William L. Kendall

ESTIMATING TEMPORARY EMIGRATION USING CAPTURE–RECAPTURE DATA WITH POLLOCK’S ROBUST DESIGN

Statistical inference for capture-recapture studies of open animal populations typically relies on the assumption that all emigration from the studied population is per- manent. However, there are many instances in which this assumption is unlikely to be met. We define two general models for the process of temporary emigration: completely random and Markovian. We then consider effects of these two types of temporary emigration on Jolly-Seber estimators and on estimators arising from the full-likelihood approach to robust design data. Capture-recapture data arising from Pollocks robust design provide the basis for ob- taining unbiased estimates of demographic parameters in the presence of temporary emi- gration, and for estimating the probability of temporary emigration. We present a likelihood- based approach to dealing with temporary emigration that permits estimation under different models of temporary emigration and yields tests for completely random and Markovian emigration. In addition, we use the relationship between capture probability estimates based on closed and open models under completely random temporary emigration to derive three ad hoc estimators for the probability of temporary emigration. Two of these should be especially useful in situations where capture probabilities are heterogeneous among indi- vidual animals. Ad hoc and full-likelihood estimators are illustrated for small-mammal capture-recapture data sets. We believe that these models and estimators will be useful for testing hypotheses about the process of temporary emigration, for estimating demographic parameters in the presence of temporary emigration, and for estimating probabilities of temporary emigration. These latter estimates are frequently of ecological interest as indicators of animal movement and, in some sampling situations, as direct estimates of breeding probabilities and proportions.

ROBUSTNESS OF CLOSED CAPTURE–RECAPTURE METHODS TO VIOLATIONS OF THE CLOSURE ASSUMPTION

Closed-population capture-recapture methods have been used extensively in animal ecology, both by themselves and within the context of Pollocks robust design and multistate models, to estimate various parameters of population and community dynamics. The defining assumption of geographic and demographic closure (i.e., no births, deaths, immigration, or emigration) for the duration of sampling is restrictive and is likely to be violated in many field situations. I evaluated several types of violations of the closure assumption and found that completely random movement in and out of a study area does not introduce bias to estimators from closed-population methods, although it decreases precision. In addition, if capture probabilities vary only with time, the closed-population Lincoln-Petersen estimator is unbiased for the size of the superpopulation when there are only births/immigration or only deaths/emigration. However, for other cases of nonrandom movement, closed-population estimators were biased when movement was Markovian (de- pendent on the presence/absence of the animal in the previous time period), when an animal was allowed one entry to and one exit from the study area, or when there was trap response or heterogeneity among animals in capture probability. In addition, the probability that an animal is present and available for capture (e.g., breeding propensity) can be estimated using Pollocks robust design only when movement occurs at a broader temporal scale than that of sampling.

Making Great Leaps Forward: Accounting for Detectability in Herpetological Field Studies

Abstract Detecting individuals of amphibian and reptile species can be a daunting task. Detection can be hindered by various factors such as cryptic behavior, color patterns, or observer experience. These factors complicate the estimation of state variables of interest (e.g., abundance, occupancy, species richness) as well as the vital rates that induce changes in these state variables (e.g., survival probabilities for abundance; extinction probabilities for occupancy). Although ad hoc methods (e.g., counts uncorrected for detection, return rates) typically perform poorly in the face of no detection, they continue to be used extensively in various fields, including herpetology. However, formal approaches that estimate and account for the probability of detection, such as capture-mark-recapture (CMR) methods and distance sampling, are available. In this paper, we present classical approaches and recent advances in methods accounting for detectability that are particularly pertinent for herpetological data sets. Through examples, we illustrate the use of several methods, discuss their performance compared to that of ad hoc methods, and we suggest available software to perform these analyses. The methods we discuss control for imperfect detection and reduce bias in estimates of demographic parameters such as population size, survival, or, at other levels of biological organization, species occurrence. Among these methods, recently developed approaches that no longer require marked or resighted individuals should be particularly of interest to field herpetologists. We hope that our effort will encourage practitioners to implement some of the estimation methods presented herein instead of relying on ad hoc methods that make more limiting assumptions.

The use of multi-state capture-recapture models to address questions in evolutionary ecology

Multi-state capture-recapture models can be used to estimate survival rates in populations that are stratified by location or by state variables associated with individual animals. In populations stratified by location, movement probabilities can be estimated and used to test hypotheses relevant to population genetics and evolutionary ecology. When the interest is in state variables, these models permit estimation and testing of hypotheses about state-specific survival probabilities. If the state variable of interest is reproductive activity or success, then the multi-state modeling approach can be used to test hypotheses about life history trade-offs and a possible cost of reproduction.

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.

On the use of secondary capture-recapture samples to estimate temporary emigration and breeding proportions

The use of the Cormack-Jolly-Seber model under a standard sampling scheme of one sample per time period, when the Jolly-Seber assumption that all emigration is permanent does not hold, leads to the confounding of temporary emigration probabilities with capture probabilities. This biases the estimates of capture probability when temporary emigration is a completely random process, and both capture and survival probabilities when there is a temporary trap response in temporary emigration, or it is Markovian. The use of secondary capture samples over a shorter interval within each period, during which the population is assumed to be closed (Pollocks robust design), provides a second source of information on capture probabilities. This solves the confounding problem, and thus temporary emigration probabilities can be estimated. This process can be accomplished in an ad hoc fashion for completely random temporary emigration and to some extent in the temporary trap response case, but modelling the complete sam...

ESTIMATING STATE‐TRANSITION PROBABILITIES FOR UNOBSERVABLE STATES USING CAPTURE–RECAPTURE/RESIGHTING DATA

Temporary emigration was identified some time ago as causing potential problems in capture–recapture studies, and in the last five years approaches have been developed for dealing with special cases of this general problem. Temporary emigration can be viewed more generally as involving transitions to and from an unobservable state, and frequently the state itself is one of biological interest (e.g., “nonbreeder”). Development of models that permit estimation of relevant parameters in the presence of an unobservable state requires either extra information (e.g., as supplied by Pollocks robust design) or the following classes of model constraints: reducing the order of Markovian transition probabilities, imposing a degree of determinism on transition probabilities, removing state specificity of survival probabilities, and imposing temporal constancy of parameters. The objective of the work described in this paper is to investigate estimability of model parameters under a variety of models that include an u...

Structured decision making as a conceptual framework to identify thresholds for conservation and management

Thresholds and their relevance to conservation have become a major topic of discussion in the ecological literature. Unfortunately, in many cases the lack of a clear conceptual framework for thinking about thresholds may have led to confusion in attempts to apply the concept of thresholds to conservation decisions. Here, we advocate a framework for thinking about thresholds in terms of a structured decision making process. The purpose of this framework is to promote a logical and transparent process for making informed decisions for conservation. Specification of such a framework leads naturally to consideration of definitions and roles of different kinds of thresholds in the process. We distinguish among three categories of thresholds. Ecological thresholds are values of system state variables at which small changes bring about substantial changes in system dynamics. Utility thresholds are components of management objectives (determined by human values) and are values of state or performance variables at which small changes yield substantial changes in the value of the management outcome. Decision thresholds are values of system state variables at which small changes prompt changes in management actions in order to reach specified management objectives. The approach that we present focuses directly on the objectives of management, with an aim to providing decisions that are optimal with respect to those objectives. This approach clearly distinguishes the components of the decision process that are inherently subjective (management objectives, potential management actions) from those that are more objective (system models, estimates of system state). Optimization based on these components then leads to decision matrices specifying optimal actions to be taken at various values of system state variables. Values of state variables separating different actions in such matrices are viewed as decision thresholds. Utility thresholds are included in the objectives component, and ecological thresholds may be embedded in models projecting consequences of management actions. Decision thresholds are determined by the above-listed components of a structured decision process. These components may themselves vary over time, inducing variation in the decision thresholds inherited from them. These dynamic decision thresholds can then be determined using adaptive management. We provide numerical examples (that are based on patch occupancy models) of structured decision processes that include all three kinds of thresholds.

First-time observer effects in the North American Breeding Bird Survey

ABsmAcr.-Currently the operational analysis of Breeding Bird Survey (BBS) data by the National Biological Service accounts for observer differences in estimating the trend for each route, but within-observer differences are not modeled. We tested for the existence of a form of within-observer differences in skill level, namely a change in ability to count birds of a given species after an observers first year on a given route. An increase in ability could positively bias the trend estimate. Removal of an observers first year of observation on each route for the period 1966 to 1991 resulted in lower average unweighted trend estimates for 415 of 459 species (90%). These reductions were statistically significant for 213 species (46%). The average reduction in trend was 1.8% change per year (SD = 5.4%). In route-regression analysis, route data are weighted by a measure of precision. Removing first-year observer counts reduced the weighted trend estimate for 275 of 416 species (66%), but differences generally were small. Received 13 July 1995, accepted 11 March 1996.

Monitoring in the Context of Structured Decision-Making and Adaptive Management

Abstract In a natural resource management setting, monitoring is a crucial component of an informed process for making decisions, and monitoring design should be driven by the decision context and associated uncertainties. Monitoring itself can play ≥3 roles. First, it is important for state-dependent decision-making, as when managers need to know the system state before deciding on the appropriate course of action during the ensuing management cycle. Second, monitoring is critical for evaluating the effectiveness of management actions relative to objectives. Third, in an adaptive management setting, monitoring provides the feedback loop for learning about the system; learning is sought not for its own sake but primarily to better achieve management objectives. In this case, monitoring should be designed to reduce the critical uncertainties in models of the managed system. The United States Geological Survey and United States Fish and Wildlife Service are conducting a large-scale management experiment on 23 National Wildlife Refuges across the Northeast and Midwest Regions. The primary management objective is to provide habitat for migratory waterbirds, particularly during migration, using water-level manipulations in managed wetlands. Key uncertainties are related to the potential trade-offs created by management for a specific waterbird guild (e.g., migratory shorebirds) and the response of waterbirds, plant communities, and invertebrates to specific experimental hydroperiods. We reviewed the monitoring program associated with this study, and the ways that specific observations fill ≥1 of the roles identified above. We used observations from our monitoring to improve state-dependent decisions to control undesired plants, to evaluate management performance relative to shallow-water habitat objectives, and to evaluate potential trade-offs between waterfowl and shorebird habitat management. With limited staff and budgets, management agencies need efficient monitoring programs that are used for decision-making, not comprehensive studies that elucidate all manner of ecological relationships.