Estimating Population Size with Noninvasive Capture-Mark-Recapture Data

Abstract:  Estimating population size of elusive and rare species is challenging. The difficulties in catching such species has triggered the use of samples collected noninvasively, such as feces or hair, from which genetic analysis yields data similar to capture-mark-recapture (CMR) data. There are, however, two differences between classical CMR and noninvasive CMR. First, capture and recapture data are gathered over multiple sampling sessions in classical CMR, whereas in noninvasive CMR they can be obtained from a single sampling session. Second, because of genotyping errors and unlike classical CMR, there is no simple relationship between (genetic) marks and individuals in noninvasive CMR. We evaluated, through simulations, the reliability of population size estimates based on noninvasive CMR. For equal sampling efforts, we compared estimates of population size N obtained from accumulation curves, a maximum likelihood, and a Bayesian estimator. For a closed population and without sampling heterogeneity, estimates obtained from noninvasive CMR were as reliable as estimates from classical CMR. The sampling structure (single or multiple session) did not alter the results, the Bayesian estimator in the case of a single sampling session presented the best compromise between low mean squared error and a 95% confidence interval encompassing the parametric value of N in most simulations. Finally, when suitable field and lab protocols were used, genotyping errors did not substantially bias population size estimates (bias < 3.5% in all simulations). The ability to reliably estimate population size from noninvasive samples taken during a single session offers a new and useful technique for the management and conservation of elusive and rare species.     

Estimator bias and efficiency for adaptive cluster sampling with order statistics and a stopping rule

Practical problems facing adaptive cluster sampling with order statistics (acsord) are explored using Monte Carlo simulation for three simulated fish populations and two known waterfowl populations. First, properties of an unbiased Hansen-Hurwitz (HH) estimator and a biased alternative Horvitz-Thompson (HT) estimator are evaluated. An increase in the level of population aggregation or the initial sample size increases the efficiencies of the two acsord estimators. For less aggregated fish populations, the efficiencies decrease as the order statistic parameter r (the number of units about which adaptive sampling is carried out) increases; for the highly aggregated fish and waterfowl populations, they increase with r. Acsord is almost always more efficient than simple random sampling for the highly aggregated populations. Positive bias is observed for the HT estimator, with the maximum bias usually occurring at small values of r. Secondly, a stopping rule at the Sth iteration of adaptive sampling beyond the initial sampling unit was applied to the acsord design to limit the otherwise open-ended sampling effort. The stopping rule induces relatively high positive bias to the HH estimator if the level of the population aggregation is high, the stopping level S is small, and r is large. The bias of HT is not very sensitive to the stopping rule and its bias is often reduced by the stopping rule at smaller values of r. For more aggregated populations, the stopping rule often reduces the efficiencies of the estimators compared to the non-stopping-rule scheme, but acsord still remains more efficient than simple random sampling. Despite its bias and lack of theoretical grounding, the HT estimator is usually more efficient than the HH estimator. In the stopping rule case, the HT estimator is preferable, because its bias is less sensitive to the stopping level.     

Addressing onsite sampling in recreation site choice models

Independent experts and politicians have criticized statistical analyses of recreation behavior, which rely upon onsite samples due to their potential for biased inference. The use of onsite sampling usually reflects data or budgetary constraints, but can lead to two primary forms of bias in site choice models. First, the strategy entails sampling site choices rather than sampling individuals—a form of bias called endogenous stratification. Under these conditions, sample choices may not reflect the site choices of the true population. Second, exogenous attributes of the individuals sampled onsite may differ from the attributes of individuals in the population—the most common form in recreation demand is avidity bias. We propose addressing these biases by combining two the existing methods: Weighted Exogenous Stratification Maximum Likelihood estimation and propensity score estimation. We use the National Marine Fisheries Service's Marine Recreational Fishing Statistics Survey to illustrate methods of bias reduction, employing both simulated and empirical applications. We find that propensity score based weights can significantly reduce bias in estimation. Our results indicate that failure to account for these biases can overstate anglers' willingness to pay for improvements in fishing catch, but weighted models exhibit higher variance of parameter estimates and willingness to pay.     

Estimation of similarity measure for multivariate normal distributions

Measures of niche overlap are used to assess the similarity or dissimilarity of two populations. Matusita's measure is one of commonly used niche overlap measures. We consider the problem of estimating Matusita's measure when samples are from multivariate normal distributions with unknown mean vectors and covariance matrices. Asymptotic variances and biases of Matusita's measure estimates are derived and bias reduction methods are proposed. Simulation results are shown to illustrate characteristics of the estimates and bias reduction methods.     

Effects of site-selection bias on estimates of biodiversity change

Estimates of biodiversity change are essential for the management and conservation of ecosystems. Accurate estimates rely on selecting representative sites, but monitoring often focuses on sites of special interest. How such site-selection biases influence estimates of biodiversity change is largely unknown. Site-selection bias potentially occurs across four major sources of biodiversity data, decreasing in likelihood from citizen science, museums, national park monitoring, and academic research. We defined site-selection bias as a preference for sites that are either densely populated (i.e., abundance bias) or species rich (i.e., richness bias). We simulated biodiversity change in a virtual landscape and tracked the observed biodiversity at a sampled site. The site was selected either randomly or with a site-selection bias. We used a simple spatially resolved, individual-based model to predict the movement or dispersal of individuals in and out of the chosen sampling site. Site-selection bias exaggerated estimates of biodiversity loss in sites selected with a bias by on average 300–400% compared with randomly selected sites. Based on our simulations, site-selection bias resulted in positive trends being estimated as negative trends: richness increase was estimated as 0.1 in randomly selected sites, whereas sites selected with a bias showed a richness change of −0.1 to −0.2 on average. Thus, site-selection bias may falsely indicate decreases in biodiversity. We varied sampling design and characteristics of the species and found that site-selection biases were strongest in short time series, for small grains, organisms with low dispersal ability, large regional species pools, and strong spatial aggregation. Based on these findings, to minimize site-selection bias, we recommend use of systematic site-selection schemes; maximizing sampling area; calculating biodiversity measures cumulatively across plots; and use of biodiversity measures that are less sensitive to rare species, such as the effective number of species. Awareness of the potential impact of site-selection bias is needed for biodiversity monitoring, the design of new studies on biodiversity change, and the interpretation of existing data.     

Using the bootstrap with two-phase adaptive stratified samples from multiple populations at multiple locations

Recently the two-phase adaptive stratified sampling design proposed by Francis (1984) has been extended by Manly et al. (2002) for situations where several biological populations are sampled simultaneously, and where this is done at several different geographical locations in order to estimate population totals or means. The method uses the results from a first phase sample to decide how best to allocate a second phase sample to locations and strata, in order to maximise a criterion (based on estimated coefficients of variation) that measures the accuracy of estimation for population totals, for all variables at all locations. One potential problem with this method is bias in the estimators of the population totals and means. In this paper bootstrapping is considered as a means of overcoming these biases. It is shown using model populations of Pacific walrus and shellfish, based on real data, that bootstrapping is a useful tool for removing about half of the bias. This is also confirmed from some simulations using artificial data.     

A method for quantifying bias in modeled concentrations and source impacts for secondary particulate matter

A method for quantifying source impacts for secondary PM_2.5 species is derived. The method provides estimates of bias in modeled concentrations. Adjusted concentrations match corresponding observations at monitored locations. Sources impacts on secondary species are estimated over the US for 20 sources. Community Multi-Scale Air Quality (CMAQ) estimates of sulfates, nitrates, ammonium, and organic carbon are highly influenced by uncertainties in modeled secondary formation processes, such as chemical mechanisms, volatilization, and condensation rates. These compounds constitute the majority of PM_2.5 mass, and reducing bias in estimated concentrations has benefits for policy measures and epidemiological studies. In this work, a method for adjusting source impacts on secondary species is developed that provides estimates of source contributions and reduces bias in modeled concentrations compared to observations. The bias correction adjusts concentrations and source impacts based on the difference between modeled concentrations and observations while taking into account uncertainties at the location of interest; and it is applied both spatially and temporally. We apply the method over the US for 2006. The mean bias for initial CMAQ concentrations compared to observations is −0.28 (OC), 0.11 (NO₃), 0.05 (NH₄), and −0.08 (SO₄). The normalized mean bias in modeled concentrations compared to observations was effectively zero for OC, NO₃, NH₄, and SO₄ after applying the secondary bias correction. 10-fold cross-validation was conducted to determine the performance of the spatial application of the bias correction. Cross-validation performance was favorable; correlation coefficients were greater than 0.69 for all species when comparing observations and concentrations based on kriged correction factors. The methods presented here address model uncertainties by improving simulated concentrations and source impacts of secondary particulate matter through data assimilation. Secondary-adjusted concentrations and source impacts from 20 emissions sources are generated for 2006 over continental US.     

Spatial statistics for modeling of abundance and distribution of wildlife species in the Masai Mara ecosystem, Kenya

This study illustrates the use of modern statistical procedures for better wildlife management by addressing three key issues: determination of abundance, modeling of animal distributions and variability of diversity in space and time. Prior information in Markov Chain Monte Carlo (MCMC) methods is used to improve estimates of abundance. Measures of autocorrelation are included when modeling distributions of animal counts, and a diversity index to indicate species abundance and richness for large herbivores is developed. Data from the Masai Mara ecosystem in Kenya are used to develop and demonstrate these procedures. The new abundance estimates are up to 35% more accurate than those obtained by existing methods. Significant temporal changes in spatial patterns are found from a space-time analysis of elephant counts over a 20-year period, with strong interactions over 5 km and 6 months space and time separations, respectively. The new diversity index is sensitive to both high abundance and species richness and is also able to capture year to year variation. It indicates an overall marginal decrease in diversity for large herbivores in the Mara ecosystem. The space-time analyses and diversity index can easily be computed thereby providing tools for rapid decision making.     

Value of time: Speeding behavior and gasoline prices

‘Value of Time’ (VOT) is a key parameter in economics and policy. This paper presents an alternative method to estimate VOT by analyzing an hourly dataset on drivers speeding behavior as a function of the gasoline price. Our identification strategy is novel as it is based on the intensive margin. In comparison, previous studies reveal VOT on the extensive margin, but choice alternatives have multiple attributes thereby potentially confounding estimates. Consistent with the range of the prior literature, we find a VOT of about 50% of the wage rate and analyze sources of bias from accidents and traffic tickets. These bias functions suggest that previous stated preference VOT estimates are likely downward whereas previous revealed preference estimates are likely upward biased.     

Reassessment of the Use of Fire as a Management Tool in Deciduous Forests of Eastern North America

Prescribed burning is increasingly being used in the deciduous forests of eastern North America. Recent work suggests that historical fire frequency has been overestimated east of the prairie–woodland transition zone, and its introduction could potentially reduce forest herb and shrub diversity. Fire‐history recreations derived from sedimentary charcoal, tree fire scars, and estimates of Native American burning suggest point‐return times ranging from 5–10 years to centuries and millennia. Actual return times were probably longer because such records suffer from selective sampling, small sample sizes, and a probable publication bias toward frequent fire. Archeological evidence shows the environmental effect of fire could be severe in the immediate neighborhood of a Native American village. Population density appears to have been low through most of the Holocene, however, and villages were strongly clustered at a regional scale. Thus, it appears that the majority of forests of the eastern United States were little affected by burning before European settlement. Use of prescribed burning assumes that most forest species are tolerant of fire and that burning will have only a minimal effect on diversity. However, common adaptations such as serotiny, epicormic sprouting, resprouting from rhizomes, and smoke‐cued germination are unknown across most of the deciduous region. Experimental studies of burning show vegetation responses similar to other forms of disturbance that remove stems and litter and do not necessarily imply adaptation to fire. The general lack of adaptation could potentially cause a reduction in diversity if burning were introduced. These observations suggest a need for a fine‐grained examination of fire history with systematic sampling in which all subregions, landscape positions, and community types are represented. Responses to burning need to be examined in noncommercial and nonwoody species in rigorous manipulative experiments. Until such information is available, it seems prudent to limit the use of prescribed burning east of the prairie–woodland transition zone. Reevaluación del Uso de Fuego como Herramienta de Manejo en Bosques Deciduos de América del Norte     

Line transect sampling of Karner blue butterflies ( Lycaeides melissa samuelis)

Line transect sampling is an effective survey method for estimating butterfly densities because it provides unbiased estimates of site-density (provided key assumptions are met), and estimates are comparable among sites. For monitoring Karner blue butterflies in Wisconsin, USA, comparable estimates are required because each year a different selection of sites will be monitored. Annual state-wide indices of species abundance can be derived from the site-surveys and compared to previous year's indices to monitor trends. We advocate that line transect sampling is preferable to Pollard-Yates transects as a survey technique for monitoring Karner blue butter- flies. The Pollard-Yates surveys do not adjust for diferences in site detectability. As a consequence, estimates of among-site from Pollard-Yates surveys can be biased. © Rapid Science 1998     

Quantifying population declines based on presence‐only records for red‐list assessments

Accurate trend estimates are necessary for understanding which species are declining and which are most in need of conservation action. Imperfect species detection may result in unreliable trend estimates because this may lead to the overestimation of declines. Because many management decisions are based on population trend estimates, such biases could have severe consequences for conservation policy. We used an occupancy‐modeling framework to estimate detectability and calculate nationwide population trends for 14 Swiss amphibian species both accounting for and ignoring imperfect detection. Through the application of International Union for Conservation of Nature Red List criteria to the different trend estimates, we assessed whether ignoring imperfect detection could affect conservation policy. Imperfect detection occurred for all species and detection varied substantially among species, which led to the overestimation of population declines when detectability was ignored. Consequently, accounting for imperfect detection lowered the red‐list risk category for 5 of the 14 species assessed. We demonstrate that failing to consider species detectability can have serious consequences for species management and that occupancy modeling provides a flexible framework to account for observation bias and improve assessments of conservation status. A problem inherent to most historical records is that they contain presence‐only data from which only relative declines can be estimated. A move toward the routine recording of nonobservation and absence data is essential if conservation practitioners are to move beyond this toward accurate population trend estimation.     

Patterns of Genetic Diversity and Its Loss in Mammalian Populations

Abstract:  Policy aimed at conserving biodiversity has focused on species diversity. Loss of genetic diversity, however, can affect population persistence, evolutionary potential, and individual fitness. Although mammals are a well-studied taxonomic group, a comprehensive assessment of mammalian genetic diversity based on modern molecular markers is lacking. We examined published microsatellite data from populations of 108 mammalian species to evaluate background patterns of genetic variability across taxa and body masses. We tested for loss of genetic diversity at the population level by asking whether populations that experienced demographic threats exhibited lower levels of genetic diversity. We also evaluated the effect of ascertainment bias (a reduction in variability when microsatellite primers are transferred across species) on our assessment of genetic diversity. Heterozygosity did not vary with body mass across species ranging in size from shrews to whales. Differences across taxonomic groupings were noted at the highest level, between populations of marsupial and placental mammals. We documented consistently lower heterozygosity, however, in populations that had experienced demographic threats across a wide range of mammalian species. We also documented a significant ( p = 0.01) reduction in heterozygosity as a result of ascertainment bias. Our results suggest that populations of both rare and common mammals are currently losing genetic diversity and that conservation efforts focused above the population level may fail to protect the breadth of persisting genetic diversity. Conservation policy makers may need to focus their efforts below the species level to stem further losses of genetic resources.     

Using unobtrusive sensors to measure and minimize Hawthorne effects: Evidence from cookstoves

People act differently when they know they are being observed. This phenomenon, the Hawthorne effect, can bias estimates of program impacts. Unobtrusive sensors substituting for human observation can alleviate this bias. To demonstrate this potential, we used temperature loggers to measure fuel-efficient cookstoves as a replacement for three-stone fires. We find a large Hawthorne effect: when in-person measurement begins, participants increase fuel-efficient stove use approximately three hours/day (53%) and reduce three-stone fire use by approximately two hours/day (29%). When in-person measurement ends, participants reverse those changes. We then examine how this Hawthorne effect biases estimates of fuel use and pollution concentrations. Our results reinforce concerns about Hawthorne effects, especially in policy-relevant impact evaluations. By measuring the Hawthorne effect we permit researchers to correct for the bias it introduces.     

Site-selection bias and apparent population declines in long-term studies

Detecting population declines is a critical task for conservation biology. Logistical difficulties and the spatiotemporal variability of populations make estimation of population declines difficult. For statistical reasons, estimates of population decline may be biased when study sites are chosen based on abundance of the focal species. In this situation, apparent population declines are likely to be detected even if there is no decline. This site-selection bias is mentioned in the literature but is not well known. We used simulations and real population data to examine the effects of site-selection biases on inferences about population trends. We used a left-censoring method to detect population-size patterns consistent with site-selection bias. The site-selection bias is an important consideration for conservation biologists, and we offer suggestions for minimizing or mitigating it in study design and analysis. Article impact statement: Estimates of population declines are biased if studies begin in large populations, and time-series data show a signature of such an effect.     

Estimation of the mean in line intercept sampling

Ratio estimation of the parametric mean for a characteristic measured on plants sampled by a line intercept method is presented and evaluated via simulation using different plant dispersion patterns (Poisson, regular cluster, and Poisson cluster), plant width variances, and numbers of lines. The results indicate that on average the estimates are close to the parametric mean under all three dispersion patterns. Given a fixed number of lines, variability of the estimates is similar across dispersion patterns with variability under the Poisson pattern slightly smaller than varia-bility under the cluster patterns. No variance estimates were negative under the Poisson pattern, but some estimates were negative under the cluster patterns for smaller numbers of lines. Variance estimates become closer to zero similarly for all spatial patterns as the number of lines increases. Ratio estimation of the parametric mean in line intercept sampling works better, from the viewpoint of approximate unbiasedness and variability of estimates, under the Poisson pattern with larger numbers of lines than other combinations of spatial patterns, plant width variances and numbers of lines.     

Untapped potential of collective intelligence in conservation and environmental decision making

Environmental decisions are often deferred to groups of experts, committees, or panels to develop climate policy, plan protected areas, or negotiate trade-offs for biodiversity conservation. There is, however, surprisingly little empirical research on the performance of group decision making related to the environment. We examined examples from a range of different disciplines, demonstrating the emergence of collective intelligence (CI) in the elicitation of quantitative estimates, crowdsourcing applications, and small-group problem solving. We explored the extent to which similar tools are used in environmental decision making. This revealed important gaps (e.g., a lack of integration of fundamental research in decision-making practice, absence of systematic evaluation frameworks) that obstruct mainstreaming of CI. By making judicious use of interdisciplinary learning opportunities, CI can be harnessed effectively to improve decision making in conservation and environmental management. To elicit reliable quantitative estimates an understanding of cognitive psychology and to optimize crowdsourcing artificial intelligence tools may need to be incorporated. The business literature offers insights into the importance of soft skills and diversity in team effectiveness. Environmental problems set a challenging and rich testing ground for collective-intelligence tools and frameworks. We argue this creates an opportunity for significant advancement in decision-making research and practice.     

Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability

Abstract:  Many researchers have obtained extinction-rate estimates for plant populations by comparing historical and current records of occurrence. A population that is no longer found is assumed to have gone extinct. Extinction can then be related to characteristics of these populations, such as habitat type, size, or species, to test ideas about what factors may affect extinction. Such studies neglect the fact that a population may be overlooked, however, which may bias estimates of extinction rates upward. In addition, if populations are unequally detectable across groups to be compared, such as habitat type or population size, comparisons become distorted to an unknown degree. To illustrate the problem, I simulated two data sets, assuming a constant extinction rate, in which populations occurred in different habitats or habitats of different size and these factors affected their detectability. The conventional analysis implicitly assumed that detectability equalled 1 and used logistic regression to estimate extinction rates. It wrongly identified habitat and population size as factors affecting extinction risk. In contrast, with capture-recapture methods, unbiased estimates of extinction rates were recovered. I argue that capture-recapture methods should be considered more often in estimations of demographic parameters in plant populations and communities.     

Sources of bias in ecological studiesof non-rare events

Ecological studies investigate relationships at the level of the group, rather than at the level of the individual. Although such studies are a common design in epidemiology, it is well-known that estimates may be subject to ecological bias. Most discussion of ecological bias has focused on rare disease events, where the tractability of the loglinear model allows some characterization of the nature of different biases. This paper concentrates on non-rare events, where the Poisson approximation to the binomial distribution is not appropriate. We limit the discussion to bias that arises from within-area variability in exposures and confounders. Our aims are to investigate the likely sizes and directions of bias and, where possible, to suggest methods for controlling the bias or for addressing the sensitivity of inference to assumptions on the nature of the bias. We illustrate that for non-rare events it is much more difficult to characterize the direction of bias than in the rare case. A series of simple numerical examples based on a chronic study of respiratory health illustrate the ideas of the paper.     

Adaptive two-stage one-per-stratum sampling

We briefly describe adaptive cluster sampling designs in which the initial sample is taken according to a Markov chain one-per-stratum design (Breidt, 1995) and one or more secondary samples are taken within strata if units in the initial sample satisfy a given condition C. An empirical study of the behavior of the estimation procedure is conducted for three small artificial populations for which adaptive sampling is appropriate. The specific sampling strategy used in the empirical study was a single random-start systematic sample with predefined systematic samples within strata when the initially sampled unit in that stratum satisfies C. The bias of the Horvitz-Thompson estimator for this design is usually very small when adaptive sampling is conducted in a population for which it is suited. In addition, we compare the behavior of several alternative estimators of the standard error of the Horvitz-Thompson estimator of the population total. The best estimator of the standard error is population-dependent but it is not unreasonable to use the Horvitz-Thompson estimator of the variance. Unfortunately, the distribution of the estimator is highly skewed hence the usual approach of constructing confidence intervals assuming normality cannot be used here.