Development and field validation of a regional,management‐scale habitat model: A koala Phascolarctos cinereus case study

Species distribution models have great potential to efficiently guide management for threatened species, especially for those that are rare or cryptic. We used MaxEnt to develop a regional‐scale model for the koala Phascolarctos cinereus at a resolution (250 m) that could be used to guide management. To ensure the model was fit for purpose, we placed emphasis on validating the model using independently‐collected field data. We reduced substantial spatial clustering of records in coastal urban areas using a 2‐km spatial filter and by modeling separately two subregions separated by the 500‐m elevational contour. A bias file was prepared that accounted for variable survey effort. Frequency of wildfire, soil type, floristics and elevation had the highest relative contribution to the model, while a number of other variables made minor contributions. The model was effective in discriminating different habitat suitability classes when compared with koala records not used in modeling. We validated the MaxEnt model at 65 ground‐truth sites using independent data on koala occupancy (acoustic sampling) and habitat quality (browse tree availability). Koala bellows (n = 276) were analyzed in an occupancy modeling framework, while site habitat quality was indexed based on browse trees. Field validation demonstrated a linear increase in koala occupancy with higher modeled habitat suitability at ground‐truth sites. Similarly, a site habitat quality index at ground‐truth sites was correlated positively with modeled habitat suitability. The MaxEnt model provided a better fit to estimated koala occupancy than the site‐based habitat quality index, probably because many variables were considered simultaneously by the model rather than just browse species. The positive relationship of the model with both site occupancy and habitat quality indicates that the model is fit for application at relevant management scales. Field‐validated models of similar resolution would assist in guiding management of conservation‐dependent species.     

A goodness‐of‐fit test for occupancy models with correlated within‐season revisits

Occupancy modeling is important for exploring species distribution patterns and for conservation monitoring. Within this framework, explicit attention is given to species detection probabilities estimated from replicate surveys to sample units. A central assumption is that replicate surveys are independent Bernoulli trials, but this assumption becomes untenable when ecologists serially deploy remote cameras and acoustic recording devices over days and weeks to survey rare and elusive animals. Proposed solutions involve modifying the detection‐level component of the model (e.g., first‐order Markov covariate). Evaluating whether a model sufficiently accounts for correlation is imperative, but clear guidance for practitioners is lacking. Currently, an omnibus goodness‐of‐fit test using a chi‐square discrepancy measure on unique detection histories is available for occupancy models (MacKenzie and Bailey, Journal of Agricultural, Biological, and Environmental Statistics, 9, 2004, 300; hereafter, MacKenzie–Bailey test). We propose a join count summary measure adapted from spatial statistics to directly assess correlation after fitting a model. We motivate our work with a dataset of multinight bat call recordings from a pilot study for the North American Bat Monitoring Program. We found in simulations that our join count test was more reliable than the MacKenzie–Bailey test for detecting inadequacy of a model that assumed independence, particularly when serial correlation was low to moderate. A model that included a Markov‐structured detection‐level covariate produced unbiased occupancy estimates except in the presence of strong serial correlation and a revisit design consisting only of temporal replicates. When applied to two common bat species, our approach illustrates that sophisticated models do not guarantee adequate fit to real data, underscoring the importance of model assessment. Our join count test provides a widely applicable goodness‐of‐fit test and specifically evaluates occupancy model lack of fit related to correlation among detections within a sample unit. Our diagnostic tool is available for practitioners that serially deploy survey equipment as a way to achieve cost savings.     

Modeling stream fish distributions using interval‐censored detection times

Controlling for imperfect detection is important for developing species distribution models (SDMs). Occupancy‐detection models based on the time needed to detect a species can be used to address this problem, but this is hindered when times to detection are not known precisely. Here, we extend the time‐to‐detection model to deal with detections recorded in time intervals and illustrate the method using a case study on stream fish distribution modeling. We collected electrofishing samples of six fish species across a Mediterranean watershed in Northeast Portugal. Based on a Bayesian hierarchical framework, we modeled the probability of water presence in stream channels, and the probability of species occupancy conditional on water presence, in relation to environmental and spatial variables. We also modeled time‐to‐first detection conditional on occupancy in relation to local factors, using modified interval‐censored exponential survival models. Posterior distributions of occupancy probabilities derived from the models were used to produce species distribution maps. Simulations indicated that the modified time‐to‐detection model provided unbiased parameter estimates despite interval‐censoring. There was a tendency for spatial variation in detection rates to be primarily influenced by depth and, to a lesser extent, stream width. Species occupancies were consistently affected by stream order, elevation, and annual precipitation. Bayesian P‐values and AUCs indicated that all models had adequate fit and high discrimination ability, respectively. Mapping of predicted occupancy probabilities showed widespread distribution by most species, but uncertainty was generally higher in tributaries and upper reaches. The interval‐censored time‐to‐detection model provides a practical solution to model occupancy‐detection when detections are recorded in time intervals. This modeling framework is useful for developing SDMs while controlling for variation in detection rates, as it uses simple data that can be readily collected by field ecologists.     

Designing occupancy surveys and interpreting non‐detection when observations are imperfect

Aim Conservation practitioners use biological surveys to ascertain whether or not a site is occupied by a particular species. Widely used statistical methods estimate the probability that a species will be detected in a survey of an occupied site. However, these estimates of detection probability are alone not sufficient to calculate the probability that a species is present given that it was not detected. The aim of this paper is to demonstrate methods for correctly calculating (1) the probability a species occupies a site given one or more non‐detections, and (2) the number of sequential non‐detections necessary to assert, with a pre‐specified confidence, that a species is absent from a site. Location Occupancy data for a tree frog in eastern Australia serve to illustrate methods that may be applied anywhere species’ occupancy data are used and detection probabilities are < 1. Methods Building on Bayesian expressions for the probability that a site is occupied by a species when it is not detected, and the number of non‐detections necessary to assert absence with a pre‐specified confidence, we estimate occupancy probabilities across tree frog survey locations, drawing on information about where and when the species was detected during surveys. Results We show that the number of sequential non‐detections necessary to assert that a species is absent increases nonlinearly with the prior probability of occupancy, the probability of detection if present, and the desired level of confidence about absence. Main conclusions If used more widely, the Bayesian analytical approaches illustrated here would improve collection and interpretation of biological survey data, providing a coherent way to incorporate detection probability estimates in the design of minimum survey requirements for monitoring, impact assessment and distribution modelling.     

Modelling occurrence and abundance of species when detection is imperfect

Relationships between species abundance and occupancy are of considerable interest in metapopulation biology and in macroecology. Such relationships may be described concisely using probability models that characterize variation in abundance of a species. However, estimation of the parameters of these models in most ecological problems is impaired by imperfect detection. When organisms are detected imperfectly, observed counts are biased estimates of true abundance, and this induces bias in stated occupancy or occurrence probability. In this paper we consider a class of models that enable estimation of abundance/occupancy relationships from counts of organisms that result from surveys in which detection is imperfect. Under such models, parameter estimation and inference are based on conventional likelihood methods. We provide an application of these models to geographically extensive breeding bird survey data in which alternative models of abundance are considered that include factors that influence variation in abundance and detectability. Using these models, we produce estimates of abundance and occupancy maps that honor important sources of spatial variation in avian abundance and provide clearly interpretable characterizations of abundance and occupancy adjusted for imperfect detection.     

Effects of point‐count duration on estimated detection probabilities and occupancy of breeding birds

Increasingly, point‐count data are used to estimate occupancy, the probability that a species is present at a given location; occupancy accounts for imperfect detection, the probability that a species is detected given that it is present. To our knowledge, effects of sampling duration on inferences from models of bird occupancy have not been evaluated. Our objective was to determine whether changing count duration from 5 to 8 min affected inferences about the occupancy of birds sampled in the Chesapeake Bay Lowlands (eastern United States) and the central and western Great Basin (western United States) in 2012 and 2013. We examined the proportion of species (two doves, one cuckoo, two swifts, five hummingbirds, 11 woodpeckers, and 122 passerines) for which estimates of detection probability were ≥ 0.3. For species with single‐season detection probabilities ≥ 0.3, we compared occupancy estimates derived from 5‐ and 8‐min counts. We also compared estimates for three species sampled annually for 5 yr in the central Great Basin. Detection probabilities based on both the 5‐ and 8‐min counts were ≥ 0.3 for 40% ± 3% of the species in an ecosystem. Extending the count duration from 5 to 8 min increased the detection probability to ≥ 0.3 for 5% ± 0.5% of the species. We found no difference in occupancy estimates that were based on 5‐ versus 8‐min counts for species sampled over two or five consecutive years. However, for 97% of species sampled over 2 yr, precision of occupancy estimates that were based on 8‐min counts averaged 12% ± 2% higher than those based on 5‐min counts. We suggest that it may be worthwhile to conduct a pilot season to determine the number of locations and surveys needed to achieve detection probabilities that are sufficiently high to estimate occupancy for species of interest.     

An improved survey method for monitoring population trends of Golden‐winged Warblers and other patchily distributed birds

Conventional surveys designed to monitor common and widespread species may fail to adequately track population changes of rare or patchily distributed species that are often of high conservation concern. We evaluated the performance of a new monitoring approach that employs both a spatially balanced sampling design and a targeted survey protocol designed to estimate population trends of one such patchily distributed species, the Golden‐winged Warbler (Vermivora chrysoptera), in the Appalachian Mountains Bird Conservation Region (BCR 28), USA. Our spatially balanced survey consisted of 105 sample quads (one‐quarter Delorme Atlas pages) across the current range of Golden‐winged Warblers within BCR 28, each with five sample points located in early successional habitat. From 2009 to 2013, collaborators visited each sample point once per year during the peak breeding season and conducted a 17‐min survey consisting of passive observation and playback of conspecific songs and mobbing vocalizations. We used multi‐season, single‐species occupancy models to estimate probability of quad occupancy, detection probability, and occupancy dynamics for Golden‐winged Warblers and closely related Blue‐winged Warblers (Vermivora cyanoptera). Our survey protocol resulted in high estimates of detection probability for Golden‐winged (92%) and Blue‐winged (79%) warblers, with 47% and 56% of quads estimated to be initially occupied, respectively. Derived population trend estimates (λ) indicated an average decline in population of 6% for Golden‐winged Warblers and 7% for Blue‐winged Warblers, resulting in estimated 21% and 22% declines, respectively, in quad occupancy after 5 yr. Our results demonstrate that coupling a spatially balanced survey design in appropriate habitat with a playback protocol to increase detection rates is a viable strategy for tracking populations of Golden‐winged Warblers in the Appalachian Mountains BCR. Similar survey methods should be considered for other rare, declining, or patchily distributed bird species that require targeted monitoring.     

Improving species occupancy estimation when sampling violates the closure assumption

Site occupancy models that account for imperfect detection of species are increasingly utilized in ecological research and wildlife monitoring. Occupancy models require replicate surveys to estimate detection probability over a time period where the occupancy status at sampled sites is assumed closed. Unlike mark–recapture models, few studies have examined how violations of closure can bias occupancy estimates. Our study design allowed us to differentiate among two processes that violate the closure assumption during a sampling season: 1) repeated destructive sampling events that result in either short‐ or long‐term site avoidance by the target species and 2) sampling occurring over a time period during which non‐random movements of the target species result in variable occupancy status. We used dynamic occupancy models to quantify the potential bias in occupancy estimation associated with these processes for a terrestrial salamander system. Our results provide strong evidence of a systematic decrease in salamander occupancy within a field season. Chronic disturbance due to repeated searches of natural cover objects accelerated natural declines in species occurrence on the forest surface as summer progressed. We also observed a strong but temporary disturbance effect on salamander detection probability associated with repeated sampling within a 24‐h. period. We generalized our findings by conducting a simulation to evaluate how violations of closure can bias occupancy estimates when local extinction occurs within a sampling season. Our simulation study revealed general sensitivity of estimates from single‐season occupancy models to violations of closure, with the strength and direction of bias varying between scenarios. Bias was minimal when extinction proba bility or the number of sample occasions was relatively low. Our research highlights the importance of addressing closure in occupancy studies and we provide multiple solutions, using both design‐ and model‐based frameworks, for minimizing bias associated with non‐random changes in occupancy and repeated sampling disturbances.     

Use of classical bird census transects as spatial replicates for hierarchical modeling of an avian community

New monitoring programs are often designed with some form of temporal replication to deal with imperfect detection by means of occupancy models. However, classical bird census data from earlier times often lack temporal replication, precluding detection‐corrected inferences about occupancy. Historical data have a key role in many ecological studies intended to document range shifts, and so need to be made comparable with present‐day data by accounting for detection probability. We analyze a classical bird census conducted in the region of Murcia (SE Spain) in 1991 and 1992 and propose a solution to estimating detection probability for such historical data when used in a community occupancy model: the spatial replication of subplots nested within larger plots allows estimation of detection probability. In our study, the basic sample units were 1‐km transects, which were considered spatial replicates in two aggregation schemes. We fit two Bayesian multispecies occupancy models, one for each aggregation scheme, and evaluated the linear and quadratic effect of forest cover and temperature, and a linear effect of precipitation on species occupancy probabilities. Using spatial rather than temporal replicates allowed us to obtain individual species occupancy probabilities and species richness accounting for imperfect detection. Species‐specific occupancy and community size decreased with increasing annual mean temperature. Both aggregation schemes yielded estimates of occupancy and detectability that were highly correlated for each species, so in the design of future surveys ecological reasons and cost‐effective sampling designs should be considered to select the most suitable aggregation scheme. In conclusion, the use of spatial replication may often allow historical survey data to be applied formally hierarchical occupancy models and be compared with modern‐day data of the species community to analyze global change process.     

Goodness‐of‐fit tests for disorder detection in NGS experiments

Next‐generation sequencing (NGS) experiments are often performed in biomedical research nowadays, leading to methodological challenges related to the high‐dimensional and complex nature of the recorded data. In this work we review some of the issues that arise in disorder detection from NGS experiments, that is, when the focus is the detection of deletion and duplication disorders for homozygosity and heterozygosity in DNA sequencing. A statistical model to cope with guanine/cytosine bias and phasing and prephasing phenomena at base level is proposed, and a goodness‐of‐fit procedure for disorder detection is derived. The method combines the proper evaluation of local p‐values (one for each DNA base) with suitable corrections for multiple comparisons and the discrete nature of the p‐values. A global test for the detection of disorders in the whole DNA region is proposed too. The performance of the introduced procedures is investigated through simulations. A real data illustration is provided.     

Lek fidelity and movement among leks by male Greater Sage‐grouse Centrocercus urophasianus: a capture‐mark‐recapture approach

Males in lek mating systems tend to exhibit high fidelity to breeding leks despite substantial evidence of skewed mating success among males. Although movements between leks are often reported to be rare, such movements provide a mechanism for an individual to improve lifetime fitness in response to heterogeneity in reproductive conditions. Additionally, estimates of apparent movements among leks are potentially biased due to unaccounted variation in detection probability across time and space. We monitored breeding male Greater Sage‐grouse Centrocercus urophasianus on 13 leks in eastern Nevada over a 10‐year period, and estimated movement rates among leks using capture‐mark‐recapture methods. We expected that male movement rates among leks would be low, despite predictions of low breeding success for most males, and that detection rates would be highly variable among leks and years. We used a robust design multistate analysis in Program mark to estimate probability of movements among leks, while accounting for imperfect detection of males. Male Sage‐grouse were extremely faithful to their leks; the annual probability of a male moving away from its original lek of capture was approximately 3% (se = 0.01). Detection probabilities varied substantially among leks (range = 0.21–0.95), and among years (range = 0.30–0.76), but remained relatively constant within years at each lek. These results suggest that male Sage‐grouse dispersal is either rare, or consists primarily of dispersal of sub‐adults from their natal areas prior to the breeding season. The study highlights the benefits of robust design multistate models over standard ‘live‐encounter’ analyses, as they not only permit estimation of additional parameters, such as movement rates, but also allow for more precise parameter estimates that are less sensitive to heterogeneity in detection rates. Additionally, as these data were collected using capture‐mark‐recapture methods, our approach to estimating movement rates would be beneficial in systems where radiotagging is detrimental to the study organism.     

Survival of Greater Sage‐Grouse broods: survey method affects disturbance and age‐specific detection probability

Investigators rely on brood surveys to estimate annual fecundity of game birds. However, investigators often do not account for factors that influence brood detection probability nor rarely document how much females and their broods are disturbed (flush rates) during surveys, which could lead to biased survival estimates. We used 45 radio‐tagged female Greater Sage‐Grouse (Centrocercus urophasianus) with broods to compare detection probabilities and document disturbance among four survey methods to allow future investigators to select the method that best meets their objectives. These methods included daytime flush, daytime visual, nocturnal spotlight, and fecal surveys at nocturnal roost sites, with the latter being a novel method. We used Cormack–Jolly–Seber (CJS) models to compare detection probability and daily survival estimates for visual and fecal surveys of broods 0–47 d post‐hatch and a double‐survey approach to compare detection probabilities among flush, fecal, and spotlight surveys ~42 d post‐hatch when investigators often determine brood fate. From CJS models, detection probability for visual surveys increased with brood age (0.618–0.881), whereas detection probability for fecal surveys did not (0.748). Daily survival probability estimates increased with brood age and differed annually based on fecal surveys (2016: 0.978–1.000 and 2017: 0.839–0.998). We detected age‐specific daily survival probability with visual surveys (0.956–0.997), but not annual differences. Based on the double‐survey approach, detection probability was high (0.857–1.000) for all methods. We flushed ~310–750% fewer females and broods during fecal and spotlight surveys than during both types of daytime surveys. Our results highlight the need to account for detection probabilities among methods and document disturbance to hens and broods that can help investigators design surveys to minimize impacts to birds. Furthermore, our result suggest that actions to improve brood survival during the first week post‐hatch may improve local recruitment.     

Estimating the abundance of burrow‐nesting species through the statistical analysis of combined playback and visual surveys

The conservation of elusive species relies on our ability to obtain unbiased estimates of their abundance trends. Many species live or breed in cavities, making it easy to define the search units (the cavity) yet hard to ascertain their occupancy. One such example is that of certain colonial seabirds like petrels and shearwaters, which occupy burrows to breed. In order to increase the chances of detection for these types of species, their sampling can be done using two independent methods to check for cavity occupancy: visual inspection, and acoustic response to a playback call. This double‐detection process allows us to estimate the probability of burrow occupancy by accounting for the probability of detection associated with each method. Here we provide a statistical framework to estimate the occupancy and population size of burrow‐dwelling species. We show how to implement the method using both maximum likelihood and Bayesian approaches, and test its precision and bias using simulated datasets. We subsequently illustrate how to extend the method to situations where two different species may occupy the burrows, and apply it to a dataset on wedge‐tailed shearwaters Puffinus pacificus and tropical shearwaters P. bailloni on Aride Island, Seychelles. The simulations showed that the single‐species model performed well in terms of error and bias except when detection probabilities and occupancies were very low. The two‐species model applied to shearwaters showed that detection probabilities were highly heterogeneous. The population sizes of wedge‐tailed and tropical shearwaters were estimated at 13 716 (95% CI: 12 909–15 874) and 25 550 (23 667–28 777) pairs respectively. The advantages of formulating the call‐playback sampling method statistically is that it provides a framework to calculate uncertainty in the estimates and model assumptions. This method is applicable to a variety of cavity‐dwelling species where two methods can be used to detect cavity occupancy.     

Estimating multiple time‐fixed treatment effects using a semi‐Bayes semiparametric marginal structural Cox proportional hazards regression model

Marginal structural models for time‐fixed treatments fit using inverse‐probability weighted estimating equations are increasingly popular. Nonetheless, the resulting effect estimates are subject to finite‐sample bias when data are sparse, as is typical for large‐sample procedures. Here we propose a semi‐Bayes estimation approach which penalizes or shrinks the estimated model parameters to improve finite‐sample performance. This approach uses simple symmetric data‐augmentation priors. Limited simulation experiments indicate that the proposed approach reduces finite‐sample bias and improves confidence‐interval coverage when the true values lie within the central “hill” of the prior distribution. We illustrate the approach with data from a nonexperimental study of HIV treatments.     

The consequences of using indirect signs that decay to determine species' occupancy

Statistical models of species' distributions rely on data on species' occupancy, or use, of sites across space and/or time. For rare or cryptic species, indirect signs, such as dung, may be the only realistic means of determining their occupancy status across broad spatial extents. However, the consequences of sign decay for errors in estimates of occupancy have not previously been considered. If signs decay very rapidly, then false‐negative errors may occur because signs at an occupied site have decayed by the time it is surveyed. On the other hand, if signs decay very slowly, false‐positive errors may occur because signs remain present at sites that are no longer occupied. We addressed this issue by quantifying, as functions of sign decay and accumulation rates: 1) the false‐negative error rate due to sign decay and, 2) the expected time interval prior to a survey within which signs indicate the species was present; as this time interval increases, false‐positives become more likely. We then applied this to the specific example of koala Phascolarctos cinereus occupancy derived from faecal pellet surveys using data on faecal pellet decay rates. We show that there is a clear trade‐off between false‐negative error rates and the potential for false‐positive errors. For the koala case study, false‐negative errors were low on average and the expected time interval prior to surveys that detected pellets indicate the species was present within less than 2–3 yr. However, these quantities showed quite substantial spatial variation that could lead to biased parameter estimates for distribution models based on faecal pellet surveys. This highlights the importance of observation errors arising from sign decay and we suggest some modifications to existing methods to deal with this issue.     

Ignoring Imperfect Detection in Biological Surveys Is Dangerous: A Response to ‘Fitting and Interpreting Occupancy Models'

In a recent paper, Welsh, Lindenmayer and Donnelly (WLD) question the usefulness of models that estimate species occupancy while accounting for detectability. WLD claim that these models are difficult to fit and argue that disregarding detectability can be better than trying to adjust for it. We think that this conclusion and subsequent recommendations are not well founded and may negatively impact the quality of statistical inference in ecology and related management decisions. Here we respond to WLD''s claims, evaluating in detail their arguments, using simulations and/or theory to support our points. In particular, WLD argue that both disregarding and accounting for imperfect detection lead to the same estimator performance regardless of sample size when detectability is a function of abundance. We show that this, the key result of their paper, only holds for cases of extreme heterogeneity like the single scenario they considered. Our results illustrate the dangers of disregarding imperfect detection. When ignored, occupancy and detection are confounded: the same naïve occupancy estimates can be obtained for very different true levels of occupancy so the size of the bias is unknowable. Hierarchical occupancy models separate occupancy and detection, and imprecise estimates simply indicate that more data are required for robust inference about the system in question. As for any statistical method, when underlying assumptions of simple hierarchical models are violated, their reliability is reduced. Resorting in those instances where hierarchical occupancy models do no perform well to the naïve occupancy estimator does not provide a satisfactory solution. The aim should instead be to achieve better estimation, by minimizing the effect of these issues during design, data collection and analysis, ensuring that the right amount of data is collected and model assumptions are met, considering model extensions where appropriate.     

The importance of incorporating imperfect detection in biodiversity assessments: a case study of small mammals in an Australian region

Aim Assessments of biodiversity are an essential requirement of conservation management planning. Species distributional modelling is a popular approach to quantifying biodiversity whereby occurrence data are related to environmental covariates. An important confounding factor that is often overlooked in the development of such models is uncertainty due to imperfect detection. Here, I demonstrate how an analytical approach that accounts for the bias due to imperfect detection can be applied retrospectively to an existing biodiversity survey data set to produce more realistic estimates of species distributions and unbiased covariate relationships. Location Pilbara biogeographic region, Australia. Methods As a component of the Pilbara survey, presence/absence (i.e. undetected) data on small ground‐dwelling mammals were collected. I applied a multiseason occupancy modelling approach to six of the most common species encountered during this survey. Detection and occupancy rates, as well as extinction and colonization probabilities, were determined, and the influence of covariates on these parameters was examined using the multi‐model inference approach. Results Detection probabilities for all six species were considerably lower than 1.0 and varied across time and species. Naïve estimates of occupancy underestimated occupancy rates corrected for species detectability by up to 45%. Seasonal variation in occupancy status was attributed to changes in detection for two of the focal species, while reproductive events explained variation in occupancy in three others. Covariates describing the substrate strongly influenced site occupancy for most of the species modelled. A comparison of the occupancy model with a generalized linear model, assuming perfect detection, showed that the effects of the covariates were underestimated in the latter model. Main conclusions The application of the multiseason occupancy modelling approach to the Pilbara mammal data set demonstrated a powerful framework for examining changes in site occupancy, as well as local colonization and extinction rates of species which are not confounded by variable species detection rates.     

Estimating site occupancy rates for aquatic plants using spatial sub-sampling designs when detection probabilities are less than one

Estimation of site occupancy rates when detection probabilities are <1 is well established in wildlife science. Data from multiple visits to a sample of sites are used to estimate detection probabilities and the proportion of sites occupied by focal species. In this article we describe how site occupancy methods can be applied to estimate occupancy rates of plants and other sessile organisms. We illustrate this approach and the pitfalls of ignoring incomplete detection using spatial data for 2 aquatic vascular plants collected under the Upper Mississippi River's Long Term Resource Monitoring Program (LTRMP). Site occupancy models considered include: a naïve model that ignores incomplete detection, a simple site occupancy model assuming a constant occupancy rate and a constant probability of detection across sites, several models that allow site occupancy rates and probabilities of detection to vary with habitat characteristics, and mixture models that allow for unexplained variation in detection probabilities. We used information theoretic methods to rank competing models and bootstrapping to evaluate the goodness-of-fit of the final models. Results of our analysis confirm that ignoring incomplete detection can result in biased estimates of occupancy rates. Estimates of site occupancy rates for 2 aquatic plant species were 19–36% higher compared to naive estimates that ignored probabilities of detection <1. Simulations indicate that final models have little bias when 50 or more sites are sampled, and little gains in precision could be expected for sample sizes >300. We recommend applying site occupancy methods for monitoring presence of aquatic species.     

A Bayesian multinomial logistic exposure model for estimating probabilities of competing sources of nest failure

Understanding causes of nest loss is critical for the management of endangered bird populations. Available methods for estimating nest loss probabilities to competing sources do not allow for random effects and covariation among sources, and there are few data simulation methods or goodness‐of‐fit (GOF) tests for such models. We developed a Bayesian multinomial extension of the widely used logistic exposure (LE) nest survival model which can incorporate multiple random effects and fixed‐effect covariates for each nest loss category. We investigated the performance of this model and the accompanying GOF test by analysing simulated nest fate datasets with and without age‐biased discovery probability, and by comparing the estimates with those of traditional fixed‐effects estimators. We then exemplify the use of the multinomial LE model and GOF test by analysing Piping Plover Charadrius melodus nest fate data (n = 443) to explore the effects of wire cages (exclosures) constructed around nests, which are used to protect nests from predation but can lead to increased nest abandonment rates. Mean parameter estimates of the random‐effects multinomial LE model were all within 1 sd of the true values used to simulate the datasets. Age‐biased discovery probability did not result in biased parameter estimates. Traditional fixed‐effects models provided estimates with a high bias of up to 43% with a mean of 71% smaller standard deviations. The GOF test identified models that were a poor fit to the simulated data. For the Piping Plover dataset, the fixed‐effects model was less well‐supported than the random‐effects model and underestimated the risk of exclosure use by 16%. The random‐effects model estimated a range of 1–6% probability of abandonment for nests not protected by exclosures across sites and 5–41% probability of abandonment for nests with exclosures, suggesting that the magnitude of exclosure‐related abandonment is site‐specific. Our results demonstrate that unmodelled heterogeneity can result in biased estimates potentially leading to incorrect management recommendations. The Bayesian multinomial LE model offers a flexible method of incorporating random effects into an analysis of nest failure and is robust to age‐biased nest discovery probability. This model can be generalized to other staggered‐entry, time‐to‐hazard situations.     

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.