Variability Of Indices Of Animal Abundance

A key influence on power to detect a given population trend is the variability of the population index used. Power to detect trends is inversely related to the magnitude of index variability and monitoring programs must be designed around the component of index variability that cannot be controlled (Ger-rodette 1987). In other words, sufficient numbers of plots must be monitored frequently enough to capture trends despite the inherent variability of the population index. Without pilot studies, however, researchers often have no estimate of population variability. Lacking estimates of this critical parameter impairs the ability of animal ecologists to design statistically powerful monitoring programs.

A ready source of data on the variability of population indices can be found in published time series of population counts. Hundreds of long-term population studies for a variety of taxa have been published in the last century, albeit mostly for temperate-zone organisms. Because most of these population series were generated using population indices, not population censuses, presumably variation in these count series reflects both environmental variation in the populations and sampling error associated with the counting methodology. As long as the time series are of sufficient and comparable duration, significant trends have been removed from them, and sufficient numbers of studies have been made, approximations of index variability can be estimated. Further-

Table 7.1 Monte Carlo Simulation Procedure Used to Estimate the Power of Population-Monitoring Programs to Detect Trends

Step Procedure

1. Basic structure of the monitoring program is defined (i.e., number of plots surveyed, survey frequency, and a series of survey years).

2. Deterministic linear trends are projected from the initial abundance index on each plot over the series of survey years.

3. Sample counts are generated at each survey occasion across all plots and for each trend. Sample counts are random deviates drawn from a normal distribution (truncated at 0) with mean equal to the deterministic projection on a particular monitoring occasion and with a variance approximated by the standard deviation in initial abundance (constant variances over time).

4. The slope of a least-squares regression of sample abundances versus survey occasion is determined for each plot and each trend.

5. The mean and variance for slope estimates are calculated across plots for each trend.

6. Whether the mean slope estimate is statistically different from zero for each trend is determined.

7. Steps 1 through 6 are repeated many times, whereupon the proportion of repetitions in which the mean slope estimate was different from zero is determined. The resulting proportion represents the power estimate, which ranges from 0 (low power) to 1 (high power) and indicates how often the survey program correctly detected an ongoing trend.

more, these estimates can be integrated with power analyses to provide general guidance on sampling protocols that animal ecologists can use to design robust monitoring programs for local populations.

To this end, count series of local animal and plant populations that extended more than 5 years were obtained by examining 25 major ecology journals published from 1940 to the present (nonwoody plants are also presented here because animal ecologists often must monitor plant populations in the course of their animal studies). Variability of each count series thus obtained was estimated by dividing the standard deviation of the counts by the mean count to determine the coefficient of variation (CV). To remove trends in the counts (which might have inflated variance estimates), the standard deviation was determined from the standardized residuals of a linear regression of counts against time. Furthermore, because the variability of a time series is related in part to its length (Warner et al. 1995), a 5-year moving CV (similar in concept to a moving average) was calculated for each count series. (However, most studies of birds, moths, and butterflies failed to present raw counts that could be detrended and standardized, so the means and error terms as presented in these studies were used. The index variabilities for these groups are therefore potentially biased high in relation to those estimates for other taxa). CVs were subsequently averaged within groups of taxonomically and ecologically related species.

A total of 512 time series for local animal and plant populations were analyzed (appendix 7.1), which provided estimates to calculate average index variabilities for each of 24 separate taxonomic and ecological groups (table 7.2). Few groups had low variability indices (CV below 25 percent), including large mammals, grasses and sedges, and herbs. A larger number had intermediate variability indices (CV 25-50 percent), including turtles, terrestrial salamanders, large birds, lizards, salmonid fishes, and caddis flies. Most groups had indices with CVs between 50-100 percent, including snakes, dragonflies, small-bodied birds, beetles, small mammals, spiders, medium-sized mammals, nonsalmonid fishes, pond-breeding salamanders, moths, frogs and toads, and bats. Finally, only butterflies and drosophilid flies had average indices with CVs above 100 percent. Although a pilot study is clearly preferable, lacking one of their own animal ecologists can refer to the specific studies (appendix 7.1) or to the summary (table 7.2) for information useful for designing monitoring programs for a particular species.

It is important to note that index variabilities (table 7.2) reflect temporal variation inherent in populations as well as sampling error associated with the counting methods. For example, direct count methods were used most often for those groups with the lowest index variability, including large mammals, all plants, terrestrial salamanders, and large-bodied birds. An exception was butterflies, which typically were counted with time-constrained visual searches. Nets and traps were used to capture individuals in most remaining groups. Trapping methods that sampled only a segment of a population (e.g., frogs, toads, and pond-breeding salamanders on breeding migrations) or that relied on attractants (e.g., most small- and medium-sized mammals at bait stations, moths and caddis flies at light traps, and drosophilid flies at fruit baits) were associated with high index variabilities. Similarly, most studies of small-bodied birds were based on counts of singing individuals and also displayed high variability. Both method-associated sampling error and inherent population variability clearly make important contributions to overall index variability, and the recommendations that follow assume that researchers will use the same standardized counting methods used by the researchers who generated the count series analyzed here (appendix 7.1).

Table 7.2 Variability Estimates for Local Populations

Group

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