  State-space models (SSMs) are increasingly used in ecology to model
time-series such as animal movement paths and population dynamics. This type of
hierarchical model is often structured to account for two levels of
variability: biological stochasticity and measurement error. SSMs are flexible.
They can model linear and nonlinear processes using a variety of statistical
distributions. Recent ecological SSMs are often complex, with a large number of
parameters to estimate. Through a simulation study, we show that even simple
linear Gaussian SSMs can suffer from parameter- and state-estimation problems.
We demonstrate that these problems occur primarily when measurement error is
larger than biological stochasticity, the condition that often drives
ecologists to use SSMs. Using an animal movement example, we show how these
estimation problems can affect ecological inference. Biased parameter estimates
of a SSM describing the movement of polar bears (\textit{Ursus maritimus})
result in overestimating their energy expenditure. We suggest potential
solutions, but show that it often remains difficult to estimate parameters.
While SSMs are powerful tools, they can give misleading results and we urge
ecologists to assess whether the parameters can be estimated accurately before
drawing ecological conclusions from their results.
