Estimation of local extinction rates when species detectability covaries with extinction probability: is it a problem?

Estimating the rate of change of the composition of communities is of direct interest to address many fundamental and applied questions in ecology. One methodological problem is that it is hard to detect all the species present in a community. Nichols et al. presented an estimator of the local extinction rate that takes into account species probability of detection, but little information is available on its performance. However, they predicted that if a covariance between species detection probability and local extinction rate exists in a community, the estimator of local extinction rate complement would be positively biased.
Here, we show, using simulations over a wide range of parameters that the estimator performs reasonably well. The bias induced by biological factors appears relatively weak. The most important factor enhancing the performance (bias and precision) of the local extinction rate complement estimator is sampling effort. Interestingly, a potentially important biological bias, such as the covariance effect, improves the estimation for small sampling efforts, without inducing a supplementary overestimation when these sampling efforts are high. In the field, all species are rarely detectable so we recommend the use of such estimators that take into account heterogeneity in species detection probability when estimating vital rates responsible for community changes.     

Latitudinal gradients in North American avian species richness,turnover rates and extinction probabilities

A decline in species richness moving from equatorial regions to polar regions is a common, but not universal, macroecological pattern. Many studies have focused on this pattern, but few have focused on how the vital rates responsible for species richness patterns, local rates of species extinction and turnover, vary with latitude. We examine patterns of richness, turnover and extinction in North American avian communities inhabiting three ecoregions, using methods that account for failure to detect all species present. We use breeding bird point count data from > 1000 routes in the Breeding Bird Survey collected from 1982 to 2001 to estimate richness, extinction probability and turnover rates. Our analyses differ from others in 1) the use of annual estimates derived at specific locations rather than index data accumulated over numbers of years, 2) the use of estimators that incorporated detection probabilities and 3) a focus on dynamical processes (colonization, extinction) in addition to static patterns (species richness). We find average species richness estimates (48 to 135 species) increasing with latitude for all three regions, contradicting predictions based on the latitudinal diversity gradient. The estimated rates of extinction and turnover declined with latitude across the three ecoregions. We speculate that higher richness might be linked to periods of superabundant food supply in northern areas that support greater numbers of resident and migrant species. Our primary ecological conclusions are that the latitudinal gradient in species richness is reversed for North American birds in the studied ecoregions, and that both local extinction and turnover decrease from southern to northern latitudes. Thus, the vital rates that determine richness show evidence of greater stability and reduced dynamics in northern areas of higher richness. We recommend additional studies examining patterns of colonization, extinction and turnover in communities, that use clearly defined estimators that deal with detection probability.     

Comparative dynamics of avian communities across edges and interiors of North American ecoregions

Aim Based on a priori hypotheses, we developed predictions about how avian communities might differ at the edges vs. interiors of ecoregions. Specifically, we predicted lower species richness and greater local turnover and extinction probabilities for regional edges. We tested these predictions using North American Breeding Bird Survey (BBS) data across nine ecoregions over a 20‐year time period. Location Data from 2238 BBS routes within nine ecoregions of the United States were used. Methods The estimation methods used accounted for species detection probabilities < 1. Parameter estimates for species richness, local turnover and extinction probabilities were obtained using the program COMDYN. We examined the difference in community‐level parameters estimated from within exterior edges (the habitat interface between ecoregions), interior edges (the habitat interface between two bird conservation regions within the same ecoregion) and interior (habitat excluding interfaces). General linear models were constructed to examine sources of variation in community parameters for five ecoregions (containing all three habitat types) and all nine ecoregions (containing two habitat types). Results Analyses provided evidence that interior habitats and interior edges had on average higher bird species richness than exterior edges, providing some evidence of reduced species richness near habitat edges. Lower average extinction probabilities and turnover rates in interior habitats (five‐region analysis) provided some support for our predictions about these quantities. However, analyses directed at all three response variables, i.e. species richness, local turnover, and local extinction probability, provided evidence of an interaction between habitat and region, indicating that the relationships did not hold in all regions. Main conclusions The overall predictions of lower species richness, higher local turnover and extinction probabilities in regional edge habitats, as opposed to interior habitats, were generally supported. However, these predicted tendencies did not hold in all regions.     

Understanding implications of detection heterogeneity in wildlife abundance estimation

Negative bias in mark-recapture abundance estimators due to heterogeneity in detection (capture) probability is a well-known problem, but we believe most biologists do not understand why heterogeneity causes bias and how bias can be reduced. We demonstrate how heterogeneity creates dependence and bias in mark-recapture approaches to abundance estimation. In comparison, heterogeneity, and hence estimator bias, is not as problematic for distance sampling and mark-resight methods because both techniques estimate detection probabilities based on a known quantity. We show how the introduction of a known number of individuals planted into a study population prior to a mark-recapture survey can reduce bias from heterogeneity in detection probability. We provide examples with simulation and an analysis of motion-sensitive camera data from a study population of introduced eastern wild turkeys (Meleagris gallopavo silvestris) of known size with a subset of telemetered birds. In choosing a method for abundance estimation, careful consideration should be given to assumptions and how heterogeneity in detection probability can be accommodated for each application.     

Testing metapopulation concepts: effects of patch characteristics and neighborhood occupancy on the dynamics of an endangered lagomorph

Metapopulation ecology is a field that is richer in theory than in empirical results. Many existing empirical studies use an incidence function approach based on spatial patterns and key assumptions about extinction and colonization rates. Here we recast these assumptions as hypotheses to be tested using 18 years of historic detection survey data combined with four years of data from a new monitoring program for the Lower Keys marsh rabbit. We developed a new model to estimate probabilities of local extinction and colonization in the presence of nondetection, while accounting for estimated occupancy levels of neighboring patches. We used model selection to identify important drivers of population turnover and estimate the effective neighborhood size for this system. Several key relationships related to patch size and isolation that are often assumed in metapopulation models were supported: patch size was negatively related to the probability of extinction and positively related to colonization, and estimated occupancy of neighboring patches was positively related to colonization and negatively related to extinction probabilities. This latter relationship suggested the existence of rescue effects. In our study system, we inferred that coastal patches experienced higher probabilities of extinction and colonization than interior patches. Interior patches exhibited higher occupancy probabilities and may serve as refugia, permitting colonization of coastal patches following disturbances such as hurricanes and storm surges. Our modeling approach should be useful for incorporating neighbor occupancy into future metapopulation analyses and in dealing with other historic occupancy surveys that may not include the recommended levels of sampling replication.     

Spatial dynamics of an invasive bird species assessed using robust design occupancy analysis: the case of the Eurasian collared dove (Streptopelia decaocto) in France

Aim The study of the spatial dynamics of invasive species is a key issue in invasion ecology. While mathematical models are useful for predicting the extent of population expansions, they are not suitable for measuring and characterizing spatial patterns of invasion unless the probability of detection is homogeneous across the distribution range. Here, we apply recently developed statistical approaches incorporating detection uncertainty to characterize the spatial dynamics of an invasive bird species, the Eurasian collared dove (Streptopelia decaocto). Location France. Methods Data on presence/absence of doves were recorded from 1996 to 2004 over 1045 grid cells (28 × 20 km) covering the entire country. Each grid cell included five point counts spaced along a route, which was visited twice a year, allowing for an estimation of detection probability. Each route was assigned to one of six geographical regions. We used robust design occupancy analysis to assess spatial and temporal variation in parameters related to the spatial dynamics of the species. These parameters included occupancy rate, colonization and local extinction probabilities. Our inference approach was based on the selection of the most parsimonious model among competitive models parametrized with conditional probabilities. Results The probability of detecting the presence of doves on a given route was high. However, we found evidence to incorporate detection uncertainty in inference processes about spatial dynamics, since detection probability was neither perfect (i.e. it was < 1), nor constant over space and time. Results showed a clear positive trend in occupancy rate over the study period, increasing from 55% in 1996 to 76% in 2004. In addition, occupancy rate differed among regions (range: 37–79%) and further analysis showed that colonization probability by region was positively related to occupancy rate. Finally, local extinction probability was lower than colonization probability and showed a tendency to decrease over the study period. Main conclusions Our results emphasize the importance of estimating detection probabilities in order to draw proper inferences about the spatial and temporal dynamics of the invasion pattern of the collared dove. In contrast to the perceived spatial dynamics from national atlas surveys, we provide evidence that the range of this species is currently increasing in France. Other results, such as regional specificity in colonization probabilities and time variation in local extinction are consistent with expectations from invasion and metapopulation theory.     

Five interval estimators for proportion ratio under a stratified randomized clinical trial with noncompliance

It is not uncommon that we may encounter a randomized clinical trial (RCT) in which there are confounders which are needed to control and patients who do not comply with their assigned treatments. In this paper, we concentrate our attention on interval estimation of the proportion ratio (PR) of probabilities of response between two treatments in a stratified noncompliance RCT. We have developed and considered five asymptotic interval estimators for the PR, including the interval estimator using the weighted-least squares (WLS) estimator, the interval estimator using the Mantel-Haenszel type of weight, the interval estimator derived from Fieller's Theorem with the corresponding WLS optimal weight, the interval estimator derived from Fieller's Theorem with the randomization-based optimal weight, and the interval estimator based on a stratified two-sample proportion test with the optimal weight suggested elsewhere. To evaluate and compare the finite sample performance of these estimators, we apply Monte Carlo simulation to calculate the coverage probability and average length in a variety of situations. We discuss the limitation and usefulness for each of these interval estimators, as well as include a general guideline about which estimators may be used for given various situations.     

Optimizing surveys for marsh songbirds: does timing matter?

Analysis of data from point counts, a common method for monitoring bird population trends, has evolved to produce estimates of various population parameters (e.g., density, abundance, and occupancy) while simultaneously estimating detection probability. An important consideration when designing studies using point counts is to maximize detection probability while minimizing variation in detection probability both within and between counts. Our objectives were to estimate detection probabilities for three marsh songbirds, including Marsh Wrens (Cistothorus palustris), Swamp Sparrows (Melospiza georgiana), and Yellow‐headed Blackbirds (Xanthocephalus xanthocephalus), as a function of weather covariates and to evaluate temporal variability in detection probability of these three species. We conducted paired, unlimited radius, 10‐min point counts during consecutive morning and evening survey periods for our three focal species at 56 wetlands in Iowa from 20 April to 10 July 2010. Mean detection probabilities ranged from 0.272 (SE = 0.042) for Marsh Wrens to 0.365 (SE = 0.052) for Swamp Sparrows. Time of season was positively correlated with detection probability for Swamp Sparrows, but was negatively correlated with detection probability for Yellow‐headed Blackbirds, suggesting that detection probability increased during the breeding season for Swamp Sparrows and was highest early in the breeding season for Yellow‐headed Blackbirds. Understanding how detection probabilities of marsh songbirds vary throughout the breeding season allows targeted survey efforts that maximize detection probabilities for these species. Furthermore, consistent detection probabilities of marsh songbirds during morning and evening survey periods mean that investigators have more time to conduct surveys for these birds, allowing greater flexibility to increase spatial and temporal replication of surveys that could provide more precise estimates of desired population parameters.     

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.     

The shrinking ark: patterns of large mammal extinctions in India

Mammal extinctions are widespread globally, with South Asian species being most threatened. We examine local extinctions of 25 mammals in India. We use historical records to obtain a set of locations at which each species was known to have been present at some time in the last 200 years. We then use occupancy estimation models to draw inferences about current presence at these same locations based on field observations of local experts. We examine predictions about the influence of key factors such as protected areas, forest cover, elevation, human population density and cultural tolerance on species extinction. For all 25 species, estimated local extinction probabilities (referenced to a 100 year time frame) range between 0.14 and 0.96. Time elapsed since the historical occurrence record was an important determinant of extinction probability for 14 species. Protected areas are positively associated with lower extinction of 18 species, although many species occur outside them. We find evidence that higher proportion of forest cover is associated with lower extinction probabilities for seven species. However, for species that prefer open habitats (which have experienced intensive land-use change), forest cover alone appears insufficient to ensure persistence (the complement of extinction). We find that higher altitude is positively associated with lower extinction for eight species. Human population density is positively associated with extinction of 13 species. We find that ‘culturally tolerated’ species do exhibit higher persistence. Overall, large-bodied, rare and habitat specialist mammals tend to have higher extinction probabilities.     

Heterogeneous capture rates in low density populations and consequences for capture-recapture analysis of camera-trap data

Closed population capture-recapture analysis of camera-trap data has become the conventional method for estimating the abundance of individually recognisable cryptic species living at low densities, such as large felids. Often these estimates are the only information available to guide wildlife managers and conservation policy. Capture probability of the target species using camera traps is commonly heterogeneous and low. Published studies often report overall capture probabilities as low as 0.03 and fail to report on the level of heterogeneity in capture probability. We used simulations to study the effects of low and heterogeneous capture probability on the reliability of abundance estimates using the M_h jack-knife estimator within a closed-population capture-recapture framework. High heterogeneity in capture probability was associated with under- and over-estimates of true abundance. The use of biased abundance estimates could have serious conservation management consequences. We recommend that studies present capture frequencies of all sampled individuals so that policy makers can assess the reliability of the abundance estimates.     

Population size influences amphibian detection probability: implications for biodiversity monitoring programs

Monitoring is an integral part of species conservation. Monitoring programs must take imperfect detection of species into account in order to be reliable. Theory suggests that detection probability may be determined by population size but this relationship has not yet been assessed empirically. Population size is particularly important because it may induce heterogeneity in detection probability and thereby cause bias in estimates of biodiversity. We used a site occupancy model to analyse data from a volunteer-based amphibian monitoring program to assess how well different variables explain variation in detection probability. An index to population size best explained detection probabilities for four out of six species (to avoid circular reasoning, we used the count of individuals at a previous site visit as an index to current population size). The relationship between the population index and detection probability was positive. Commonly used weather variables best explained detection probabilities for two out of six species. Estimates of site occupancy probabilities differed depending on whether the population index was or was not used to model detection probability. The relationship between the population index and detectability has implications for the design of monitoring and species conservation. Most importantly, because many small populations are likely to be overlooked, monitoring programs should be designed in such a way that small populations are not overlooked. The results also imply that methods cannot be standardized in such a way that detection probabilities are constant. As we have shown here, one can easily account for variation in population size in the analysis of data from long-term monitoring programs by using counts of individuals from surveys at the same site in previous years. Accounting for variation in population size is important because it can affect the results of long-term monitoring programs and ultimately the conservation of imperiled species.     

Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring

We propose nonparametric estimators of the stage occupation probabilities and transition hazards for a multistage system that is not necessarily Markovian, using data that are subject to dependent right censoring. We assume that the hazard of being censored at a given instant depends on a possibly time-dependent covariate process as opposed to assuming a fixed censoring hazard (independent censoring). The estimator of the integrated transition hazard matrix has a Nelson-Aalen form where each of the counting processes counting the number of transitions between states and the risk sets for leaving each stage have an IPCW (inverse probability of censoring weighted) form. We estimate these weights using Aalen's linear hazard model. Finally, the stage occupation probabilities are obtained from the estimated integrated transition hazard matrix via product integration. Consistency of these estimators under the general paradigm of non-Markov models is established and asymptotic variance formulas are provided. Simulation results show satisfactory performance of these estimators. An analysis of data on graft-versus-host disease for bone marrow transplant patients is used as an illustration.     

Opposite effects of environmental variability and species richness on temporal turnover of species in a complex habitat mosaic

Species are continuously lost and added to a local community. Dynamics of this process in a complex habitat mosaic (multiple habitats in a landscape), particularly of its rates (species turnover) are of primary concern for biodiversity conservation. Various studies suggest that species traits such as habitat specialization should affect species turnover. In communities where habitat specialization is a function of abiotic constraints, habitat specialists should respond faster to changing environment than generalists. We thus predicted a higher temporal turnover for specialists than for generalists in the presence of environmental variability (EV). In addition, we predicted that temporal turnover should decrease with increasing species richness of the communities they live in. We tested these predictions in a model system of 49 natural rock pools inhabited by 70 invertebrate species for which long-term (9 years) environmental and population dynamics data are available. We computed standard deviation of salinity measurements to represent EV for each pool. We further obtained the number of combined colonization and extinction events weighted by the number of years a species was recorded as a temporal turnover for each species in individual pools. We found that EV induced greater temporal turnover, however, the turnover depended on the species habitat traits (habitat specialization)—it has been higher in specialists but that relationship between EV and temporal turnover dissolved with increasing niche breadth (generalists). We further found that for some species, temporal turnover decreased with higher species richness and for other species, temporal turnover increased with higher species richness. The effect of species richness on temporal turnover was unrelated to species traits. This study suggests that whenever habitat is complex and heterogeneous and species pool diversified, local community dynamics becomes a composite of differential responses.     

Robustness of close‐kin mark–recapture estimators to dispersal limitation and spatially varying sampling probabilities

1. Close‐kin mark–recapture (CKMR) is a method for estimating abundance and vital rates from kinship relationships observed in genetic samples. CKMR inference only requires animals to be sampled once (e.g., lethally), potentially widening the scope of population‐level inference relative to traditional monitoring programs.
2. One assumption of CKMR is that, conditional on individual covariates like age, all animals have an equal probability of being sampled. However, if genetic data are collected opportunistically (e.g., via hunters or fishers), there is potential for spatial variation in sampling probability that can bias CKMR estimators, particularly when genetically related individuals stay in close proximity.
3. We used individual‐based simulation to investigate consequences of dispersal limitation and spatially biased sampling on performance of naive (nonspatial) CKMR estimators of abundance, fecundity, and adult survival. Population dynamics approximated that of a long‐lived mammal species subject to lethal sampling.
4. Naive CKMR abundance estimators were relatively unbiased when dispersal was unconstrained (i.e., complete mixing) or when sampling was random or subject to moderate levels of spatial variation. When dispersal was limited, extreme variation in spatial sampling probabilities negatively biased abundance estimates. Reproductive schedules and survival were well estimated, except for survival when adults could emigrate out of the sampled area. Incomplete mixing was readily detected using Kolmogorov–Smirnov tests.
5. Although CKMR appears promising for estimating abundance and vital rates with opportunistically collected genetic data, care is needed when dispersal limitation is coupled with spatially biased sampling. Fortunately, incomplete mixing is easily detected with adequate sample sizes. In principle, it is possible to devise and fit spatially explicit CKMR models to avoid bias under dispersal limitation, but development of such models necessitates additional complexity (and possibly additional data). We suggest using simulation studies to examine potential bias and precision of proposed modeling approaches prior to implementing a CKMR program.

     

Population trends and calling phenology of anuran populations surveyed in Ontario estimated using acoustic surveys

Many acoustic surveys have been initiated to monitor anuran populations in North America. We used the Ontario Backyard Frog Survey to examine temporal and spatial trends, from 1994 to 2001. Our data suggest that there have been no consistent trends in site occupancy during this time period, but there were some differences among years. Both American toads and northern leopard frogs were more prevalent in 1995 than in 1994. Similarly, species richness was higher in 1995 and 1996 compared to most other years. Individual populations of species, however, often were not stable. Extinction and colonization rates varied among species, and ranged from 1.5 to 19.5% per year, and site occupancy was negatively correlated with extinction rates. Daily detection probabilities were often quite low, and were primarily driven by the perceived calling intensity. We recommend: (i) that monitoring programs attempt to preserve common survey routes, despite heavy turnover of volunteers, (ii) calling surveys be timed to maximize detection probabilities, and (iii) analyses based upon landscape features and GIS approaches should be used to determine localized changes in site occupancy or species richness.     

Estimating Incidence Rates from Population‐Based Case‐Control Studies in the Presence of Nonrespondents

In population‐based case‐control studies, it is of great public‐health importance to estimate the disease incidence rates associated with different levels of risk factors. This estimation is complicated by the fact that in such studies the selection probabilities for the cases and controls are unequal. A further complication arises when the subjects who are selected into the study do not participate (i.e. become nonrespondents) and nonrespondents differ systematically from respondents. In this paper, we show how to account for unequal selection probabilities as well as differential nonresponses in the incidence estimation. We use two logistic models, one relating the disease incidence rate to the risk factors, and one modelling the predictors that affect the nonresponse probability. After estimating the regression parameters in the nonresponse model, we estimate the regression parameters in the disease incidence model by a weighted estimating function that weights a respondent's contribution to the likelihood score function by the inverse of the product of his/her selection probability and his/her model‐predicted response probability. The resulting estimators of the regression parameters and the corresponding estimators of the incidence rates are shown to be consistent and asymptotically normal with easily estimated variances. Simulation results demonstrate that the asymptotic approximations are adequate for practical use and that failure to adjust for nonresponses could result in severe biases. An illustration with data from a cardiovascular study that motivated this work is presented.     

Site occupancy models with heterogeneous detection probabilities

Models for estimating the probability of occurrence of a species in the presence of imperfect detection are important in many ecological disciplines. In these "site occupancy" models, the possibility of heterogeneity in detection probabilities among sites must be considered because variation in abundance (and other factors) among sampled sites induces variation in detection probability (p). In this article, I develop occurrence probability models that allow for heterogeneous detection probabilities by considering several common classes of mixture distributions for p. For any mixing distribution, the likelihood has the general form of a zero-inflated binomial mixture for which inference based upon integrated likelihood is straightforward. A recent paper by Link demonstrates that in closed population models used for estimating population size, different classes of mixture distributions are indistinguishable from data, yet can produce very different inferences about population size. I demonstrate that this problem can also arise in models for estimating site occupancy in the presence of heterogeneous detection probabilities. The implications of this are discussed in the context of an application to avian survey data and the development of animal monitoring programs.     

Estimating the richness of species with variable mobility

The vast majority of species are animals that, unlike most plants and fungi, are variably and often highly mobile. While species' mobility affects species' probabilities of being sampled, effects of movement on the estimation of species richness have yet to be systematically investigated. Information-rich abundance-based estimators may be able to address variably mobile species but the accuracy of these estimators has also yet to be investigated. Here, we address both issues by variably sampling simulated landscapes with up to 250 species and evaluating the performance of ten non-parametric estimators and one species accumulation curve. Our results show that some abundance-based estimators are as accurate as better known and tested incidence-based estimators. Increased movement heterogeneity between the species reduced estimator performance by reducing the sample coverage, which systematically determined which estimator was most accurate. Based on these findings, we present the first decision framework for choosing the most accurate of many available abundance-based species-richness estimators. These decisions, based on data coverage, can significantly improve investigators' ability to estimate faunal species richness.     

Estimation of Heritability in Heteroscedastic One‐Way Unbalanced Random Model

A modified estimator of heritability is proposed under heteroscedastic one way unbalanced random model. The distribution, moments and probability of permissible values (PPV) for conventional and modified estimators are derived. The behaviour of two estimators has been investigated, numerically, to devise a suitable estimator of heritability under variance heterogeneity. The numerical results reveal that under balanced case the heteroscedasticity affects the bias, MSE and PPV of conventional estimator, marginally. In case of unbalanced situations, the conventional estimator underestimates the parameter when more variable group has more observations and overestimates when more variable group has less observations, MSE of the conventional estimator decreases when more variable group has more observations and increases when more variable group has less observations and PPV is marginally decreased. The MSE and PPV are comparable for two estimators while the bias of modified estimator is less than the conventional estimator particularly for small and medium values of the parameter. These results suggest the use of modified estimator with equal or more observations for more variable group in presence of variance heterogeneity.