  State-space models (SSMs) are an important modeling framework for analyzing
ecological time series. These hierarchical models are commonly used to model
population dynamics, animal movement, and capture-recapture data, and are now
increasingly being used to model other ecological processes. SSMs are popular
because they are flexible and they model the natural variation in ecological
processes separately from observation error. Their flexibility allows
ecologists to model continuous, count, binary, and categorical data with linear
or nonlinear processes that evolve in discrete or continuous time. Modeling the
two sources of stochasticity separately allows researchers to differentiate
between biological variation (e.g., in birth processes) and imprecision in the
sampling methodology, and generally provides better estimates of the ecological
quantities of interest than if only one source of stochasticity is directly
modeled. Since the introduction of SSMs, a broad range of fitting procedures
have been proposed. However, the variety and complexity of these procedures can
limit the ability of ecologists to formulate and fit their own SSMs. We provide
the knowledge for ecologists to create SSMs that are robust to common, and
often hidden, estimation problems, and the model selection and validation tools
that can help them assess how well their models fit their data. In this paper,
we present a review of SSMs that will provide a strong foundation to ecologists
interested in learning about SSMs, introduce new tools to veteran SSM users,
and highlight promising research directions for statisticians interested in
ecological applications. The review is accompanied by an in-depth tutorial that
demonstrates how SSMs models can be fitted and validated in R. Together, the
review and tutorial present an introduction to SSMs that will help ecologists
to formulate, fit, and validate their models.
