Data Analysis: Cool things networks are doing and planning

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Data Analysis Cool things networks are doing and
planning
Meeting of the Networks Fifth IM
Meeting San Diego, Feb. 6-10, 2006 S. Garman
- NCPN
Contributors to this Presentation E. Beever
(GLKN) W. Cohen/R. Kennedy (USDA FS) R.
DenBleyker (NCPN) F. Dieffenbach (NETN) S. Gende
(SEAN) C. Hoffman, J. Freilich (NCCN) M. Kunze
(GRSM) G. Rowell (HTLN-Prairie Cluster) B.
Thompson (SWAN) A. Williams (SHEN)
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What is Cool?
Monitoring plans describe solid approaches to
data summary, status and trend analyses lots of
brain power in the IM program! Cool things -
approaches to data analysis (display, summary,
stats) that are - pushing the envelope -
non-traditional - simple, yet highly
effective - critical given unique aspects of
IM data
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Topics
Change Detection Directed Change-vector Analysis
Trend, Status Bayesian Geostatistical
Benthic ABC Kendall for WQ
Data Summary/Display ATBI Data Summary
Systems Climate Web Tool
Summary Methods for Reporting Condition
Thresholds Bayesian Belief Nets
Under development on WEB version of talk
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Thematic maps (from satellite imagery) useful in
monitoring landcover. Change detection
sometimes based on differencing maps
(determining theme-class changes) between years

theme changes
Time t
Time t1
Change based on differences in thematic classes
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Differencing themes is not a good approach. Theme
maps are model-based, subject to error
propagation. Different classification methods
among years also introduces error.
theme changes
Time t
Time t1
NOT COOL
Change based on differences in thematic maps
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NCCN - Landcover Change

• Monitor using spectral-change information only,
  not relying on initial, thematic maps
• Monitor state over time by tracking spectral
  values in tasseled-cap space (Directed Change
  Vector analysis - DCV)

TC Greenness
TC Brightness
source R. Kennedy
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• Identify keystone types in spectral space

Keystone Broadleaf
DATE 1
Keystone Old Conifer
Keystone Barren
Keystone Snow
source R. Kennedy
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• Identify keystone types in spectral space
• Characterize change vector relative to keystone
  types

Keystone Broadleaf
DATE 1
DATE 2
Keystone Old Conifer
Keystone Barren
Keystone Snow
source R. Kennedy
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NCPN, SCPN Landcover Mapping and Change
Time t - determine/store location of pixels in
TC space - thematic map from
Keystone/Veg-map data
Time t1 apply DCV - identify real change
- identify new thematic class of change -
update thematic map of land cover
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Bayesian Trend Analysis
Increasing number of Networks propose to
consider Bayesian methods for Trend Analyses
Conventional statistical analyses (frequentist
statistics) calculate the probability of
observing data given a specific value for a
parameter, such as the null hypothesis
Bayesian methods calculate the probability of a
parameter value given the observed data
- use prior knowledge/beliefs (prior prob.
distribution) - update beliefs (posterior
prob. distribution) - can evaluate the
probability of many values of a parameter
Wade, P. R. 2000. Conservation Biology
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Frequentist Trend Analysis
No slope 0
(alpha0.05) Pop A - sign. slope Pop B
non-sign. slope
Slope -0.03 P 0.048

• Tell park staff
• To begin to worry
• about Pop A
• 2) Not sure about Pop B
• looks like a decline but
• lack statistical evidence
• need more data!

Slope -0.10 P 0.053
Wade, P. R. 2000. Con. Biol.
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Bayesian Trend Analysis
Prior distribution previous information about
parameter values - the belief
component Likelihood distribution prob. of
observing the data for every possible parameter
value derived from sample data
Likelihood
Prior (uniform in this case)
Wade, P. R. 2000. Con. Biol.
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Bayesian Trend Analysis
Posterior distribution integral of the
product of prior and likelihood distributions
- prob. distribution of parameter values
used to make inference about parameters - in
subsequent analysis of a new sample, this
posterior becomes the new prior i.e.,
updated knowledge
Posterior
Prior (uniform in this case)
Wade, P. R. 2000. Con. Biol.
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Bayesian Trend Analysis
Posterior distribution for example
A
B
Pop A Pop B Odds Ratio stable
vs. 5 decline evidence 5 decline is 5 X
for stable more probable
Pop A Pop B Prob. of 5 or faster
decline 0.0 0.86
Wade, P. R. 2000. Con. Biol.
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POP QUIZ Select the most correct answer
Bayesian Trend Analysis is

• An excuse not to use real statistics
• Cool, given my prior beliefs!
• Another tool for the toolbox!
• - IM trend data likely to be noisy
• - Risk of missing an early warning signal too
  great to ignore benefits of approach
• d) Not sure what it really is, need more info
• - attend/see slides from Data Analysis
  break-out session
• - talk with Scott Gende (SEAN)

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Geostatistical Analysis of Plant Communities at
Tallgrass Prairie National Preserve Kansas L.
Monika Moskal Jennifer Haack Gareth Rowell and
Mike DeBacker
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Semivariogram
Sill
Semivariance
Range
Nugget
Separation Distance
The semivariogram - summarizes the magnitude,
spatial scale and pattern of the variation in the
region of interest
source G. Rowell
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Spatial pattern - Legumes cover
2001 Range 1000 m Exp. Model r2 0.82
Semivariance
Separation distance (m)
2004 Range 655 m Exp. Model r2 0.40
Semivariance
Separation distance (m)
source G. Rowell
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Change from 2001 to 2004

• No local decrease in legumes, but the spatial
  homogeneity reduced
• Use Range metric to assess spatial trends?

Range (spatial continuity)
cover
2001
2004
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Aquatic (freshwater) Macro-Invert. Trends - NCCN
NCCN Aquatic Systems - relatively
pristine - very narrow disturbance
gradients - subtle changes expected over time
- critical to detect subtle changes to
preserve pristine conditions - existing
benthic monitoring methods designed to
detect large changes (pristine vs.
impacted site comparisons)
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• Propose development/use of Abundance
• Biomass Comparison (ABC)
• The ABC Concept -

Under stable pristine conditions, where
benthic community approaches equilibrium,
biomass dominated by few large species
numerical dominants, however, are smaller
species K-dominance curves (KDC) show relative
proportions of biomass and numbers
attributable to each species, and illustrate
system conditions based on theory
NCCN motivation reference sites not needed with
ABC - changes in KDC curve shapes can
be used in trend assessments
Warwick, R. M. 1986. Marine Biology. NCCN
PMIS Proposal (2005)
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KDC for pristine biomass above numbers
curve KDC for degraded conditions opposite of
pristine KDC for intermediate conditions
congruent curves
Unpolluted (pristine)
Grossly polluted
Hypothetical k-dominance curves
Warwick, R. M. 1986. Marine Biology
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Methods to roll-up monitoring results for
scorecard reporting NETN - Condition
Thresholds SWAN Bayesian Belief Nets (BBNs)
State of the Park Scorecard
source - NETNs Monitoring Plan a version of S.
Fancys state of the park
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NETN Vital Signs Scorecard

• Condition Threshold approach assigns individual
  metrics of a Vital Sign to a condition class
  (good, caution, sign. concern) for each
  monitoring plot. Class bounds defined by
  literature, experts, data, etc

VS Forest Vegetation Metrics Tree Mortality
Rate (TMR) - Live Tree Basal Area
(LTBA) - 8 others. Condition Class
Rating Good (5 pts) Caution (3 pts)
Sign. Concern (1 pt) TMR lt3 3-10
gt10 LTBA gt20 10-20 lt10 .
(source - NETN Monitoring Plan, Chapter 7)
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NETN Vital Signs Scorecard

• Ratings (numeric scores) assigned to each
  condition class

VS Forest Vegetation Metrics Tree Mortality
Rate (TMR) - Live Tree Basal Area
(LTBA) - 8 others. Condition Class
Rating Good (5 pts) Caution (3 pts)
Sign. Concern (1 pt) TMR lt3 3-10
gt10 LTBA gt20 10-20 lt10 .
(source - NETN Monitoring Plan, Chapter 7)
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• Condition class of
• metric(s) can be
• Mapped
• Ratings of metrics
• can be summed to
• provide a
• condition score
• for a Vital Sign
• ________________
• Spatial
• representation
• is Cool!

(source NETN contrived example)
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NETN Vital Signs Scorecard

• Aggregate metrics into indices to report
• on Scorecard categories - methods TBD

Forest Vegetation metrics
Herps metrics
3 other VSs
weighted averages of ratings, of condition
scores?
complex algorithms?, etc
Biological Integrity
Scorecard categories
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Dashboard Displays graphical display of
inventories, trends, rolled-up summary of
status (ratings scaled from -1 to 1)
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• 3 pieces of information displayed in each dial
• current rolled-up value (bottom center)
• resource condition (color code)
• green - good, yellow - caution, red concern
• change in value (up or down arrow, horizontal
  bar)

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Bayesian Belief Nets (BBNs) SWAN

• BBNs
• use directed, acyclic graphs to
• represent a system
• use probability theory to represent
• dependencies among knowledge components of
• a system incorporates uncertainty
• provides ability to forecast system change
• can be updated with new knowledge

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A Very Simple BBN
Root Node
First define system components - watershed
history - habitat condition - fish pop.
trends Second define states (levels) within a
node that are mutually exclusive states of
higher-level nodes result in states
of lower-level nodes Third define prob. of
relationships among states
Fish
Leaf Node
source SWAN Monitoring Plan, Appendix IV
(taken from Lee, D. 2000)
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Data, expert opinion, simulation models
The is the conditional probability table that
quantifies relationships between watershed
history and habitat condition (the probability
of a habitat condition resulting for a type of
watershed-level disturbance)
source SWAN Monitoring Plan Appendix IV
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Probabilities of each state level are required
(belief vectors), and should reflect
current/historical conditions of the
area/population of interest. If unknown,
probabilities can be initiated proportionally.
NOTE prob. are shown as in this example.
source SWAN Monitoring Plan Appendix IV
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• Given conditional probs. and state-level probs.,
  a BBN is mathematically solved
• Probabilities of Habitat Condition are
• derived from watershed history initial state
  probs.
• - Probabilities for the different types of
  population trends are a key result

source SWAN Monitoring Plan Appendix IV
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Hypothetical example of a BBN for reporting
S. Garman
In the early days of monitoring, BBNs useful to
capture trend/stauts uncertainty
Disturbance Undis. Mod.Dis. Highly Dis.
Cond. Prob. Table based on historical
evidence, beliefs
Vital Sign C Rapid Slow Nochange Slow
Rapid
Vital Sign B Rapid Slow Nochange Slow
Rapid
Vital Sign A Trend Rapid Slow Nochange Slow
Rapid
Cond. Prob. Table based on historical
evidence, beliefs
Biological Integrity Improv., Nochange, Deteriora
ting Good, Caution, Concern
Reportcard Category (prob. statements re trends
status)
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Hypothetical example of a BBN for reporting
S. Garman
Over time, monitoring data contributes to CP
table
Disturbance Undis. Mod.Dis. Highly Dis.
Cond. Prob. Table based on monitoring data ,
beliefs
Vital Sign C Rapid Slow Nochange Slow
Rapid
Vital Sign B Rapid Slow Nochange Slow
Rapid
Posterior Dist.
Vital Sign A Trend Rapid Slow Nochange Slow
Rapid
Cond. Prob. Table based on monitoring
data, beliefs
Biological Integrity Improv., Nochange, Deteriora
ting Good, Caution, Concern
Reportcard Category (prob. statements re trends
status)
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http//165.83.102.13/ATBI_Start.cfm
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ATBI display
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ATBI display
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Data Summary System for Aquatic
MacroInvertebrates Alan Williams - Shenandoah NP
See http//science.nature.nps.gov/im/monitor/mee
tings/Austin_05/GRowell_DataSummaries.ppt

• Features
• Multiple summary metrics drawn into a standard
  format
• Compartmentalizes each metric calculation
• Facilitates uniform presentation

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Alans User Interface for Summary Operations
See http//science.nature.nps.gov/im/monitor/mee
tings/Austin_05/GRowell_DataSummaries.ppt
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Data Summary Viewer Tool
See http//science.nature.nps.gov/im/monitor/mee
tings/Austin_05/GRowell_DataSummaries.ppt
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NCPN Climate Web Tool Interactive analysis of
climatic extremes
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Water Quality Trends - GLKN
Seasonal Kendall test is one of several
preferred nonparametric tests for evaluating
interannual trends in water quality. One can
analyze data by months, seasons, or by
limnological strata. The average of slopes
becomes the final trend line. Handles strong
within-yr variability while being efficient for
understanding interannual trends