Darryl I. MacKenzie

ESTIMATING SITE OCCUPANCY RATES WHEN DETECTION PROBABILITIES ARE LESS THAN ONE

Nondetection of a species at a site does not imply that the species is absent unless the probability of detection is 1. We propose a model and likelihood-based method for estimating site occupancy rates when detection probabilities are 0.3). We estimated site occupancy rates for two anuran species at 32 wetland sites in Maryland, USA, from data collected during 2000 as part of an amphibian monitoring program, Frogwatch USA. Site occupancy rates were estimated as 0.49 for American toads (Bufo americanus), a 44% increase over the proportion of sites at which they were actually observed, and as 0.85 for spring peepers (Pseudacris crucifer), slightly above the observed proportion of 0.83.

ESTIMATING SITE OCCUPANCY, COLONIZATION, AND LOCAL EXTINCTION WHEN A SPECIES IS DETECTED IMPERFECTLY

Few species are likely to be so evident that they will always be detected when present. Failing to allow for the possibility that a target species was present, but undetected, at a site will lead to biased estimates of site occupancy, colonization, and local extinction probabilities. These population vital rates are often of interest in long-term monitoring programs and metapopulation studies. We present a model that enables direct estimation of these parameters when the probability of detecting the species is less than 1. The model does not require any assumptions of process stationarity, as do some previous methods, but does require detection/nondetection data to be collected in a manner similar to Pollocks robust design as used in mark-recapture studies. Via simulation, we show that the model provides good estimates of parameters for most scenarios considered. We illustrate the method with data from monitoring programs of Northern Spotted Owls ( Strix occiden- talis caurina) in northern California and tiger salamanders (Ambystoma tigrinum) in Min- nesota, USA.

Assessing the fit of site-occupancy models

Few species are likely to be so evident that they will always be detected at a site when present. Recently a model has been developed that enables estimation of the proportion of area occupied, when the target species is not detected with certainty. Here we apply this modeling approach to data collected on terrestrial salamanders in the Plethodon glutinosus complex in the Great Smoky Mountains National Park, USA, and wish to address the question “how accurately does the fitted model represent the data?” The goodness-of-fit of the model needs to be assessed in order to make accurate inferences. This article presents a method where a simple Pearson chi-square statistic is calculated and a parametric bootstrap procedure is used to determine whether the observed statistic is unusually large. We found evidence that the most global model considered provides a poor fit to the data, hence estimated an overdispersion factor to adjust model selection procedures and inflate standard errors. Two hypothetical datasets with known assumption violations are also analyzed, illustrating that the method may be used to guide researchers to making appropriate inferences. The results of a simulation study are presented to provide a broader view of the methods properties.

Improving inferences in population studies of rare species that are detected imperfectly

For the vast majority of cases, it is highly unlikely that all the individuals of a population will be encountered during a study. Furthermore, it is unlikely that a constant fraction of the population is encountered over times, locations, or species to be compared. Hence, simple counts usually will not be good indices of population size. We recommend that detection probabilities (the probability of including an individual in a count) be estimated and incorporated into inference procedures. However, most techniques for estimating detection probability require moderate sample sizes, which may not be achievable when studying rare species. In order to improve the reliability of inferences from studies of rare species, we suggest two general approaches that researchers may wish to consider that incorporate the concept of imperfect detectability: (1) borrowing information about detectability or the other quantities of interest from other times, places, or species; and (2) using state variables other than abundance (e.g., species richness and occupancy). We illustrate these suggestions with examples and discuss the relative benefits and drawbacks of each approach.

Modeling the Probability of Resource Use: The Effect of, and Dealing with, Detecting a Species Imperfectly

Abstract Resource-selection probability functions and occupancy models are powerful methods of identifying areas within a landscape that are highly used by a species. One common design/analysis method for estimation of a resource-selection probability function is to classify a sample of units as used or unused and estimate the probability of use as a function of independent variables using, for example, logistic regression. This method requires that resource units are correctly classified as unused (i.e., the species is never undetected in a used unit), or that the probability of misclassification is the same for all units. In this paper, I explore these issues, illustrating how misclassifying units as unused may lead to incorrect conclusions about resource use. I also show how recently developed occupancy models can be utilized within the resource-selection context to improve conclusions by explicitly accounting for detection probability. These models require that multiple surveys be conducted at each of a sample of resource units within a relatively short timeframe, but given the growing evidence from simulation studies and field data, I recommend that such procedures should be incorporated into studies of resource use.

HOW SHOULD DETECTION PROBABILITY BE INCORPORATED INTO ESTIMATES OF RELATIVE ABUNDANCE

Determination of the relative abundance of two populations, separated by time or space, is of interest in many ecological situations. We focus on two estimators of relative abundance, which assume that the probability that an individual is detected at least once in the survey is either equal or unequal for the two populations. We present three methods for incorporating the collected information into our inference. The first method, proposed previously, is a traditional hypothesis test for evidence that detection probabilities are unequal. However, we feel that, a priori, it is more likely that detection probabilities are actually different; hence, the burden of proof should be shifted, requiring evidence that detection probabilities are practically equivalent. The second method we present, equivalence testing, is one approach to doing so. Third, we suggest that model averaging could be used by combining the two estimators according to derived model weights. These differing approaches are applied to a mark–recapture experiment on Nuttalls cottontail rabbit (Sylvilagus nuttallii) conducted in central Oregon during 1974 and 1975, which has been previously analyzed by other authors.

Modeling species occurrence dynamics with multiple states and imperfect detection

Recent extensions of occupancy modeling have focused not only on the distribution of species over space, but also on additional state variables (e.g., reproducing or not, with or without disease organisms, relative abundance categories) that provide extra information about occupied sites. These biologist-driven extensions are characterized by ambiguity in both species presence and correct state classification, caused by imperfect detection. We first show the relationships between independently published approaches to the modeling of multistate occupancy. We then extend the pattern-based modeling to the case of sampling over multiple seasons or years in order to estimate state transition probabilities associated with system dynamics. The methodology and its potential for addressing relevant ecological questions are demonstrated using both maximum likelihood (occupancy and successful reproduction dynamics of California Spotted Owl) and Markov chain Monte Carlo estimation approaches (changes in relative abundance of green frogs in Maryland). Just as multistate capture-recapture modeling has revolutionized the study of individual marked animals, we believe that multistate occupancy modeling will dramatically increase our ability to address interesting questions about ecological processes underlying population-level dynamics.

SAMPLING DESIGN TRADE‐OFFS IN OCCUPANCY STUDIES WITH IMPERFECT DETECTION: EXAMPLES AND SOFTWARE

Researchers have used occupancy, or probability of occupancy, as a response or state variable in a variety of studies (e.g., habitat modeling), and occupancy is increasingly favored by numerous state, federal, and international agencies engaged in monitoring programs. Recent advances in estimation methods have emphasized that reliable inferences can be made from these types of studies if detection and occupancy probabilities are simultaneously estimated. The need for temporal replication at sampled sites to estimate detection probability creates a trade-off between spatial replication (number of sample sites distributed within the area of interest/inference) and temporal replication (number of repeated surveys at each site). Here, we discuss a suite of questions commonly encountered during the design phase of occupancy studies, and we describe software (program GENPRES) developed to allow investigators to easily explore design trade-offs focused on particularities of their study system and sampling limitations. We illustrate the utility of program GENPRES using an amphibian example from Greater Yellowstone National Park, U.S.A.

Tigers on trails: occupancy modeling for cluster sampling.

Occupancy modeling focuses on inference about the distribution of organisms over space, using temporal or spatial replication to allow inference about the detection process. Inference based on spatial replication strictly requires that replicates be selected randomly and with replacement, but the importance of these design requirements is not well understood. This paper focuses on an increasingly popular sampling design based on spatial replicates that are not selected randomly and that are expected to exhibit Markovian dependence. We develop two new occupancy models for data collected under this sort of design, one based on an underlying Markov model for spatial dependence and the other based on a trap response model with Markovian detections. We then simulated data under the model for Markovian spatial dependence and fit the data to standard occupancy models and to the two new models. Bias of occupancy estimates was substantial for the standard models, smaller for the new trap response model, and negligible for the new spatial process model. We also fit these models to data from a large-scale tiger occupancy survey recently conducted in Karnataka State, southwestern India. In addition to providing evidence of a positive relationship between tiger occupancy and habitat, model selection statistics and estimates strongly supported the use of the model with Markovian spatial dependence. This new model provides another tool for the decomposition of the detection process, which is sometimes needed for proper estimation and which may also permit interesting biological inferences. In addition to designs employing spatial replication, we note the likely existence of temporal Markovian dependence in many designs using temporal replication. The models developed here will be useful either directly, or with minor extensions, for these designs as well. We believe that these new models represent important additions to the suite of modeling tools now available for occupancy estimation in conservation monitoring. More generally, this work represents a contribution to the topic of cluster sampling for situations in which there is a need for specific modeling (e.g., reflecting dependence) for the distribution of the variable(s) of interest among subunits.

OCCUPANCY ESTIMATION AND MODELING WITH MULTIPLE STATES AND STATE UNCERTAINTY

The distribution of a species over space is of central interest in ecology, but species occurrence does not provide all of the information needed to characterize either the well-being of a population or the suitability of occupied habitat. Recent methodological development has focused on drawing inferences about species occurrence in the face of imperfect detection. Here we extend those methods by characterizing occupied locations by some additional state variable (e.g., as producing young or not). Our modeling approach deals with both detection probabilities <1 and uncertainty in state classification. We then use the approach with occupancy and reproductive rate data from California Spotted Owls (Strix occidentalis occidentalis) collected in the central Sierra Nevada during the breeding season of 2004 to illustrate the utility of the modeling approach. Estimates of owl reproductive rate were larger than naïve estimates, indicating the importance of appropriately accounting for uncertainty in detection and state classification.