ETHZQuantMethods

Course materials for the demographic structure module (2017 Quantitative Methods at ETH Zurich).

This 3-week module introduces structured population models and explores the unique dynamics that arise when individuals are not demographically identical.

Key concepts:

Individual variation
Population dynamics
Density- and frequency-dependence
Optimization of life history

Tools:

Matrix population models (biology -> model -> analysis)
Sensitivity analysis
Differential equations

25 April 2017: Introduction to matrix population models

Instructor: Will Petry

Lecture (30-45 min)
- What is population structure?
  - N1 = rN0
  - Demographic differences between life stages
  - Biological examples
- Mapping life cycles to transition matrices
  - Drawing life cylces for different organisms
  - EX: drawing life cycles
  - From life cycle to matrix model
  - EX: converting life cylces <--> matrix models
- Basic analysis of matrix population models
  - Matrix multiplication with population vector
  - P + F = T
  - Ergodic equilibria
  - [Eigenvalues]
  - [Transient dynamics]
Demonstration of Shiny app
Exercises
- Density-independence
- Gestalt feel for sensitivity/elasticity

2 May 2017: Sex-structured population models, nonlinearities, and dynamic equilibria

Instructors: Will Petry & Chris Johnson

Lecture, part 1 (20 min)
- Adding multiple structuring variables (sex as a case study)
- EX:
- Paradox of two models
Exploration of two-sex model Shiny app
Analyses of non-linear matrix population models
Lecture, part 2
- Differential equations
- Oscillations/dynamic equilibria

9 May 2017: Environmental sensitivity of demographic rates

Instructor: Chris Johnson

Lecture
- Vital rate responses to temperature
- Multivariate optimization of fitness components

References

Caswell, H. (2001). Matrix population models. John Wiley & Sons, Ltd., Chicago.