# WILDLIFE POPULATION MODELING (WIS 6466)

## COURSE DESCRIPTION:

Matrix population models are standard tools for the study of life history and population dynamics of age- or stage-structured populations. These models have become popular in population biology because they can be applied to organisms with diverse life-histories and population structures. This course is designed to provide a rigorous background in theory of matrix population models, and application of these tools to address basic and applied ecological questions. Relevant concepts in matrix algebra will be reviewed to provide necessary mathematical background. Computer exercises will involve analysis of real-life data using MATLAB.

## COURSE OBJECTIVES:

By the end of the semester, students will:

• have a thorough understanding of the process of modeling the dynamics and persistence of biological populations
• be able to construct and analyze life tables, and age- and stage- structured matrix population models,
• be able to conduct prospective and retrospective perturbation analyses and population viability analysis, and
• be able to apply matrix population models to address basic and applied ecological questions using MATLAB and other software packages.

## COURSE OUTLINE

PART I. PRELIMINARIES

Introduction to MATLAB
2. Introduction to matrix algebra
3. Review of life table analysis

PART II. AGE-STRUCTURED (LESLIE MATRIX) MODELS

1. Model formulation and parameterization
2. Population projection
3. Population growth rate, stable age distribution, reproductive values,…
4. Sensitivity analysis (sensitivities and elasticities)
5. Lower level sensitivities
6. Sensitivity analysis using partial life-cycle models
7. Second derivatives of population growth rate; sensitivity of elasticities

PART III. STAGE-STRUCTURED MODELS

1. Parameterization of stage-structured models
2. Population growth rate, stable stage distribution, reproductive values
3. Sensitivity/elasticity analysis
4. Age-specific traits from stage-specific models

PART IV. PARAMETER ESTIMATION

1. Estimation of transition probabilities
2. Estimation of reproductive parameters

PART V. ANALYSIS OF LIFE TABLE RESPONSE EXPERIMENTS (LTRE)

1. An overview of LTRE analyses
2. Fixed effect designs
3. Random effect designs

PART VI. ANALYSIS OF TRANSIENT DYNAMICS

1. Damping ratio, and population momentum
2. Sensitivity analysis of transient dynamics

PART VII. STATISTICAL INFERENCE

1. Confidence intervals
2. Loglinear analysis

PART VIII. STOCHASTIC MODELS

1. Why stochasticity matters
2. Environmental stochasticity
a. Formulation of stochastic models
b. Stochastic growth and stochastic sensitivities/elasticities
c. Environmental stochasticity and probability of extinction
3. Demographic stochasticity
a. Dealing with demographic stochasticity
b. Demographic stochasticity and probability of extinction

PART IX. POPULATION VIABILITY ANALYSIS: OVERVIEW

1. Introduction to PVA
2. Sources of variation
3. Estimating extinction parameters: alternative approaches
4. PVA using matrix model

PART X. DENSITY-DEPENDENT MODELS

1. Incorporating density-dependence into matrix models
2. Analysis of density-dependent matrix models

PART XI. MATRIX METAPOPULATION MODELS

1. The concept and relevance of metapopulations
2. Matrix metapopulation model: construction and analyses

PART XII. POTPOURRI

REQUIRED TEXT:

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