# State-space models in ecology

In this workshop, I'm focusing on a state-space model that arises from theory on intrinsic population dynamics. But state-space models are also very useful for testing relationships between dynamics and extrinsic variables (like temperature, pollution levels, etc). They can be used to test hypotheses about relationships and also to get estimates of population size given observations only of the extrinsic variables. The state-space model gives you a way to do this and to explicitly incorporate both process and non-process error in your population model (rather than just assuming non-process, or measurement error). A few examples of state-space models used in this way are shown here. You'll want to click 'view full size' to read on-line (the older papers are a bit grainy, but that is due to the old pdf software use to generate them).

Other fairly readable non-ecological (engineering and economics) references on state-space models are

Chapter 3 Harvey, A. C. 1989. Forecasting, structural time series models and the Kalman filter. Cambridge University Press.

Chapter 1. Maybeck, P. S. 1979. Stochastic models, estimation and control. Vol 1.

Greg Welch maintains a comprehensive Kalman filter site where you can download code, course material, and Maybeck's chapter (among many other things)

http://www.cs.unc.edu/~welch/kalman/

Other fairly readable non-ecological (engineering and economics) references on state-space models are

Chapter 3 Harvey, A. C. 1989. Forecasting, structural time series models and the Kalman filter. Cambridge University Press.

Chapter 1. Maybeck, P. S. 1979. Stochastic models, estimation and control. Vol 1.

Greg Welch maintains a comprehensive Kalman filter site where you can download code, course material, and Maybeck's chapter (among many other things)

http://www.cs.unc.edu/~welch/kalman/

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