Wildife Population Analysis Spring 2016

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: 3236 Forestry and Wildlife Sciences Building E-mail: grandjb@auburn.edu Class web site: www.auburn.edu/~grandjb/wildpop

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.

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

Grading There will be no exams. Grades will be assigned on a 10-point scale (e.g. 90-100=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.

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

Analysis of Animal Populations Theory and Scientific Process

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

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

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

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!

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

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

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

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

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).

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

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

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

… 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

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

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

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.

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

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)

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)

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)

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

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.

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

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

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.

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