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.