Grand Overview

1
Grand Overview

• Environmental Problems are generally characterize
  by noisy and ambiguous data.
• Understanding errors and data reliability/bias is
  key to implementing good policy

2
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

3
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 gt data organization and
  reduction data visualization statistical
  analysis
• Comparing different models

4
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.

5
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

6
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

7
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

8
Global Warming I
9
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

10
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

11
Trend Extrapolation Techniques
12
Trend Estimation

• Exponential vs linear models
• Exponential Exhaustion Timescales
• Why R doesnt matter so much
• Why is exhaustion timescale driven mostly by the
  consumption rate, k
• Exponential doubling times

13
The Importance of Trend Extrapolation
14
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

15
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 t-test)
• KS test is excellent for testing observed
  distribution for normality (Excel random number
  generator ? normal distribution)

16
Predator Prey Relations

• 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

17
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

18
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

19
Applied Ecology

• Know what the terms mean and understand what an
  iterative solution is

20
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?

21
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?

22
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

23
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!

24
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.

25
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