sampling design for long-term regional trends in marine rocky intertidal communities

Sampling design for long-term regional trends in marinerocky intertidal communities

Gail V. Irvine & Alice Shelly

Received: 29 March 2012 /Accepted: 2 January 2013 /Published online: 19 February 2013# Springer Science+Business Media Dordrecht (outside the USA) 2013

Abstract Probability-based designs reduce bias andallow inference of results to the pool of sites fromwhich they were chosen. We developed and testedprobability-based designs for monitoring marine rockyintertidal assemblages at Glacier Bay National Parkand Preserve (GLBA), Alaska. A multilevel designwas used that varied in scale and inference. The levelsincluded aerial surveys, extensive sampling of 25sites, and more intensive sampling of 6 sites. Aerialsurveys of a subset of intertidal habitat indicated thatthe original target habitat of bedrock-dominated siteswith slope ≤30° was rare. This unexpected findingillustrated one value of probability-based surveys andled to a shift in the target habitat type to includesteeper, more mixed rocky habitat. Subsequently, weevaluated the statistical power of different sampling

methods and sampling strategies to detect changes inthe abundances of the predominant sessile intertidaltaxa: barnacles Balanomorpha, the mussel Mytilustrossulus, and the rockweed Fucus distichus subsp.evanescens. There was greatest power to detect trendsin Mytilus and lesser power for barnacles and Fucus.Because of its greater power, the extensive, coarse-grained sampling scheme was adopted in subsequentyears over the intensive, fine-grained scheme. Thesampling attributes that had the largest effects onpower included sampling of “vertical” line transects(vs. horizontal line transects or quadrats) and increas-ing the number of sites. We also evaluated the powerof several management-set parameters. Given equalsampling effort, sampling more sites fewer timeshad greater power. The information gained throughintertidal monitoring is likely to be useful in assessingchanges due to climate, including ocean acidification;invasive species; trampling effects; and oil spills.

Keywords Probability design .Monitoring .Marine .

Rocky intertidal . Statistical power . Extensive .

Intensive . Sampling methods . Alaska . Glacier Bay

Introduction

The marine intertidal zone is inhabited by diverse,highly productive communities with strong ecologicalties to both marine and terrestrial systems (e.g., Mengeand Branch 2001; Peterson and Estes 2001). Given

Environ Monit Assess (2013) 185:6963–6987DOI 10.1007/s10661-013-3078-6

Electronic supplementary material The online version of thisarticle (doi:10.1007/s10661-013-3078-6) contains supplementarymaterial, which is available to authorized users.

G. V. Irvine (*)Alaska Science Center, US Geological Survey,4210 University Drive,Anchorage, AK 99508, USAe-mail: [email protected]

A. ShellyTerraStat Consulting Group,17014 NE 158th St.,Woodinville, WA 98072, USA

http://dx.doi.org/10.1007/s10661-013-3078-6

these connections, effects from various stressors maybe translated into changes that are observable andmore easily studied in the intertidal zone than in thepelagic realm. The high ecological and conservationvalue of these systems, and in areas, economic andsubsistence value, argue for our continued attention(e.g., Castilla and Duran 1985; Steneck and Carlton2001). In addition, the rich history of experimental andtheoretical studies of intertidal communities provides astrong context for designing studies and interpretingchanges (e.g., Connell 1961a, b; Paine 1966, 1969,1977; Dayton 1971; Underwood and Denley 1984;Roughgarden et al. 1988).

Tracking changes in the environment over timeis critical for ecological understanding and forincreasing our ability to separate anthropogeniceffects from natural variation. When designingand implementing a regional monitoring program,one of the challenges is balancing the desire tosample across broad physical scales for greaterspatial inference with the need to sample inten-sively enough to detect temporal changes occurringwithin biological communities. Frequently, investi-gators or managers choose to conduct intensivesampling over smaller scales, and inference maybe limited to selected habitat types, sites, plots,and/or species (e.g., Richards and Davis 1988).

Environmental monitoring has increasingly focusedon detecting broad-scale or regional changes over longtime periods (e.g., National Resources Inventory(Nusser and Goebel 1997; Nusser et al. 1998); ForestInventory and Analysis (McRoberts and Hansen1999); Forest Health Monitoring Survey (Eager et al.1991); National Wetlands Inventory (Ernst et al.1995); Environmental Monitoring and AssessmentProgram (EMAP; Overton et al. 1990); GlobalObservation Research Initiative in Alpine Environments(e.g., Grabherr et al. 2000); British Countryside Surveys(e.g., Brandt et al. 2002); National Inventory ofLandscapes in Sweden (e.g., Stahl et al. 2011)) or thedevelopment of standardized approaches that would en-able such monitoring (e.g., Bunce et al. 2008).Longitudinal monitoring, the repeated sampling of mul-tiple random sites within a region, is an important tool fordiscovering changes in species abundances and otherenvironmental parameters. Because of the long-term as-pect of this type of monitoring, the initial sampling designis critically important to the success of the program.Testing designs initially, prior to implementation, is

preferred to changing designs after monitoring has begun,which can lead to loss of data and higher costs.

Probability-based designs, which use a randomiza-tion process to select sampling units, are commonlyused in terrestrial systems, but are uncommon in marine(or aquatic) systems (Olsen et al. 1999). The EMAP-Estuaries program is the most prominent probability-based design in marine coastal areas (Summers et al.1995). A few intertidal monitoring programs or studieshave also taken this route (e.g., Schoch and Dethier1996; this study—Irvine 1998, 2010; Irvine andMadison 2008; Bodkin et al. 2008), but most samplingof rocky intertidal environments has relied on selectedsites (Channel Islands National Park [NP]—Richardsand Davis 1988; Kinnetic Laboratories, Inc. 1992;Partnership for Interdisciplinary Study of CoastalOceans—Schoch et al. 2006; and Multi-AgencyRocky Intertidal Network [MARINe]—Ambrose et al.1995; Raimondi et al. 1999), often with selected plots ortransects, or a mixed approach (Olympic NP—Fradkinand Boetsch 2012). Because probability-based designsare not common, we stress their advantage for thebroader inference of their results.

To be effective, a monitoring design must be cou-pled with sampling that produces sufficient power todetect trends in identified parameters. Statistical pow-er, the ability to detect trends, is influenced by thenatural variability in spatial and temporal patterns ofspecies abundances, the level of sampling error, theselected sample sizes, and type 1 error (alpha level). Itmay be more difficult to detect trends in rare species orspecies with very patchy abundance (i.e., high spatialvariance). Sampling variance may be reduced and thepower to detect change increased by stratifying pop-ulations and communities along known gradients ofvariation or by increasing sampling effort.

This study focuses on the development and test-ing of a probability-based design for trend monitor-ing of sessile intertidal assemblages inhabitingprotected rocky substrates in Glacier Bay NationalPark and Preserve (GLBA), Alaska (Fig. 1). Theprobability-based design provides inference to sim-ilar habitat along the >1,000 km coast of GlacierBay proper (the large bay within the park; hereafterreferred to as Glacier Bay). Sampling was con-ducted from 1997 to 2001 using a variety of sam-pling regimes, methods, and intensities. Samplingyielded data on the abundance of multiple intertidalspecies through space and time. These data are a

6964 Environ Monit Assess (2013) 185:6963–6987

valuable resource for the planning of future inter-tidal monitoring in this region. In this paper, weuse the 1997–2001 data to compare trend detectioncapabilities of different sampling methods and sce-narios. We include recommendations for samplingof key sessile taxa that are pertinent to this generalgeographical region and to Glacier Bay. Althoughthe data used are from Glacier Bay, the probability-based approach is broadly applicable.

We devised a multilevel survey and samplingscheme, detailed in the succeeding paragraphs, thatallowed us to adapt sampling methods to conditionsthat were discovered in initial stages. The levelsincluded:

1. Aerial surveys of a systematically selected subsetof coastal segments to characterize habitat attrib-utes, assess the frequency of different habitattypes, and provide a pool of sites of known habitattype for further sampling;

2. Extensive, lower-intensity sampling of a largenumber of randomly selected sites of a selectedhabitat type (labeled CG for coarse-grained sam-pling); and

3. More intensive and experimental sampling of asubset of sites with more restricted habitat (labeledFG for fine-grained sampling).

In the first stage, aerial surveys were conductedto classify coastal segments and determine the loca-tions of rocky substrates. Based on categorical datafrom the aerial surveys, the target habitat type wasdefined to be intertidal areas comprised of bedrock(>1 %) and/or ≥76 % cobble/boulder substrate withslopes ≤60°. Extensive sampling was conducted at25 randomly selected sites under the CG samplingregime. More intensive sampling of 6 sites from thelower half of the bay (a subset of the 25) consti-tuted the FG sampling (Fig. 2). These FG siteswere all cobble/boulder-dominated sites.

Fig. 1 Location of Glacier Bay (gray box) within GLBA in Southeast Alaska (black box in inset map of Alaska)

Environ Monit Assess (2013) 185:6963–6987 6965

Data analyzed here are from sampling that primar-ily targeted macro sessile species. Glacier Bay has arelatively low diversity rocky shore, especially com-pared to other sites in the NE Pacific. Our analysesfocus on detecting changes in the three most abundantsessile taxa in the sampled habitat type: barnacles, themussel Mytilus trossulus, and the rockweed Fucusdistichus subsp. evanescens. Quantifying the abun-dance of these three taxa describes the intertidal zoneremarkably well. The results of the sampling con-ducted from 1997 to 2001 have inference withinGlacier Bay to bedrock and cobble/boulder habitats

for CG sampling and to a narrower geographic band ofcobble/boulder habitats for FG sampling.

We examined the ability of different samplingmethods and regimes to detect trends in the predomi-nant sessile species through statistical power analyses.Power can be defined as the ability to detect a changewhen one is occurring. Statistically, power is the prob-ability of rejecting the null hypothesis (e.g., no trend)when it is false (e.g., trend exists) and should berejected (Zar 1984). As part of the power analyses,sampling attributes, such as the number of sites, trans-ects, and intensity of point sampling, were varied to

Fig. 2 Locations and segment numbers of the coarse-grained (n=25) and fine-grained (n=6) sites in GLBA. Fine-grained sites are asubset of the coarse-grained sites


examine their effect on the power of particular sam-pling plans to detect change. The effect of severalmanagement-set parameters (e.g., acceptable errorlevel; frequency and scope of surveys) on power wasalso examined.

Field surveys and sampling methods

Field work was carried out in 1997, 1998, 1999, and2001. The methods used in the three levels of surveysand sampling listed previously are described in detailin Irvine (2010). They are reviewed in the succeedingsubsections, followed by description of the analyticalmethods.

Aerial surveys and description of habitat types

The goal of the aerial surveys was to characterizeintertidal habitat types and their frequencies inGlacier Bay, as well as to define survey sites. Thecategorical abundances of substrate and spatially dom-inant sessile biota, as well as slope, were described foreach segment surveyed. Substrate types were bedrock,cobble/boulder, pebble/gravel, sand/silt/mud, andcoarse sand. Taxa categorized were barnacles, mus-sels, and the rockweed Fucus. Slope categories were0–30°, 31–60°, and 61–90°.

Our first step in defining a set of survey siteswas to divide a digitized coastline of GLBA(Geiselman et al. 1997) into 200-m length seg-ments. The 1,109-km coast of Glacier Bay proper,the main bay in GLBA, yielded 5,545 segments.We estimated that 250 segments could be aeriallysurveyed during one low (minus) tide series.Beginning with a random start in Glacier Bay, each23rd segment was selected to be surveyed. From afixed-wing plane, 241 of the 250 segments wereclassified categorically for habitat type, slope, andbiota. Nine of the 250 segments could not be sur-veyed or were found to be inappropriate (i.e., theywere not intertidal beaches [several were streambanks]; they were snow-covered; or the segmentmaps did not resemble the current coast due tolarge changes since the last chart was made) andwere not classified (Irvine 2010). The describedsegments then formed a pool of sites with knownhabitat types that were available for subsequentstages of intertidal sampling.

Extensive (CG) sampling

Prior to the aerial surveys, the original target habitat typewas bedrock-dominated segments with slope ≤30°.However, only 1 of the 241 segments classified by airhad those characteristics. When the slope was increasedto ≤60°, only two more segments were added to thepool. As a consequence, the habitat selection was broad-ened to include both bedrock (greater than or equal tocategory 2, 1–25 %) and/or cobble/boulder (category 5,76–100 %) habitat with slopes ≤60°. Of the 241 aeriallyclassified segments, 111 segments met these habitatcriteria and became the pool available for CG sampling.From this pool, 30 sites were randomly selected for CGsampling (Fig. 2). Five sites were later eliminated be-cause they were either too steep, were not true beaches(e.g., had no land exposed at high tide and thus might notallow the same elevational band of the intertidal to besampled), or were not accessible because the site was in awildlife protection area (Irvine 2010). The 25 randomlyselected sites were primarily cobble/boulder-dominated(n=15), with the remainder bedrock-dominated (n=3), ora combination of bedrock and cobble/boulder (n=7).

CG sampling was conducted in 1997, 1998, 1999,and 2001. The area sampled was the area betweenmean higher high water (MHHW), defined by biolog-ical characteristics (see below), and the 0-m tide level(mean lower low water), set with information from thetide program Tides & Currents for Windows, version2.5a (Nautical Software 1993–1997). A horizontalsegment line delimiting the upper bound of the sitewas laid parallel to the shoreline along the MHHWcontour, defined as the lower edge of the Verrucaria(black lichen) zone (approximately 20 % cover ofVerrucaria); this was usually close to the juncture ofthe barnacle and Verrucaria zones. On some beaches,beach wrack or beach grass was used as an indicator ofthe highest tide levels. Six “vertical” line transectsrunning parallel to the elevational gradient and per-pendicular to the shoreline were laid from MHHW tothe 0-m tide level. The lengths of vertical transectsvaried due to changes in slope across a beach bothwithin and among sites. The start of the first verticaltransect was determined randomly within the first33 m of the horizontal segment line; the succeedingtransect lines were laid out systematically at 33-mintervals with respect to the first. If a vertical transectfell on a section of the segment that was unsampleabledue to steep slope or fresh water input, then the


locations of that transect and the remaining transectswere shifted the horizontal distance of the unsample-able area to the right, facing shore. The locations of thetransects were re-randomized each year, in part be-cause the park was reluctant to have permanentmarkers established; also, there was some uncertaintyabout the ability to effectively mark and resample thesame locations over time even if markers could beestablished, based on the mixed and potentially mobilesubstrates often present. Re-randomizing transectseach year likely increases temporal variation associat-ed with sampling (thus reducing trend detection), butalso increases the spatial knowledge of a site. Sessilespecies were targeted by three-dimensional (3D)point–intercept sampling along the vertical transects.All species (both sessile and mobile), including mul-tiple layers of the same species under the point, wererecorded, from top to bottom, until the first substratewas encountered. The substrate was also recorded.Species identifications were made to the lowest taxo-nomic level possible in the field during all surveys.

In 1997, the CG sampling began with a samplingintensity of 1 point/m along each vertical transect.This sampling intensity was selected based on the timeit took to do the 3D sampling in an initial field test,coupled with the objective of sampling one site perday. As field crews became more experienced andmost sites were found to have shorter transects thanthose in the field test, the number of points sampledper meter was increased (Irvine 2010). Therefore, in1997, the sampling intensity varied from 1 to5 points/m; however, the common sampling intensityfor all sites was 1 point/m. Beginning in 1998, thesampling intensity was increased to 5 points/m at all25 sites to increase the probability of detecting less-common species and to increase the precision of theestimates. Although the sampling intensity was con-sistent, the number of points sampled per transectvaried because the lengths of transects varied.

Intensive (FG) sampling

In 1997 only, the more intensive and diverse FGsampling was conducted at 6 of the 25 CG sites(Fig. 2). Although these sites were a subset of theoriginal random set, they were selected to facilitatesite access and to focus on cobble/boulder habitats. FGsampling required multiple days of effort at each site.Consequently, only sites from the lower half of the bay

(below the juncture of the two upper arms) wereconsidered due to their faster access by skiff from parkheadquarters (located near site 59; Fig. 2). Also, cob-ble/boulder habitats have a greater prevalence withinGlacier Bay and thus were of particular interest to thepark. Therefore, only those sites with ≥76 % cobble/-boulder substrate located in the lower half of the baywere considered for inclusion. Of eight such sites, themost distant northern and southern sites within thisband were dropped. The FG data from the six siteshave inference to the range of cobble/boulder habitatwithin the band or region that the sites occupy, as thesesites were also part of the CG set of sites, which hadbeen randomly selected from the pool of the selectedhabitat type. Thus, the FG sites are an approximatelyrandom sample of predominantly cobble/boulder hab-itat within the exact band they occupy.

The FG sampling consisted of multiple types ofsampling (Fig. 3), which are detailed in Irvine(2010). We briefly describe three of the samplingtypes here: (1) vertical transect via the point–inter-cept method described for CG sampling; (2) hori-zontal transect via point–intercept, and (3) quadrat,by point–intercept. Point–intercept sampling targetsmacro sessile taxa, but all macro taxa under apoint are recorded, as well as substrate. For theFG sites, point–intercept sampling was conductedalong ten vertical transects sampled consistently at5 points/m. The vertical transects were laid out ina similar manner as those in the CG sampling,except that the sampling of ten (rather than six)transects led to a smaller (20-m) systematic dis-tance between adjacent transects.

For horizontal transect sampling, three horizontaltransects (length of 10 m) were established on each ofthe ten vertical transects. A random location withinone third of the vertical transect was selected for theorigin of the first horizontal transect. The other twohorizontal transects were set at systematic intervalsfrom the first within the two other vertical zones ofthe beach. Sampling along horizontal transects usedthe same intensity (5 points/m) and sampling method-ology as employed for vertical transects.

In the third sampling method, a quadrat was sam-pled at each juncture of the vertical and horizontaltransects, with three arrayed per vertical transect.Quadrats were 1/9 m2 in area and contained a grid of36 intersections at which points were sampled.Quadrat point–intercept sampling used the same 3D


methodology as employed for both vertical and hori-zontal transects.

Analytical methods—estimating abundanceand power analyses

Percent cover was the metric of abundance for sessilespecies at the transect and site level. For each transect,the percent cover was estimated by dividing the num-ber of hits of the chosen taxon by the number of pointscounted along the transect. For quadrats, the numberof hits of a taxon for all three quadrats on a transectline was divided by the number of points sampledwithin the three quadrats. Because points were sam-pled three-dimensionally and multiple layers of a tax-on could be encountered at each point, the percentcover could potentially exceed 100 %. The averagepercent cover for the site in the sampled year wasestimated by the average of the percent cover esti-mates for each transect, weighted by the length of eachtransect.

The analyses focus on the predominant sessile spe-cies or taxa: (1) the mussel, M. trossulus; (2) thebrown alga or rockweed, F. distichus subsp. evanes-cens (formerly known as Fucus gardneri (Gabrielsonet al. 2006)); and (3) all barnacles (Balanus glandula,Semibalanus balanoides, Semibalanus cariosus,Chthamalus dalli, Balanomorpha, and barnacle spat/-cyprids). It is important to note that, in the field, allspecies were recorded to the lowest taxonomic levelpossible and barnacle spat were discriminated, but forthe purposes of analysis, all barnacle taxa and catego-ries (e.g., spat/cyprids) were combined.

Power analyses were designed to evaluate the effi-ciency of different sampling methods for detectinglong-term exponential trends in these three taxa atthese sites or similar sites. This power analysisassumes that any new monitoring established wouldbe for future trends. That is, we assume that samplingmethods might differ, and the time gap would precludethe existing data from being included in future trendanalyses. Nonetheless, the analytical results will beuseful for designing future monitoring.

VerticalTransectLine

Point-contactQuadrat

Segment line(MHHW)

MLLW (0’ tide level)

Horizontaltransect line

Total of 10verticaltransects

Water

Fig. 3 Layout of the various sampling methods used during the fine-grained surveys


After estimating required parameters from existingdata and setting assumptions for hypothesized trends,statistical power was estimated via simulations run us-ing a custom program written in R statistical software(version 2.10.0; R Foundation for Statistical Computing2009).

The parameters and scenarios tested for statisticalpower are summarized in Table 1. We examined theeffects of using fewer sites vs. fewer transects and theeffect of reducing the number of points sampled permeter on vertical transects. In addition, we examinedthe power and bias of different sampling methods (ver-tical transects vs. horizontal transects and quadrats).Overall bias can only be estimated if the populationmean is known, so bias is estimated only for the hori-zontal transect and quadrat sampling methods, relativeto the vertical transect sampling method. Unless thepopulation exhibits systematic trends parallel to theshoreline, the systematic sampling of vertical transectsshould result in unbiased estimates. We also examinedthe effect of varying alpha and altering sampling fre-quency and number of sites within a 10-year period.

We ran the main set of simulations for the dominantCG sampling plan. The following methods furtherdefine the simulation process:

1. Our simulations use the existing site means (av-eraged 1998–2001) as a representative sample ofexpected site means. Starting values for each sitewere estimated by mean percent cover for 1998–2001 for each of the 25 CG sites sampled usingvertical transects. These means were used for allsampling methods (e.g., quadrat sampling) un-less large biases to the mean (i.e., >10 %) were

observed. If biases were observed, corrections weremade and noted.

The transects vary in length, so a weighted meanestimator was used. For each site s in year t, themean percent cover was estimated as:

yst ¼Pn

i¼1Miyi

Pn

i¼1Mi

ð1Þ

where n is the number of sampled transects, Mi isthe number of possible subsamples on transect i,

yi ¼Pmi

j¼1

yij

mi, yij is the species count for the jth sub-

sample on the ith transect, and mi is the number ofsubsamples taken on transect i.

Mi is proportional to the length of transect i, sothe length of the transect is used in Eq. 1. For pointsampling in 1998–2001 (all 5 points/m), mi is pro-portional to Mi, so mi can be substituted into theabove equations. In this case, Eq. 1 simplifies to:

yst ¼

Pn

i¼1

Pmi

j¼1yij

Pn

i¼1mi

: ð2Þ

2. Exponential trends ranging from −20 to +20 %were added to the starting values for each plot.A no-trend result (0 %) was run as a check onthe nominal alpha level—the rejection rate inthis case should be approximately equal toalpha.

Table 1 Parameters and scenar-ios used in the power analyses Parameter categories Parameter options

Species Sessile dominants Mytilus, Fucus, all barnacles

Hypothesized trends Exponential trends ±0–20 % annual increases

Sampling attributes Number of sites 25, 20, 15, 10

Number of Transects 10 vs. 6

Sampling method Vertical transects, horizontaltransects, quadrats

Number of points per meter 5 vs. 1 point/m

Frequency of sampling 3, 4, or 5 sampling times over10 years

Management parameters Alpha level 0.05, 0.10

Length of monitoring program 10 years


3. We evaluated the relative power for a 10-yearmonitoring program.Most of the simulations wererun assuming samples are collected every 3 years(i.e., years 1, 4, 7, and 10).We also ran the main set(six vertical transects per site, 5 points/m) withthree sampling periods in 10 years (years 1, 5,and 10) and with five sampling periods in 10 years(years 1, 4, 6, 8, and 10).

4. There are two types of variance that affect power formonitoring trend—process variance and samplingvariance. Process variance is defined as differencesin the population level among years unrelated to anoverall trend in population level—essentially natu-ral variability in the system. For example, thesedifferences may be caused by weather or changesin local environmental conditions. Sampling vari-ance is the variance of the site mean within a singleyear due to sampling error and spatial variancewithin the site.

Because we have multiple samples within ayear (i.e., multiple transects) and across years, wecan estimate both types of variance (or “partition”the total variance) and model them separately inthe simulations. There are several ways to partitionvariance, all of which require assumptions. Weassumed a constant coefficient of variation (CV,standard deviation divided by the mean)—allow-ing the standard deviation to vary linearly with themean through time. Both the process and samplingCVs are assumed to be constant. The plots inFig. 4 show that both types of standard deviationsincrease with the mean. We further assume thatthere are no trends in this short time period, whichshould result in conservative variance estimates.

The total variance at a site is estimated as thedeviance of the three means around the overallaverage mean:

TV s ¼Pn

t¼1ðyst � ys Þ2

ðn � 1Þ

where t indexes year and ys is the average of theannual means at each site.

The sampling variance for each site is estimatedas:

SVs ¼ ðcv s � ys Þ2

where cvs is the average coefficient of variationacross years at site s. The CV for each year isestimated by:

cvst ¼ffiffiffiffiffiffiffiffiffiffiffiffiffivðy st Þ

p

y s t

where v(yst), the variance for the mean estimator inEq. 1, is approximated by:

vðystÞ ffiPn

i¼1M2

i ðyi � yÞ2

nðn� 1ÞM 2 ð3Þ

and M ¼Pn

i¼1

Mi

n . The formula is approximate be-cause another variance term, the variance within atransect, becomes relevant if the proportion of thepopulation sampled (i.e., the proportion of possi-ble transects sampled) becomes non-negligible.

Then the process variance for each site is esti-mated by TVs−SVs. In some cases, the estimate ofsampling variance is greater than the estimate oftotal variance. In these cases, we assume that thesampling variance is a better estimate due to morereplication and that the process variance is 0.

5. Because the simulated values are means (acrosstransects), normal distributions are assumed forthe sampling distributions (mean=0, variance asdiscussed in item no. 4).

6. Because negative cover values are not possible,any simulated negative values are set to 0.

7. Because the hypothesized trends are exponentialand the variance is related to the mean, all sam-ples are log-transformed (after adding 1 to ac-count for zeros) prior to estimating linear slopes.

8. The set of resulting slopes is tested for differencesfrom zero using the nonparametric Wilcoxon testwith alpha=0.05 and 0.10 for two-tailed tests.

9. Data are available for a total of 25 plots. Power forfewer plots was estimated by randomly selectingfewer slopes to test within each simulation run.

10. One thousand simulationswere run on each scenario.We estimated the reduction in sampling

variance that would result from sampling tenrather than six transects for each site usingdata from the six FG sites sampled in 1997.Weighted means and variances were estimated


for the full ten-transect data set, then for thereduced data set using only transects 1, 3, 5,6, 8, and 10. If the transects were equal inlength, the reduction in sampling variancewould be known—the variance of the meanis the (variance of y) divided by n, so increas-ing to ten transects would decrease the vari-ance by 6/10=0.60. However, these transectsare not equal in length (due to variation inslope within and between sites), so insteadwe use the empirical variance results for thesix FG sites, assuming that the variabilityamong transect lengths is similar to that whichwill be seen in future monitoring. Process

variance could not be estimated (only 1 yearof FG sampling) and was assumed unchanged.

Data from the six FG sites sampled in 1997were also used to estimate the changes tosampling variance that would result from us-ing horizontal transect or quadrat samplinginstead of vertical transect sampling. Meansand variances were estimated for the six sitesusing the three different sampling methods;the mean and variance estimates were thencompared. We used these results to adjust themeans (correct for bias) and the variances forsimulations (e.g., multiply all variance esti-mates by 1.2).

0 20 40 60 80 100

010

2030

4050

Barnacles

Mean Percent Cover

Sam

plin

g S

tand

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Dev

iatio

n

0 20 40 60 80 1000

1020

3040

50

Fucus

Mean Percent Cover

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010

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Mytilus

Mean Percent Cover

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n

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Fig. 4 Standard deviations plotted against mean percent cover for each taxon (in columns, barnacles, Fucus, andMytilus). The top rowis sampling error, and the bottom row is process error. The linear regression line (with 0 intercept) is shown on each plot


In order to estimate expected changes toparameters for less intensive sampling, all1997–2001 CG transects were subsampled at1 point/m. Means and both types of varianceswere reestimated on this data set which hadfewer points but one additional year of data.

Results

Based on the average 1998–2001 values for each site,barnacles had a more truncated distribution of meanpercent cover at sites than the other two major taxa,with a maximum cover of 40 % (Fig. 5; OnlineResource 1: Table 1.1). Fucus had the most broadlydistributed mean percent covers, with a maximumpercent cover at a site of 97 %; Mytilus had a distri-bution that was intermediate between the other twoand a maximum site mean percent cover of 56 %(Fig. 5; Online Resource 1: Table 1.1). These valuesare influenced by the relative incidence and magnitudeof multiple hits of a taxon at a point (a product of the3D sampling). Fucus and, to a lesser extent, Mytilusmore commonly have multiple hits at a point than dobarnacles. Mytilus had lower mean site CVs, on aver-age, than barnacles and Fucus (Fig. 6), while Fucushad the broadest distribution of CVs.

The major taxa varied in the percent of total vari-ance at sites that was sampling variance (rather thanprocess variance) (Fig. 7). Barnacles had the leastsampling variance, while Fucus and Mytilus hadbroader distributions of percent sampling varianceand Mytilus had the greatest frequency of sites with100 % sampling variance (Fig. 7). Process variancewas greater than sampling variance (Fig. 4).

Parameter estimates and power results are pre-sented in detail in the supplementary online material(Online Resource 1).The power to detect trends for themain simulation set (six vertical transects, 5 points/m,alpha=0.05) was consistently greatest for Mytilus,with lower and similar power for barnacles andFucus (Fig. 8). Note that, for this plot and all powerplots not focused on varying the number of sites, thetrajectory for 20 sites is depicted. This is primarilybecause the results for the different taxa are moredistinguishable for 20 sites than for the 25-site scenar-io, where power results are higher. Decreasing thenumber of sites had a strong negative effect on power(Fig. 9). Sampling of 20 or more sites provided a

power of ≥80 % to detect ±10 % annual trends forthese 3 taxa. There was considerably less power todetect trends when ten sites were sampled. Poweranalysis results for varying numbers of sites and sam-pling scenarios are presented in Online Resource 1:Tables 1.6–1.8.

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Fig. 5 Distributions of site mean percent cover for barnacles,Fucus, and Mytilus at the 25 sites


In comparing the sampling of ten vs. six verticaltransects, bias in the mean was variable across sites, butthe median and mean biases were <5 % of the ten-transect mean (relative bias %=100×(6 transect mean−

10 transect mean)/10-transect mean). Therefore, the sitemean estimates were unchanged from the main simula-tion set.

For Fucus, two of the six FG sites had samplingvariance increase by using ten transects (one of thetransects was somewhat anomalous in both cases),

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Fig. 6 Histograms comparing the distribution of CVs for bar-nacles, Fucus, and Mytilus at the 25 sites

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while the other four sites showed variance ratios (tentransect variance/six transect variance) ranging from0.40 to 0.65. There did not appear to be a relationshipbetween mean level or variance level with change invariance. Because of the wide variation in results, weused the median ratio across sites as the most robustestimate of likely changes. Ratios for barnacles andMytilus were more consistent. The median ratios were

0.54 (Fucus), 0.52 (barnacles), and 0.46 (Mytilus),e.g., for Fucus, (10-transect variance)=0.54×(6-tran-sect variance). These multipliers were applied to sam-pling variance only—process variance cannot beestimated from the existing data, so we assume it isunchanged by the increase in number of transects.Note that the variability in transect lengths adds tothe overall sampling variance and the decreases in

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Fig. 8 Estimated statisticalpower for detecting trendsin 3 taxa using vertical tran-sect sampling at 20 siteswith 6 vertical transectssampled at 5 points/m(alpha=0.05)

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Fig. 9 Estimated statisticalpower for detecting trendsin three taxa using verticaltransect sampling at differ-ing numbers of sites with sixvertical transects sampled at5 points/m (alpha=0.05)


variance for sampling more transects is less thanwould be achieved for equal transect lengths.

Increasing the number of transects sampled at asite from six to ten has only a small positive effecton power (Fig. 10). This is in contrast to the largeeffect observed from varying the number of sites(Fig. 9).

Bias to the mean for horizontal transect samplingand quadrat sampling relative to vertical transectmeans is shown in Table 2. Using horizontal trans-ects or quadrat point contact sampling caused gen-erally negative biases to the mean estimates (i.e.,underestimated means). Although the means werelower, the variance increased overall (as expectedfor fewer number of points sampled). The magni-tude of variance differences was inconsistent, butthe CV ratios were more consistent. Table 2 alsoshows the median CV ratio for each method andtaxon. There is no good way to estimate partitionedvariances for 25 sites for these different samplingmethods, since this has to be done on a site-by-sitebasis. Therefore, we held the process variance constant,decreased the means, and increased the sampling

variances so that the CVs were increased to match theresults in Table 2. Results are presented in OnlineResource 1: Tables 1.6–1.8.

For all three major sessile taxa, vertical transect sam-pling provided the greatest power to detect change, withmuch reduced power for the horizontal transect andquadrat sampling (Fig. 11). Less intensive samplingalong transects (as reflected by the number of pointssampled per meter) resulted in negative bias in the meanestimates, particularly for Fucus. The median relativebias for Fucus was 21 %, for barnacles 3 %, and forMytilus 8 %. Median relative bias across sites wascalculated as: (mean across years using 1 point/m−mean using 5 points/m)/(mean using 5 points/m).

The distributions of site CV ratios for sampling at 1vs. 5 points/m were fairly similar for Fucus andMytilus, with the exception of one site with a highCV ratio for Mytilus (Fig. 12). Barnacles had a higheroccurrence of ratios <1—meaning the CVs werehigher with more frequent sampling. The CVs wereincreased by 10–30 % by using only 1 point/m (seeFig. 12). For Fucus, the net result was actually lowervariances because the means were so much lower.

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Fig. 10 Estimated statisticalpower for detecting trendsin 3 taxa using verticaltransect sampling at 20 siteswith 6 or 10 vertical trans-ects sampled at 5 points/m(alpha=0.05)


Decreasing the intensity of point sampling from 5to 1 point/m had a relatively small negative effect onpower for Mytilus, a greater negative effect at smallertrends for Fucus, and a slightly positive effect forbarnacles (Fig. 13). Increasing alpha from 0.05 to0.10 increased the power to detect trends for all thethree major taxa (Fig. 14). For Mytilus, power for themain simulation set was already so high that the in-crease was negligible. In comparing equal samplingeffort over different survey times, we found that sam-pling 25 sites 3 times over 10 years provided morepower to detect trends for all 3 major taxa than didsampling 15 sites 5 times over 10 years (Fig. 15).

Discussion

Our study results indicate that it is possible to developprobability-based monitoring of rocky intertidalassemblages at a landscape scale that has high powerto detect changes in abundance of the predominanttaxa. Through examination of the differences in powerof various sampling methods and regimes, we provideinformation that can be used to design the most effec-tive (in terms of effort and power) intertidal monitor-ing plan for this locale, Glacier Bay. Even though thespecific results have regional pertinence, the multilev-el survey and sampling approach used has broad

Table 2 Median response (from six FG sites) for using horizontal transects or quadrat sampling instead of vertical transects

Fucus Barnacles Mytilus

Horizontal Quadrat Horizontal Quadrat Horizontal Quadrat

Bias (%) −20 −39 −31 −15 −17 −12CV ratio 3.7 5.9 3.7 4.2 3.7 4.9

Bias is relative change from vertical transects. All values are rounded to two significant figures. CV ratio is the median across sites

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Fig. 11 Estimated statisticalpower for detecting trends in3 taxa at 20 sites comparinghorizontal and quadrat sam-pling to 6 vertical transectssampled at 5 points/m(alpha=0.05)


applicability. Also, results of power analyses of par-ticular sampling methods may maintain their relativeranking when applied in other locations.

Study design

Although we devised a multilevel probability-baseddesign, there were some reductions in inference ateach level based on segments that could not be sur-veyed or were inappropriate (aerial surveys), segmentsthat could not be sampled (CG sampling), or geo-graphical and habitat restrictions (FG sampling).

The results of the aerial surveys led to a revision inthe characteristics of habitat types selected for themonitoring program. The finding that bedrock-dominated habitat with slope ≤60° was actually rarewas unanticipated, even by resident National ParkService staff. In retrospect, perhaps it should not havebeen too surprising, as the glacial action that createdthe bay carved steep-sided bedrock habitat as glaciersadvanced. Finer sediments occupy more gently slopedenvirons. The unexpected results of the aerial surveysillustrate one of the values of probability-based sur-veys for avoiding bias. The systematically selected setof characterized segments is also available for otherstudies, thus facilitating further establishment ofprobability-based studies in Glacier Bay. This poolof sites has since been used by researchers examiningthe effects of invading sea otters (Enhydra lutris) onintertidal clams (Bodkin et al. 2007).

The prevalence of cobble/boulder habitat in themore protected waters of Glacier Bay, where it islikely to be stable, led to its inclusion along withbedrock, as the habitats of focus (Irvine 1998, 2010).Most ecologists have avoided monitoring biota onpotentially less stable substrates, as detecting trendsmay be made more difficult by adding another factor(disturbance) that differentially affects various sizeclasses of substrates and has been shown to affectspecies diversity (Sousa 1979). However, Eckert(2009) found no effect of substrate (cobble vs. bed-rock) on temporal variability of marine algal popula-tions in the Gulf of Alaska, but a significantly greatervariability for marine invertebrates on bedrock vs.cobble or soft-sediment substrates. This latter resultwas unexpected and needs further investigation.Although different substrate types were not found tobe related to a significant effect on population variabilityfor some groups, there was high variability among the

marine plants and invertebrates examined, leading to theconclusion that it would be difficult to detect trends(based on the studies examined; Eckert 2009).

In our study, the CG and FG sampling plans weredesigned to examine the ability to effectively sample

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Fig. 12 Histograms comparing the distribution of CV ratios(1 point/m CV divided by 5 points/m CV) for 6 vertical transectsat the 25 sites for barnacles, Fucus, and Mytilus


the variation expressed in intertidal communitiesacross different scales. The scales reflected geographicvariation, sampled by increasing the number of sitesand their geographic scope, and within-site variation,addressed by varying the intensity of sampling.

Increased geographic spread of sites under the CGsampling plan encompasses strong clines in environmentalgradients (e.g., salinity, temperature) within Glacier Baythat reflect the relative proximity and influence of tidewaterglaciers (Etherington et al. 2007). The narrower geographicband occupied by the FG sites includes a somewhat re-duced range of environmental conditions; however, thereis still considerable environmental variation present due tothe varied location of these sites (e.g., some in side baysinfluenced by local glaciers, rivers, or ice; Etherington et al.2007; Irvine, unpublished data).

For within-site sampling that targeted sessile taxa,vertical transects were chosen as a sampling techniquefor several reasons. First, they sample across the eleva-tional zones of species, one of the major sources ofvariation in intertidal communities (e.g., Stephensonand Stephenson 1949, 1972; Southward 1958), andour primary question is how sites, not a particular

species or zone, vary. Second, if climate changeoccurs, the vertical distribution of species could beaffected. For example, zones could shift verticallywithout the relative abundance of a species changingacross a beach. If fixed quadrats or horizontal transectsare initially located within zones, then changes notedin the abundance of a species or an assemblage mightreflect changes for that position, but might not reflectchanges occurring across the beach. If vertical trans-ects were fixed in location, then changes in the verticaldistribution of species on a beach segment could beassessed.

Vertical transects also provide a good approach forsampling sessile biota in cobble/boulder habitat, as thedraped transect lines sample topographically diversesubstrates better than quadrats due to the variation insurface area that would be sampled among quadrats. Inaddition to these rationales for using vertical transects,we found that vertical transect sampling had muchgreater power to detect changes in abundance of themajor sessile taxa compared to the other point–inter-cept methods tested (quadrats and horizontal transects;Fig. 11). Further support for the effectiveness of

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Fig. 13 Estimated statisticalpower for detecting trends in3 taxa using vertical transectsampling at 20 sites with 6vertical transects sampled at 1vs. 5 points/m (alpha=0.05)


vertical transects comes from a study on bedrock sub-strates in Southern California that found that samplingof randomly placed vertical transects more accuratelyestimated the percent cover of intertidal species thandid randomly placed quadrats and generally providedsimilar or greater accuracy than the best stratifiedquadrat plans (Miller and Ambrose 2000).

Power, trend detection, and setting parameters

Power is the ability to detect a trend if one is, in fact,occurring. The power and design of a monitoring pro-gram will be influenced by both management-set param-eters (e.g., the desired power, level of change to bedetected, and alpha level) and sampling parameters(e.g., number of sites, transects, quadrats, etc.). The bio-logical data provide the foundation for assessing how tosample to achieve management-set parameters. Effort orcost can also greatly affect the ultimate sampling design.

There are no universally agreed upon levels for power,although Cohen (1988) suggested that at least an 80 %power level was desirable. Some have argued that alpha

should equal beta, which would affect power (1−beta)(e.g., Peterman 1990) or that alpha may be relaxed as ameans of increasing power (e.g. Toft and Shea 1983;Peterman 1990; Fairweather 1991). Fairweather (1991)has elaborated further on issues of power and effectivedesign of environmental monitoring.

The levels that are set for power and other aspectsof a monitoring design vary among programs. ChannelIslands NP (Ventura, CA, USA) has set, as their goalfor monitoring, a power of 80 % to detect a 40 %change in species abundance through time, with analpha of 0.05. It is not clear over what time frame this40 % change is computed or whether this simplyrepresents an impact level of change. The NorthAmerican Amphibian Monitoring Program (http://www.pwrc.usgs.gov/naamp/) previously stated ontheir website that monitoring programs should be ableto detect population trends with a power of 90 %, butan alpha of 0.20. Their rationale for setting a relativelyhigh alpha value is that it is more important, from aconservation standpoint, to detect declines than to becorrect about whether they are occurring (S. Droege,

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Fig. 14 Estimated statisticalpower for detecting trends inthree taxa using verticaltransect sampling with sixvertical transects sampled at5 points/m with alpha=0.05and 0.10


http://www.pwrc.usgs.gov/naamp/

http://www.pwrc.usgs.gov/naamp/

US Geological Survey, personal communication,2009). The signaling of a decline could initiate furthersampling or research to clarify the trend or investigatecauses. Setting the levels of change to be detected is amanagement decision, but it should be made withcognizance of how short-term changes compoundover time. Even small annual changes of 5 % quicklyaccelerate over time to appreciable levels of change(e.g., 5 % annual trend after 5 years=22.6 %, after10 years=40.1 %, after 20 years=64.2 %).

Our power analyses indicated that the CG samplingof 20–25 sites, with 6 vertical transects per site, sampledat 5 points/m, had ≥80 % power to detect 10 % annualchanges in the 3 predominant sessile taxa, with alpha=0.05. Power analyses of intertidal data collected atOlympic NP, which employed Monte Carlo simulationsof historical data for sessile taxa (from random pointcounts arrayed in proximity to horizontal transects),indicated that, at individual sites, it appeared possibleto detect 10 % annual changes in abundance after10 years of monitoring, with a power of 80 %, basedon annual sampling and alpha=0.10 (Fradkin andBoetsch 2012 citing Nielson and McDonald 2005).

An alternative approach to evaluating the effective-ness of a monitoring program’s design has been a pre-impact analysis, where the ability of monitoring todetect a certain magnitude of change (impact) isassessed. A combination of monitoring data and sim-ulations can be used to either evaluate the ability todetect change (e.g., Minchinton and Raimondi 2001,2005) or optimize environmental sampling designs(e.g., Benedetti-Cecchi 2001a). Minchinton andRaimondi (2001, 2005) used before–after analyses todetermine if rocky intertidal monitoring data inCentral and Southern California could detect 50 %changes in the abundances of target species with apower of 80 % at alpha=0.05. In both sets of analyses,monitoring had ≥80 % power to detect 50 % changesin abundance at alpha=0.05 for many species and sitecombinations (basically all that met the assumptionsof the power analyses), and for 67–88 % of the com-parisons, it was possible to detect 20 % changes inabundance (Minchinton and Raimondi 2001, 2005).However, the great majority of species and site com-binations did not meet the assumptions for the poweranalyses and thus could not be examined (Minchinton

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Fig. 15 Estimated statisticalpower for detecting trends inthree taxa using verticaltransect sampling with sixvertical transects sampled at5 points/m (alpha=0.05).The two displayed scenarioshave equal sampling effortover 10 years


and Raimondi 2005). Several factors likely increasedthe power to detect change: (1) the before–after designanalyses compared data from single sites and (2) thefixed quadrats were established in locations with highand relatively uniform abundances of a species(Minchinton and Raimondi 2005).

Although the other monitoring programs discussedhave determined that their sampling methods allow thedetection of change at specified or acceptable levels,the use of selected sites and/or selected plots targetinghigh abundances of certain taxa limits the inference ofthe results, depending on the design.

Variation in the ability to detect change among taxa

Power to detect change varied consistently among thethree predominant sessile taxa in our study (Fig. 8) andwas inversely related to the magnitude of the CVs(Fig. 6). The range of variation of the CVs also affect-ed power to a lesser extent, for example, the medianoverall CVs for barnacles and Fucus were almostidentical at 55 %, but Fucus had several sites withvery high CVs (Fig. 6) which may account for theslightly lower power.

Eckert (2009), in her synthesis of variability innearshore Gulf of Alaska marine populations (whichdid not include this study), calculated mean CVs forM. trossulus as 93 %, barnacles (S. balanoides/B.glandula) as 110 %, and Fucus gardneri (= F. dis-tichus subsp. evanescens) as 64 %. Our study obtainedmuch lower mean CVs for Mytilus (30 % vs. Eckert’s93 %) and barnacles (55 % vs. Eckert’s 110 %) and avery similar mean CV for Fucus (65 % vs. Eckert’s64 %), which indicate that we have increased ability todetect changes for Mytilus and barnacles than didmany other Alaskan studies.

In addition to examining the CVs, we partitioned thevariance, which provides some insight into differencesamong the taxa (Fig. 7). It appears that process variancedrives the power results. Among the three taxa, Mytilushad the lowest percentage of variance attributable toprocess variance, and it had the uniformly highest sta-tistical power. This makes sense—if there are greatchanges in abundance among years not attributable totrends, it is more difficult to discern trends, even withvery low sampling variance within years. Thus, whenthere is high process variance, it becomes more impor-tant to sample permanent transects and to sample overlong time periods to discern trends.

Power analyses of Channel Islands (Ventura, CA,USA) rocky intertidal data also show differences amongtaxa, with greatest power to detect changes for rock-weeds, lower power for the California mussel Mytiluscalifornianus and for barnacles, and lowest power forEndocladia muricata, a red alga (Minchinton andRaimondi 2001). Since the species comprising thesetaxonomic groups, as well as their abundances and ecol-ogy, differ from those in Glacier Bay, it is not surprisingthat the power relationships among taxa are not the same.For example, the rockweeds are comprised of entirelydifferent taxa: Silvetia compressa (formerly Pelvetia fas-tigiata) and Hesperophycus californicus (formerlyHesperophycus harveyanus) (MARINe website: http://www.marine.gov/Research/CoreSurveys/SeaweedOfCalifornia.html). Various ecological and design factorscould affect the relative power “hierarchies” of similartaxa in different areas or in different analyses. For exam-ple, the Glacier Bay sites are protected, while theChannel Island sites are exposed rocky (bedrock) habitat.The suites of species present and their interactions differ.The study design also influences the power results; sincemany of the plots at Channel Islands were selected to bewithin zones dominated by these target taxa (Richardsand Davis 1988), the abundances of the target taxa wereat least initially high. The geographical variation in pow-er for similar taxa (e.g., rockweeds) indicates that weshould use caution when borrowing information fromother areas to guide power analyses.

Power of different sampling and management-setparameters

We have focused on comparing the ability of differentparameters to detect trends in the predominant sessilespecies. Note that all parameters for evaluatingchanges to statistical power for modified samplingmethods and more or less intensive sampling withina site were based on data collected from only six sitesin only 1 year and in a more limited geological stratumthan the full complement of CG sites.

Varying the number of sites sampled had a strong effecton power (Fig. 9). Sampling 20 or more sites is recom-mended to achieve a power of ≥80 % to detect ±10 %annual trends for the 3 major taxa, with alpha=0.05.

When the number of vertical transects sampled wasincreased from six to ten, there was virtually nochange in statistical power to detect changes in percentcover, particularly for barnacles (Fig. 10). This may be


http://www.marine.gov/Research/CoreSurveys/SeaweedOfCalifornia.html



because process variance was the more importantcomponent for barnacles (50 % of sites had <8 %sampling variance; Fig. 7), and process variance wasnot adjusted for the increase in number of transects.Fucus had higher sampling variances and higher per-centages of total variance as sampling variance(Fig. 7), so there is a somewhat greater change to theoverall power for Fucus. Even so, the combinedresults show smaller effects than might be expectedfor the large increase in sampling effort.

When sampling effort was reduced along transects(reduced number of points per meter), both Mytilusand Fucus had modest declines in power (Fig. 13).Both species had increased CVs overall (Fig. 12). Theoverall CVs for barnacles decreased at most sites(Fig. 12), and this resulted in slight increases in theestimated power for detecting trends using fewerpoints on transects. Also, the reduction in variancefor barnacles was process variance, which had a great-er effect on trend detection than sampling variance.

Vertical transect sampling had high power. However,the power results for horizontal and quadrat samplingwere very low (Fig. 11), as expected due to much higherCVs for these methods (Table 2). The differences inCVs are at least partially due to less sampling effortrather than the methods themselves—it is difficult todiscern how large an effect this is with the current data.Sampling effort for horizontal transects was 85 % andfor quadrats was 61 % of that for vertical transects.Nonetheless, these results are intriguing and it wouldbe interesting to explore their biological underpinnings.

Benedetti-Cecchi (2001b) argues for the impor-tance of considering both vertical and horizontal sour-ces of variation when evaluating spatial patterns inabundance of intertidal taxa. There are two main com-ponents to the patterning of species in the intertidal:zonation and patchiness. Strong patterns in verticalzonation (bands) of species with distance from theshoreline lead to a preference for vertical transectsampling. The larger number of samples in the verticaldirection increases the probability of obtaining a real-istic representation of species occurrence. With strongvertical bands, if you sampled only at three locationsvertically (as for horizontal transects and quadrats),then you have a good chance of missing a zone orpatch. This bias tendency is likely increased by the useof a systematic sample rather than a random sample.We would expect this bias to be reduced with morehorizontal transects or quadrats.

If a taxon has a strong pattern of vertical bandingwith smaller distances between organisms or patchesin the vertical dimension, then there may be a morenegative bias to the mean for few horizontal transects(because you may miss sampling the zone) and a lessnegative bias for quadrat sampling (because you havea larger sample along the vertical axis than the singlepoint for a horizontal transect). These are the resultsfor barnacles.

If a taxon occurs in small patches in the vertical(or horizontal) dimension, then increasing the num-ber of points sampled should increase the power;we observed such a result for vertical transect sam-pling of Fucus. If the species is patchy and doesnot appear in dense vertical bands, then increasingthe number of samples in the horizontal directionshould decrease the negative bias, which is theresult observed for Fucus. That is, quadrat sam-pling had a strong negative bias and horizontalpoint sampling had less bias. The fairly high butlesser bias exhibited by Fucus for horizontal tran-sect sampling suggests more random patchiness butnot as well-developed a band as for barnacles.

Although these contrasting patterns for Fucus andbarnacles suggest differences in their spatial patterningon the beaches sampled, the vertical transect samplingwas overall a much more effective (powerful) sam-pling technique, especially when sampled at 5 points/m(for Fucus and Mytilus). In addition, when the numberof vertical transects was increased, there was almostno effect on power for barnacles. This suggests thatthe across-beach patterning of barnacles is generallyconsistent and that the sampling of six vertical trans-ects captures it well.

We examined two types of management-set param-eters, in addition to considering the levels at whichpower could be set. We found that increasing alphafrom 0.05 to 0.10 also increased the power; the effectwas rather straightforward (Fig. 14). This is a man-agement option that might be employed if the numberof sites were reduced or in other situations where thereis a desire to increase power without increasing thesampling effort.

We also considered the effect of varying thenumber of sites surveyed and the survey interval.With a consistent exponential trend over 10 years,sampling 3 time periods with 25 sites resulted inhigher statistical power than sampling 5 time peri-ods with 15 sites (Fig. 15). Note that each sampling


regime had an equal sampling effort of 75 sitevisits over 10 years. The difference in power canbe attributed to the wide variation among sites andsite parameters—resulting in variability in the mag-nitude of trends among sites. Sampling more sites,therefore, resulted in reduced variability and greaterpower.

Power synopsis

Vertical transect sampling had much greater power todetect trends than did point–intercept sampling ofhorizontal transects and quadrats. Increasing the num-ber of sites, number of transects, or intensity of pointssampled per meter all increased the power to detecttrends. The effect of increasing sites was pronounced,especially as the number of sites reached 15 or more(Fig. 9). Increasing the number of points sampled from1 to 5 points/m generally created a greater gain inpower than increasing the number of transects fromsix to ten (Figs. 10 and 13). Increasing the number ofpoints per meter generally had a larger effect for Fucus(Fig. 13); this and the strong negative bias for quadratmeans suggest a more patchy distribution for Fucus.Increasing alpha had a direct positive effect on power.Analysis of equal sampling effort over 10 years, ap-portioned by inverses of number of sites and samplingfrequencies, indicates that power is increased by sam-pling a greater number of sites fewer times.

General considerations

These results suggest that, for these species in thishabitat at this location, sampling effort for trend de-tection should focus on getting broad spatial coveragerather than sampling a few individual sites intensively.A similar conclusion has been reached by others(Holland-Bartels et al. 1995; Murray et al. 2006) andis the foundation for other regional or nationalprobability-based studies (e.g., FIA, EMAP). The ver-tical transects were a very effective sampling methodfor these common sessile taxa. Monitoring for status,as opposed to trend, may require some sites withintensive sampling. Power could also be increased bymaking the vertical transects at the sites fixed in loca-tion, thereby reducing process variation over time.This should increase power to detect change for otherspecies that are less common or that have patchydistributions. Also, if fixed quadrats for the sampling

for small mobile invertebrates were coupled with fixedvertical transect sampling, trend detection should in-crease through the reduction of spatial variation.

In addition to better power to detect trends, there isvalue in having a large number and good spatial dis-tribution of sites. Sampling a larger number of sites islikely to increase the capture of particular types ofeffects, events, or changes, as well as ensuring thatthese sites better reflect the overall condition of thebay. If there are impacts that affect a small subset ofthe sites (e.g., ice scour, trampling effects), having alarger number of sites increases the ability to compareaffected vs. unaffected sites. Even if the number ofsites is reduced, logistic costs of visiting a few, quitedispersed sites could be very high, although this wouldbe at least partially offset by the reduced cost ofsampling fewer sites. An alternative approach formaintaining a high number of sites but reducing yearlysampling costs is to employ panel survey designswhere subsets of the sites are sampled each year, withvarious possible patterns (see review by McDonald2003). Overall, sampling a larger number and spreadof sites is preferred.

Since this study was initiated, another probability-based approach has been developed, the generalizedrandom-tessellation stratified (GRTS) survey design(McDonald 2004; Stevens and Olsen 2004). TheGRTS survey design creates a spatially balanced sam-ple and has flexibility for altering sampling units whilemaintaining the spatial balance. Thus, it improves onboth systematic and simple random designs. This ap-proach should be considered by those establishingnew surveys or programs.

An additional factor that should be considered inevaluating the power to detect trends for particular taxais that the abundances of the major space-holding spe-cies in the intertidal have been treated here as thoughthey are independent, which they are not. Competitionfor space occurs and can be mediated by predation anddisturbance (e.g., Connell 1961a, b; Paine 1966; Dayton1971; Sousa 1979). Thus, variation in one species canaffect variation in other species. Currently, there are notechniques for multispecies power analyses. Similarproblems should occur in evaluating sampling for othermultispecies communities with similar structuringmechanisms, such as terrestrial plant assemblages.

If additional species become more common inGlacier Bay as glaciers recede or as climate warms,then the relative abundances and, hence, power to


detect change in barnacles, Mytilus, and Fucus maychange. Other species could become dominant in thefuture. Although current CG sampling records all spe-cies under each point–intercept, species with lowabundances will be more difficult to detect (e.g.,Elzinga et al. 1998). The CG surveys could be com-bined periodically with more intensive sampling, sitesurveys, or timed surveys to increase detection of less-common species. The development of protocols toeffectively sample small and large mobile inverte-brates, which can also have strong direct and indirecteffects on sessile taxa under both natural conditionsand following oil spills (e.g., Paine 1966; Cubit andConnor 1993; Wooten 1993; Highsmith et al. 1996;Irvine 2000; Menge and Branch 2001), would greatlystrengthen an intertidal monitoring program and in-crease understanding of changes occurring in thesecommunities.

In conclusion, the probability-based survey andsampling approaches used in this study provide abroad characterization of selected intertidal habitatswithin Glacier Bay, as well as statistical powerestimates for sampling approaches varying in design,methods, and intensity. Extensive sampling of manysites (the CG sampling plan) had more power to detectchange in the predominant sessile taxa, than didmore intensive sampling of fewer sites (the FGplan). This sampling provided a power of 80 %or greater to detect 10 % annual changes for all threestudied taxa at alpha=0.05.

The analyses provide substantial information thatwill be useful in designing and implementing a long-term intertidal monitoring program in Glacier Bay orin geographically similar areas. Although the resultsare most pertinent regionally, the probability-basedapproach is much more broadly applicable. We rec-ommend that managers and investigators consider theconsiderable benefits of developing probability-basedsurveys.

Acknowledgments This project has benefited from the statisti-cal and design advice of L. McDonald (WEST, Inc.) and M.Udevitz. Project and field support was provided by J. Bodkin, K.Kloecker, T. Gage, M. Ferguson, K. Vandersall, G. Esslinger, D.Monson, Jennifer Mondragon, Jeffrey Mondragon, A. Delorenzo,T. Stoltey, E. Madison, J. de la Bruere, D. Douglas, M. Whalen,and K. Oakley of the US Geological Survey (USGS); M.Lindeberg of the National Oceanic and Atmospheric Administra-tion; J. Williams of Sitka National Historical Park; and L.Sharman, W. Eichenlaub, M.B. Moss, and L. Basch of GlacierBay National Park and Preserve (NP&P). We thank boat captain

Jim Luthy and the crew of theNunatak (NPS) and boat captain Jimde la Bruere and the crew of the Alaska Gyre (USGS) for greatfield support. Initial funding was from USGS Natural ResourcePreservation Program; additional support was provided by GlacierBay NP&P and the USGS. We thank P. Geissler, S. Fradkin, andan anonymous review for their constructive comments on drafts ofthis manuscript. Any mention of trade names is for descriptivepurposes only and does not represent endorsement by the USgovernment. With kind remembrance of C.A. Toft (died 2011)and her contributions to ecology.

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