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1 December 2005 Mark-resight superpopulation estimation of a wintering elk Cervus elaphus canadensis herd
William R. Gould, Samuel T. Smallidge, Bruce C. Thompson
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Abstract

We executed four mark-resight helicopter surveys during the winter months January–February for each of the three years 1999–2001 at 7–10 day intervals to estimate population size of a wintering elk Cervus elaphus canadensis herd in northern New Mexico. We counted numbers of radio-collared and uncollared elk on a simple random sample of quadrats from the study area. Because we were unable to survey the entire study area, we adopted a superpopulation approach to estimating population size, in which the total number of collared animals within and proximate to the entire study area was determined from an independent fixed-wing aircraft. The total number of collared animals available on the quadrats surveyed was also determined and facilitated detectability estimation. We executed superpopulation estimation via the joint hypergeometric estimator using the ratio of marked elk counted to the known number extant as an estimate of effective detectability. Superpopulation size estimates were approximately four times larger than previously suspected in the vicinity of the study area. Despite consistent survey methodology, actual detection rates varied within winter periods, indicating that multiple resight flights are important for improved estimator performance. Variable detectability also suggests that reliance on mere counts of observed individuals in our area may not accurately reflect abundance.

Mark-resight techniques have been used to estimate abundance for a wide variety of animal populations including mammals (Hein & Andelt 1995, McCullough et al. 2000, Focardi et al. 2002), birds (Collazo & Bonilla-Martinez 2001, Ganter & Madsen 2001), and fish (Young & Hayes 2001). In addition, population size estimates from mark-resight studies have been used in a comparative manner to assess the reliability of indices (Fuller et al. 2001, Young & Hayes 2001) and other estimation methods (Casagrande & Beissinger 1997, Bender & Spencer 1999, Fisher et al. 2000). Estimator developments in which individual animals must be identifiable (Minta & Mangel 1989, Arnason et al. 1991, Bowden & Kufeld 1995, Gardner & Mangel 1996), and Bayesian estimation approaches (Ananda 1997) have also received attention.

The Lincoln-Petersen estimator (Petersen 1896, Lincoln 1930) or Chapman's (1951) estimator, which is a less-biased version of the former, are typically used for estimating population size on the individual surveys. Rather than simply averaging individual estimates from multiple resighting events, Bartmann et al. (1987) concluded that the joint hypergeometric estimator (JHE) was more efficient. The JHE is found by maximizing (numerically) the likelihood,

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where N̂ is the estimated abundance, Mi is the number of marked individuals in the population on the ith occasion, ni is the number of sighted individuals (marked and unmarked) on the ith occasion and mi is the number of marked animals sighted during the ith occasion.

The JHE assumes that 1) the population is closed demographically and geographically, 2) all animals have equal, independent detection probabilities on a given survey occasion, 3) marks are not lost and all are reported, and 4) animals are sampled without replacement. Neal et al. (1993) estimated relative bias, precision and confidence interval coverage via simulation when the second assumption was violated. When sighting probabilities were not independent, bias for estimated population size was negligible, although confidence interval coverage was lowered. Heterogeneous sighting probabilities were more likely to bias population estimates and lower confidence interval coverage, but in general the bias was small and obviated the need for using the Minta & Mangel (1989) estimator that allows for unequal sighting probabilities.

In most capture-recapture studies, recapture events are conducted over the entire area of interest. Due to the large size of our study area (~1,750 km2), we were not able to resight animals over the entire study area. We randomly sampled the study area on which to conduct helicopter surveys. Skalski (1994) presented a framework for combining finite sampling theory and density estimation techniques for making statistical inference when the study area is sampled. Skalski's (1994) approach relied on combining population estimates from the individually sampled area units. Bowden et al. (2003) extended Skalski's work by developing estimators that allowed correlated quadrat-specific estimates, primarily motivated by a need to pool information across quadrats.

Our present study differs from these approaches in two ways. First, quadrat-specific abundance estimates for use in traditional finite sampling approaches (e.g. see Thompson 2002) were not feasible due to low numbers of marked animals within quadrats. Secondly, we adopted a ‘superpopulation’ approach (Kendall 1999) to abundance estimation via mark-resight techniques in which individuals were not individually identifiable in our resight surveys. The superpopulation refers to the group of animals that have a non-zero probability of being located and detected on the study area during the wintering survey periods. Thus, geographic closure of the wintering population was not assumed.

We present an example of superpopulation estimation for a Rocky Mountain elk Cervus elaphus canadensis herd in northern New Mexico. In previous years, aerial surveys of our study area had been conducted by the New Mexico Department of Game and Fish (NMDGF), but these surveys assumed 100% detectability in surveyed units (e.g. see Kufeld et al. 1980). The advantage of having known numbers of marked elk in the population is that we were able to estimate the effective detection probability, thus achieving less-biased abundance estimates than those based on unadjusted counts. Additionally, we consider model assumptions and evaluate the impact of assumption violations on our population estimates.

Study area

San Antonio Mountain (3,325 m a.s.l.) lies in north-central New Mexico approximately 30 km equidistant northwest