Using Hidden Markov Models to develop ecosystem indicators from non-stationary time series

Ecological indicators are important mechanisms for understanding ecosystem change and implementing Ecosystem Based Fishery Management, but the development of useful indicators must account for ecosystem shifts that result in non-stationary processes over time. This necessitates the adoption of more adaptable statistical modeling approaches. Hidden Markov Models (HMMs) provide a robust framework for distinguishing underlying ecosystem shifts from noisy time-series data. In this paper, we illustrate the power of HMMs to develop model-based ecological indicators of non-stationary systems, focusing on two case studies from the California Current Large Marine Ecosystem. In the first case study, we analyze four temperature time series from 1998 to 2022 that are used as indicators for environmental conditions experienced by juvenile salmon in the northern portion of the system. We apply a three-state HMM incorporating temporal trends to account for non-stationarity in the means over time due to overall ocean warming. Output from this model reveals increasing temperatures for all four metrics in the California Current, with most years being assigned to the warmest estimated state. In our second case study, we analyze nine time series of seabird densities in the northern California Current from 2003 to 2022, to demonstrate how HMMs can be useful to identify sets of indicators that reflect different ecosystem processes, including potential seabird predation pressure on juvenile salmon, and have different variances. We found the strongest support for the existence of two distinct temporal regimes in the seabird data, with an abrupt shift occurring after 2010. While mean densities changed slightly for some species, this regime shift can be best characterized with a shift in variances: sooty shearwaters (Ardenna grisea) and Cassin's auklets (Ptychoramphus aleuticus) represented species with densities becoming more variable, while common murres (Uria aalge) and gulls were estimated to have become less variable after 2010. Common murres, Cassin's auklets, sooty shearwaters, pink-footed shearwaters (Ardenna creatopus) and gulls all represent species that may be useful indicators of change in the northern California Current, because of their differential responses to this regime change. Overall, our analysis provides a first step illustrating the potential applications of HMMs to developing ecosystem indicators in non-stationary systems and a framework that is widely useful for applications to ecosystems around the world.