TRENDS OVER TIME IN ECOLOGICAL RESOURCES OF A REGION

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DESIGNING PANEL SURVEYSSPECIFICALLY RELEVANT TO
NATIONAL PARKSIN THE NORTHWEST

• N. Scott Urquhart
• Senior Research Scientist
• Department of Statistics
• Colorado State University
• Fort Collins, CO 80527-1877

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INFERENCE PERSPECTIVES

• Design Based
• Inferences rest on the probability structure
  incorporated in the sampling plan
• Completely defensible very minimal assumptions
• Limiting relative to using auxiliary information
• Model Assisted
• Uses models to compliment underlying sampling
  structure
• Has opportunities for use of auxiliary
  information
• Model Based (eg spatial statistics)
• Ignores sampling plan
• Defensibility lies in defense of model

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APPROACH OF THIS PRESENTATION

• Use tools from the arena of
• Model assisted and
• Model based analyses
• To study the performance of
• Design based
• Model-assisted analyses
• WHY?
• Without models,
• performance evaluations need simulation
• Before substantial data have been gathered
• No basis for values to enter into simulation
  studies

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STATUS TRENDS OVER TIME IN ECOLOGICAL
RESOURCES OF A REGIONMAJOR POINTS

• Regional trend ¹ site trend
• Detection of trend requires substantial elapsed
  time
• Regional OR intensive site
• Almost all indicators have substantial patterns
  in their variability
• Design to capitalize on this dont fight it.
• Minimize effect of site variability with planned
  revisits specific plans will be illustrated
• Design tradeoffs TREND vs STATUS

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REGIONAL TREND ¹ SITE TREND

• The predominant theme of ecology
• Ecological processes
• How does a specific kind of ecosystem function
• Energy flows
• Food webs
• Nutrient cycling
• Most studies of such functions must be temporally
• Temporally intensive
• What material goes from where to where?
• Consequently spatially restrictive
• In this situation Temporal trend site trend

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REGIONAL TREND ¹ SITE TREND( - CONTINUED)

• The predominant theme of ecology versus
• A Substantial (any) Agency Focus
• All of an ecological resource
• In an area or region
• Across all of the variability present there
• Most government regulations
• Apply to a whole area or region
• Only a few apply to specific sites
• The definition of a region certainly depends on
  what agency makes the regulation

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REGIONAL TREND ¹ SITE TREND( - CONTINUED - III)

• The predominant theme of ecology versus
• A substantial agency (EPA) focus
• An entire region, like
• Lakes in the Adirondack Mountains
• All lakes in Northeastern US
• All (wadeable) streams the mid-Appalachian
  Mountains
• Or National Park Service
• All riparian areas in Olympic National Park
• All riparian areas in National Parks in the
  coastal Northwest

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TREND ACROSS TIME - What is it?

• Any response which changes across time in a
  generally
• Increasing or
• Decreasing
• Manner shows trend
• Monotonic change is not essential.
• If trend of this sort is present, it will be
  detectable as linear trend.
• This does NOT mean trend must be linear
  (examples follow)
• Any specified form is detectable
• Time years, here

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TREND ACROSS TIME - What is it?(continued)
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TREND DETECTION REQUIRES SUBSTANTIAL ELAPSED TIME

• IT IS NEARLY IMPOSSIBLE TO DETECT TREND IN LESS
  THAN FIVE YEARS. WHY?

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BIOLOGICAL INDICATORS HAVE SOMEWHAT MORE
VARIABILITY THAN PHYSICAL INDICATORS BUT THIS
VARIES, TOO

• Subsequent slides show the relative amount of
  variability
• Ordered by the amount of residual variability
  least to most (aquatic responses)
• Acid Neutralizing Capacity
• Ln(Conductance)
• Ln(Chloride)
• pH(Closed system)
• Secchi Depth
• Ln(Total Nitrogen)
• Ln(Total Phosphorus)
• Ln(Chlorophyll A)
• Ln( zooplankton taxa)
• Ln( rotifer taxa)
• Maximum Temperature

And others, both aquatic and terrestrial
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IMPORTANT COMPONENTS OF VARIANCE

• POPULATION VARIANCE
• YEAR VARIANCE
• RESIDUAL VARIANCE

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IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED)

• POPULATION VARIANCE
• Variation among values of an indicator (response)
  across all sites in a park or group of related
  parks, that is, across a population or
  subpopulation of sites

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IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED II)

• YEAR VARIANCE
• Concordant variation among values of an indicator
  (response) across years for ALL sites in a
  regional population or subpopulation
• NOT variation in an indicator across years at a
  single site
• Detrended remainder, if trend is present
• Effectively the deviation away from the trend
  line (or other curve)

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IMPORTANT COMPONENTS OF VARIANCE ( - CONTINUED -
III)

• Residual component of variance
• Has several contributors
• YearSite interaction
• This contains most of what ecologists would call
  year to year variation, i.e. the site specific
  part
• Index variation
• Measurement error
• Crew-to-crew variation (minimize with documented
  protocols and training)
• Local spatial protocol variation
• Short term temporal variation

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SOURCE OF DATA FOR ESTIMATES OF COMPONENTS OF
VARIANCE

• EMAP Surface Waters Northeast Lakes Pilot
  1991 - 1994
• About 450 observations
• Over four years
• Including about 350 distinct lakes
• Design allowed estimation of several residual
  components

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SOURCE OF COMPONENTS OF VARIANCE FROM NW HABITAT

• Oregon Department of Fisheries and Wildlife
  stream habitat survey
• GRADIENT Stream gradient measured on site
• WIDTH  Wetted stream width
• ACW Active Channel
• ACH Active Channel Height
• UNITS100 Number of distinct habitat units per
  100 meters of stream length
• NOPOOLS Number of pools in the surveyed reach
• POOLS100 Number of pools per 100 meters
• PCTPOOL of reach length in pools
• PCTFINES stream substrate that is sand or
  finer particle size
• PCTGRAVEL of stream stubstrate that is gravel
  sized particles
• RIFSNDOR of riffle stream length that is sand
  or finer particle size
• RIFGRAV of riffle stream length that is
  gravel sized particles
• SHADE stream channel shaded
• LOG(PIECESLWD 0.01) Number of pieces of large
  woody debris per 100 meters.
• LOG(VOLUMELWD 0.01) Volume of large woody
  debris (m3/100 meters)
• RESIDPD Volume of residual pools (pools
  remaining if streamflow stopped)

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SOURCE OF COMPONENTS OF VARIANCE FROM GRAND CANYON

• Grand Canyon Monitoring and Research Center
• Effects of Glen Canyon Dam on the near River
  Habitat in the Grand Canyon
• At various heights above the river
• Height is measured as the height of the rivers
  water at various flow rates
• Eg 15K cfs, 25K cfs, 35K cfs, 45K cfs 60K
  cfs
• Using first two years data
• Mike Kearsley UNA
• Design spatially balanced
• With about 1/3 revisited

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ALL VARIABILITY IS OF INTEREST

• The site component of variance is one of the
  major descriptors of the regional population
• The year component of variance often is small to
  small to estimate. It is a major enemy for
  detecting trend over time.
• If it has even a moderate size, sample size
  reverts to the number of years.
• In this case, the number of visits and/or number
  of sites has no practical effect.

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ALL VARIABILITY IS OF INTEREST( - CONTINUED)

• Residual variance characterizes the inherent
  variation in the response or indicator.
• But some of its subcomponents may contain useful
  management information
• CREW EFFECTS gt training
• VISIT EFFECTS gt need to reexamine definition
  of index (time) window or evaluation protocol
• MEASUREMENT ERROR gt work on laboratory/measurem
  ent problems

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DESIGN TRADE-OFFS TREND vs STATUS

• How do we detect trend in spite of all of this
  variation?
• Recall two old statistical friends.
• Variance of a mean, and
• Blocking

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DESIGN TRADE-OFFS TREND vs STATUS( - CONTINUED)

• VARIANCE OF A MEAN
• Where m members of the associated population
  have been randomly selected and their response
  values averaged.
• Here the mean is a regional average slope, so
  "s2" refers to the variance of an estimated
  slope ---

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DESIGN TRADE-OFFS TREND vs STATUS( - CONTINUED
- II)

• Consequently
• Becomes
• Note that the regional averaging of slopes has
  the same effect as continuing to monitor at one
  site for a much longer time period.

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DESIGN TRADE-OFFS TREND vs STATUS( - CONTINUED
- III)

• Now, s2, in total, is large.
• If we take one regional sample of sites at one
  time, and another at a subsequent time, the site
  component of variance is included in s2.
• Enter the concept of blocking, familiar from
  experimental design.
• Regard a site like a block
• Periodically revisit a site
• The site component of variance vanishes from the
  variance of a slope.

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NOW PUT IT ALL TOGETHER

• Question What kind of temporal design should
  you use for Northwest National Parks?
• Well investigate two (families) of recommended
  designs.
• All illustrations will be based on 30 site
  visits per year, as Andrea recommended.
• General relations are uninfluenced by number of
  sites visited per year, but specific performance
  is.
• Well use the panel notation Trent set out.

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RECOMMENDATION OF FULLER and BREIDT

• Based on the Natural Resources Inventory (NRI)
• Iowa State US Department of Agriculture
• Oriented toward soil erosion
• Changes in land use
• Their recommendation
• Pure panel 1-0 Always Revisit
• Independent 1-n Never Revisit
• Evaluation context
• No trampling effect remotely sensed data
• No year effects
• Administrative reality of potential variation in
  funding from year to year

MATH RECOME 100 50 0 50
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TEMPORAL LAYOUT OF (1-0), (1-n)
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1-0 X X X X X X X X X X X X X X X X X X X X
1-n X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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FIRST TEMPORAL DESIGN FAMILY

• 30 site visits per year

1-0 30 20 10 0
1-n 0 10 20 30
ALWAYS REVISIT NEVER REVISIT
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POWER TO DETECT TRENDFIRST TEMPORAL DESIGN
FAMILY NO YEAR EFFECT
Always Revisit
Never Revisit
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POWER TO DETECT TRENDFIRST TEMPORAL DESIGN
FAMILY, MODEST ( SOME) YEAR EFFECT
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POWER TO DETECT TRENDFIRST TEMPORAL DESIGN
FAMILYBIG ( LOTS) YEAR EFFECT
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FOREST INVENTORY ANALYSIS (FIA) HAS A SYSTEMATIC
SPATIAL DESIGN WITH 1-9
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X

• Doesnt match up well with 1-0 and 1-n
• We need to investigate alternatives

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SERIALLY ALTERNATING TEMPORAL DESIGN (1-3)4
SOMETIMES USED BY EMAP
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X
(1-3)4 X X X X X X
X X X X X
X X X X X
X X X X X
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SERIALLY ALTERNATING TEMPORAL DESIGN (1-3)4
SOMETIMES USED BY EMAP
YEAR 1 2 3 4 5 6 7 8 9 10 11
FIA X X
(1-3)4 X X X
X X X
X X X
X X

• Unconnected in an experimental design sense
• Very weak design for estimating year effects, if
  present

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SPLIT PANEL (1-4)5 , ---
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X
(1-4)5 X X X X X
X X X X
X X X X
X X X X
X X X X

• AGAIN, Unconnected in an experimental design
  sense
• Matches better with FIA
• Still a very weak design for estimating year
  effects, if present

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SPLIT PANEL (1-4)5 ,(2-3)5
YEAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
FIA X X X
(1-4)5 X X X X X
X X X X
X X X X
X X X X
X X X X
(2-3)5 X X X X X X X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X

• This Temporal Design IS connected
• Has three panels which match up with FIA

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SECOND TEMPORAL DESIGN FAMILY

• 30 site visits per year

1-4 30 20 10 0
2-3 0 5 10 15
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POWER TO DETECT TRENDSECOND TEMPORAL DESIGN
FAMILY NO YEAR EFFECT
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POWER TO DETECT TRENDSECOND TEMPORAL DESIGN
FAMILYSOME YEAR EFFECT
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POWER TO DETECT TRENDSECOND TEMPORAL DESIGN
FAMILYLOTS OF YEAR EFFECT
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COMPARISON OF POWER TO DETECT TRENDDESIGN 1 2
ROWS
YEAR EFFECT NONE
SOME
LOTS
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POWER TO DETECT TRENDVARYING YEAR EFFECT AND
TEMPORAL DESIGN
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 1, NO
YEAR EFFECT
TOTAL OF 30 SITES
110 SITES VISITED BY YEAR 5
410 SITES VISITED BY YEAR 20
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 1, SOME
YEAR EFFECT
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 1, LOTS
OF YEAR EFFECT
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 2, NO
YEAR EFFECT
TOTAL OF 75 SITES
TOTAL OF 150 SITES
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 2, SOME
YEAR EFFECT
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STANDARD ERROR OF STATUSTEMPORAL DESIGN 2, LOTS
OF YEAR EFFECT
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SO WHAT?

• Regardless of evaluation circumstances,
• Trend detection improves the more the same sites
  are revisited
• Status estimation improves as the number of
  distinct sites visited increases
• Temporal design 2 is better than temporal design
  1 in relevant cases
• Its power is only slightly influenced by split
  between panels

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METADATA

• Really important for your successors
• Like your grandchildrens generation
• Ill comment about this later in the conference
  if you want me to

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FUNDING ACKNOWLEDGEMENT
The work reported here today was developed under
the STAR Research Assistance Agreement CR-829095
awarded by the U.S. Environmental Protection
Agency (EPA) to Colorado State University. This
presentation has not been formally reviewed by
EPA.  The views expressed here are solely those
of presenter and STARMAP, the Program he
represents. EPA does not endorse any products or
commercial services mentioned in this
presentation.
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TEMPORAL DESIGN 1ALWAYS REVISIT
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TEMPORAL DESIGN 2NEVER REVISIT
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TEMPORAL DESIGN 3AUGMENTED SERIALLY ALTERNATING
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TEMPORAL DESIGN 4 SPLIT PANELSERIALLY
ALTERNATINGPLUS SERIALLY ALTERNATING WITH
CONSECUTIVE YEAR REVISITS
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