Quantifying Extinction Probabilities from Sighting Records: Inference and Uncertainties

Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.     

Sequential hypothesis testing with spatially correlated presence-absence data

A pest management decision to initiate a control treatment depends upon an accurate estimate of mean pest density. Presence-absence sampling plans significantly reduce sampling efforts to make treatment decisions by using the proportion of infested leaves to estimate mean pest density in lieu of counting individual pests. The use of sequential hypothesis testing procedures can significantly reduce the number of samples required to make a treatment decision. Here we construct a mean-proportion relationship for Oligonychus perseae Tuttle, Baker, and Abatiello, a mite pest of avocados, from empirical data, and develop a sequential presence-absence sampling plan using Bartlett's sequential test procedure. Bartlett's test can accommodate pest population models that contain nuisance parameters that are not of primary interest. However, it requires that population measurements be independent, which may not be realistic because of spatial correlation of pest densities across trees within an orchard. We propose to mitigate the effect of spatial correlation in a sequential sampling procedure by using a tree-selection rule (i.e., maximin) that sequentially selects each newly sampled tree to be maximally spaced from all other previously sampled trees. Our proposed presence-absence sampling methodology applies Bartlett's test to a hypothesis test developed using an empirical mean-proportion relationship coupled with a spatial, statistical model of pest populations, with spatial correlation mitigated via the aforementioned tree-selection rule. We demonstrate the effectiveness of our proposed methodology over a range of parameter estimates appropriate for densities of O. perseae that would be observed in avocado orchards in California.     

An Evaluation of Plotless Sampling Using Vegetation Simulations and Field Data from a Mangrove Forest

In vegetation science and forest management, tree density is often used as a variable. To determine the value of this variable, reliable field methods are necessary. When vegetation is sparse or not easily accessible, the use of sample plots is not feasible in the field. Therefore, plotless methods, like the Point Centred Quarter Method, are often used as an alternative. In this study we investigate the accuracy of different plotless sampling methods. To this end, tree densities of a mangrove forest were determined and compared with estimates provided by several plotless methods. None of these methods proved accurate across all field sites with mean underestimations up to 97% and mean overestimations up to 53% in the field. Applying the methods to different vegetation patterns shows that when random spatial distributions were used the true density was included within the 95% confidence limits of all the plotless methods tested. It was also found that, besides aggregation and regularity, density trends often found in mangroves contribute to the unreliability. This outcome raises questions about the use of plotless sampling in forest monitoring and management, as well as for estimates of density-based carbon sequestration. We give recommendations to minimize errors in vegetation surveys and recommendations for further in-depth research.     

Estimating the influence of population density and dispersal behavior on the ability to detect and monitor Agrilus planipennis (Coleoptera: Buprestidae) populations

Emerald ash borer, Agrilus planipennis Fairmaire (Coleoptera: Buprestidae), a phloem-feeding pest of ash (Fraxinus spp.) trees native to Asia, was first discovered in North America in 2002. Since then, A. planipennis has been found in 15 states and two Canadian provinces and has killed tens of millions of ash trees. Understanding the probability of detecting and accurately delineating low density populations of A. planipennis is a key component of effective management strategies. Here we approach this issue by 1) quantifying the efficiency of sampling nongirdled ash trees to detect new infestations of A. planipennis under varying population densities and 2) evaluating the likelihood of accurately determining the localized spread of discrete A. planipennis infestations. To estimate the probability a sampled tree would be detected as infested across a gradient of A. planipennis densities, we used A. planipennis larval density estimates collected during intensive surveys conducted in three recently infested sites with known origins. Results indicated the probability of detecting low density populations by sampling nongirdled trees was very low, even when detection tools were assumed to have three-fold higher detection probabilities than nongirdled trees. Using these results and an A. planipennis spread model, we explored the expected accuracy with which the spatial extent of an A. planipennis population could be determined. Model simulations indicated a poor ability to delineate the extent of the distribution of localized A. planipennis populations, particularly when a small proportion of the population was assumed to have a higher propensity for dispersal.     

Estimating the abundance of rare and elusive carnivores from photographic-sampling data when the population size is very small

Conservation and management agencies require accurate and precise estimates of abundance when considering the status of a species and the need for directed actions. Due to the proliferation of remote sampling cameras, there has been an increase in capture–recapture studies that estimate the abundance of rare and/or elusive species using closed capture–recapture estimators (C–R). However, data from these studies often do not meet necessary statistical assumptions. Common attributes of these data are (1) infrequent detections, (2) a small number of individuals detected, (3) long survey durations, and (4) variability in detection among individuals. We believe there is a need for guidance when analyzing this type of sparse data. We highlight statistical limitations of closed C–R estimators when data are sparse and suggest an alternative approach over the conventional use of the Jackknife estimator. Our approach aims to maximize the probability individuals are detected at least once over the entire sampling period, thus making the modeling of variability in the detection process irrelevant, estimating abundance accurately and precisely. We use simulations to demonstrate when using the unconditional-likelihood M ₀ (constant detection probability) closed C–R estimator with profile-likelihood confidence intervals provides reliable results even when detection varies by individual. If each individual in the population is detected on average of at least 2.5 times, abundance estimates are accurate and precise. When studies sample the same species at multiple areas or at the same area over time, we suggest sharing detection information across datasets to increase precision when estimating abundance. The approach suggested here should be useful for monitoring small populations of species that are difficult to detect.     

Estimation of genetically effective breeding numbers using a rejection algorithm approach

Polygynous mating results in nonrandom sampling of the adult male gamete pool in each generation, thereby increasing the rate of genetic drift. In principle, genetic paternity analysis can be used to infer the effective number of breeding males (Nebm). However, this requires genetic data from an exhaustive sample of candidate males. Here we describe a new approach to estimate Nebm using a rejection algorithm in association with three statistics: Euclidean distance between the frequency distributions of maternally and paternally inherited alleles, average number of paternally inherited alleles and average gene diversity of paternally inherited alleles. We quantify the relationship between these statistics and Nebm using an individual-based simulation model in which the male mating system varied continuously between random mating and extreme polygyny. We evaluate this method using genetic data from a natural population of highly polygynous fruit bats (Cynopterous sphinx). Using data in the form of mother-offspring genotypes, we demonstrate that estimates of Nebm are very similar to independent estimates based on a direct paternity analysis that included data on candidate males. Our method also permits an evaluation of uncertainty in estimates of Nebm and thus facilitates inferences about the mating system from genetic data. Finally, we investigate the sensitivity of our method to sample size, model assumptions, adult population size and the mating system. These analyses demonstrate that the rejection algorithm provides accurate estimates of Nebm across a broad range of demographic scenarios, except when the true Nebm is high.     

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.     

Evaluating the performance of a multilocus Bayesian method for the estimation of migration rates

Bayesian methods have become extremely popular in molecular ecology studies because they allow us to estimate demographic parameters of complex demographic scenarios using genetic data. Articles presenting new methods generally include sensitivity studies that evaluate their performance, but they tend to be limited and need to be followed by a more thorough evaluation. Here we evaluate the performance of a recent method, bayesass , which allows the estimation of recent migration rates among populations, as well as the inbreeding coefficient of each local population. We expand the simulation study of the original publication by considering multi-allelic markers and scenarios with varying number of populations. We also investigate the effect of varying migration rates and F _ST more thoroughly in order to identify the region of parameter space where the method is and is not able to provide accurate estimates of migration rate. Results indicate that if the demographic history of the species being studied fits the assumptions of the inference model, and if genetic differentiation is not too low ( F _ST ≥ 0.05), then the method can give fairly accurate estimates of migration rates even when they are fairly high (about 0.1). However, when the assumptions of the inference model are violated, accurate estimates are obtained only if migration rates are very low ( m  = 0.01) and genetic differentiation is high ( F _ST ≥ 0.10). Our results also show that using posterior assignment probabilities as an indication of how much confidence we can place on the assignments is problematical since the posterior probability of assignment can be very high even when the individual assignments are very inaccurate.     

A Comparison of Grizzly Bear Demographic Parameters Estimated from Non-Spatial and Spatial Open Population Capture-Recapture Models

Capture-recapture studies are frequently used to monitor the status and trends of wildlife populations. Detection histories from individual animals are used to estimate probability of detection and abundance or density. The accuracy of abundance and density estimates depends on the ability to model factors affecting detection probability. Non-spatial capture-recapture models have recently evolved into spatial capture-recapture models that directly include the effect of distances between an animal’s home range centre and trap locations on detection probability. Most studies comparing non-spatial and spatial capture-recapture biases focussed on single year models and no studies have compared the accuracy of demographic parameter estimates from open population models. We applied open population non-spatial and spatial capture-recapture models to three years of grizzly bear DNA-based data from Banff National Park and simulated data sets. The two models produced similar estimates of grizzly bear apparent survival, per capita recruitment, and population growth rates but the spatial capture-recapture models had better fit. Simulations showed that spatial capture-recapture models produced more accurate parameter estimates with better credible interval coverage than non-spatial capture-recapture models. Non-spatial capture-recapture models produced negatively biased estimates of apparent survival and positively biased estimates of per capita recruitment. The spatial capture-recapture grizzly bear population growth rates and 95% highest posterior density averaged across the three years were 0.925 (0.786–1.071) for females, 0.844 (0.703–0.975) for males, and 0.882 (0.779–0.981) for females and males combined. The non-spatial capture-recapture population growth rates were 0.894 (0.758–1.024) for females, 0.825 (0.700–0.948) for males, and 0.863 (0.771–0.957) for both sexes. The combination of low densities, low reproductive rates, and predominantly negative population growth rates suggest that Banff National Park’s population of grizzly bears requires continued conservation-oriented management actions.     

Predicting leatherjacket population frequencies in Northern Ireland

Annual surveys of leatherjacket (Tipula spp. larvae) were made in Northern Ireland to provide warning of the likelihood of damage to spring sown cereals after grass. A climate-based multiple regression model was developed to estimate mean annual populations. Ades distributions were fitted to the annual data of leatherjacket counts to provide common estimates of parameters r and r. These values were then held constant to provide yearly estimates of A, the third parameter. The relationship between A and the sample mean was established so that a frequency distribution could be generated for any estimated mean population density. The ability of these models to predict leatherjacket frequency distributions was validated by using weather data for 1985–1988 to predict the number of fields with populations in excess of thresholds of 0.5,0.75 and 1 times 10⁵ha^-1. It is concluded that the predictions were of sufficient accuracy to substitute for the annual leatherjacket survey.     

Edge Effect on Density Estimates of a Radiotracked Population of Yellow-Necked Mice

ABSTRACT Density estimates for small-mammal populations from capture-mark-recapture (CMR) data have played an important role in many studies of theoretical and applied ecology. Defining effective trapping area (ETA) is one of the main issues affecting accuracy of density estimates. Our objective was to assess sensitivity of CMR density estimates to correctors based on movement parameters calculated from trapping and radiotelemetry data. From May to November 2005, we conducted monthly CMR trapping in a beech (Fagus sylvaticus) forest of the province of Trento, northern Italy. In conjunction with CMR, we radio-marked 32 yellow-necked mice (Apodemus flavicollis) captured from July to October and located them daily using radiotelemetry. We estimated population size (N) by model averaging with Program MARK. We calculated ETA using several definitions of the boundary strip, including full and half mean maximum distance moved (MMDM) from capture-recapture and telemetry data and mean radius of mean monthly home ranges. The boundary strip (W) increased with the amount of behavioral information embodied in the estimates. The largest W and lowest density values were based on radius of mean home ranges followed by MMDM calculated from telemetry data. The ETA based on movement distances increased more than proportionally when N decreased, suggesting that low population density combined with scarce resources results in rodents moving more in search of food, thus leading to overestimated ETA and underestimated density values. Although robust behavioral information would certainly improve density estimates, we suggest caution in relating ranging movements to capture probability and hence in using correctors based on movement distances to infer density values.     

Methods for Estimating Population Density in Data-Limited Areas: Evaluating Regression and Tree-Based Models in Peru

Obtaining accurate small area estimates of population is essential for policy and health planning but is often difficult in countries with limited data. In lieu of available population data, small area estimate models draw information from previous time periods or from similar areas. This study focuses on model-based methods for estimating population when no direct samples are available in the area of interest. To explore the efficacy of tree-based models for estimating population density, we compare six different model structures including Random Forest and Bayesian Additive Regression Trees. Results demonstrate that without information from prior time periods, non-parametric tree-based models produced more accurate predictions than did conventional regression methods. Improving estimates of population density in non-sampled areas is important for regions with incomplete census data and has implications for economic, health and development policies.     

The adequacy of aging techniques in vertebrates for rapid estimation of population mortality rates from age distributions

As a key parameter in population dynamics, mortality rates are frequently estimated using mark–recapture data, which requires extensive, long‐term data sets. As a potential rapid alternative, we can measure variables correlated to age, allowing the compilation of population age distributions, from which mortality rates can be derived. However, most studies employing such techniques have ignored their inherent inaccuracy and have thereby failed to provide reliable mortality estimates. In this study, we present a general statistical model linking birth rate, mortality rate, and population age distributions. We next assessed the reliability and data needs (i.e., sample size) for estimating mortality rate of eight different aging techniques. The results revealed that for half of the aging techniques, correlations with age varied considerably, translating into highly variable accuracies when used to estimate mortality rate from age distributions. Telomere length is generally not sufficiently correlated to age to provide reliable mortality rate estimates. DNA methylation, signal‐joint T‐cell recombination excision circle (sjTREC), and racemization are generally more promising techniques to ultimately estimate mortality rate, if a sufficiently high sample size is available. Otolith ring counts, otolithometry, and age‐length keys in fish, and skeletochronology in reptiles, mammals, and amphibians, outperformed all other aging techniques and generated relatively accurate mortality rate estimation with a sample size that can be feasibly obtained. Provided the method chosen is minimizing and estimating the error in age estimation, it is possible to accurately estimate mortality rates from age distributions. The method therewith has the potential to estimate a critical, population dynamic parameter to inform conservation efforts within a limited time frame as opposed to mark–recapture analyses.     

Optimization and accuracy of faecal pellet count estimates of population size: The case of European rabbits in extensive breeding nuclei

Cost-effective indices to estimate relative abundances of species are crucial for their management and conservation. As an example, population indices are needed to monitor extensive breeding nuclei used for translocating wild rabbit populations. Based on counts of faecal pellets from four high density rabbit nuclei in southwest Spain: (i) we assess the accuracy of this population index in high-density populations; and (ii) present a simulation approach to evaluate how the reduction of the counting effort affects accuracy of the population estimates. Our findings suggest that this method provides a valid estimate in high-density rabbit populations, and, notably, estimates would have not substantially changed after a reduction of 45–65% in the number of counted plots depending on variation on rabbit density between nuclei. We provide a framework that managers and other scientists could use to improve data collection of pellet counts in order to optimize their chances of detecting relative abundance estimates of rabbits. In addition, we present a R function to implement our approach that can easily be applied in a variety of monitoring programmes for other species based on count data. This will likely help to reduce field-effort in different studies without compromising population indices estimates.     

Knowledge-based interaction potentials for proteins.

We discuss the derivation of atomic-level potentials of mean force from the known protein structures and their applicability for structural evaluation applications. In the derivation process, rigorous density estimation methodology is used to estimate the probability density functions (PDFs) for the distributions of interatomic distances in the protein structures. Potentials of mean force are then derived from these density functions using simple Boltzmann's relation. We also test the potentials against pairs of current and superseded protein structures in the Protein Data Bank. Using PDF potentials to evaluate each structure pair, we are able to identify, with high accuracy, which of the two structures is of higher resolution or better quality. This result shows that the PDF potentials are sensitive to details in protein structures as the current and superseded atomic coordinates generally do not differ by more than 1 A in root-mean-square deviation, and that the PDF potentials could potentially be used for X-ray structure refinement and protein structure prediction.     

Evaluating Methods for Counting Cryptic Carnivores

ABSTRACT Numerous techniques have been proposed to estimate carnivore abundance and density, but few have been validated against populations of known size. We used a density estimate established by intensive monitoring of a population of radiotagged leopards (Panthera pardus) with a detection probability of 1.0 to evaluate efficacy of track counts and camera-trap surveys as population estimators. We calculated densities from track counts using 2 methods and compared performance of 10 methods for calculating the effectively sampled area for camera-trapping data. Compared to our reference density (7.33 ± 0.44 leopards/100 km²), camera-trapping generally produced more accurate but less precise estimates than did track counts. The most accurate result (6.97 ± 1.88 leopards/100 km²) came from camera-trap data with a sampled area buffered by a boundary strip representing the mean maximum distance moved by leopards outside the survey area (MMDMOSA) established by telemetry. However, contrary to recent suggestions, the traditional method of using half the mean maximum distance moved from photographic recaptures did not result in gross overestimates of population density (6.56 ± 1.92 leopards/100 km²) but rather displayed the next best performance after MMDMOSA. The only track-count method comparable to reference density employed a capture-recapture framework applied to data when individuals were identified from their tracks (6.45 ± 1.43 leopards/100 km²) but the underlying assumptions of this technique limit more widespread application. Our results demonstrate that if applied correctly, camera-trap surveys represent the best balance of rigor and cost-effectiveness for estimating abundance and density of cryptic carnivore species that can be identified individually.     

Detectability in Audio-Visual Surveys of Tropical Rainforest Birds: The Influence of Species,Weather and Habitat Characteristics

Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidence-based approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for non-distance sampling data and for estimating detectability of rare species.     

Bayesian inference of recent migration rates using multilocus genotypes

A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.     

Neglecting uncertainty behind Allee effect estimation may generate false predictions of population extinction risk

Estimation of extinction thresholds arising from Allee effects (Allee thresholds) and related probabilities of population extinction is notoriously difficult. One way is to analyze adequately parameterized population models. Traditionally, a point estimate is substituted for the Allee effect strength in such models. However, each point estimate entails an underlying uncertainty. We explore how accounting for this uncertainty affects the probability of population extinction, and show that this probability decreases sigmoidally with increasing population density, even in the absence of any stochasticity. Deviations from when only a point estimate of the Allee effect strength is used can be significant, unless stochasticity is added and the stochastic noise intensity is high. Significant deviations from when only a point estimate is used also occur when the Allee threshold and the environmental carrying capacity of the species are close enough one to another. We also show that the impact of the uncertainty in the Allee effect strength estimate increases as the Allee effect strength itself increases and decreases as the species recovery potential increases. This is not a good news, since we would like to preferentially and efficiently manage slowly recovering populations prone to strong Allee effects. Still, there is a way to come up with relatively good Allee threshold estimates. Besides an obvious option of collecting as many data as possible, the impact of the uncertainty can be mitigated by diversifying Allee effect experiments such that we put more emphasis on larger size groups. This is somewhat surprising, given that frequent complaints on the (im)possibility of detecting Allee effects concern difficulties in locating, observing and experimenting on rare populations. Our results extend current theory surrounding Allee effects and have broad ramifications for applied ecology.