A Sightability Model for Mountain Goats

ABSTRACT Unbiased estimates of mountain goat (Oreamnos americanus) populations are key to meeting diverse harvest management and conservation objectives. We developed logistic regression models of factors influencing sightability of mountain goat groups during helicopter surveys throughout the Cascades and Olympic Ranges in western Washington during summers, 2004–2007. We conducted 205 trials of the ability of aerial survey crews to detect groups of mountain goats whose presence was known based on simultaneous direct observation from the ground (n = 84), Global Positioning System (GPS) telemetry (n = 115), or both (n = 6). Aerial survey crews detected 77% and 79% of all groups known to be present based on ground observers and GPS collars, respectively. The best models indicated that sightability of mountain goat groups was a function of the number of mountain goats in a group, presence of terrain obstruction, and extent of overstory vegetation. Aerial counts of mountain goats within groups did not differ greatly from known group sizes, indicating that under-counting bias within detected groups of mountain goats was small. We applied Horvitz-Thompson-like sightability adjustments to 1,139 groups of mountain goats observed in the Cascade and Olympic ranges, Washington, USA, from 2004 to 2007. Estimated mean sightability of individual animals was 85% but ranged 0.75–0.91 in areas with low and high sightability, respectively. Simulations of mountain goat surveys indicated that precision of population estimates adjusted for sightability biases increased with population size and number of replicate surveys, providing general guidance for the design of future surveys. Because survey conditions, group sizes, and habitat occupied by goats vary among surveys, we recommend using sightability correction methods to decrease bias in population estimates from aerial surveys of mountain goats.     

Mark-resight and sightability modeling of a western Washington elk population

The North Cascades (Nooksack) elk (Cervus elaphus) population declined during the 1980s, prompting a closure to state and tribal hunting in 1997 and an effort to restore the herd to former abundance. In 2005, we began a study to assess the size of the elk population, judge the effectiveness of restoration efforts, and develop a practical monitoring strategy. We concurrently evaluated 2 monitoring approaches: sightability correction modeling and mark-resight modeling. We collected data during February–April helicopter surveys and fit logistic regression models to predict the sightability of elk groups based on group and environmental variables. We used an information-theoretic criterion to compare 9 models of varying complexity; the best model predicted sightability of elk groups based on 1) transformed (log₂) group size, 2) forest canopy cover (%), and 3) a categorical activity variable (active vs. bedded). The sightability model indicated relatively steady and modest herd growth during 2006–2011, but estimates were less than minimum-known-alive counts. We also used the logit-normal mixed effects (LNME) mark-resight model to generate estimates of total elk population size and the sizes of the adult female and branch-antlered male subpopulations. We explored 15 LNME models to predict total population size and 12 models to predict subpopulations. Our results indicated individual heterogeneity in resighting probabilities and variation in resighting probabilities across sexes and some years. Model-averaged estimates of total population size increased from 639 (95% CI = 570–706) in spring 2006 to 1,248 (95% CI = 1,094–1,401) in 2011. We estimated the adult female subpopulation increased from 381 (95% CI = 338–424) in spring 2006 to 573 (95% CI = 507–639) by 2011. The branch-antlered male subpopulation estimates increased from 87 (95% CI = 54–119) to 180 (95% CI = 118–241) from spring 2006 to spring 2011. The LNME model estimates were greater than sightability model estimates and minimum-known-alive counts. We concluded that mark-resight performed better and was a viable approach for monitoring this small elk population and possibly others with similar characteristics (i.e., small population and landscape scales), but this approach requires periodic marking of elk; we estimated mark-resight costs would be about 40% greater than sightability model application costs. The utility of sightability-correction modeling was limited by a high proportion of groups with low detectability on our densely forested landscape. © 2012 The Wildlife Society.     

Variance of Stratified Survey Estimators With Probability of Detection Adjustments

Abstract: Estimates of wildlife population sizes are frequently constructed by combining counts of observed animals from a stratified survey of aerial sampling units with an estimated probability of detecting animals. Unlike traditional stratified survey designs, stratum-specific estimates of population size will be correlated if a common detection model is used to adjust counts for undetected animals in all strata. We illustrate this concept in the context of aerial surveys, considering 2 cases: 1) a single-detection parameter is estimated under the assumption of constant detection probabilities, and 2) a logistic-regression model is used to estimate heterogeneous detection probabilities. Naïve estimates of variance formed by summing stratum-specific estimates of variance may result in significant bias, particularly if there are a large number of strata, if detection probabilities are small, or if estimates of detection probabilities are imprecise. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):837–844; 2008)     

Estimation and Correction of Visibility Bias in Aerial Surveys of Wintering Ducks

Abstract: Incomplete detection of all individuals leading to negative bias in abundance estimates is a pervasive source of error in aerial surveys of wildlife, and correcting that bias is a critical step in improving surveys. We conducted experiments using duck decoys as surrogates for live ducks to estimate bias associated with surveys of wintering ducks in Mississippi, USA. We found detection of decoy groups was related to wetland cover type (open vs. forested), group size (1–100 decoys), and interaction of these variables. Observers who detected decoy groups reported counts that averaged 78% of the decoys actually present, and this counting bias was not influenced by either covariate cited above. We integrated this sightability model into estimation procedures for our sample surveys with weight adjustments derived from probabilities of group detection (estimated by logistic regression) and count bias. To estimate variances of abundance estimates, we used bootstrap resampling of transects included in aerial surveys and data from the bias-correction experiment. When we implemented bias correction procedures on data from a field survey conducted in January 2004, we found bias-corrected estimates of abundance increased 36–42%, and associated standard errors increased 38–55%, depending on species or group estimated. We deemed our method successful for integrating correction of visibility bias in an existing sample survey design for wintering ducks in Mississippi, and we believe this procedure could be implemented in a variety of sampling problems for other locations and species. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):808–813; 2008)     

Estimating mountain goat abundance using DNA from fecal pellets

Non-invasive collection of tissue samples to obtain DNA for microsatellite genotyping required to estimate population size has been used for many wildlife species but rarely for ungulates. We estimated mountain goat (Oreamnos americanus) population size on a mountain complex in southwestern British Columbia by identification of individuals using DNA obtained from fecal pellet and hair samples collected during 3 sampling sessions. We identified 55 individuals from 170 samples that were successfully genotyped, and estimated a population of 77 mountain goats (SE = 7.4). Mean capture probability was 0.38 (SE = 0.037) per session. Our technique provides one of the first statistically rigorous estimates of abundance of an ungulate species using DNA derived primarily from fecal pellets. Our technique enables managers to obtain minimum counts or population estimates of ungulates in areas of low sightability that can be used for conservation and management. © 2011 The Wildlife Society.     

Monitoring population size of mammals using a spotlight-count-based abundance index: How to relate the number of counts to the precision?

Abundance indices are widely used to study changes in population size in wildlife management. However, a truly appropriate measure of precision is often lacking in such studies. Statistically, the two crucial issues regarding the use of an abundance index are sampling and observability, which lead one to consider two kinds of errors, namely sampling and observation errors. The purpose of this methodological paper is to relate the number of counts to the precision of an abundance index by introducing the Hansen–Hurwitz–Bershad model which takes into account both sampling and observation errors. We illustrate this statistical approach in the case of a European rabbit (Oryctolagus cuniculus) abundance index based on spotlight counts, for two fixed spatial sampling units located in different ecological contexts. We show (i) that the usual sampling variance estimator is a downward-biased estimator of the total variance of the abundance index, (ii) that the bias of the usual variance estimator does not decrease when increasing the sampling size, (iii) that correlated observation errors may have a dramatic impact on the total variance, especially when the sampling size increases. The acknowledgement that the (pure) sampling variance underestimates the total variance because of observation errors is a statistical result that is neither widely known nor appreciated by most wildlife ecologists. The magnitude of this underestimation may be important and, therefore, observation errors cannot be always considered as a priori negligible in assessing the precision of a count-based abundance index.     

Improving inference for aerial surveys of bears: The importance of assumptions and the cost of unnecessary complexity

Obtaining useful estimates of wildlife abundance or density requires thoughtful attention to potential sources of bias and precision, and it is widely understood that addressing incomplete detection is critical to appropriate inference. When the underlying assumptions of sampling approaches are violated, both increased bias and reduced precision of the population estimator may result. Bear (Ursus spp.) populations can be difficult to sample and are often monitored using mark‐recapture distance sampling (MRDS) methods, although obtaining adequate sample sizes can be cost prohibitive. With the goal of improving inference, we examined the underlying methodological assumptions and estimator efficiency of three datasets collected under an MRDS protocol designed specifically for bears. We analyzed these data using MRDS, conventional distance sampling (CDS), and open‐distance sampling approaches to evaluate the apparent bias‐precision tradeoff relative to the assumptions inherent under each approach. We also evaluated the incorporation of informative priors on detection parameters within a Bayesian context. We found that the CDS estimator had low apparent bias and was more efficient than the more complex MRDS estimator. When combined with informative priors on the detection process, precision was increased by >50% compared to the MRDS approach with little apparent bias. In addition, open‐distance sampling models revealed a serious violation of the assumption that all bears were available to be sampled. Inference is directly related to the underlying assumptions of the survey design and the analytical tools employed. We show that for aerial surveys of bears, avoidance of unnecessary model complexity, use of prior information, and the application of open population models can be used to greatly improve estimator performance and simplify field protocols. Although we focused on distance sampling‐based aerial surveys for bears, the general concepts we addressed apply to a variety of wildlife survey contexts.     

ABUNDANCE OF SOUTHERN CALIFORNIA COASTAL BOTTLENOSE DOLPHINS ESTIMATED FROM TANDEM AERIAL SURVEYS

We describe a tandem aerial survey method for bottlenose dolphins ( Tursiops truncatus ) that uses two aircraft and independent observer teams to conduct consecutive surveys of the same coastal strip one hour apart. Alternatively, one aircraft with one observer team surveys the same coastal strip twice over several hours. Using mark-recapture analysis, we corrected survey counts for visibility bias resulting from missing dolphin groups at the surface and submerged groups. Dolphin groups were considered "recaptured" when we determined that both observer teams had detected the same group. This tandem method is highly useful for estimating abundance (and visibility bias) for species where population closure may be assumed between flights. We assumed population closure between flights and matched groups using geographic location, group size, and expected travel rates. We derive a new variance estimator of population size which incorporates group-size variability commonly encounteted in cetacean surveys. From six tandem surveys conducted from 1991 to 1994, we estimated the abundance of southern California coastal bottlenose dolphins to be between 78 (95% CI 60-102) and 271 (240-306) animals, with an average of 140 (128-154). Variability in abundance estimates is likely due to seasonal and interannual movement of animals along the California and Baja California coast. Abundance estimates from tandem surveys averaged 53% higher than dolphin counts obtained from individual survey flights, demonstrating the importance of correcting for visibility bias.     

Integrating distance sampling with minimum counts to improve monitoring

Minimum counts are commonly used to estimate population size and trend for wildlife conservation and management; however, the scope of inference based on such data is limited by untestable assumptions regarding the detection process. Alternative approaches, such as distance sampling, occupancy surveys, and repeated counts, can be employed to produce detection-corrected estimates of population parameters. Unfortunately, these approaches can be more complicated and costly to implement, potentially limiting their use. We explored a conceptual framework linking datasets collected at different spatial scales under different survey designs, with the goal of improving inference. Specifically, we link landscape-scale distance sampling surveys with local-scale minimum counts in an integrated modeling framework to estimate mountain goat (Oreamnos americanus) abundance at both the local and regional scale in south-central Alaska, USA, and provide an estimate of detection probability (i.e., sightability) for the minimum counts. Estimated sightability for the minimum count surveys was 0.67 (95% credible interval [CrI] = 0.52–0.83) and abundance for the entire area was 5,600 goats (CV = 9%), both in broad agreement with estimates from previous studies. Abundance estimates at the local scale (i.e., individual min. count unit) were reasonably precise ( = 18%), suggesting the integrated approach can increase the amount of information produced at both spatial scales by linking minimum count approaches with more rigorous survey designs. We propose that our integrated approach may be implemented in the context of a modified split-panel monitoring design by altering survey protocols to include frequent minimum counts within local count units and intermittent but more rigorous survey designs with inference to the entire study area or population of interest. Doing so would provide estimates of abundance with appropriate measures of uncertainty at multiple spatial scales, thereby improving inference for population monitoring and management. © 2019 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.     

Towards eliminating bias in cluster analysis of TB genotyped data

The relative contributions of transmission and reactivation of latent infection to TB cases observed clinically has been reported in many situations, but always with some uncertainty. Genotyped data from TB organisms obtained from patients have been used as the basis for heuristic distinctions between circulating (clustered strains) and reactivated infections (unclustered strains). Naïve methods previously applied to the analysis of such data are known to provide biased estimates of the proportion of unclustered cases. The hypergeometric distribution, which generates probabilities of observing clusters of a given size as realized clusters of all possible sizes, is analyzed in this paper to yield a formal estimator for genotype cluster sizes. Subtle aspects of numerical stability, bias, and variance are explored. This formal estimator is seen to be stable with respect to the epidemiologically interesting properties of the cluster size distribution (the number of clusters and the number of singletons) though it does not yield satisfactory estimates of the number of clusters of larger sizes. The problem that even complete coverage of genotyping, in a practical sampling frame, will only provide a partial view of the actual transmission network remains to be explored.     

Effects of sample size on estimates of population growth rates calculated with matrix models

Background

Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen''s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ.

Methodology/Principal Findings

Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography.

Conclusions/Significance

We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.     

MAXIMUM-LIKELIHOOD ESTIMATION OF POPULATION DIVERGENCE TIMES AND POPULATION PHYLOGENY IN MODELS WITHOUT MUTATION

In this paper we present a method for estimating population divergence times by maximum likelihood in models without mutation. The maximum-likelihood estimator is compared to a commonly applied estimator based on Wright's F_ST statistic. Simulations suggest that the maximum-likelihood estimator is less biased and has a lower variance than the F_ST-based estimator. The maximum-likelihood estimator provides a statistical framework for the analysis of population history given genetic data. We demonstrate how maximum-likelihood estimates of the branching pattern of divergence of multiple populations may be obtained. We also describe how the method may be applied to test hypotheses such as whether populations have maintained equal population sizes. We illustrate the method by applying it to two previously published sets of human restriction fragment length polymorphism (RFLP) data.     

Performance of ground-based and aerial survey methods for monitoring wildlife assemblages in a conservation area of northern Tanzania

Validating and improving field-sampling techniques for estimating wildlife community composition and population size is essential for wildlife management and conservation. We conducted ground distance sampling surveys along line transects and block counts from a small aircraft in Manyara Ranch in Northern Tanzania and contrasted estimates of species richness and species-specific densities from both sampling techniques. We used regression analyses (logistic regression and generalized linear mixed models) and model selection to investigate whether a species’ body size, group size, body color, as well as vegetation cover explained the variation in species presence/absence and relative density differences in aerial vs. ground-based sampling. Ground surveys detected significantly more species than aerial surveys. However, aerial surveys detected three species that were missed by ground surveys (African lions, African buffalo, and spotted hyena). Model selection suggested that species with smaller body mass and small group sizes were more likely to be missed in aerial surveys. Densities estimated from the aerial surveys were generally but non-significantly lower than the densities estimated from the ground surveys, with the exception of density estimates for African elephants which were slightly higher from aerial surveys. Density differences between the two methods were greater for species with small group size, light body color, and in areas with denser vegetation cover; these variables explained 75% of the variation in density differences between the two survey methods. Albeit being similar in operational costs in our relatively small study area, ground surveys yielded (1) more complete information with respect to wildlife community composition and (2) density estimates were mostly higher and (3) more precise and (4) appear more feasible to be implemented in community-based conservation schemes.     

Development of a Sightability Model for Low-Density Elk Populations in Ontario,Canada

ABSTRACT The status of recolonizing elk (Cervus elaphus) populations in Ontario, Canada, is unclear and there is a need for effective population survey methods that can be applied locally. We sought to develop a sightability model that could account for both low densities of elk and dense forest cover in elk-release areas in Ontario. We corrected winter aerial survey counts for sightability based on radiocollared animals known to be within observable distance of the aircraft. The multivariate model with the highest Akaike's Information Criterion corrected for sample size weight (w_i = 0.427) revealed that elk group size, elk activity, dominant tree type, percent canopy cover, and percent conifer cover were significant predictors of elk sightability. The group-size effect indicated that odds of sighting an elk increased by 1.353 (95% CI = 0.874-3.689) for every additional elk. Standing elk were 5.033 (95% CI = 0.936-15.541) times more likely to be observed than were resting elk, and those located in conifer cover were 0.013 (95% CI = 0.001-0.278) times less likely to be sighted than elk in deciduous cover. Furthermore, elk located in >50% canopy cover and >50% conifer cover were 0.041 (95% CI = 0.003-0.619) times and 0.484 (95% CI = 0.024-9.721) times less likely to be sighted than elk in more open habitat, respectively. During model validation, observers detected 79% (113/143) of known elk in any given area, and population and sightability model predictions (±90% CI) overlapped with the population estimate, implying that our predictive model was robust. Unsurprisingly, large groups of elk in open habitat increased model precision, which highlights difficulties of counting Ontario elk in their northern range. We conclude that our model provided increased reliability for estimating elk numbers in Ontario compared to existing methods, and that the estimator may be useful in other areas where elk density is low and sightability is poor due to dense forest cover.     

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

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

Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.     

Accounting for Sampling Error When Inferring Population Synchrony from Time-Series Data: A Bayesian State-Space Modelling Approach with Applications

Background

Data collected to inform time variations in natural population size are tainted by sampling error. Ignoring sampling error in population dynamics models induces bias in parameter estimators, e.g., density-dependence. In particular, when sampling errors are independent among populations, the classical estimator of the synchrony strength (zero-lag correlation) is biased downward. However, this bias is rarely taken into account in synchrony studies although it may lead to overemphasizing the role of intrinsic factors (e.g., dispersal) with respect to extrinsic factors (the Moran effect) in generating population synchrony as well as to underestimating the extinction risk of a metapopulation.

Methodology/Principal findings

The aim of this paper was first to illustrate the extent of the bias that can be encountered in empirical studies when sampling error is neglected. Second, we presented a space-state modelling approach that explicitly accounts for sampling error when quantifying population synchrony. Third, we exemplify our approach with datasets for which sampling variance (i) has been previously estimated, and (ii) has to be jointly estimated with population synchrony. Finally, we compared our results to those of a standard approach neglecting sampling variance. We showed that ignoring sampling variance can mask a synchrony pattern whatever its true value and that the common practice of averaging few replicates of population size estimates poorly performed at decreasing the bias of the classical estimator of the synchrony strength.

Conclusion/Significance

The state-space model used in this study provides a flexible way of accurately quantifying the strength of synchrony patterns from most population size data encountered in field studies, including over-dispersed count data. We provided a user-friendly R-program and a tutorial example to encourage further studies aiming at quantifying the strength of population synchrony to account for uncertainty in population size estimates.     

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.