Instructor Notes

Logistic Growth

• Is everyone comfortable with the basic logistic growth example?
  • If not, give a brief introduction or clarify questions
• This is an autoregressive model in that the abundance at the current time is influenced by the abundance at the previous timestep, but in a more complicated way than the ARIMA model.

Adding sources of uncertainty

• So far we’ve talked about uncertainty as a single thing: epilson ~ N(0, sigma)
• What are the different sources of uncertainty? list on board and discuss what each is as students name them
  • observation error
  • parameter uncertainty
  • initial condition uncertainty
  • process variability
  • model uncertainty
  • driver and scenario uncertainty
  • numerical approximation error
• What is the distinction between uncertainties & sources of variation?
  • uncertainties: describe ignorance about a process; should decrease asymptotically with sample size
  • sources of variability: variation in the process that are not captured by a model
• Which of items on the board are uncertainties vs. sources of variation? mark on board
  • What does the author mean when they say “if observation error was the only source of uncertainty then this forecast would have zero uncertainty”?
• How does this related to measurement error?
• Can uncertainty in initial conditions be reduced with more data?
• What is the difference between the additive process error and observation error?
• What information do covariance matrices provide?

Thinking probabilistically

• How do the boxes in the graphical model of logistic growth relate to the sources of error?

Predictability

• How does disturbance make forecasting difficult?

  • What could be done to ameliorate the influence of disturbance on forecasts?

• Which components of uncertainty (e.g., in eq. 2.1) have the potential to grow through time?

  • What implications does this have for our ability to forecast?

• What aspects of external drivers make systems easy vs. difficult to forecast?

• Are there implications of the need for different experimental designs for forecasting vs. hypothesis testing for how we should do science?

• What is the difference between parameter uncertainty and parameter variability?

• What are the implications for forecasting?

• How can we tell them apart?

• What kinds of uncertainty/variability do you think are most important in ecological systems?

• If a forecast model doesn’t include all of these sources of variance can it be a valid forecast?