WLF 503: Matrix Population Models

Dr. Sophie Gilbert

Email: sophiegilbert@uidaho.edu

Course description and goals:

Animal population dynamics are influenced by a wide array of processes, from environmental variability to predation, competition, management changes, and nutritionally-induced density dependence. As a result, researchers and managers are often keenly interested in better understanding and quantifying population dynamics. However, the complex life histories of many species require approaches such as matrix population models that can incorporate structured populations with vital rates that vary by age class or life stage, and evaluate their relative importance.   

Matrix-based population models can incorporate a multitude of ecological dynamics and provide a wide array of useful metrics, and are also a primary structure underlying an important new approach, integrated population models (not covered in this course). However, the construction and analysis of matrix models can be a barrier to use for those who have not used them previously.  The goal of this course is to provide participants with the opportunity to learn and practice the skills needed to build and analyze matrix population models, including a wide variety of structures (age-based, stage-based, 2-sex, density-dependent, stochastic, and predator-prey interactive). We will begin with basic matrix structures and then build in ecological complexity as we go, and will learn “hands on” coding of each type of model via coding exercises in program R.

Learning outcomes:

  1. Understand the structure and function of matrix population models

  2. Be able to build and analyze matrix models, including incorporating ecological complexity into model structures and analyze results

  3. Understand limitations of matrix models and derived indices


Content:


Module 0 Coding Assignment: Intro to R (optional)

This first week of the course, I asking that those who are not well versed in program R take this time to learn about basic R functionality. To this end, I recommend that you go through the following 2 tutorials:

  1. Intro to R

  2. Troubleshooting

For those that are more advanced with R, I recommend looking at the rest of the tutorials here, plus their great links to many other R learning resources. Of course, there are many, many other great R learning resources out there, many tailored towards ecologists. Some links to check out:

-  R for Data Science free online book with exercises (https://r4ds.had.co.nz/)

- R for Fish and Wildlife Grads (https://sites.google.com/site/rforfishandwildlifegrads/)

- R Bootcamp (https://r-bootcamp.netlify.app/)

Module 1: Brief introduction.

A basic introduction to structured population models and why we bother with them.

Module 2: Basic structure

How to construct a matrix model, including how we can start with what each row and column means,

Module 3: Pre- vs. post-breeding matrix

The critical difference between these two basic structures of matrices, and how we often get it wrong!

Module 4: Perturbation analysis

Answering our basic “what if” question… if we could change them, which vital rate is most important for growth?

Module 5: Stage structured populations

Age is a pretty limited way to describe population structure… stages are much more flexible!

Module 6: Size structured populations

A classic subset of “stage” structure are populations where size dictates fitness and vital rates.

Module 7: Sex and site structured populations

  • Video

  • Reading

  • Code: gulls 2-site (STARTER and SOLUTION)

Module 8: Environmental Stochasticity I

Module 9: Environmental Stochasticity II

Module 10: Density Dependence

Module 11: Predator-Prey

Module 12: Transience

Take-Home Exercise (EXERCISE)