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Sampling Requirements for Detecting Trends in Amphibian Populations

James P. Gibbs

Center for Environmental Research and Conservation
Columbia University
New York, New York 10027
e-mail: jamesgibbs@aol.com


Estimating temporal trends in amphibian populations is a common goal of many herpetologists and managers. Trends are typically inferred from counts of individuals made on sample plots over time. A common problem in trend detection is that sources of "noise" in counts obscure the "signal" associated with ongoing trends. This is a particular problem in amphibian monitoring because many amphibian populations, monitored with standard methods, are characterized by striking variability.

The probability that a monitoring program will detect a trend in sample counts when the trend is occurring, despite the "noise" in the count data, represents its statistical power. Although statistical power is central to every monitoring effort, it is rarely assessed. Consequences of ignoring it include collection of count data insufficient to make reliable inferences about population trends or collection of data in excess of what is needed.

The purpose of this paper is to (1) estimate the variability of amphibian populations using published, long-term count series and (2) to incorporate these estimates in a power analysis to determine the sampling intensities needed to detect trends of various strengths in amphibian populations. The results are intended to provide general guidance to herpetologists on sampling protocols, specifically, the number of plots or subpopulations to monitor and number of counts to make per year.

Data Sources
Count series of local amphibian populations that extended over at least 5 years were obtained from the literature. The variability of these count series was estimated by dividing the standard deviation of the counts by the mean count, that is, the coefficient of variation. To remove the effects of any trends in the counts that might have inflated the variance estimates, the standard deviations were determined from the residuals of a linear regression of counts against time. Coefficients of variation were averaged within groups of taxonomically- and ecologically-related amphibian species, as well as those monitored with similar techniques. In cases where multiple, local populations were monitored in a single study, a detrended coefficient of variation was calculated for each population and then averaged to obtain a single value per study.

Power Analysis
I conducted a power analysis that assumed the following logistical constraints: resources available for a regional amphibian monitoring program would permit surveys of < 250 plots or subpopulations on 1-5 occasions annually over a monitoring period of 10 years. Within this framework, I assessed goals for detecting overall changes in amphibian population indices of 10%, 25%, and 50% for each group of amphibians during the monitoring period.

Power to detect linear trends in abundance was assessed by coupling a route-regression approach with Monte Carlo simulation. The following procedure was used: (1) I identified a number of plots or subpopulations to be surveyed (n = 10, 20, 30, ..., 250 plots or subpopulations), a frequency at which they were surveyed each year (n = 1, 2, 3 visits), and a time series of survey occasions (surveys always at 1, 2, 3, ..., 10 years); (2) deterministic linear trends were projected from the initial abundance index on each plot; (3) sample abundances were generated at each monitoring occasion across all plots and for each trend as random deviates 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 was determined for each plot and each trend; (5) the mean and variance for slope estimates were calculated across plots for each trend; (6) whether the slope estimate was different from zero for each trend was determined with a two-sided t-test at alpha = 0.1; and (7) the process was repeated 250 times, after which the proportion of repetitions in which the slope estimate was different from zero was determined. Thus, the resultant power estimate, measured from alpha (low power) to 1 (high power), indicated how often a survey program would correctly detect an ongoing trend. The simulation software ("monitor.exe") has been adapted for general use on DOS-based microcomputers and is available from me or via the internet at: "ftp.im.nbs.gov" or "".

Results
Three general groupings of amphibians were made: (1) terrestrial and streamside salamanders directly counted on small, terrestrial plots, (2) pool-breeding salamanders counted on breeding migrations with drift fences and pit-falls, and (3) frogs and toads counted on breeding migrations with drift fences and pit-falls Table 1. Average coefficients of variation for these groups were 0.303 for terrestrial salamanders (8 studies), 0.533 for frogs and toads (6 studies), and 0.695 for pool-breeding salamanders (6 studies). The power analysis ( Table 2) indicated that infrequent monitoring (for example, once per year) at a small sample of sites (for example, < 30) would reliably detect strong population trends (that is, a 50% drop over 10 years) in all groups. For streamside and terrestrial salamanders the sampling estimates are quite modest for all trends owing to the inherent stability of their numbers and the precision of litter plot counts as a population index. More intensive monitoring is needed to detect trends in the other groups, but nevertheless is still at logistically feasible level for many state- or province-level monitoring programs. For example, the most demanding sampling situation identified was 110 sites monitored 5 times per year to detect a 10% trend over 10 years in pool-breeding salamander populations Table 2.

Recommendations
It is important to emphasize that any conclusions drawn from this study are directly contingent on the initial statement of the monitoring program's objectives. While power estimates are influenced by many factors controlled to large extent by researchers, e.g., duration and interval of monitoring, count means and variances, and number of sites and counts made per season, several other, entirely arbitrary factors exert an important influence on power estimates. These include trend strength (effect size), significance level (Type I error rate), and the number of tails to employ in statistical tests. For these reasons, it is critical that explicit and well-reasoned monitoring objectives be established prior to the initiation of any amphibian monitoring program. Minimally, these goals should address what magnitude of change in the population index is sought for detection, what probability of false detections is to be tolerated (alpha level), and what frequency of failed detections is acceptable (power). An initial statement of objectives is important because subsequent efforts to judge the success or failure of a monitoring program are made relative to those objectives. Conducting power analyses during the pilot phase of a monitoring program also is critical because it permits an assessment of a program's potential for meeting its stated goals while the opportunity for altering the program's structure is still available. The computer program developed for this study can provide researchers such an option (see Methods).

Post-script
I searched the literature thoroughly to find the studies used in this analysis. The relatively small number of long-term studies located indicates just how little we know about amphibian population dynamics and trends. If any readers are aware of other published count series for local amphibian populations that extend for 5 years or more, I would appreciate learning of them. This applies also to unpublished count series. If you have any counts that extend over 5 years or more, I would be happy to receive them, analyze them, and make them available to the amphibian monitoring community in a format similar to this paper.

Table 1. Variability estimates for amphibian populations. Values are coefficients of variation (standard deviation/mean) for detrended count series.

Table 2. Sampling intensities needed to detect overall changes of 50%, 25%, and 10% over 10 years of annual monitoring of amphibian populations. Values are the number plots or subpopulations that should be monitored to detect a trend at alpha = 0.1 with a likelihood (power) of > 0.90 given 5, 4, 3, 2, or 1 annual count(s) of each plot or subpopulation. All estimates were made with the "monitor.exe" program with 250 replications.

U.S. Department of the Interior
U.S. Geological Survey
Patuxent Wildlife Research Center
Laurel, MD, USA 20708-4038
http://www.pwrc.usgs.gov/naamp3/naamp3.html
Contact: Sam Droege, email: Sam_Droege@usgs.gov
Last Modified: June 2002