An Approach to Estimate Probability of Presence and Richness of Fish Species

—Absence of a species when it is not observed from a given area is ensured only when the probability of observation, when present, is 1. This condition is rarely satisfied in surveys of animals in natural environments, particularly with elusive targets such as fish. Detectability (probability of species encounter) is a function of probability of individual capture, which varies widely with sampling method, fish size, physical habitat, and number of individuals present in a given area. An empirical Bayesian approach was developed for estimating probability of presence for zero-catch samples, in which the number of individuals present for a species is predicted from independent samples and used as an empirical prior. The model was illustrated for 16 species of fish sampled in 121 blocked-off stream reaches in which samples were collected using one of five primary gear methods; treatment with an ichthyocide followed. All species present were caught by the primary gear in only 17 (14%) of the samples. Of the empirical Bayesian predictions of presence or absence from zero-catch samples, 69% were correct. Of these zero-catch samples, 20% of samples in which a species was present and 93% of samples in which a species was absent were correctly predicted. The mean species richness was 10.3, compared with 7.4 for species richness from catch data of (mean bias of 227.4%). The model predicted a mean of 9.6 species (mean bias of 23.3%). Sampling design and subsequent analysis should account for catchability and fish densities (predicted as functions of physical habitat variables) and area sampled in order to reliably estimate probability of presence by species and, subsequently, species richness. Analyses of the presence and absence of species individually and collectively (e.g., species richness) are increasingly being used by fishery biologists to examine the influence of natural and anthropogenic factors on fish distribution and community structure (e.g., Tonn and Magnuson 1982; Matthews and Robinson 1988; Kruse et al. 1997; Sekine et al. 1997; Dunham and Rieman 1999) and for developing biodiversity conservation strategies (Burley 1988; Lee et al. 1997). Estimates of species presence and species richness are usually only based on catch, but are assumed or implied to be representative of the identity and numbers of species actually present in the sampled area. Unfortunately, complete observation or capture of all species is frequently impossible for mobile, aquatic organisms such as fish (Zalewski and Cowx 1990; Dolloff et al. 1996). Consequently, species presence and species richness estimates from samples underestimate true values to varying degrees. * Corresponding author: [email protected] Received May 8, 2000; accepted January 23, 2001 Approaches to minimize the influence of incomplete observation or capture on estimates of species presence and fish species richness can be roughly categorized as ‘‘sampling effort’’ and ‘‘inferential.’’ Sampling-effort approaches to detect the presence of individual species in a region of interest (sampling frame) rely on a predetermined number of samples and usually are based on an arbitrary threshold density and presumed statistical distribution (Bonar et al. 1997). Hence, inferences regarding species presence are restricted to the region of interest rather than at the site (sampling unit) level. For species richness estimates, the sampling-effort approach depends on cumulative catches indicating an asymptotic value of richness as the sampled area increases (Lyons 1992; Angermeier and Smogor 1995). Subsequently, a sampled area is predetermined for each sample (usually a streamreach length that is a constant multiple of its mean width) in which the catch is estimated to be a fixed proportion of the asymptotic value. The sampling-effort approach therefore attempts to optimize the individual sample procedure 621 ESTIMATING FISH SPECIES AND PRESENCE rather than the sampling design covering the region of interest. In contrast, inferential approaches explicitly account for imperfect detectability and can be used with existing data that are consistent with an overall design. Although there are currently no inferential approaches for individual species presence, a variety of species richness estimators have been developed to take into account species that may have been missed during sampling (Sugihara 1980; Smith and Belle 1984; Palmer 1990; Bunge and Fitzpatrick 1993; Solow 1994). These estimators assume that individuals are encountered at random and that probability of detection does not differ among individuals or species (however, see jackknife approach of Burnham and Overton 1979; Boulinier et al. 1998). However, detectability (the probability of detecting a species), is a function of the number of vulnerable individuals in a given area and the probability of individual capture (i.e., catchability or sampling efficiency), both of which may be influenced by habitat features. Furthermore, differences in catchability due to method (e.g., Figure 1), species, and individual size can also strongly affect detectability. Failure to account for differences in detectability can introduce different biases into estimates of species presence when catchability is strongly influenced by changes in habitat type and scale and the types of species present (Bayley and Dowling 1993). Therefore, a model predicting probability of presence that specifically accounts for empirically derived abundance and catchability estimates of each species is a more desirable approach to estimating species richness and would also provide useful information on distributions of individual species. Here we describe one such approach. We developed a model that predicts probability of presence by species. Using several sampling methods and a gear-efficiency calibration method, we derived empirical relationships predicting abundance and catchability of 16 fish species in warmwater streams of the midwestern United States. This information was then incorporated in a Bayesian model to estimate probability of species presence for each sample in which a species was not collected (henceforth: ‘‘zero-catch sample’’). All probabilities of species presence, including those caught, were then used to estimate species richness by sample. We validated the accuracy of model predictions by comparing them with presence determined by a combination of several gear passes and subsequent rotenone treatment.