On the Use of Enumeration Estimators for Interspecific Comparisons, with Comments on a "Trappability" Estimator

Abstract

Recently, Adler et al. (1984) studied the population dynamics of the meadow jumping mouse, Zapus hudsonius, in Massachusetts. As is typical of contemporary capture-recapture studies on small mammals, they used enumeration estimates of population size and survival despite the known biases of these estimators (Jolly and Dickson, 1983; Nichols and Pollock, 1983). Adler et al. (1984:390) noted that of density and survival rate during the active season for Zapus hudsonius in our study population were considerably lower than those obtained by Nichols and Conley (1982). They also compared estimates of 7 demographic for 3 species trapped on their grids: Z. hudsonius, Peromyscus leucopus, and Microtus pennsylvanicus. They found substantial differences between estimates for Z. hudsonius and the other 2 species. For example, the parameter they termed overall survival (14-day rate) was estimated at 0.13 and 0.09 for Zapus males and females, respectively, and 0.73 and 0.78 for Microtus males and females (Adler et al., 1984:389). On our Michigan study area, W. Conley and I found very similar point estimates of weekly survival probability for these 2 species (0.84 for Zapus, 0.89 for Microtus; Nichols and Conley, 1982), and these estimates did not differ significantly. In this note I do not argue that the apparent interspecific differences reported by Adler et al. (1984) are nonexistent. It may well be that such differences did exist on their study area. Instead, I point out that enumeration estimates are especially inappropriate for such interspecific comparisons and that they cannot be used to draw reasonable inferences about the underlying parameters of interest. This inappropriateness results largely from the fact that enumeration estimators estimate complicated functions of survival and capture probabilities (Nichols and Pollock, 1983) and that different species are often likely to have different capture probabilities. The relevance of capture probability to this argument leads to a second point, which involves the inappropriateness of an estimator for trappability that appears in Adler et al. (1984) and throughout the small mammal literature. The expected value of the enumeration survival rate estimator for capture period i, includes the survival and capture probabilities for every capture period subsequent to i in the entire experiment (see Nichols and Pollock, 1983: eq. 6). Because of this dependence on capture probability, 2 studied populations with identical survival probabilities but different capture probabilities would be expected to yield different enumeration survival estimates. Numerical examples of this problem appear in Figs. 1D and 1E of Nichols and Pollock (1983). These 2 examples show enumeration survival estimates for a single population with constant true survival over 12 capture periods. The difference between the survival estimates for periods with high (0.7) and low (0.3) capture probabilities exemplifies the problem that exists with interspecific comparisons in which the species do not have equal capture probabilities. Even if true survival probabilities are equal, the species with the lower capture probabilities will have lower enumeration survival estimates. W. Conley and I found substantial differences in the Jolly-Seber capture probability estimates for Z. hudsonius and M. pennsylvanicus trapped at the same times on the same grid (Table 1). Estimates for Zapus were consistently lower than those for Microtus until mid-September. We speculated that the crimped oats bait may have been especially attractive during the period of rapid weight gain preceding hibernation, resulting in the high Zapus capture probabilities in September. In any case, these differences in capture probability would have caused problems if we had used enumeration estimates to compare these 2 species. Enumeration estimates of population size and survival rate would have been biased low for both species, but the absolute value of the relative bias would have been greater for Zapus because of the lower capture probabilities. Thus, even if survival rate was similar for the 2 species, as was the case in our study, the enumeration estimate would have been lower for Zapus. Five of the 7 parameter estimates used in the interspecific comparisons of Adler et al. (1984) are functions of capture probability. Any differences between estimates for the different species may then reflect either true differences in the parameter of interest or differences in capture probability. For 3 of these estimators, average density, overall survival, and transiency rate, the effects of differences in capture probability 590 Vol. 67, No. 3