammal populations are subject to the impacts of environmental change, increasing anthropogenic disturbance and the effects of management measures. Survival estimates are essential to improve our understanding of population dynamics and help predict how future pressures may impact populations, but obtaining robust information on the life history of long‐lived species is challenging. Our study illustrates how knowledge of survival can be increased by applying a robust analytical framework to photoidentification data.     

Modeling the prehistoric Maori population

Skeletal and comparative evidence of mortality is combined with fertility estimates for the precontact Maori population of New Zealand to determine the implied rate of precontact population growth. This rate is found to be too low to populate New Zealand within the time constraints of its prehistoric sequence, the probable founding population size, and the probable population size at contact. Rates of growth necessary to populate New Zealand within the accepted time span are calculated. The differences between this minimum necessary rate and the skeletally derived rate are too large to result solely from inadequacies in the primary data. Four alternative explanations of this conundrum are proposed: 1) skeletal evidence of precontact mortality is highly inaccurate; 2) skeletal evidence of fertility is severely underestimating actual levels; 3) there was very rapid population growth in the earliest part of the sequence up to 1150 A.D., from which no skeletal evidence currently is available; or 4) the prehistoric sequence of New Zealand may have been longer than the generally accepted 1,000-1,200 years. These alternatives are examined, and a combination of the last two is found to be the most probable. The implications of this model for New Zealand prehistory and Oceanic paleodemography are discussed.     

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.     

Occupancy Patterns of Breeding American Black Ducks

Occupancy patterns can assist with the determination of habitat limitation during breeding or wintering periods and can help guide population and habitat management efforts. American black ducks (Anas rubripes; black ducks) are thought to be limited by habitat and food availability during the winter, but breeding sites may also limit the size or growth potential of the population. The Canadian Wildlife Service conducts an annual breeding waterfowl survey that we used to explore the hypothesis that black duck carrying capacity is limited by wetlands available for breeding in Québec, Canada. We applied single-visit, multi-species occupancy models to the 1990–2015 population survey data to determine if there was evidence the black duck population was limited by breeding habitat. Using a dynamic (multi-season) occupancy modeling approach, we estimated latent occupancy (occupancy accounting for imperfect detection) of black ducks and then used latent occupancy estimates to derive occupancy, colonization, and extirpation rates. We jointly modeled the occupancy dynamics of black ducks and other duck species in wetlands where both species were present. Throughout the duration of the survey, 44% of wetlands were never observed to be occupied by black ducks. Occupancy models showed wetland size was positively associated with occupancy at the first time step (initial occupancy) and colonization. All 2-species models indicated initial black duck occupancy, persistence (continued occupancy), and colonization were positively associated with the presence of a second species. Colonization rate over the 26-year period ranged from 7% to 27% across all models. Extirpation rates were similar and were constant through time within each model. Low occupancy rates, combined with approximately equal colonization and extirpation rates, suggest there are available wetlands for breeding black ducks in their core breeding area. If breeding habitats are not saturated, this suggests migration or wintering areas may be more limiting to black duck population abundance. © 2019 The Wildlife Society.     

Demography and population trends of Whooping Cranes

ABSTRACT Previous studies of Whooping Crane demography used estimates of fecundity rates based on females in captivity, and breeding success was estimated based on either the number of unbanded pairs nesting or the number arriving in wintering areas with chicks. We analyzed demographic data from 12 cohorts of banded Whooping Cranes (Grus americana) from the Aransas National Wildlife Refuge/Wood Buffalo National Park (ANWR/WBNP) population that had not been compiled previously into a single data base and had not been included in previous population analyses. We estimated age‐specific survival and natality, parameterized an age‐structured density‐dependent model, and projected population sizes assuming two different estimates of wintering ground carrying capacity. Sixty‐seven of 132 birds banded between 1977 and 1988 formed nesting pairs, females first produced hatchlings when 3 to 7 yrs old, and the annual proportion of mature females that reproduced successfully ranged from 0.566 to 0.606. Population projections indicate that the down‐listing criterion of reaching a population size of 1000 individuals might be attained considerably later than the target year (2035) indicated in the Whooping Crane recovery plan. Even assuming that all suitable habitat within a ～100‐km radius of their current winter range could be occupied, projections suggest that population size may be ～700 in 2035, and might not reach 1000 individuals until the mid‐2060s. Based on their territorial behavior on the wintering grounds, long generation time and faithfulness to their migratory route, we suspect that the population growth rate may decrease markedly in the near future and the ANWR/WBNP population may remain below the target down‐listing size of 1000 individuals.     

Variations in elk aggregation patterns across a range of elk population sizes at Wall Creek,Montana

In the Greater Yellowstone Ecosystem, growing concern over increasing rates of brucellosis seroprevalence in wildlife has challenged wildlife managers to develop strategies for minimizing the potential for pathogen exchange within and between wildlife populations. Recent evidence suggests that increases in elk seroprevalence may be associated with increasing elk densities and/or increasing size of elk aggregations. However, the interactions between elk population density, landscape factors, and elk aggregation patterns are not well-understood, making appropriate management responses challenging. Using a unique, long-term elk aggregation dataset collected across a wide range of elk population sizes, we investigated relationships between elk population size, landscape factors, and elk aggregation responses (group size and group density) with goals of clarifying how changes in elk population size may affect elk aggregation patterns. Overall, landscape attributes and weather had a stronger influence on elk aggregation patterns than factors such as elk population size that are within management control. We found little evidence that elk population size affected mean elk group sizes, but we did find evidence that the size and density of the largest elk aggregations increased as elk population size increased. We also found some evidence that group densities increased following the establishment of wolves. However, across the relatively wide range of elk population sizes observed in this study, only modest changes in elk group density were observed, suggesting that dramatic reductions in population sizes would be necessary to produce measureable reductions in elk group density to affect frequency-dependent transmission. Management actions designed to lower disease transmission are likely to negatively affect other objectives related to elk management and conservation. We therefore suggest that a first step in managing disease transmission risk is agreement among stakeholders interested in elk management of all objectives related to elk management, including acknowledgment that disease transmission is undesirable. © 2011 The Wildlife Society.     

Reproduction in a population of wild pigs (Sus scrofa) subjected to lethal control

The continued range expansion of wild pigs (Sus scrofa) in North America is an increasing cause for concern because of the numerous negative impacts that wild pigs have on ecosystem structure and function. Once populations are established, wild pigs have proven to be extremely difficult to control, and close to impossible to eradicate. If effective control and removal techniques are to be developed, we must determine if wild pig populations respond to reductions in density by increasing reproductive output. This study was designed to examine if reproductive parameters of female wild pigs display a density-dependent response following a concentrated removal effort. We compared reproductive parameters and condition of adult sows that were collected between a control area and a treatment area where lethal removal occurred. From August 2004 to May 2006, we focused a concentrated removal effort within the treatment area. Although the population density was more than 65% greater in the control area than the treatment area during the study, we did not detect differences between areas for condition, litter size, ovarian mass, corpus luteum mass, or corpora lutea number. Several years of heavy mast production during the study may have negated any effect on condition and subsequent reproduction between the 2 study areas. These data suggest that reproductive parameters of wild pigs do not exhibit density-dependence during periods when pig populations are in good condition. © 2012 The Wildlife Society.     

Bear historical ranges revisited: Documenting the increase of a once-extirpated population in Nevada

Black bears (Ursus americanus) were once abundant in Nevada and distributed throughout the state, yet recognition of the species' historical occurrence in the state is uncommon and has therefore been ignored in published distribution maps for North America. The lack of representation on distribution maps is likely due to the lack of any scientific data or research on bears in Nevada until 1987. Historical records dating back to the 1840s compiled by Nevada Department of Wildlife (NDOW) biologist Robert McQuivey indicate presence of black bears throughout the state in the 1800s through about 1930. The paucity of historical references after 1931 suggest extirpation of black bears from Nevada's interior mountain ranges by this time. We report on historical records of black bears in the state of Nevada and the results of a current population estimate of black bears derived from a sample of marked bears (n = 420) captured 707 times between 1997 and 2008. Using Pradel and Cormack–Jolly–Seber models in Program MARK, we estimated overall population size, finite rate of growth (λ = 1.16), quarterly and annual survival rates for males and females, seasonal capture probabilities, and recruitment rates. Our results indicate an overall population size of 262 ± 31 adult black bears in western Nevada. These results suggest that the once abundant, then extirpated population of black bears in Nevada is increasing at an annual average rate of 16%. Although the current distribution is limited to the western part of the state, our findings suggest possible expansion of the population into historical habitat within the interior and eastern portions of the state that have been absent of bears for >80 years. Finally, based on historical records, we present suggested revised historical distribution maps for black bears that include the Great Basin ranges in Nevada. © 2013 The Wildlife Society.     

Combining band recovery data and Pollock's robust design to model temporary and permanent emigration

Capture-recapture models are widely used to estimate demographic parameters of marked populations. Recently, this statistical theory has been extended to modeling dispersal of open populations. Multistate models can be used to estimate movement probabilities among subdivided populations if multiple sites are sampled. Frequently, however, sampling is limited to a single site. Models described by Burnham (1993, in Marked Individuals in the Study of Bird Populations, 199-213), which combined open population capture-recapture and band-recovery models, can be used to estimate permanent emigration when sampling is limited to a single population. Similarly, Kendall, Nichols, and Hines (1997, Ecology 51, 563-578) developed models to estimate temporary emigration under Pollock's (1982, Journal of Wildlife Management 46, 757-760) robust design. We describe a likelihood-based approach to simultaneously estimate temporary and permanent emigration when sampling is limited to a single population. We use a sampling design that combines the robust design and recoveries of individuals obtained immediately following each sampling period. We present a general form for our model where temporary emigration is a first-order Markov process, and we discuss more restrictive models. We illustrate these models with analysis of data on marked Canvasback ducks. Our analysis indicates that probability of permanent emigration for adult female Canvasbacks was 0.193 (SE = 0.082) and that birds that were present at the study area in year i - 1 had a higher probability of presence in year i than birds that were not present in year i - 1.     

Boreal Caribou Can Coexist with Natural but Not Industrial Disturbances

For species at risk, it is important that demographic models be consistent with our most recent knowledge because alternate model versions can have differing predictions for wildlife and natural resource management. To establish and maintain this consistency, we can compare predicted model values to current or past observations and demographic knowledge. When novel predictor information becomes available, testing for consistency between modeled and observed values ensures the best models are used for robust, evidence-based, wildlife management. We combine novel information on the extent of historical disturbance regimes (industrial and fire) to an existing demographic model and predict historical and projected demographics of woodland caribou (Rangifer tarandus caribou). Exploring 6 simulation experiments across 5 populations in Alberta, Canada, we identify the relative importance of industrial disturbance, fire, and population density to observed population size and growth rate. We confirm the onset of significant declines across all 5 populations began approximately 30 years ago, demonstrate these declines have been consistent, and conclude they are more likely due to industrial disturbance from the oil and gas sector within contemporary population ranges than historical fire regimes. These findings reinforce recent research on the cause of woodland caribou declines. Testing for consistency between observations and models prescribed for species recovery is paramount for assessing the cause of declines, projecting population trends, and refining recovery strategies for effective wildlife management. We provide a novel simulation method for conducting these tests. © 2020 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.     

Measurement error and survey design in sightability model development

Measurement error of explanatory variables used in sightability models can result in biased population estimates and associated measures of precision. We developed a Monte Carlo simulation procedure that can be implemented within the sightability model framework when measurement error is present. Additionally, we developed simulation and sample survey methods, for determining the optimal allocation of survey effort to maximize precision of population estimates for a fixed survey cost, when a complete survey of a study area is not feasible. We used data from aerial surveys of elk during 2004–2006 in Michigan to demonstrate the application of these techniques. By accounting for measurement error and applying appropriate survey design practices, managers employing sightability models may be able to generate more accurate and cost-effective population estimates and accompanying measures of precision than is possible if these techniques are ignored. © 2011 The Wildlife Society.     

Hidden population size estimation and diagnostics using two respondent-driven samples with applications in Armenia

Estimating the size of hidden populations is essential to understand the magnitude of social and healthcare needs, risk behaviors, and disease burden. However, due to the hidden nature of these populations, they are difficult to survey, and there are no gold standard size estimation methods. Many different methods and variations exist, and diagnostic tools are needed to help researchers assess method-specific assumptions as well as compare between methods. Further, because many necessary mathematical assumptions are unrealistic for real survey implementation, assessment of how robust methods are to deviations from the stated assumptions is essential. We describe diagnostics and assess the performance of a new population size estimation method, capture–recapture with successive sampling population size estimation (CR-SS-PSE), which we apply to data from 3 years of studies from three cities and three hidden populations in Armenia. CR-SS-PSE relies on data from two sequential respondent-driven sampling surveys and extends the successive sampling population size estimation (SS-PSE) framework by using the number of individuals in the overlap between the two surveys and a model for the successive sampling process to estimate population size. We demonstrate that CR-SS-PSE is more robust to violations of successive sampling assumptions than SS-PSE. Further, we compare the CR-SS-PSE estimates to population size estimations using other common methods, including unique object and service multipliers, wisdom of the crowd, and two-source capture–recapture to illustrate volatility across estimation methods.