DEVELOPMENTS IN TREND DETECTION IN AQUATIC SURVEYS

1. DEVELOPMENTS IN TREND DETECTION IN AQUATIC SURVEYS N. Scott Urquhart STARMAP Program Director Department of Statistics Colorado State University

2. PATH FOR TODAY • Review a model I have used to project power of EMAP-type revisit or temporal designs • Recent developments • Impact of removing planned revisits – Grand Canyon • Power of differences in trend – Oregon plan & others • Generalize model to allow distribution of trends • Each part has different collaborators

3. A SIMPLE MODEL for a SURVEYED ECOLOGICAL RESPONSE • Consistent with annual or less frequent observation • Represent the response time series by an annual departure • Represent space by a site effect only • Allow sites to be visited in panels • Regard trends across time as a contrast over the panel by annual response means

4. A STATISTICAL MODEL • where • i INDEXES PANELS 1, 2, ... , s • (all sites in a panel have the same revisit pattern) • j INDEXES TIME PERIODS ( years in EMAP) • k INDEXES SITES WITHIN A PANEL 1, 2, ... , ni • and (uncorrelated):

5. A STATISTICAL MODEL - continued • Consider the entire table of the panel by time-period means, • Without regard to, as yet, whether the design prescribes gathering data in any particular cell • Ordered by panel within time period (column wise) With this ordering, we get

6. STATISTICAL MODEL - continued • Now let X denote a regressor matrix containing a column of 1’s and a column of the numbers of the time periods. The second element of contains an estimate of trend.

7. STATISTICAL MODEL - continued • But this estimate of b cannot be used because it is based on values which, by design, will not be gathered. • Reduce X, Y and F to X*, Y*, and F*, where these represent that subset of rows and columns from X, Y, and F corresponding to where data will be gathered. Then

8. A STANDARDIZATION • Note thatcan be rewritten as • Consequently power, a measure of sensitivity, can be examined relative to

9. TOWARD POWER • Trend: continuing, or monotonic, change. Practically, monotonic trend can be detected by looking for linear trend. • We will evaluate power in terms of ratios of variance components and where this denominator depends on the ratios of variance components and the revisit or temporal design.

10. POWER REFERENCE • Urquhart, N. S., S. G. Paulsen and D. P. Larsen. (1998). Monitoring for policy-relevant regional trends over time. Ecological Applications 8: 246 - 257.

11. DESIGN and POWER ofVEGETATION MONITORING STUDIESforTHE RIPARIAN ZONE NEAR THE COLORADO RIVER in THE GRAND CANYON COOPERATORS Mike Kersley, University of Northern Arizona, and Steven P. Gloss, Program Manager-Biological Resources Grand Canyon Monitoring & Research Center, USGS

12. POWER TO DETECT TREND IN VEGETATION COVER,ZONE = 15, VARYING % TREND 1%, 2%, 3% 5% PER YEAR

13. Available Info – Probably not for today TODAY’S PATH • Bit of historical background • Distribution of sample sites along river • Inquiry about your stat backgrounds • Variation and its structure • Power • Responses • Zone • Responses to some questions asked during oral presentation • How the sample sites were selected • How the power was calculated

14. VIEW DOWN TRANSECT AT MILE 12.3

15. MARKING TRANSECT AT MILE 12.3

16. MIKE & SCOTT AT THE END!

17. CLIFF AT MILE 135.2(PARTIAL HEIGHT)

18. LOCATION OF SITES BY RIVER MILE RevisitSites 2002 Sites 2001 Sites

19. RESPONSE SIZE AND VARIATION • Data 2001 & 2002, including revisit sites • Vegetation cover • Other responses, but not discussed here • Analysis model • River Width (fixed) • Year (random) – proxy for roughness of immediate terrain • Station = river mile (random) • Residual = Year by Station interaction/remainder

20. MEAN and STANDARD DEVIATIONof VEGETATION COVER vs ZONE (RIVER FLOW LEVEL)

21. STRUCTURE OF VARIANCE • The common formulas for estimating (computing) variance assume UNCORRELATED data. • Reality: This rarely is true. • Examples - • Data from the same SITE, but different years are correlated • Data from the same YEAR, but different years are correlated • Total variance = var(site) + var(year) + var(residual) • Subsequent figures show this

22. COMPONENTS of VARIANCE of VEGETATION COVERSITE, YEAR, and RESIDUAL

23. SAMPLE SIZE ASSUMPTIONSFOR POWER • 25 revisit sites • Revisited annually • 30 sites to be visited on a three-year rotating cycle • “Augmented Rotating Panel Design”

24. POWER TO DETECT TREND IN VEGETATION COVER,ZONE = 15, VARYING % TREND 1%, 2%, 3% 5% PER YEAR

25. RESPONSE TO A QUESTION • “What would be the effect of revisiting sites only in alternating years after the first?” • Response 1: My greatest concern would be retaining the skills and knowledge of those doing the evaluations. (Changing personnel would almost certainly change response definitions in subtle, but unrecognized ways.) • Response 2: Power to detect trend would be delayed somewhat. (Actually a bit more than I initially thought!) • This is illustrated in the next two slides.

26. ALTERNATE REVISIT PLAN and SAMPLE SIZES ASSUMPTIONS FOR POWER • 25 revisit sites • Revisited annually, for first three years (as planned), then in alternating years • 30 sites to be visited on a three-year rotating cycle • A revisit plan with no specific name

27. POWER TO DETECT TREND (2%PER YEAR) IN COVER by ZONE and REVISIT PLANS: CURRENT = n ; ALTERNATE =l

28. OBSERVATIONS RELATIVE TO POWER UNDER THE BIANNUAL REVISIT PLAN • The loss of power for biannual revisits compared to the augmented serially alternating design has some noteworthy characteristics: • Power is the order of a quarter to a third for all years less than a decade. • The time required to get to a given level of power is extended by 3-5 years in the biannual revisit design. • The "years" on the x-axis represents the starting point for ANY comparison • Power accrues from accumulating data, elapsed time, and accumulating trend • Detection of moderate trends requires a commitment to the continuing acquisition consistent and comparable data. • These power evaluations DO NOT relate to comparing years 10 to 11, or any specific two years.

29. MODEL ADAPTATION • Have a set of panels for the “untreated” sites, another for the “treated” sites. • Change X*, but not Y*or F*:

30. POWER TO DETECT DIFFERENCES IN TREND(BETWEEN “TREATED and “UNTREATED”) COOPERATORS Phil Larsen, WED (Part of a presentation for the American Fisheries Society next week) Oregon Plan Team

31. SOURCE OF ESTIMATES OF VARIANCE COMPONENTS • Data source ----- • Response is log of large woody debris • Log10(LWD+0.1) • Variance components values were selected as low and high • All plans assume annual revisit • Number of sites in each set = 5, 10, 15, 20, 25

32. ALL POWER CURVES – SET #1 (8/16/05)

33. POWER CURVES FOR DETECTING DIFFERENCES IN TREND(LOW VALUES OF VARIANCE COMPONENTS)

34. POWER CURVES FOR DETECTING DIFFERENCES IN TREND(HIGH VALUES OF VARIANCE COMPONENTS)

35. POWER CURVES FOR DETECTING DIFFERENCES IN TREND(LOW vs HIGH VALUES OF VARIANCE COMPONENTS, n = 10 EACH)

36. POWER CURVES n = 20ALWAYS REVISIT SAME SITES versusAUGMENTED SERIALLY ALTERNATING FOR HIGH VALUES OF VARIANCE COMPONENTS

37. POWER CURVES FOR HIGH VALUES OF VARIANCE COMPONENTS; AUGMENTED ROTATING PANEL DESIGN

38. TOWARD POWER TO DETECT REGIONAL TRENDWHEN TREND VARIES BY SITE COOPERATORS Phil Larsen, WED, EPA Tim Gerrodette, National Marine Fisheries Service, Southwest Science Center, La Jolla, CA Dawn Van Leeuwen, New Mexico State Univ Will use Oregon Plan data

39. INITIAL SIMPLIFYING CONDITIONS • Every site in a region is revisited every year, and • Some relevant response is evaluated.

44. WHERE NEXT WITH RANDOM SLOPES? • Model adapts to matrices and varied revisit plans • should be incorporated into power calculations • Estimate magnitude of • Montana Bull Trout • Various Oregon Plan responses • Develop web-based software • This is where Tim Gerrodette enters – This generalizes something he did earlier