Estimating Harvest Rates of Bears from Sex Ratio Changes

Abstract

Using simulation modeling, we assessed the potential for estimating harvest rates for generalized bear (Ursus spp.) populations from changes in kill sample sex ratios (Paloheimo and Fraser 1981, Fraser 1984). Models underlying these techniques require assumptions that may be violated in the field. We found that both estimators were sensitive to violations of 4 critical assumptions, and that bias was generally most pronounced when applied to bear populations with low harvest rates, moderate differences in hunting vulnerability between sexes, and complex age structures. Additionally bears typically occur in low densities and yield small harvests, producing limited data from which harvest estimates are produced. Chance deviations from the expected patterns occurred with small (20-180) samples of harvested bears, producing substantial variability in year-to-year estimates. J. WILDL. MANAGE. 51(4):802-811 Data analyses based on mathematical models are now commonplace in wildlife studies. Models inevitably make simplifying assumptions that will be violated in nature to some degree. In addition, many models are deterministic, thereby providing no way to assess the variability of the technique when applied to field data. When possible, analytical methods are validated under controlled field conditions where the parameters of interest are known, quantifying bias and variability directly. Empirical assessments of this sort are now common in the literature; e.g., Robinette et al. 1974, Greenwood et al. 1985, Conner et al. 1986. However, some analyses are intended to help biologists estimate parameters in situations where controlled field conditions are difficult or impossible. In such cases a biologist must either apply a technique in which unmet assumptions produce unknown consequences, or dispense with the technique entirely. Many will proceed with the analysis, adding a note that assumptions may be violated. Managers and administrators often place credence on the results of such studies, ignoring accompanying qualifiers and disclaimers regarding assumption violations or insufficient sample size. Simulation modeling can identify some consequences of unmet model assumptions with realistic amounts of data. In this paper we use simulated grizzly (Ursus arctos) and black bear (U. americanus) populations to assess a harvest rate estimator developed by Fraser (1976, 1984). Obtaining precise population estimates for bears, especially grizzlies, is exceedingly difficult in practice, making field verification of harvest rates virtually impossible. The analysis, originally developed by Fraser (1976) for moose (Alces alces), considers a cohort that starts with equal numbers of males and females, in which males are consistently more vulnerable to harvest. As the cohort ages and th more vulnerable males are depleted by hunting, the standing age structure increasingly favors females. In more intensely harvested populations, females predominate more quickly. Fraser (1976, 1984) found that the reciprocal of the age at which females 1st predominate aproximated the composite harvest rate (T of M and F harvest rates) over a broad range of harvest rates and differential vulnerabilities. Consequently, harvest rate could be estimated by regressing percent males on age. Four assumptions underlie the model: (1) males and females are equally represented in the age class prior to the 1st age of harvest or, alternately, that sex ratios can be determined empirically; (2) no systematic changes occur with age in the relative male and female vulnerabilities to hunting; (3) both sexes experience equal non-harvest sources of mortality; and (4) harvest effort is constant during the period analyzed. Other than the last, these assumptions also underlie the more general model (Paloheimo and Fraser 1981) on which this analysis is based. These 4 assumptions may be violated in bear populations. Production of cub (age 0.5 year) grizzly bears in Yellowstone National Park was biased toward males (Craighead et al. 1974, Knight and Eberhardt 1985), violating Assumption 1. Conversely, sex ratios of preharvest age ' Present address: Alaska Fish and Wildlife Research Center, 101 12th Ave., Fairbanks, AK 99701.