# 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?