Evaluation of the Petersen: Lincoln Estimator for a White-Tailed Deer Population

We tested the accuracy of the Petersen-Lincoln estimate on the enclosed white-tailed deer (Odocoileus virginianus) population of the George Reserve in Michigan, where the approximate size and composition of the population was known. Up to 68% of the population and 80% of the adult females were marked individually during the study. Recapture was based on observation of marked animals in the field. Petersen-Lincoln estimates were obtained for 32 consecutive months, from September 1968 through April 1971. Because births and deaths were known, and the enclosing fence prevented ingress and egress, the Bailey (1952) model for a closed population was applied. Petersen-Lincoln estimates by month were frequently inaccurate and were skewed toward overestimation. Eighty percent of the females were marked but estimates of females were inaccurate. There was no relationship between standard error of the estimate and accuracy. Increasing the percent of the population marked did not improve accuracy. The number of marked animals observed was an important variable for sample sizes 10. Sex and age classes were not captured or observed in proportion to their presence in the population. Age, spatial location of home range, and habitat all contributed to observability bias of females. J. WILDL. MANAGE. 52(3):534-544 Accurate estimates of wildlife populations are a major objective of most management programs. A number of theoretically sound estimation methods (Seber 1973, Caughley 1977, Davis and Winstead 1980) fail in practice because underlying assumptions cannot be met or the criteria for application are too restricted to be achievable under field conditions. Achievable techniques that produce reasonable results despite limitations need to be verified by empirical studies. Many ungulates are relatively observable and lend themselves to mark-resight methods (Rice and Harder 1977). Nevertheless, the method is seldom employed because of high cost and effort in capture for marking (Silvy et al. 1977) and the prevalent belief that the method is inaccurate. The best known evaluation of the Petersen-Lincoln estimate on ungulates was by Strandgaard (1967), who found that about 75% of a population of roe deer (Capreolus capreolus) needed to be marked before reasonable estimates were obtained. Recently Bartmann et al. (1987) reported that >45% of a mule deer (Odocoileus hemionus) population needed to be marked to obtain reliable population estimates. Mark-recapture methods are particularly sensitive to violation of the assumption that animals have equal catchability (heterogeneity) and observability (Burnham and Overton 1978, Otis et al. 1978, White et al. 1982). Catchability varies by season, weather, and sex and age class (Mattfeld et al. 1974, Garrott and White 1982, Bartmann et al. 1987). Unfortunately, tests on sample data for assumptions of equal catchability are usually insensitive to violation of the assumptions (Eberhardt 1969, Roff 1973). Comparison of mark-recapture estimates with alternative estimates (Dasmann and Taber 1955, Flyger 1959, Krebs 1966, Smith 1968) are better than no validation but do not rule out equal inaccuracy among several methods, or suggest which is more accurate when results differ. In this paper we report on an empirical test of the Petersen-Lincoln estimate as an estimator of white-tailed deer population size during 32 consecutive months on the Edwin S. George Reserve in southeastern Michigan. This 464-ha area This content downloaded on Wed, 19 Dec 2012 22:19:23 PM All use subject to JSTOR Terms and Conditions J. Wildl. Manage. 52(3):1988 ESTIMATES OF DEER * McCullough and Hirth 535 is enclosed by a deer-proof fence, and reconstructed population estimates were accurate (McCullough 1979, 1982b). Because immigration and emigration were eliminated by the deerproof fence, and the number of deer born and dying were known, many of the difficulties with mark-recapture methods were avoided; a simple statistical model for closed populations could be used. Furthermore, because the age and sex structure of the population was known from reconstruction, the contribution of biases in capturing and subsequent observation by sex and age to inaccuracy of population estimates could be evaluated; i.e., were animals captured and observed in proportion to their presence in the population? Data from the George Reserve deer population allow empirical evaluation of accuracy of the Petersen-Lincoln estimates, empirical variance of the Petersen-Lincoln estimate, influence of sample sizes on bias of estimators of model parameters, and influence of unequal catchability and observability on accuracy. Equal catchability could be tested by comparing the sex and age composition in the reconstructed population to that of the trapped sample. Equal observability could be tested in 2 ways: compare sex and age composition in the reconstructed population to that in the observed sample or compare marked to unmarked ratios in the reconstructed population by sex and age to that in the observed sample. We thank N. G. Hairston and F. C. Evans for their cooperation in making this research possible. B. E. Coblentz, J. Garry, E. Baker, P. G. Mickelson, H. M. Wilbur, and J. P. Clark helped with trapping and marking deer, and B. E. Coblentz helped with observation surveys. W. J. Zielinski and T. E. Kucera assisted in data analysis. M. C. Conner, D. C. Erman, M. L. Morrison, K. H. Pollock, S. J. Williamson, and several anonymous reviewers suggested improvements in the manuscript. The field work was done while we were at the School of Natural Resources, University of Michigan, Ann Arbor. The study was supported by the National Science Foundation grants GB-6171 and GB-12958 to DRM, and a Caulkins Foundation fellowship and National Science Foundation traineeship to DHH.