Ecology and conservation require reliable data on the occurrence of animals and plants. A major source of bias is imperfect detection, which, however, can be corrected for by estimation of detectability. In traditional occupancy models, this requires repeat or multi-observer surveys. Recently, time-to-detection models have been developed as a cost-effective alternative, which requires no repeat surveys and hence costs could be halved.
We compared the efficiency and reliability of time-to-detection and traditional occupancy models under varying survey effort. Two observers independently searched for 17 plant species in 44 100 m2 Swiss grassland quadrats and recorded the time-to-detection for each species, enabling detectability to be estimated with both time-to-detection and traditional occupancy models. In addition, we gauged the relative influence on detectability of species, observer, plant height and two measures of abundance (cover and frequency).
Estimates of detectability and occupancy under both models were very similar. Rare species were more likely to be overlooked; detectability was strongly affected by abundance. As a measure of abundance, frequency outperformed cover in its predictive power. The two observers differed significantly in their detection ability.
Time-to-detection models were as accurate as traditional occupancy models, but their data easier to obtain; thus they provide a cost-effective alternative to traditional occupancy models for detection-corrected estimation of occurrence.
Sampling species in the field provides most of the basic data on which our knowledge in ecology and conservation is based. However, several potential mechanisms might lead to biased assessments of state variables such as occurrence or abundance (Yoccoz, Nichols & Boulinier 2001; Albert et al. 2010), most importantly imperfect detection. Not accounting for ‘overlooking’ typically leads to underestimates of abundance (Kéry, Gregg & Schaub 2005) or occurrence (Kéry, Gardner & Monnerat 2010), overestimation of extinction probability (Kéry et al. 2006), missing eradication opportunities in invasive species (Bogich, Liebhold & Shea 2008; Hauser & McCarthy 2009), erroneous conclusion about treatment difference (Archaux, Henry & Gimenez 2012), and biased inference on habitat preference (Kéry 2004), taxonomic diversity (Archaux 2009) or population trajectories (Alexander, Slade & Kettle 1997; Shefferson et al. 2001). Probability of detection, or detectability for short, is therefore a critical parameter to assess in ecological studies and biodiversity surveys. However, detectability is far from being commonly accounted for by ecologists (Archaux, Henry & Gimenez 2012), mainly due to the effort and cost necessary for obtaining the multiple surveys required by the traditional approaches to estimate it.
A wide array of field protocols and associated statistical models are available for estimating detectability of species, including traditional occupancy models and time-to-detection occupancy models. Traditional occupancy (or site-occupancy) models are based on repeat surveys at the same site, either by the same or by different observers (MacKenzie et al. 2002, 2006), generating binary detection/non-detection (misleadingly also called ‘presence–absence’) data. These models use such data to estimate the probability that at least one individual of a species occurs at a site (occupancy) and the probability that an occupied site is recognized as such, that is, that at least one individual is detected at an occupied site (detectability). These protocols and the associated statistical models are now widely used in animal sampling, but are still rare in plant studies.
Time-to-detection occupancy models (Garrard et al. 2008; denoted TTD models from now) have recently been proposed as an alternative to traditional occupancy models to estimate detectability and occupancy. TTD models use the time required to detect a species to estimate detectability as a sort of survival analysis: a species ‘survives’ until it is detected and the time to the detection event is modelled as a function of an encounter rate parameter, which can itself be modelled as a function of covariates. All else equal, it appears that survey costs may be halved compared to traditional occupancy models, since TTD models require neither repeat surveys nor multiple observers. Given that resources are always limited, TTD models appear as a very appealing alternative to traditional occupancy models to save a lot of money. However, in spite of its promise, the method has not yet received much attention (Garrard et al. 2013; McCarthy et al. 2013), nor has it been evaluated in the field in a comparison with another design.
We carried out a field experiment to compare traditional occupancy models (MacKenzie et al. 2002) with TTD models (Garrard et al. 2008). Like Garrard et al. (2013), we extended previous models to incorporate multiple species and multiple observers. We worked in Swiss grassland sites and asked the following questions:
How similar are estimates of detectability and occupancy under the two models?
How do survey effort and observer skills affect the estimates of detectability?
How is detectability related to two measures of abundance, cover and frequency?
Materials and methods
Study site and study species
We conducted the study in the Gurnigel–Gantrisch region (46°44′20′′N, 7°26′45′′E) in the Swiss Alps at an elevation of 1450–1510 m a.s.l. The study area is composed of a mosaic of different open habitats including wet meadows with dryer outcrops and patches of fens and bogs. The area is used as an extensive cattle pasture, adding some small-scale disturbances due to trampling and grazing. We randomly chose the locations of 44 of 10 m × 10 m quadrats and selected 17 plant species with different growth form, height and colour (Table S1) and thus different conspicuousness. The fieldwork was conducted from 16 to 31 August 2011, a period short enough to ensure that changes in occurrence and phenology of the study species remained negligible, thus not challenging the closure assumption made by occupancy models. During our study, most species had finished flowering and were in the fruiting stage; three occurred exclusively in the vegetative stage (Table S1).
Two observers (CNB and LB), both experienced field botanists, surveyed each quadrat independently and for all 17 study species simultaneously. The list of species occurring in a quadrat was unknown beforehand. The habitat was suitable for most study species in most quadrats, but it was reasonable to suppose that several species did not grow in all quadrats. The maximum survey effort per quadrat and observer was 8 min, as this was deemed sufficient to detect most species based on a preliminary study carried out by CNB and LB. While searching for the species, observers were allowed to enter the quadrat and move around freely. Once a species was detected, the stopwatch was paused, and time-to-detection of the species and the height of the detected individual were recorded. Very conspicuous species, which could be detected at a glance right at the start of the experiment while standing outside the quadrat, were given a time-to-detection of 1 sec, and the height of the detected individual was measured at the end of the search to avoid the accidental detection of other, less conspicuous species. For analyses with traditional occupancy models, the outcome of the search experiments was summarized in the form of binary detection/non-detection data yi, j, k, where yi,j,k = 1 denotes detection of species k (k = 1…17) at site i (i = 1…44) by observer j (j = 1,2) and yi,j,k = 0 non-detection.
Factors influencing detectability
We assessed the influence of the following factors on detectability: observer, species, abundance, plant height. Each observer measured the plant height of the first detected individual of each species in each quadrat as described above. The abundance of all occurring species was assessed after both observers had searched a given quadrat using two of the most commonly used measures of plant abundance: cover and frequency. Frequency was assessed by dividing the 10 m × 10 m quadrats into 16 subquadrats of 2·5 m × 2·5 m and counting the number of subquadrats in which a given species grew (i.e. rooted subquadrat frequency, Wilson 2011). As the frequency assessment required 15–30 min per quadrat, each observer assessed the frequency of half of the study species in each quadrat. Each observer assessed alternatively one or the other part of the study species in different quadrats. Cover was assessed as the percentage of the ground area covered by a given species and estimated visually by consensus among both observers using a continuous scale ranging from 0·5% to 100% with increments of 0·5%. This assessment required only 2 min. To assess cover, visual estimates were preferred to more accurate and objective methods such as point-quadrat or point-intercept methods (Vittoz & Guisan 2007; Wilson 2011; Wintle et al. 2013) in order to avoid damaging the vegetation by these more labour-intensive methods. This was especially necessary, as extremely many points would have been required to accurately assess the cover of the rare species, because most target species occurred at very low abundance and because point methods are prone to miss such rare species (Everson, Clarke & Everson 1990; Vittoz & Guisan 2007). Sometimes, during the extra time spent in each quadrat for the frequency and cover estimation, previously missed species were detected and their abundance was assessed. This information was used in further analyses (binomial GLMMs) to model the influence of factors on detectability for all species ever detected.
Estimation of occupancy and detectability in the two survey protocols
We jointly estimated the occupancy and detection probability using a multispecies generalization of traditional occupancy models (MacKenzie et al. 2006) and of time-to-detection occupancy models (Garrard et al. 2008, 2013) fit to the detection/non-detection and the time-to-detection data, respectively. Both represent hierarchical models that accommodate false-negative observations by distinguishing two linked processes: an ecological process for species occurrence and an observation process for species detection. The outcome of the observation process is specified conditional on that of the ecological process: a species can only be detected where it is occurring. Hence, we made the typical assumption of no false positives. The outcome of the observation process, that is, the observed data, is also affected by other variables, such as the observer ability.
In both occupancy models, the description of the ecological process underlying the latent state of occurrence, presence or absence, zi,k, of species k in quadrat i, is treated as a Bernoulli random variable,
where ψi,k is the probability of occurrence of species k in quadrat i.
When analysing the detection/non-detection data, the observation process is modelled as another Bernoulli random variable such that the observed detection/non-detection data, yi,j,k given the true presence or absence of a species zi,k is analogous to a coin flip:
where pi,j,k is the detection probability for species k in quadrat i by observer j.
For the TTD data, the observation process describes the time until first detection of a species, which is modelled as a censored exponential random variable that is also conditional on the outcome of the Bernoulli random variable z. Hence, for the observed TTD ti,j,k, we assume at a quadrat where the species is present:
where ti,j,k is the time until first detection of an individual of species k in quadrat i during survey j, and λi,j,k is the expected number of detections per time unit (detection rate) of a Poisson process for species k in quadrat i during survey j (note that two observers are treated identical to two surveys). To accommodate the fact that every survey must end at some time, say at time T, we modelled TTD at an occupied quadrat as a censored exponential random variable:
where the censoring at time T is denoted by C(T). That is, whenever a species is not detected after 8 min, the observation is censored at T. Similarly, for an absent species, the observation of time-to-detection is also censored at T. Detection probability (D) until some time t is a function of the detection rate λ and time t (Garrard et al. 2008):
We treated the effect of individual species k on probability of occurrence ψ, detectability p and detection rate λ as random effect. As in virtually all generalized linear mixed models in ecology, we assumed that species-specific random effects come from a Normal distribution with mean μ and variance σ2 that were both estimated. We estimated an observer-specific detectability for each species by modelling the effect of survey j on detectability p and on detection rate λ.
We compared the efficiency of both models under a range of survey efforts (2–8 min). To test whether TTD models provide accurate estimates of occupancy after a single visit only, we ran them with observations of each observer singly.
We analysed the models using Bayesian methods with vague priors meant to introduce little or no information. For a detailed description of our models in the BUGS language as well as the data sets used in the analyses, see Appendices S1 and S2 in the Supporting Information.
We carried out the analysis in the free, general Bayesian modelling software JAGS 3.3.0 (Plummer 2003), which we called from R (R Development Core Team 2012) through package R2jags (Su & Yajima 2012). We ran three Markov chains for 36 000 iterations each, discarded the first 6000 as a burn-in and thinned the remainder by 2. The Gelman–Rubin Rhat statistic (Gelman & Rubin 1992) indicated acceptable convergence for all parameters (i.e. Rhat values were close to 1). We report posterior means as point estimates and central 95% percentiles of the posterior samples as Bayesian credible intervals (CRI).
Effect of covariates on detection
In our two hierarchical models, we estimated only the effect of observer on the estimated detectability but did not introduce any other covariates (e.g. cover, frequency), because they could not be measured independently from the survey outcomes (i.e. whether a species was detected or not). Hence, in a second step, we assumed that the true occupancy was known at the end of the extra time spent conducting the abundance assessments, and we estimated the influence of other covariates for those species that were detected at least once. Based on Eqn 5, it turned out that all species have an estimated detectability >0·99 after 30 min; therefore, the assumption of known true occupancy seems realistic.
We modelled the influence of frequency, cover, observers and the height of the first detected individual on the probability of detection after 30 min using a binomial generalized linear mixed model (GLMM) using the lmer function in the R package lme4 (Bates, Maechler & Bolker 2011). We used the binary detection/non-detection data after 8-min survey by observers A and B in all quadrats where the species was observed at least once during the 8-min survey or in the extra time taken to conduct the abundance assessment.
We modelled the influence of frequency, cover, observers and the height of the first detected individual on the time-to-detection using a gamma GLMM with the hglm function of the hglm R package (Ronnegard, Shen & Alam 2010). Species were entered in both models as random effects, and frequency and cover were log-transformed. To overcome a spike in the model residuals at 1 s, we generated new detection times for all cases of detection at first glance by taking random numbers from an exponential distribution with rate = 2 (i.e. mean detection time = 0·5 s). It is reasonable to assume that what we called detection at first glance is well modelled in such a way.
Most species were found in >70% of the quadrats, but at low abundance (Tables 1 and S1, Fig. 1). Observed occurrence of the 17 species ranged from 18 to 44 (median 34) quadrats after the regular 8-min survey. For 8 of the 17 species, observed occurrence increased after the extra effort associated with abundance assessments and ranged from 20 to 44 quadrats (median 35, Table 1). The two different measures of abundance (cover and frequency) were strongly correlated (Spearman's rho = 0·77, P < 0·001), but expressed two different aspects of abundance (Fig. 1). Cover never exceeded 15%, and most species had extremely low cover values (median 1%, minimum 0·5%). In contrast, in terms of frequency, several species showed maximum values of 16 (median 7) subquadrats (Table 1). Hence, none of the 17 species was dominating the community, but many were spatially evenly distributed (Fig. 1).
Table 1. Observed and estimated occurrence of the 17 study species in 44 quadrats of 10 m × 10 m. Species name follows Lauber & Wagner (2007). oA,B = observed occurrence after 8-min searching time by observers A and B, respectively. otot = observed occurrence by both observers A and B (each with 8-min searching time). oextra = observed occurrence after an extra search of more than 15 min. oocc = estimated occurrence based on traditional occupancy model (mean, SD). ottd = estimated occurrence based on time-to-detection model (mean, SD)
Estimates of detectability and occupancy obtained with TTD and traditional occupancy models were in good agreement (Fig. 2), highlighting the ability of TTD models to provide reliable estimates after a single visit only. However, traditional occupancy models (with two surveys per site) provided much more precise estimates than TTD models with a single survey (Figs 2 and 3), but not when the TTD models were fitted to both surveys (Fig. S1).
Survey effort had a strong effect on the precision of the parameter estimates (Figs 2 and 3). After 2 min, estimates were fairly imprecise (Figs 2a, d), although those of occupancy for observer B were already precise and presumably also accurate (i.e. close to the putatively true value) for nine out of 17 species (Fig. 3). After 4 min, traditional occupancy models provided accurate occupancy estimates for 14 species and TTD models for 11 species using the data from observer A (Fig. 3) and for 14 species using observer B's data (Fig. 3). After the regular survey time of 8 min, most estimates of detectability were much more precise but also >0·9 (Fig. 2c), indicating an overall high probability to detect a given species within the 10 m × 10 m quadrats. With a survey effort of 8 min, occupancy estimates under traditional occupancy models were accurate for all species (Fig. 3), but still imprecise for one species (Fig. 3, species Aj). Occupancy estimates under TTD models were likewise accurate for all species when using data from observer B, but only for 14 species when using data from observer A (Fig. 3).
The ability of both TTD and traditional occupancy models to correct for imperfect detection was apparent in the close match between the observed occurrence after 30 min and the estimated occupancy under both models (Table 1, Fig. 3).
TTD times were exponentially distributed (Figs 4 and S2), supporting our modelling assumption. This reflects that most of the detection events occurred soon after the beginning of the survey (Fig. S2), except for species that are hard to detect (e.g. Lotus and Ajuga, Fig. 4). Inspection of detection-effort curves indicated that 8-min searching time was not sufficient for all species, since the curves did not always reach a plateau after 8 min (Figs 4 and S2).
Detectability varied widely between observers (Table 2, Figs 2 and 5) and was strongly influenced by abundance (Table 2, Fig. 5). The relative importance of the covariates appeared to be similar when analysing either detection/non-detection data (Table 2a) or the TTD data (Table 2b); the effect of frequency was the strongest, followed by that of observer, cover and plant height. In addition to significant differences between observers in their detection ability, both models indicated a strong influence of the frequency on the survey outcome (Table 2, Fig. 5). Cover, the other measure of abundance, had a much weaker predictive power in comparison with frequency (Table 2), but was influential in models where frequency was not introduced as covariate (Table S2).
Table 2. Relationships between (a) probability of detection and (b) time-to-detection, and abundance (frequency and cover), observer, plant height and species under a binomial GLMM (in a) and a gamma GLMM (in b) for all 17 study species. The response variable in (a) is the detection/non-detection of species by each observer (binary data) obtained assuming that all species were detected either during the 8-min survey or in the extra 15–30 min taken to conduct the abundance assessment in each quadrat. The response variable in (b) is the time-to-detection during the 8 min. Estimated variance components due to species: (a) 0·199 (SE = NA), (b) 0·282 (SE = 0·360)
Estimate (±standard error)
Estimate (±standard error)
Our field study highlights the cost efficiency of time-to-detection (TTD) designs: detectability estimates under a TTD model, based on a single visit only, were almost identical to those under a traditional occupancy model requiring two surveys. Although traditional occupancy models need on average shorter visits than time-to-detection models, this advantage is cancelled out by the cost of a second survey, for example travel time or salary of a second observer. In other words, survey costs could essentially be halved by using TTD designs. Given the typical resource limitation, we believe that TTD designs should be of great interest for ecologists and conservationists since the extra resources (money, time, personnel) required traditionally to estimate detectability based on repeat surveys may be better spent in other part of the monitoring or management of threatened or invasive species.
Survey effort and observer effect
The positive influence of survey effort on detectability has already been noted (Chen et al. 2009; Moore et al. 2011) and was very apparent in our study. Detectability increased with survey effort (Fig. 2A–C), and after 8 min, more than 80% of the species had more than 90% detectability, which is very high in comparison with former studies (e.g. Kéry et al. 2006; Chen et al. 2009), most likely because these invested less survey effort per area. Still, 8 min were not enough for one of the observers to get accurate estimates for two species. Moreover, a greater survey effort would have improved the precision of the estimate of inconspicuous species. This stresses the importance to assess and adapt the necessary survey effort to observer skills or to the desired precision of the estimates.
The two observers differed markedly in their detection ability. Strong observer differences have already been reported (Archaux et al. 2006; Moore et al. 2011; McCarthy et al. 2013; but see Chen et al. 2009). Clearly, only explicitly estimating detectability can in practice remove such effects. If perfect observations are desired (i.e. no detection error), our findings confirm that basing the survey effort on expert opinion can be misleading. For instance, experts strongly underestimated the survey effort in our study; following a qualitative test of the method, survey effort was set at 8 min, although TTD models finally showed that 30 min would have been required for detecting the most inconspicuous species. This underlines that the required effort to achieve a desired accuracy in the observed data should be calculated with TTD models (Garrard et al. 2008). Detection-effort curves offer a useful graphical tool to express the relationship between survey ‘catch’ and survey effort (Figs 4 and S2; Delaney & Leung 2010). For instance, detection-effort curves of Ajuga reptans or Lotus corniculatus (Fig. 4) showed clearly that 8 min were not enough to detect these species perfectly. However, during the fieldwork, none of the observers felt that 8-min effort was insufficient to detect the study species. This biased feeling may be due to observers having fewer opportunities to train their eyes to the search image of species occurring at low occupancy or at low abundance. Moreover, one could suspect that observer expectations about the putative presence of a common vs. rare species influence their focus or the amount of effort spent searching for it. Observers are likely to focus part of their searching time looking for some common species that they have not found yet but that they expect to be present. Similar investment is less likely for rare species, since observers’ expectation is that a rare species must be normally absent in a fraction of the sites surveyed. Such causes may well lead observers to an overconfidence that species that are hard to detect must also be truly absent, even if this feeling is severely biased. Given that ecologists are prone to overestimate the information content of their data (Burgman 2005; Martin et al. 2012; Wintle et al. 2013), quantitative methods such as TTD models are essential to objectively estimate survey effort.
Survey effort is a key parameter to optimally monitoring biodiversity. In small sites such as our 100 m2 quadrats, it is naturally expressed by recording TTD times. But when very large sites are surveyed, effort is arguably better assessed spatially. Few studies report survey effort in terms of area surveyed (Chen et al. 2009; Moore et al. 2011), but given the distribution of the detection events in relation to effort, we expect that models that treat spatial effort alike to temporal effort might provide useful estimates as well. The equivalence between time and length of a search route merits further study (see also Guillera-Arroita et al. (2012), for models of occurrence for continuous detection data along transects).
Effect of abundance
Not surprisingly, rare species were more likely to be overlooked. A negative relationship between abundance and detectability has been reported several times (Gaston 1994; Archaux et al. 2006; Vittoz & Guisan 2007; Chen et al. 2009; Delaney & Leung 2010; McCarthy et al. 2013). In our study, detectability was much more affected by frequency than cover, probably because frequency reflects the spatial distribution of a species within a quadrat, whereas cover values <1% occurred for situations where a species occurred in only a few patches (i.e. at low frequency) and where a species occurred everywhere in the quadrat (Fig. 1). The higher predictive power of frequency compared with cover suggests that many species occurred in clumps and thus that a relatively even occurrence in the quadrat (which was reflected by higher values of frequency) was more important for high detectability. However, assessing frequency is much more time demanding than assessing cover and thus cannot be recommended as a general solution for every plant survey.
The effect of abundance on detection has raised concerns about potential biases in our understanding of biological patterns and processes for a long time (Gaston 1994). The issue is especially important in conservation where many species of concern occur at low abundance. For example, assessment of extinction of endangered species (Kéry et al. 2006; Garrard et al. 2008) and early detection of invasive species (Bogich, Liebhold & Shea 2008; Hauser & McCarthy 2009) are situations in which detection of species at low abundance is crucial. To estimate the necessary survey effort for situations where the species occur at low abundance, Delaney & Leung (2010) proposed an empirical model using sites with known density of a target species. Recently, McCarthy et al. (2013) proposed a theoretical model using measured detectability at known abundance to predict detectability across a range of abundances.
However, the abundance–detection relationship should not only be seen as a nuisance. It could be exploited to monitor abundance (Royle & Nichols 2003; McCarthy et al. 2013). Indeed, any decrease in the species abundance will be related to an increase in the effort required until the species is detected. Such an approach could reduce the efforts required for abundance monitoring. It could be particularly useful for species whose abundance is hard to assess with conventional techniques, or when very large sites are surveyed in which cover estimation or counting of individual is impossible to carry out. The main issue with this approach is that variation in observer skills may also affect the survey effort in addition to species abundance. The approach may still be valuable, for example, as an early warning system, in sampling schemes where observer skills are monitored, or when no observers are involved (e.g. automatic tape recording of animal calls, McCarthy et al. 2013).
Benefits of multiple visits
TTD provided reliable estimates of detectability after a single visit. However, multiple visits may still be desirable in particular situations, at least in a fraction of the surveyed sites. First, multiple visits can help to detect false positives due to species misidentifications. Indeed, visits done at the same site by another observer allows for detecting such false positives under certain assumptions (Archaux et al. 2009; Miller et al. 2011). Secondly, multiple visits may be important when there is temporary emigration in organisms with movement, that is, animals. Thirdly, they allow one to deal with temporary unavailability to detection due to species phenology. This issue is important in large-scale and/or multispecies surveys where the timing of the visits cannot be optimized for all species and hence multiple visits are required. To deal with the issue of temporary unavailability, TTD models could be extended to use the extra information from visits at different seasons. The structure of such a three-level hierarchical model with occupancy, availability and detection would be very similar to what has been implemented in traditional three-level occupancy modelling (e.g. Nichols et al. 2008), that is, a time-to-detection design would simply have to be conducted at multiple occasions during the growing season (see Kéry et al. (2009) for a similar design with occupancy surveys in a butterfly meta-community). Note that the advantage of requiring fewer visits of TTD designs carries over to this situation as well. Indeed, to estimate availability separately from occupancy and detection, two visits per site are enough with TTD models. However, with traditional occupancy models, four visits would be required, that is, two visits within each two seasons (or more when more occasions in a season should be covered).
Therefore, it is advisable to allocate some of the resources saved by the cost-efficient estimation of detectability through TTD design to repeat visits by another observer, among seasons or even within a season. Since TTD models performed as well as traditional occupancy model when run with data from two visits (Fig. S1), the methodological issue is not to choose between TTD and traditional occupancy models, but to assess in which situation a second visit may provide useful data and to find the optimal sampling strategy given some logistical and biological constraints (e.g. Joseph et al. 2006). Since the exact amount of sites where multiple visits would be required is strongly affected by the scope of the study (i.e. local monitoring of a single species vs. large-scale monitoring of multiple species), the target species and the number of observers involved as well as their skill, there is unfortunately not a single standard solution for the issue of resource allocation.
Conclusion and outlook
The time-to-detection design offers a cost-effective way to achieve two main goals of reproducible and therefore scientifically defensible surveys: controlling the sampling effort and estimating species detectability. Our study shows that the TTD design is easily implemented in the field is quick and provides detectability estimates that are essentially identical to those obtained with traditional occupancy models. Given the cost efficiency and ease of implementation of the method, the TTD design appears very interesting for monitoring many different types of organisms.
An interesting future avenue will be expanding TTD approaches to situations where effort is expressed spatially in terms of transect length or search area. Secondly, the TTD is so tightly related with abundance that one could take advantage of this relationship to monitor abundance, even of species whose abundance is hard to assess otherwise (e.g. along the lines of McCarthy et al. 2013).
We thank O. Bossdorf, A. Kempel and four anonymous reviewers for providing very valuable comments on the manuscript. This work was financially supported by the Federal Office of the Environment (FOEN) of Switzerland.