Ecological systems can often be characterised by changes among a  set of underlying states pertaining to individuals, populations, communities, or entire ecosystems through time. Owing to the inherent difficulty of empirical field studies, ecological state dynamics operating at any level of this hierarchy can often be unobservable or "hidden". Ecologists must therefore often contend with incomplete or indirect observations that are somehow related to these underlying processes. By formally disentangling state and observation processes based on simple yet powerful mathematical properties that can be used to describe many ecological phenomena, hidden Markov models (HMMs) can facilitate inferences about complex system state dynamics that would otherwise be intractable. However, while HMMs are routinely applied in other disciplines, they have only recently begun to gain traction within the broader ecological community. We provide a gentle introduction to HMMs, establish some common terminology, and review the immense scope of HMMs for applied ecological research  . By illustrating how practitioners can use a simple conceptual template to customise HMMs for their specific systems of interest, revealing methodological links between existing applications, and highlighting some practical considerations and limitations of these approaches, our goal is to help establish HMMs as a fundamental inferential tool for ecologists.
Ecological systems can often be characterised by changes among a finite set of underlying states pertaining to individuals, populations, communities, or entire ecosystems through time. Owing to the inherent difficulty of empirical field studies, ecological state dynamics operating at any level of this hierarchy can often be unobservable or "hidden". Ecologists must therefore often contend with incomplete or indirect observations that are somehow related to these underlying processes. By formally disentangling state and observation processes based on simple yet powerful mathematical properties that can be used to describe many ecological phenomena, hidden Markov models (HMMs) can facilitate inferences about complex system state dynamics that might otherwise be intractable. However, while HMMs are routinely applied in other disciplines, they have only recently begun to gain traction within the broader ecological community. We provide a gentle introduction to HMMs, establish some common terminology, and review the immense scope of HMMs for applied ecological research . We also provide a supplemental tutorial on some of the more technical aspects of HMM implementation and interpretation . By illustrating how practitioners can use a simple conceptual template to customise HMMs for their specific systems of interest, revealing methodological links between existing applications, and highlighting some practical considerations and limitations of these approaches, our goal is to help establish HMMs as a fundamental inferential tool for ecologists.
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finite
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would
might
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. We also provide a supplemental tutorial on some of the more technical aspects of HMM implementation and interpretation