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 1s 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
TODAYS 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
Revisit Sites
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 (2PER 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 Yor 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(LWD0.1)
• 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
versus AUGMENTED 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.

40
(No Transcript)
41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
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