Designs for Evaluating Local and Regional Scale Trends

The declining status of numerous plant and animal populations valued by contemporary society has prompted their listing as threatened or endangered under the Endangered Species Act. Many populations have declined so severely that their loss is evident to the casual eye—through reduced commercial harvests, smaller recreational catches, or informal observation over the years at favorite places. In many cases, restorative measures have been initiated through bans on commercial or recreational harvest, changes in land management activities thought to be detrimental to these populations, and direct alteration of habitat features to improve degraded conditions. In addition, monitoring programs of varying degrees of scientific sophistication have been established. Interest in detecting trends in the condition of ecological resources can be expected to underscore the requirement for rigorous monitoring networks capable of detecting trends, either improving or declining, in a timely manner. A common monitoring framework for trend detection consists of repeated measurements over time of attributes of interest at specific geographic locations. Attention might be focused on a single location, or it might cover a region by using a network of sites. Monitoring locations can be points on the landscape (e.g., chemical sampling at points on a stream network); linear transects, such as those used in Breeding Bird Surveys; or areas, such as the plots used by the National Agricultural Statistics Service. The attributes of interest can be physical, chemical, or biological, or a combination of these. The data derived from a general monitoring framework can be summarized as a matrix of locations (or sites) by time, with attribute scores in the elements of the matrix. The simplest design is an array of sites at which measurements are made within and across years. Among basic design choices for the chosen attributes are the number of sites to include in the network, when and how often to visit a site within a year, and the duration of the network. Although numerous modifications can be made during the evolution and refinement of a design, this basic framework serves as a sound foundation. In addition, knowing the relative magnitude of an attribute's temporal, spatial, and residual variation is crucial for making efficient design decisions. Thus, estimating the magnitude of the components of variation and assessing their implications for trend detection is an important part of developing and evaluating monitoring designs. Stevens and Urquhart (2000) distinguish two important concepts in the development of monitoring plans: the sampling design and the response design. The sampling design refers to the spatial and temporal pattern of locations where measurements are to be made. It involves making critical design choices that govern allocation of the sampling effort within and among years and across sites. It also entails continually reevaluating the allocation of sampling effort as information about the structure of variation is gathered. The response design incorporates numerous decisions about how to measure the attribute of interest accurately. Naturally occurring organisms range in size from microbes to elephants and whales; the places in which they are studied may range from square meters (or less) to many square kilometers. All features of the definition of a response—the manner in which it is evaluated in the field (including observation or measurement bias), the size of the plot on which it is measured, and the consequences for analysis of quantitative responses—reside in the response design. Features of the response design can have major impacts on the appropriate analysis and interpretation of an observational study, and these features are often attribute-specific. Here, however, we focus on the sampling design as a framework within which many of the questions about an indicator's performance can be evaluated. In this article, we generally assume that response design issues have been dealt with responsibly, consistent with the organism or phenomenon under consideration, though we also explicitly address some problems with responses. First, we describe two components of variation to which single-site trend detection is sensitive. Second, we extend this description to encompass two additional components of variation important for multiple-site trend detection. We then summarize two case studies to illustrate the magnitude of variance components, and we conclude by describing how these variance components affect trend detection capability. Because we want to consider a class of responses broader than population size, we use the term indicator as a descriptor of an ecological attribute of interest in the sense that Gibbs et al. (1998) use the term index as an indicator of a population's size. Gibbs et al. (1998) have provided a valuable service by compiling estimates of temporal variability across a wide range of plant and animal taxa, by developing tools for designing monitoring networks to estimate population trends, by advocating power analyses to evaluate alternative designs, and by making much of this information available on the Internet. They correctly emphasize the important influence that variability exerts on the ability (power) to detect trends across time (usually across years). However, their approach does not distinguish between two components of temporal variation—namely, coherent and ephemeral (or interaction) variation (Platt and Filion 1973, Magnuson et al. 1990, Kratz et al. 1995, Stoddard et al. 1996, Urquhart et al. 1998)—that are critical for the cost-effective design of networks of sites. We make that distinction here by describing the components of variation both at a single site and at a network of sites. The temporal pattern of a hypothetical ecological indicator across years at a single site incorporates two components of variation—within year and across years—whose separation is important for evaluating trend detection capability. Measurements made within a year make it possible to estimate the status of the indicator for that year. How well yearly status is described depends on various factors: whether a temporal window (an index window) is used for measurements, the natural variability of the indicator within the selected window, variation and errors in the measurement protocol, and the number of samples allocated to describing that indicator, for example. Variability in the estimate of yearly status is one of the important components of variation relevant for trend detection at an individual site. A comparison of the two panels of Figure 1 illustrates the second component, year-to-year variation in the status of an ecological indicator at a site. Figure 1a illustrates the temporal pattern of a hypothetical indicator whose yearly status is precisely estimated and whose year-to-year variation is small. Figure 1b is the same as Figure 1a, except that greater year-to-year variation has been introduced. In both panels, yearly status is estimated with the same precision and the same linear trend has been incorporated. The relative scatter of points around the linear trend in the two panels reflects this second important component of variation. The trend is more evident in Figure 1a than in Figure 1b, illustrating the importance of the year-to-year component of variation. The design of single-site monitoring programs should allow for the evaluation of within- and across-year components of variation, because the relative magnitude of these components delimits the cost-effectiveness of revisiting a site during the year. Trend detection capability depends upon the magnitude of the combined sources of variation. The ability to estimate yearly status can be enhanced through design decisions, especially by within-year sample size and by attention to refinements of the response design. However, the effect of natural year-to-year variation cannot be controlled through changes in sample size. If year-to-year variation is large, the ability to detect relatively small trends depends on the duration of the sampling program; adding or deleting sampling within a given year will have little effect on trend detection capability under these circumstances. Consequently, for purposes of design, identifying and decomposing within-year and across-year variation is important. Now consider a network of sites at which indicator measurements are made. Suppose there is an underlying linear trend among all sites, expressed as the average across the site-specific trends (Gibbs et al. 1998). Four important components of variation can be described. The first, what we call residual variation, is analogous to the within-year variation at a site; it represents the average within-year variation across all sites in the network. The second and third are year-to-year components of variation. When multiple sites are monitored, year-to-year variation can be decomposed into two parts, one of which describes the coherent or synchronous year-to-year variation expressed by all of the sites together (Figure 2a; Magnuson et al. 1990). Coherent variation occurs when all sites in the network are in a consistent years might indicator scores across the years might coherent component of temporal variation an important in trend analogous to the that year-to-year variation in single-site trend detection (Figure choices are by the magnitude of this coherent component of temporal variation. The second part of multiple-site year-to-year variation represents the average year-to-year variation at the variation to site-specific (Figure component of variation has been ephemeral spatial, ephemeral temporal, or the variation (Platt and Filion 1973, Magnuson et al. 1990, Kratz et al. 1995, Urquhart et al. 1998). The precision with which a yearly average across multiple sites can be estimated depends on the of the residual and components of variation, which can be controlled by the allocation of sampling effort within and across sites. precision in evaluating an average trend is by the number of sites than by within-year to individual sites. However, the of adding sites for trend detection depends on the relative magnitude of the component of variation. If variation is revisiting sites within the year adding sites can have much effect et al. Urquhart and The in the magnitude of an attribute the component of variation et al. variation in site-specific that the magnitude of the ecological attribute of interest as variation in or the of the site for specific animal or plant habitat might greater animal than or some or might in stream networks than variation, not for in the design of monitoring can influence trend detection capability. variation, which variation not by year, and site components, incorporates within-year variation from a of circumstances. not all sites in a network can be at the same temporal variation during the in which the of sites is to the residual many are to spatial A might be at sites might a indicator can also from in how multiple field of which may be well sampling in a network of sites. In cases, measurement in field and analyses of to residual variation. among these components of variation is important for sample the between the number of sites in a network and the number of to sites within and across years. sites within a year the effect of residual variation on trend adding sites to a network the effect of both and residual variation. However, coherent variation trend detection a not controlled by adding sites. because the component of a monitoring is often the of to sites and making the measurements, an efficient allocation of sampling effort is for to the variance components and are year, and sample size are number of sites, number of and number of to a site within a year. assume a design in a with to all sites year. for variance components when repeated measures are which not all sites are within a year, are all sites the same framework is used for estimating variance components, the are more The relative magnitude of these variance components can be by on two case studies for which we have The is a of populations in are of many animal and plant population monitoring programs in which the of a of interest is across many sites for many years. 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However, sampling design for single-site trend detection are relatively the choices are how many to measure the indicator within the year and what yearly pattern to use (e.g., to make measurements year or to make trend detection more sampling design the allocation of sampling effort within and across years and the allocation of effort across multiple sites. multiple-site more sampling design are available for trend detection. the effect of site on estimates of precision can be by a design that to sites across years. sites across years variation in the same that in studies the variation across The of residual and can be by choices of to sites or additional sites in the However, it is from that the number of within-year to sites the number of sites both residual and Consequently, for trend of are the same as for sites, greater trend is by adding sites to the at the of However, at a adding more sites will not affect trend detection precision because the in the by year. with single-site trend when year is sampling design choices are trend detection capability as the duration of the Although is for evaluating some sampling design design can be more by an evaluation of power to detect In to sample size, and time a of trend detection trend magnitude and the of the when it is or it when it is is the of detecting a trend one is Trend can be evaluated by power as a of the it et al. 1996, Urquhart et al. 1998). illustrate how the variance components affect trend detection we and trend year. the we used a design and combined and residual then year and across the in data 1 and we the number of sites as A wide of can be evaluated with this We selected a to emphasize the of trend detection to the magnitude of year by varying magnitude from to (Figure The of detecting a year trend when year is about years with sites, when year is power to than and is by sample size in the range of to sites. year power does not approach years. is at an of magnitude greater than year 1 and and trend detection capability is not so to in magnitude (Figure with year and a network of sites, power is years when from to The between adding sites and for the of years is when year and the of detecting a trend years is about with sites. However, power is years with sites (Figure Thus, the of trend detection by a of years is the of the number of sites by this design is Although the use a design in which a network of sites is year, yearly of site can be efficient for trend detection. Urquhart and (1998) and Urquhart and evaluated the of for estimating multiple-site trend detection. They that designs, in which sites are year for a of are an alternative to revisiting site year. a might of sites in of the years. in the year, sites in year 1 are in the year, those in year are and so pattern can be for as as the information derived from the is can various of within and across years for the purposes of estimating the variance components or to improve trend detection in the term et al. 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