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Grand Overview
Environmental Problems are generally
characterize by noisy and ambiguous
data.
Understanding errors and data
reliability/bias is key to implementing
good policy
Goals of this Course
• To gain practice in how to frame a problem
• To practice making toy models involving data
organization and presentation
• To understand the purpose of making a model
• To understand the limitations of modeling and
that models differ mostly in the precision of
predictions made
• Provide you with a mini tool kit for analysis
Sequence for Environmental Data
Analysis
• Conceptualization of the problem  which data
is most important to obtain
• Methods and limitations of data collection 
know you biases
• Presentation of Results => data organization
and reduction; data visualization; statistical
analysis
• Comparing different models
Three Problems with Environmental
Data
• Its usually very noisy
• It is often unintentionally biased because
the wrong variables are being measured to
address the problem in question.
• A control sample is usually not available.
Some Tools
Linear Regression  predictive power
lies in scatter
Slope errors are important
Identify anomalous points by sigma
clipping (1-cycle)
Learn to use the regression tool in
Excel
Least squares method used for best
fit determination
More Tools
Chi square test
Understand how to determine your
expected frequencies
Two chi square statistic requires
marginal sum calculations
Chi square statistic used to accept or
reject the null hypothesis
Know how to compute it
Estimation Techniques
Extremely useful skill  makes you
valuable
 Devise an estimation plan  what factors
do you need to estimate
 Scale from familiar examples when
possible
 Perform a reality check on your estimate
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Global Warming I
Global Warming II
Understand basics of “greenhouse effect”
 Ice core data and lag time issue
 What are best indicators of global climate
change
 Why is global mean temperature a poor
proxy
 Spatial distribution of temperature
changes is most revealing
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Global Warming III
Why is methane such a potential problem?
 What are anthropogenic sources of
methane emission and how can they be
curtailed
 What is the hydrate problem?
 What are some other smoking guns for
global warming/climate change?
 120 Tornadoes Touch down March 12,
2006
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Trend Extrapolation Techniques
Trend Estimation
Exponential vs linear models
 Exponential Exhaustion Timescales
 Why R doesn’t matter so much
 Why is exhaustion timescale driven mostly
by the consumption rate, k
 Exponential doubling times
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The Importance of Trend
Extrapolation
Statistical Distributions
Why are they useful?
 How to construct a frequency distribution
and/or a histogram of events.
 Frequencies are probabilities
 How the law of large numbers manifests
itself  central limit theorem; random
walk; expectation values
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Comparing Distributions
• Why?  to identify potential differences and
environmental drivers
• KS test  uses the entire distribution by
comparing cumulative frequency distributions
(cfd)  more powerful than tests based on
means and standard deviations (e.g. Z-test; ttest)
• KS test is excellent for testing observed
distribution for normality (Excel: random number
generator  normal distribution)
Predator Prey Relations
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Non linear in nature  small changes in one
part of the system can produce rapid population
crashes
Density dependent time lags are important
“Equilibrium” is intrinsically unstable
Logistic growth curve makes use of carrying
capacity concept, K
Negative feedback occurs as you approach K
R selected vs. K selected mammals
Human Population Projections
What assumptions are used?
 Does human population growth respond to
the carrying capacity concept?
 World population growth rate is in
continuous decline (but still positive)  will
this continue indefinitely?
 What role does increased life expectancy
have?  changing population pyramids
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Non Normal Distributions
Positive and Negative skewness 
median value more relevant than mean
 Bi modal  sum of two normal
distributions if the peaks are well
separated
 Poisson Distribution for discrete arrival
events  review this
 Exponential Distribution for continuous
arrival events
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Applied Ecology
 Know what the terms mean and
understand what an iterative solution is:
Applied Ecology II
 Understand from the point of view of the
framework (e.g. the equations) why stability is
very hard to achieve
 What role does finite reproductive age play?
 What makes human growth special within this
framework.
 Understand concepts of equilibrium occupancy
and demographic potential
 Why is error assessment so important here?
Probabilistic Outcomes
 Why is “natural selection” best
described in this way?
 What parameters determine the
outcomes?
 What are the differences between
stabilization, directional, and
disruptive forms of evolution?
Techniques for Dealing with Noisy
Data
Boxcar smoothing (moving average)
 Exponential smoothing
 Binning the data into two groups and
comparing means via the Z-test (e.g.
rainfall broken up into two distinct time
periods)
 Construction of a waveform and
comparison of waveforms
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The Data Rules
Always, always ALWAYS plot your data
 Never, never NEVER put data through
some blackbox reduction routine without
examining the data themselves
 The average of some distribution is not
very meaningful unless you also know the
dispersion. Always calculate the dispersion
and then know how to use it!
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More Data Rules
Always compute the level of significance
when comparing two distributions
 Always know your measuring errors. If
you don't then you are not doing science.
 Always calculate the dispersion in any
correlative analysis. Remember that a
correlation is only as good as the
dispersion of points around the fitted line.
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The Biggest Rules
Always require someone to back up their
"belief statements" with credible data.
 Change the world. Stop being a passive
absorber of some one else's belief system.
 Frame all environmental problems
objectively and seek reliable data to
resolve conflicts and make policy
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