Species occurrence is of central importance in ecology and its applications. The collection of sites where a species occurs represents the distribution of that species (Guisan & Thuiller 2005), while the collection of species occurring at a site represents species richness, the most widely used metric of biodiversity (Gotelli & Colwell 2001). However, occurrence is typically not observed perfectly; instead, there are two possible errors that can be made when dealing with species distributions: false-negative errors, also called errors of omission or nondetection, and false-positive errors, also called errors of commission or misclassification (Miller et al. 2011). Given the widespread nature of detection errors (Yoccoz, Nichols & Boulinier 2001), species occurrence is at least partly a latent state that needs to be estimated for unbiased inference about species distributions and species richness (Royle & Dorazio 2008). Treating observed occurrence and species distributions as the true occurrence and distribution, that is failing to make amendments for imperfect detection, may lead to problems in species distribution studies (Kéry 2011), habitat models (Gu & Swihart 2004) and biodiversity management (Chades et al. 2008).
Over the last decades, a plethora of statistical models has been developed to correct for imperfect detection in population analyses for inference about distribution, abundance and vital rates (Seber 1982; Buckland et al. 2001; Borchers, Buckland & Zucchini 2002; Williams, Nichols & Conroy 2002; Royle & Dorazio 2008; King et al. 2010; Kéry & Schaub 2012). However, with few exceptions, use of these models and the associated sampling designs has been restricted to studies in animal ecology. Plant ecologists have been slow to acknowledge the possible need for such methods in their research, presumably because they know that plants do not run away (Harper 1977).
Only a handful of plant distribution studies have formally dealt with the problem of imperfect detection. For instance, in several vegetation surveys, 20–30% species were overlooked (Nilsson & Nilsson 1985; Scott & Hallam 2002; Archaux et al. 2006). Trained botanists recorded more species in plant inventories than untrained ones (Ahrends et al. 2011). The overlooking of some species was recognized as a methodological problem when estimating turnover of plants on islands (Nilsson & Nilsson 1982, 1983). Nevertheless, only very few studies have formally estimated the magnitude of detection errors in plants using adequate protocols and analytical methods (e.g. Alexander, Slade & Kettle 1997; Shefferson et al. 2001; Kéry & Gregg 2003; Slade, Alexander & Kettle 2003; Kéry et al. 2006; Chen et al. 2009). In all of these, detection probability was found to be less than one and sometimes depended on covariates such as plant size or life state.
Nevertheless, these studies give an incomplete description of imperfect detection of plants because species were not selected randomly and survey methods between studies are not comparable. However, they do emphasize a need to better understand the magnitude and the patterns of imperfect detection in space and time and its influence on plant distribution studies (Kéry, Gardner & Monnerat 2010a; Kéry 2011).
In this study, we estimate detection probability and study patterns in detection because of life-form (LF), space and time for a large random sample from an entire national flora. We conducted two analyses, one for a random sample to obtain the best possible estimate of average detection probability in the entire flora and another for a stratified random sample restricted to more common species (operationally defined as those with at least 18 detections) to obtain estimates of the magnitude and of the patterns of detection and occurrence as related to biotic and abiotic covariates. We used data from the Swiss Biodiversity Monitoring (BDM; Weber, Hintermann & Zangger 2004), where detection/nondetection data are collected twice in each year at each sample site. This within-season replication in the sampling protocol enables site-occupancy models (MacKenzie et al. 2002; Tyre et al. 2003) to be applied to jointly estimate occurrence and detection probability. We applied a recently developed multispecies site-occupancy model (Dorazio & Royle 2005; Russell et al. 2009; Zipkin, Dewan & Royle 2009), which combines data from multiple species in a hierarchical model to estimate mean and variance of hyperdistributions describing the variability among species. Treating the effects of individual species as random is consistent with the intended scope of our analyses, namely the entire Swiss flora. Thus, the two samples of 100 species actually studied were simply regarded as replicates of the larger, statistical population of species that could have been selected in our study, that is all Swiss vascular plant species except for the very rare ones.
Our study had three aims. First, we assessed the magnitude of imperfect detection caused by false-negative errors in field survey for plants in a well-designed and well-conducted national BDM program. Secondly, we explored the differences in detection errors among species and LFs. And thirdly, we aimed to identify factors affecting detection probabilities over space and time.