# WIS 6466

Wildlife Population Modeling

Instructor:
Madan K. Oli

324 Newins-Ziegler Hall

Phone: 846-0561

E-mail: olim@wec.ufl.edu

Course description:

Population models are important tools that are routinely used to understand, explain and predict the dynamics and persistence of biological populations. This course is designed to provide rigorous background in the theory of population models, and application of these tools to address basic and applied ecological questions. The primary focus of this course will be the matrix population models because they are powerful, flexible and can be applied to organisms with diverse life-histories and population structures; consequently, matrix models are the most popular models in basic and applied ecology. However, we will also explore topics in lie table analysis, integral projection models (IPMs) and individual- (or agent-) based models (IBMs). Relevant concepts in matrix algebra will be reviewed to provide students with necessary mathematical background. Computer exercises will involve analysis of real-life data using MATLAB or other relevant programming languages.

## COURSE OUTLINE

PART I. PRELIMINARIES

- Introduction to population models
- Review of life table analysis
- Introduction to MATLAB

PART II. A “CRASH COURSE” IN MATRIX ALGEBRA (Guest lecture by Dr. David Wilson)

- Definitions and matrix notations
- Matrix operations
- Determinants, inverses
- Eigenvalues and eigenvectors

PART III. AGE-STRUCTURED (LESLIE MATRIX) MODELS

- Model formulation and parameterization
- Population projection
- Population growth rate, stable age distribution, reproductive values,...
- Sensitivity analysis
- Sensitivity
- Elasticity

PART IV. STAGE-STRUCTURED MODELS

- Parameterization of stage-structured models
- Population growth rate, stable stage distribution, reproductive values, ...
- Sensitivity analysis
- Age-specific traits from stage-specific models

PART V. SENSITIVITY ANALYSIS REVISITED

- Lower level sensitivities
- Second derivatives of eigenvalues and sensitivity of elasticities
- Sensitivity analysis using partial life-cycle models
- Sensitivity analysis of transient dynamics

PART VI. LIFE TABLE RESPONSE EXPERIMENTS

- Fixed effect designs
- Random effect designs

PART VII. PARAMETER ESTIMATION

- Estimation of transition probabilities
- Estimation of reproductive parameters (fecundity, breeding probabilities)

PART VIII. STATISTICAL INFERENCE

- Confidence interval
- Loglinear analysis
- Radomization methods

PART IX. STOCHASTIC MODELS

- Environmental stochasticity
- Demographic stochasticity
- Incorporating sources of variation into matrix models

PART X. DENSITY-DEPENDENT MODELS

- Incorporating density-dependence into matrix models
- Analysis of density-dependent matrix models

PART XI. MATRIX METAPOPULATION MODELS

- What are metapopulations?
- Matrix metapopulation model: construction and analyses

PART XII. POPULATION VIABILITY ANALYSIS (PVA)

- Introduction to PVA
- PVA models based on estimates of abundnace
- PVA using matrix population models

## Required Text

Caswell, H. 2001. Matrix population models. Second edition. Sinauer, Sunderland, MA.