Northern Prairie Wildlife Research Center
We report results for gray wolves (Canis lupus), coyotes (C. latrans), red foxes (Vulpes vulpes), skunks (mostly Mephitis mephitis, but also Spilogale putorius), raccoons (Procyon lotor), and bobcats (Felis rufus). These species have been monitored elsewhere with scent stations and embody diverse physical and behavioral adaptations that may affect the usefulness of scent-station surveys. Where possible, we present P-values to enable readers to judge statistical significance for themselves; where unavoidable, we infer significance from P ≤ 0.05. Many biologists, however, consider the consequences of Type II errors more serious than those of Type I errors when testing for population trend and are thus willing to accept Type I error rates much greater than P = 0.05 (up to P = 0.20 for scent-station data; Zielinski and Stauffer 1996).
We analyzed 2 indices: (1) the proportion of stations (station index), and (2) the proportion of lines (line index) within a biogeographic section (section; Fig. 1) at which a species was detected. For some goodness-of-fit tests, data were grouped by county within section (when section boundaries subdivided counties, each portion was treated separately). When calculating annual means for the entire state, we corrected for nonrandom sampling by weighting results for each section in proportion to its area. Because of the limited geographic extent and small sample size of the South Superior section, results were combined with those of the West Superior section. Visitation rates were estimated 2 ways: (1) from the entire dataset, and (2) with the geographic extent of surveys restricted to sections where species were detected at least once.
For each species, we used linear regression to compare the rank order of index values with the temporal ordering of surveys and thereby determine whether index values exhibited sustained increasing or decreasing trends. We included section, year, and their interaction in regression models and tested statewide trends when interactions were nonsignificant. We tested trends separately for each section when interactions were detected. We also plotted indices against time to check for evidence of non-monotonic trends with management significance.
The binomial distribution is sometimes regarded as a statistical model for the number of scent stations visited (Sumner and Hill 1980, Diefenbach et al. 1994, Smith et al. 1994). For each species and county, we computed expected numbers of lines receiving i = [0,...,10] visits from a binomial distribution and the average visitation rate. Summing across counties gave expected values of a multinomial distribution with 11 cells, with the frequency in cell i corresponding to the numbers of lines receiving i = [0,...,10] visits. We used chi-square goodness-of-fit tests to compare field data to expected values. Significant differences implied local spatial heterogeneity of visitation rates or spatial correlations among visits, and hence inadequacy of the binomial distribution as a model for visitation for the species in question. This method was also used to compare observed numbers of lines visited per county with expected values computed from section-specific visitation rates. We present results obtained after combining number-of-visits categories until expected values exceeded 5, which assured chi-square distributions for test statistics (Sprent 1989), but combining categories did not affect conclusions. To safeguard against Type II errors, we used Fisher's inverse chi-square test (Hedges and Olkin 1985) to determine whether P-values were uniformly distributed when the null hypothesis could not be rejected for any species.
We used indicator variograms (Rossi et al. 1992) to examine spatial correlations among visits to scent stations. We excluded data collected during 1992-93 from this analysis because they were provided in a format that did not distinguish the position of stations within lines. We also excluded lines receiving <2 visits in a year because they did not provide information about spatial relations among multiple visits. We used remaining data to plot average squared differences between results (1 = visit, 0 = no visit) for stations within lines and years against 480-m separation intervals ranging from 480 to 4,320 m. Because average squared differences are larger when data are independent than when they are positively spatially correlated, trends in variograms provided visual evidence if correlations were related to the distance between stations (Rossi et al. 1992).
We simulated data similar to those Smith et al. (1994) would have obtained if their population estimates were correct, distributional assumptions of their logistic analyses were met, and raccoons visited scent stations at a rate linearly related to population size. Although Smith et al. (1994) included data from 20 surveys in their analyses, we simulated only 14 surveys. We omitted 6 consecutive surveys conducted during winter, when raccoons never visited scent stations. We set Sj to correspond to the number of stations and Nj to correspond to the estimated population size for survey j. The binomial probability, PNj, was linearly related to Nj, by the equation
and where xi was the number of visits, Si was the number of stations, and i was the estimated size of the raccoon population for the ith survey. Thus, was the average number of visits observed per raccoon per station. Finally, we used Sj, PNj to generate datasets of 14 binomial [BIN(Sj, PNj)] random variables, . Simulated data did not vary seasonally, so we did not incorporate seasonal effects in our model, but otherwise used the same methods of analysis as Smith et al. (1994). Distributions of Spearman's rank correlations and of P-values for logistic analyses were estimated by analyzing 10,000 simulated datasets generated by the RANBIN function of SAS (SAS Institute 1988).
The second experiment we reevaluated was conducted by Diefenbach et al. (1994), who introduced bobcats onto Cumberland Island, Georgia, during September of 1988. Diefenbach et al. (1994) conducted 14 scent-station surveys as the population expanded from periodic introductions of additional bobcats and, after the first year, from reproduction as well. They used linear regression to relate inverse visitation rates (1/rate) to estimates of bobcat abundance after deleting 1 survey considered an outlier. We used the same data and multiple regression to determine whether the relation between inverse visitation rates and estimated abundance (Diefenbach et al. 1994) could be explained as plausibly by confounding factors that differed between 2 time periods (before 28 Feb and after 11 Sep, 1989). During the first time period, the bobcat population included only recently introduced individuals. During the second time period, the bobcat population included adults from the original introduction and their progeny, in addition to recently introduced animals. We compared models with respect to explained variation and adherence to assumptions of multiple regression.