Introduction
The marine ecological and fisheries literature is increasingly replete with references to regime shifts (Möllmann et al. 2015). A common approach is to describe, through one means or another, an abrupt temporal change in a measure of biological productivity as a regime shift and to then explore other data to identify causal drivers of the shift. Temporally abrupt changes in biological productivity are clearly of importance from basic ecological and management perspectives, as they can affect population dynamics, species viability, ecosystem structure and function, and fisheries sustainability (de Young et al. 2008; Möllmann et al. 2009).
However, what constitutes a regime shift is not always clear. Many definitions explicitly refer to ecosystems and incorporate the necessity that a shift from one regime to another must be difficult to reverse, asserting that regimes represent stable alternative states in community structure (Conversi et al. 2015) or ecosystem configuration (Scheffer and Carpenter 2003).
A second issue is methodological in nature. Some analyses are based on empirical but ultimately subjective impressions resulting from visual observation, such as an over-grazed kelp bed (Ling et al. 2015) or coral bleaching (Graham et al. 2015). When evidence of a regime shift is visually striking and arguably self-evident, there is perhaps less need for the methodological objectivity that long-term, continuously variable information usually demands. Under such circumstances, sequentialt -tests are not uncommon (Rodionov 2004; Weijerman et al. 2005; Vert-pre et al. 2013; Jaagus et al. 2017), although the selection of years applied is frequently based on the researcher’s perception of the magnitude of the effect of the purported regime shift.
We offer an alternative, operationally objective means of identifying regime shifts in time-series data that involves application of a Bayesian online change point detection (BOCPD) algorithm (Adams and MacKay 2007). Perälä and Kuparinen (2015) introduced this approach to detect regime shifts in the fisheries ecology literature. Their method utilized normal-gamma conjugate priors for the normal observation model, resulting in an analytically tractable procedure that is able to simultaneously detect shifts in the mean and(or) variance parameter of the data-generating process. Using sequential Monte Carlo (SMC) methods, Perälä et al. (2016) expanded the methodology so that it can be used to detect shifts in any parameter of the underlying predictive model with arbitrary prior distributions. They applied the method to Beverton-Holt and Ricker fisheries stock-recruitment models and detected shifts, for example, in maximum per capita reproductive output parameters.
The BOCPD algorithm continually and sequentially updates (i) the posterior probability distribution since the latest regime shift together with (ii) the posterior probability distributions of the parameters of the data-generating process. A high probability of a change point (regime shift) results from poor compatibility of the model prediction with an observed data point, as determined by the posterior predictive density function evaluated at the new observation. Here, we use the SMC implementation of the algorithm for a normal observation model with uniform priors for the mean and variance parameters of the model.
Our overarching objective is to use the BOCPD algorithm to detect regime shifts in a measure of biological productivity (a nearly century-long time series of juvenile Atlantic cod, Gadus morhua, abundance) and hypothesized drivers of cod productivity (Fromentin et al. 1998; Beaugrand and Reid 2003; de Young et al. 2004, 2008; Stige et al. 2006): North Atlantic Oscillation (NAO); zooplankton abundance; and water temperature. We use the BOCPD algorithm to identify regime shifts in all time series. The degree to which these time series overlap with one another will be used to infer potential causal drivers of regime shifts in cod productivity. In addition to these metrics of climate, food supply, and temperature, we applied the BOCPD algorithm to temporal estimates of fishing mortality to explore its role as a driver (Neubauer et al. 2013) and as a factor that might conditionally affect the strength of other suspected drivers.