Imperfect detectability is a critical source of variation that limits ecological progress and frustrates effective conservation management. Available modelling methods provide valuable detectability estimates, but these are typically species-specific.
We present a novel application of time-to-detection modelling in which detectability of multiple species is a function of plant traits and observer characteristics. The model is demonstrated for plants in a temperate grassland community in south-eastern Australia.
We demonstrate that detectability can be estimated using observer experience, species population size and likelihood of flowering. The inclusion of flower colour and species distinctiveness improves the capacity of the model to predict detection rates for new species.
We demonstrate the application of the general model to plants in a temperate grassland community, but this modelling method may be extended to other communities or taxa for which time-to-detection models are appropriate.
Detectability is influenced by traits of the species and the observer. General models can be used to derive detectability estimates where repeat survey data, point counts or mark-recapture data are not available. As these data are almost always absent for species of conservation concern, general models such as ours will be useful for informing minimum survey requirements for monitoring and impact assessment, without the delays and costs associated with data collection.
Biological surveys underpin most ecological studies. They may be used to determine the distribution and abundance of species, monitor changes in populations or communities and as part of ecological impact assessments. However, numerous studies have demonstrated that detections of plant and animal species are imperfect, so species can remain undetected during a biological survey despite being present (McArdle 1990; Kéry 2002; Kéry & Gregg 2003; Slade, Alexander & Kettle 2003; Tyre et al. 2003; Bailey, Simons & Pollock 2004; de Solla et al. 2005; Wintle et al. 2005; MacKenzie et al. 2006; Alexander et al. 2009). Failure to account for imperfect detectability in biological surveys may bias estimates of abundance or species richness, impair detection of change or identification of differences due to management actions, misinform management decisions and increase the risk of extinction of rare and endangered species (Wintle et al. 2012). Imperfect detection should be considered when designing surveillance programs (Regan et al. 2006; Hauser & McCarthy 2009), and early detection is critical for the successful management of invasive species (Timmins & Braithwaite 2002).
Various methods now exist for characterising detectability, including mark-recapture methods (Nichols 1992; Kéry & Gregg 2003; Alexander et al. 2009), N-mixture models (Royle 2004; Joseph et al. 2009), zero-inflated binomial and other occupancy models (MacKenzie et al. 2002; Tyre et al. 2003; Wintle et al. 2005) and time-to-detection models (Garrard et al. 2008). While these methods differ in their objectives and data requirements, they are similar in that they are specific to a species or individuals within a species. With unlimited time and resources, species-specific detectability models would be constructed for all species for which the probability of detection during a survey is important. However, estimating species detectability can be onerous, often requiring a large investment in data collection. Given the large number of species for which detectability estimates are important, it may be useful to utilise what is known about the detectability of species with similar traits or characteristics, rather than rely on limited or no data for a species-specific detectability model. This requires a multi-species model of detectability that focuses on the characteristics of species that influence detectability.
In this article, we present a general model of plant detectability based on the single-species time-to-detection modelling approach introduced by Garrard et al. (2008). We begin by describing a multi-species model of mean time-to-detection. Then, using a case study in a native temperate grassland plant community located near Melbourne, Australia, we identify characteristics that influence the detection of plant species during flora surveys. We conclude by discussing implications of general models of detectability for ecological monitoring, management and policy.
Materials and methods
Consider a survey that aims to detect a species, j, at a one-hectare site, i. Observer k may search the site for a period of time, T minutes. There is some probability, pij, that the species is present at the site. The species cannot be detected where it is not present, but may or may not be detected at a site where it is present. The probability that the species is detected during a survey of an occupied site is determined by attributes of the observer, species traits that affect visibility or identification and the duration of the survey. By compiling data on the time at which J species are first detected at I sites in K surveys, as well as information about plant traits and observer attributes that might influence detection, it is possible to characterise the average time to detection as a function of traits. From this information, the probability that a species with a given set of traits will be detected in an occupied site during a survey of duration T can be estimated.
Exponential detection time model
The detection time model described by Garrard et al. (2008) is related to the exponential survival model (or ‘constant hazard’ model: Cox & Oakes 1984). This model assumes that detection times are distributed exponentially and that the rate of detection, λ, is constant. The mean time to detection, , is modelled as a function of explanatory variables, xn:
where βn are model coefficients describing the magnitude of influence of explanatory variables xn (e.g. plant traits such as size and colour, environmental conditions or observer characteristics) on mean detection time.
Observations where the species is not detected during the survey are censored observations, containing only partial information about the detection time (i.e. the detection time is longer than the period of survey). We denote δ as an indicator variable, which equals one when the species is detected and zero otherwise. Under a traditional exponential survival model, the likelihood of observing a detection time, t, for a species given a constant detection rate, λ, is (Cox & Oakes 1984):
where λ is the rate at which detection events occur, and T is the survey duration, such that t = T when the species is not detected (i.e. when δ = 0).
The standard survival model assumes that the species will eventually be detected during a survey provided T is sufficiently large. This assumption is untenable in our application, as there is some probability that the species is truly absent from the site. To account for this, the likelihood functions are modified (Garrard et al. 2008):
where p is the probability that the species occupies the site being surveyed. The likelihood for censored observations (i.e. when δ = 0) now includes two possibilities; the species was present at the site and remained undetected (p.exp−λt) and the species was truly absent from the site (1−p).
Multi-species detection time model
The model presented in eqn (eqn 3) can accommodate variation in plant detection times across multiple sites, i, and species, j:
where pij is the probability of species j occurring at site i, tij is the detection time for species j recorded at site i, and λj is the expected rate of detection for a species j as a function of the explanatory variables according to eqn (eqn 1), and can include various random effect terms to accommodate variation that is not accounted for by the fixed effects.
Finally, it is necessary to account for the additional information that may be gained from multiple surveys at each site. Consider the situation in which observer k does not observe species j at site i. If species j is recorded by another observer at site i, observer k's observation is known to be a failed detection because the species' presence is known. The likelihood for this censored observation is exp (−λT). However, if that species is not observed during K surveys of the site, then observer k's observation might be because the species was absent from the site or because all the observers failed to detect it. Therefore, the likelihoods for species j of the combined observations by all K observers at site i are given as:
where δijk is an indicator identifying whether observer k found species j at site i (δijk equals one when detected and zero when not). The first line accounts for the case where species j is seen by at least one of the K observers at site i, and the second line accounts for the case where no observers detected the species.
Case study data
Detection time data were collected during a multi-site, multi-observer field study in October and November, 2006. This period was chosen to coincide with the peak flowering period for a majority of the native grassland plants (Groves 1965). Surveys were conducted in one-hectare plots at 16 treeless native grassland sites in Victoria, Australia. Observers were allocated 90 min to survey each plot and recorded the time they first detected each species. Any species that remained undetected after 90 min was recorded as unobserved for that observer at that site. The modelling data consisted of 62 observations for 78 species by 11 observers across 14 sites. Observers were experienced in botanical surveys; however, a distinction was made between those with extensive experience and knowledge of grassland species (experienced) and those who were not familiar with the vegetation community prior to beginning surveys for this study (intermediate).
Models were constructed using time-to-detection data for forbs, small shrubs, ferns and non-grassy graminoids. Many native grasses in this community are extremely difficult to identify to species level in the field so grasses were removed from the analysis to ensure the accuracy of the data used in the model.
Like other models designed to explicitly model observation processes with imperfect detection (sensu MacKenzie et al. (2002) and Tyre et al. (2003)), the time-to-detection model may be sensitive to false positives. A single false-positive observation of a given species among a set of true-negative observations at a location will overestimate the average detection time (underestimating detection probability) of that species (Garrard et al. 2008). We took a conservative approach to reducing the possibility of including experiment-wide false positives by excluding species recorded only once across all sites. We included singleton observations at individual sites, as these may represent species that are difficult to detect.
Species traits that influence detectability
Detection of species during a survey may be influenced by a number of factors that affect visibility and/or identification. These include the size or form of the plant (Kéry & Gregg 2003; Slade, Alexander & Kettle 2003; Brown, Harris & Timmins 2004), the presence of flowers (Kéry & Gregg 2003; Burrows 2004) and the rarity or local population size of the species (McCarthy et al. in press). For example, a plant with a small local population is less likely to be detected during a survey than one that is locally common (Chen et al. 2009; McCarthy et al. in press). In contrast, large species or species that grow in clumps may be visible from a greater distance than small species or those that grow as isolated individuals.
Plants may be more detectable when flowering, and species with large or conspicuous flowers should be more easily detected than those without such features (Kéry & Gregg 2003; Burrows 2004). In addition, it is reasonable to assume that detectability would increase with leaf size. Lastly, identification to species level may be difficult if there are many similar species within the ecological community being surveyed.
Model fitting & comparison
We identified plant traits thought to influence detection (Table S1). The simplest model considered was one in which average time to detection is explained by observer experience and local abundance (hereafter referred to as the Base model), as these variables are known to influence plant detection (Garrard et al. 2008; Chen et al. 2009; McCarthy et al. in press). Because our time-to-detection models were relatively slow to converge (e.g. requiring a burn-in of up to 100 000 samples at around 0·5 s per sample), testing all combinations of explanatory variables was not feasible. We tested each variable separately by adding them to the Base model. Random effect terms, res, reo and resp for site, observer and species, respectively, were also included. Traits that were found to have little influence on average detection time were not considered further.
Next, we identified eight a priori models for investigation, representing different hypotheses about the influences of traits on detectability (Table 1). Models tested were ‘Base’, ‘Temporal’, ‘Visual, ‘Spatial’, ‘Identification’ and three combinations of these models, including the full model, in which all of the hypotheses about the detection process were represented. Data limitations meant that model simplicity was prioritised, and for this reason, no interactions between variables were included.
Table 1. Candidate trait-based detection time models representing hypotheses about how traits influence detection. Also shown are the difference in DIC from the Base model and R2 values for the relationship between predicted and observed proportion of sites detected (for all species included in model fitting) and, for a hold-out set of eight species, the relationship between the average detection times predicted by the multi-species and single-species time-to-detection models. exper is observer experience, abund is a measure of local population size, inpeak indicates whether the survey occurred during peak flowering month (1) or not (0), LA is leaf area, clump indicates whether species grows in clumps (1) or not (0), flcol is flower colour, and nosp is the number of grassland species in genus. α is the intercept, β1 : 9 are variable coefficients, and εsp, εs and εo are random effects for species, site and observer, respectively. Detailed information on covariates is presented in Table S1 and posterior parameter estimates are presented in Table S3
Where β4 : 7∙flcol = (β4∙YW + β5∙BP + β6∙RP + β7∙BGIC), and YW = yellow or white flowers, BP = blue or purple flowers, RP = red or pink flowers and BGIC = black, green or inconspicuous flowers. DIC, Deviance Information Criterion.
Models were run in OpenBUGS version 3.2.1, a freely-available Bayesian statistical modelling program (Lunn et al. 2000). Vague prior distributions were specified to ensure posterior estimates were driven by the data. The probability of species j occurring at site i, pij, was assumed to be constant and assigned a uniform prior distribution (dunif(0,1)). Random effects for site, observer and species were drawn from a normal distribution with a mean of zero and standard deviation to be estimated. The prior distribution for the standard deviation of the random effects was specified as uniform between 0 and 100 (Gelman 2006). Prior distributions for the regression coefficients on detectability variables were specified as normal distributions with a mean of zero and a standard deviation of 1000.
Some explanatory variables were transformed to improve model parameter estimation. Continuous variables that were unconstrained with skewed positive distributions were transformed using the natural logarithm. We used the complementary log–log transformation of estimated abundance in all models so that the regression coefficient associated with the effect of abundance on detection rate can be interpreted as the factor by which detectability scales with abundance (McCarthy et al. in press). Due to the large number of candidate variables relative to the number of independent data points, linear relationships were assumed between the logarithm of detection times and continuous explanatory variables to reduce the number of predictor degrees of freedom. This may have implications for the reliability of inference if the true, underlying relationship is not adequately approximated by a linear function.
We ran two MCMC chains to ensure that convergence was reached and centred continuous variables where appropriate to hasten convergence. An initial set of samples was discarded as a burn-in, and posterior estimates were calculated from post-convergence sampling. The number of necessary samples varied across models, but was typically around 20 000 for the burn-in and 300 000 for estimating posterior distributions. Candidate models were assessed for fit and parsimony using the Deviance Information Criterion (DIC: Spiegelhalter et al. 2002).
Evaluating model calibration
Evaluation of detectability models is not trivial. Where a species is detected at a site, the true occupancy of that site is known. An absence observation has two possible ‘truths’: the species is either truly absent from the site or it is present and has remained undetected. Therefore, unless occupancy is experimentally controlled, field validation of detectability models is impeded. Furthermore, because the true value of censored observations is unknown, evaluation of time-to-event models such as the one presented here is difficult (Hosmer, Lemeshow & May 1999).
Model calibration was assessed by comparing the predicted and observed proportion of sites at which each species occurred. The observed proportion of sites is the proportion of the 14 sites in this study at which each species was observed at least once. The time-to-detection model simultaneously estimates the rate of detection and the probability of occupancy for each species. When the probability of occupancy is modelled as a constant across all sites, as was done here, it estimates the proportion of sites at which species j is present, . We estimated the predicted proportion of sites at which species j would be detected, :
where is an estimate of the probability that species j would be detected in a 90-minute survey, equal to and is the estimated average detection rate for species j at a typical site for an experienced observer.
We evaluated the predictive performance of each candidate model by comparing the average detection times for eight hold-out species predicted by the multi-species model with average detection times predicted using single-species models. The eight species were chosen to represent a range of characteristics included in the candidate models (Table S2). During evaluation, these species were withheld from the data used to fit each multi-species model, so we could test its capacity to predict to new species. For the multi-species models, predictions were made for experienced and intermediate observers assuming average site, observer and species effects (i.e. res = reo = resp = 0).
Single-species models for the eight evaluation species were constructed using the likelihoods in eqn (eqn 3). For each species, average time to detection was modelled as a function of observer experience and the per cent cover of the dominant grass, Themeda triandra (Garrard et al. 2008). Average detection time for each species was predicted for experienced and intermediate observers assuming average Themeda cover (35%). There were insufficient data at the species level to adequately model site and observer random effects. Consequently, the precision of parameter estimates for these models will be overestimated.
The posterior density distributions of the predicted average times to detection were positively skewed with long tails. We compared the natural logarithm of the median posterior estimates of average detection time for the eight species, as predicted by the multi- and single-species models.
There was little difference between the candidate models when comparing measures of fit (Table 1, Fig. 1a–c), indicating that the benefit of the information provided by additional trait variables may be offset by the associated reduction in degrees of freedom. All candidate models perform reasonably well when comparing the fitted and predicted proportion of sites at which each species is detected during 90 min surveys (Fig. 1a–c, Table 1). These models explain between 82% and 87% of the variation in the observed detections. However, there is some bias in the predictions, with all models tending to underestimate the proportion of sites at which detections would occur. This indicates that the predicted average detection times may be over-estimated (detection rate is underestimated).
There was a clear effect of abundance in all models, indicating that more abundant species have shorter average detection times. Experienced observers tend to have shorter detection times than observers with less grassland experience, although the 95% credible interval for the effect of observer experience includes zero (Fig. 2a, Table S3). Leaf area, clumpiness and number of species did not explain a substantial amount of variation in detection times in this data set (Fig. 2a). Plant trait variables peak flowering month and flower colour explain a small amount of variation in detectability, although wide coefficient standard errors indicate substantial uncertainty about these effects (Fig. 2a). Species whose peak flowering month overlaps with the month of survey tend to be detected more quickly than those species that are not in their peak flowering month when surveys occurred (Fig. 2a). Average detection times are almost 50% longer when surveys occur outside the peak flowering month. In addition, species with blue/purple flowers appear more easily detected than those with white/yellow flowers, and species with red/pink flowers are detected most rapidly. Species with black or inconspicuous flowers have the longest average detection times.
The effect of flower colour is potentially as large as the influence of relative abundance (Fig. 2a), although the standard errors are large for flower colour. Including flower characteristics does not appear to substantially improve the fit of the Temporal, Visual and Combination 1 models over the Base model (as measured by DIC and correlation between predicted and observed proportion of sites occupied). However, the ability of the model to predict average detection times of species not included in the model-fitting data set is substantially improved when peak flowering period, flower colour and species distinctiveness information are included in the model (Table 1, Fig. 1d–f).
There is strong support for including site, observer and species random effects in all models tested (Fig. 2b). All random effects have a standard deviation that is clearly different from zero, suggesting that there is variation in detection time across sites, observers and species that is not explained by the fixed effects examined here. The standard deviation of the species random effect is significantly greater than that of the site and observer random effects, indicating that there is greater unexplained variation among species than among sites or observers.
A general detection time model
Our multi-species model of plant detection time is a novel and potentially extremely useful approach to characterising species' detectability. To date, the detectability literature has focussed on estimating detection probabilities of individual species. Consequently, detectability estimates are species-specific and available for few species. Trait-based detectability models will be valuable as they can be used to inform minimum survey effort requirements for species lacking the survey data necessary to estimate species-level detection probabilities.
The general models presented here fit the data well, explaining up to 87% of the variation in detection times across 78 grassland species. When information on flowering period and flower colour is included, general models predict well to grassland species not included in the model-fitting data set. Predictions of average detection time exhibit some bias when predicting to fitted and new species (Fig. 1). In general, average times to detection are overestimated (detection rates are underestimated). The bias is greater for species with low detection times (high detection rates), and less when detection times are longer (low detection rates). Bias in detectability estimates has been demonstrated when using zero-inflated binomial or mark-recapture models; however, these models tend to overestimate detection probability when the true detectability is low (≤0·2: Wintle et al. 2004). Further investigation into the bias in time-to-detection models is warranted; however, comprehensive evaluation of detection rate estimates can only be achieved by experimentally controlling species' presence and absence (Moore et al. 2011; McCarthy et al. in press).
Our study highlights the importance of using multiple measures to evaluate models. If we based our inference purely on a measure of fit (DIC), we may have decided that species' characteristics beyond abundance were of little importance in explaining variation in species' detectability. However, when predicting to new species, flower information has some value. It is common for studies to use an information criterion such as DIC to choose between models. Our result reinforces the view that information criteria are best used in conjunction with other model selection methods, including expert opinion and common sense (Austin 2002; Burnham & Anderson 2002; Spiegelhalter et al. 2002; Wintle et al. 2005; Millar 2009).
Detectability and abundance
While we found a positive relationship between detectability and abundance (a negative relationship between abundance and average detection time), detectability did not scale linearly with abundance, as has been demonstrated in McCarthy et al.(in press). A scaling factor of <1, such as ours, is typical of a situation in which species are not distributed randomly or detected independently, but are instead clumped or grouped in some way. In our case, the less-than-linear scaling may also likely be attributable to: extra variance in detection times introduced by the fact that observers were looking for multiple species at once; the existence of influences on detectability not modelled in this study; and the fact that we have used a proxy for abundance, rather than measuring abundance at each site. The benefit of the abundance proxy we have used here is that it can be estimated a priori, which is essential for predicting detection time and survey effort for new species at new sites. Using generalised ‘classes of rarity’ (sensu Rabinowitz 1981) is an alternative to utilising explicit estimates of abundance in cases where no such estimate can be obtained. We found expert-assigned rarity class to be almost as powerful a predictor of detection times as explicit abundance estimates for the grassland species used in this case study (G. Garrard, unpublished data).
Constructing multi-species time-to-detection models requires information on the time at which each species is first detected during a survey, as well as species trait information. Trait information can be compiled from published flora and trait databases, meaning that only detection time data must be collected in the field. It is possible that such information could be routinely collected during environmental impact assessments with only a small modification to current practices. For example, where an ecological study or assessment involves compiling a comprehensive species list at a site, it is relatively simple to also record the time to initial detection of each species. Environmental impact assessments and ecological reports undertaken by environmental consultants now account for a significant proportion of collected ecological data (McDonnell, Williams & Hahs 1999). If such assessments were to collect detection time data, it is possible that general models of detection time could be constructed for a range of ecological communities with relatively little effort.
Detectability and survey design
Because they can estimate detection rates for species where no species-specific detection time model exists, general models of detectability are important when designing ecological surveys. They can be used to identify plant traits or characteristics that contribute to low detection probabilities (i.e., low abundance, inconspicuous flowers, surveys outside of peak flowering period), thereby flagging situations where extra survey effort may be necessary. It is similarly important to consider variation in detectability due to observers when specifying survey requirements (Fig. 2a), as the experience of the person conducting the survey is influential in single (Garrard 2009) and now multiple species plant detectability models.
Estimates of average detection time can be used to calculate the survey effort required to achieve a specified level of certainty that a species will be detected if it is present, and the number of sequential non-detections necessary to achieve some minimally acceptable posterior probability of occupancy (Garrard et al. 2008; Wintle et al. 2012). Where no species-specific detectability information exists, trait-based detectability models may provide a defensible means for determining prior estimates of detection probabilities and survey effort requirements. Estimates of average time to detection from our model range from 60 to more than 200 min per hectare. The survey effort required to achieve a 0·90 probability of detection for species with an average detection time of 60 min is more than 2 h per hectare, which is well above the effort expended in most environmental impact assessments in this ecosystem (Garrard 2009). Our model could be used to help specify minimum survey effort requirements for monitoring programs or impact assessment surveys, including consultations under Section 7 of USA's Endangered Species Act and referrals under Australia's Environment Protection and Biodiversity Conservation Act 1999.
We showed that flowering traits such as timing and colouration are likely to influence detectability. In our study, the average time to detection was c. 32% shorter for species that were in their peak flowering month at the time of survey. Many plant species will be difficult to detect when they are not flowering, particularly lilies, orchids and other species that die back to belowground organs in unfavourable seasons. Care should be taken to undertake surveys at a time when target species are likely to be flowering. Where this is not possible, survey effort should be increased to compensate for the reduced detectability. Our results indicate that survey effort should be increased by around 50% to achieve this, although this figure will vary depending on how detectable the plant is when not flowering.
The models presented here account for a large percentage of the variation in detection times for grassland species, but some variation remains unmodelled. We have shown that there is variation attributable to site, observer and species not captured by the variables investigated and that much of the unmodelled variation is at the species level (Fig. 2b). This may arise because our measurement of the traits that influence detection is imperfect, or because there are traits that influence detection which we have not included. When making predictions for new species, it is common to assume, as we did, that the species effect is zero (i.e. that the species is ‘average’). However, the large species effect indicates that some species are much easier or more difficult to detect, even when accounting for influential species traits. A standard deviation of 0·9 means that for species within one standard deviation of the ‘average’, predicted detection times can vary from 22 to 134 min ha−1 when the ‘average’ species has a mean time to detection of 55 min ha−1. Further investigation of species traits and characteristics that influence detection may reduce the size of the species random effect and improve the fit, generality and predictive capacity of our model. For example, we demonstrated a potential, but uncertain, relationship between detectability and flower colour using coarse colour categories. Measuring colour by spectral reflectance (Chittka 1992; Thomas 2011) might help understand the relationship between colour and detectability.
While our results are specific to the community investigated, the trait-based time-to-detection modelling approach is widely applicable and may be used to develop models of detection time in other vegetation communities, as well as other taxa for which time-to-detection modelling is appropriate (e.g. birds: Alldredge et al. 2007). A compilation of multi-species models that relate detection time to species traits for a range of communities would be a valuable resource for ecologists and land managers, providing a basis for determining survey effort requirements where no species-level detection information exists. While not being able to perfectly predict individual species' detection probabilities, trait-based models of detectability should provide sensible, bounded estimates of detection rates to underpin species survey designs. We envisage that detection times can be modelled as a function of plant traits, observer and environment, with possible interactions between these parameters.
This research was supported by Australian Research Council (LP0454979 and DP0985600) and the Australian Centre for Excellence in Risk Analysis. GEG, MMC, SAB and BAW were supported by funding from the National Environment Research Program Environmental Decisions Hub and the ARC Centre of Excellence for Environmental Decisions. Peter Vesk and Joslin Moore, and two external reviewers provided valued feedback during preparation of the manuscript. Monique Hallett helped compile species' trait information.