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?


  • 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?