1. Wildife Population Analysis
Spring 2016

2. Wildlife Population Analysis
3 units credit
Lectures:
Thursday 11:00-11:50 FWS 1219
Labs:
Tuesdays 12:00 – 1:50pm FWS 2218 (Computer Lab)
Instructor: Dr. James (Barry) Grand,
Office: Forestry and Wildlife Sciences Building
Class web site:

3. General Information
Lecture and laboratory material will focus on maximum-likelihood estimation of population parameters
Survival
Recruitment
Abundance
Distribution (patch occupancy)
Model-based estimation
Use of information theoretic methods for model selection, and
Parameterization and analysis of matrix population models.

4. Course Objectives
Introduce state-of-the art methods for design and analysis of studies of demography and abundance.
Provide experience in sample design, analysis, and inference from data sets for the analysis of marked populations.
Introduce methods for using matrix models in the analysis of wild populations.
Provide experience in matrix model design, analysis, and inference for wildlife populations

5. Grading There will be no exams.
Grades will be assigned on a 10-point scale (e.g =A, 80-89=B, etc.) and calculated in the following way:
Participation 25%
Laboratory exercises 50%
Term project 25%
All graded items (e.g. lab assignments, term projects) must be delivered on time for full credit.

6. Course Schedule http://www.auburn.edu/~grandjb/wildpop/
Conflicts & fieldwork
Revised schedule

7. Analysis of Animal Populations
Theory and Scientific Process

8. Objectives Review the basic theory of animal population dynamics
Lay the foundation for the analysis of animal populations
Place in context of good scientific process

9. Theory of population dynamics
Population state (size and distribution) is driven by four vital rates:
Births
Deaths
Immigration
Emigration
The analysis of animal populations concerns estimating the state(s) or the vital rates of a population and the factors that influence them.
Population N
Mortality (1 - S )
Natality
Fertility (F
Emigration
Immigration

10. Vital rates & fitness
Rates – population level contributions of the four basic population processes
Fitness – probability of individual contributions to population
Subtle differences
Estimated in similar ways

11. Why do we care? Conservation & management Sustaining small populations
Controlling large populations
Managing harvestable surplus
Contribution to science
Understanding life history & ecology
Population theory
Either should employ good scientific process!

12. Scientific method Theory Hypotheses Prediction
Observation (data collection)
Comparison of predictions to data (analysis)
Conclude

13. Causation and Science
Causes – explanations for patterns we observe i.e., what is “truth?”
Science – attempts to use logic to establish cause

14. Causation and logic Necessary causation
Must be present for the statement to be true
Sufficient causation
If present assures the statements truth
Deductive logic
Start with premise (assume true)
Determine what else should also be true
Inductive logic
Starts with data and attempts to develop general conclusions

15. Causal relationship Science – attempts to use logic to establish cause
Hypothetical statement:
A  B
Read: If A then B
Antecendent – premise
Consequence – conclusion

16. Logic of Causality
A  B
Affirmation of premise A implies affirmation of conclusion B
Assymetrical – affirmation of B does not affirm A
Example:
If my dog is here (A), then slobber will be on the floor (B)
If there is slobber on the floor (B), then my dog is here (A)?
B  A
Causation established scientifically by identifying cause (C) and effect (E) as either premise (A) or conclusion (B).

17. Necessary causation E  C Equivalent: ~C  ~E (“~” = “not”)
Sets effect (E) as premise (A), and cause (C) as conclusion (B),
E  C
Observing effect means you can conclude cause was present.
If effect (E) is present, cause (C) must be also.
Examples:
photosynthesis (E)  light (C)
forest fire (E)  fuel loads (C)
Equivalent: ~C  ~E (“~” = “not”)
Absence of the effect follows from absence of the cause

18. Sufficient causation C  E
Sets cause (C) as premise (A), and effect (E) as conclusion (B),
C  E
Observing cause means you can conclude the effect must be present.
If effect is present, cause may or may not be present. (alternative causes exist)
Examples:
Heat causes fluid dynamics
Drought causes physiological stress in plants

19. Logical Rigor
Necessary causation logically stronger than sufficient causation:
Necessary: C alone ensures E
Sufficient: C is one condition (possibly among many) that must be present for E
Example:
Heat source = sufficient cause of fire
Fire  Heat Source
Heat + fuel + O2 = necessary cause of fire
Heat  Fire

20. … and in Science Attain necessary causation through manipulation
Control (~C) and treatment (C)
If effect is observed in treatment but not in control, C is sufficient cause of E
If no control used, observed effect in treatment indicates C is necessary cause of E
Use of a control in research = rigor!
Sufficient
C  E
Necessary
E  C

21. Strength of inference (rigor)
Experimental manipulation
Using appropriate controls, replication & randomization
Impact studies (before and after)
Observational studies
Based on a priori hypotheses
Based on a posteriori description
Inference
Strong
Weak
Most studies in ecology
To be avoided

22. Hypothesis Development
a priori Hypotheses = {T} + H
Adds to theory
With experimentation
Leads to sufficient causation & scientific rigor
With observation
Leads to necessary causation
a posteriori description
Just storytelling

23. Models “All models are wrong; some are useful.” (G. Box 1979)
Approximations of reality.
Conceptual  Mathematical
A statistical model is a mathematical expression that help us predict a response (dependent) variable from an hypothesis as a function of explanatory (independent) variables based on a set of assumptions that allow the model not to fit exactly.

24. Modeling One-to-one correspondence with hypotheses Allows prediction
Determines what data is collected
Used to identify parameters of interest
Used to confront predictions with data
Determine strength of evidence

25. Modeling example 1
Observation: Large numbers of dead waterfowl with ingested lead shot in gizzard
Theory: Lead is toxic in many vertebrates
Hypothesis: Ingested lead shot (C) is causing waterfowl mortality (E)
Treatment (C) – mallard fed lead shot
Control (~C) – mallard fed seeds
Model: S~C = SC + E
Prediction: S~C > SC
Observation: S~C > SC
Causation?
Necessary (EC)
Sufficient (CE)

26. Modeling example 2 Theory
Daily survival rates (DSR) of nests increases with nest age because vulnerable nests are found by predators first.
DSR also varies each year because of functional and numerical responses of predators
Hypothesis
Model
DSR varies by nest age
DSR = f(age)
DSR varies annually and by nest age and the effect of age is similar each year
DSR = f(year + age)
DSR varies annually and by nest age and the effect of age is different each year
DSR = f(year x age)

27. Modeling example 2 Several working hypotheses
One model for each hypothesis
Only plausible models not every possible model
Builds from theory
Causation?
Necessary (EC)
Sufficient (CE)

28. Modeling & truth Do models represent truth?
Models are approximations of reality
Searching for the best approximating model
How do we do that?
Confront the model with data
Examine the strength of evidence

29. Parsimony Defined - Economy in the use of means to an end.
…[using] the smallest number of parameters possible for adequate representation of the data.”
Box and Jenkins (1970:17)
In the context of our analyses, we strive to be economical in the use of parameters to explain the variation in data.

30. Trade-off between precision and bias.
As K, the number of parameters increases, bias increases and variance decreases.
Best Approximating Model

31. Precision versus bias Unbiased; Precise Biased; Precise
Biased; Imprecise
Unbiased; Imprecise

32. Information Theoretic Methods
Kullback-Leibler (Kullback and Liebler 1951) “distance," or “information" seeks to quantify the information contained in a model
i.e., distance from “truth”
Information Theoretic Methods use measures of information for data-based model selection.

33. Assignment Read Williams (1977) & Johnson (1999)
Download the Lab exercise & follow the instructions
We will discuss on Tuesday